Citation

## Material Information

Title:
Measurement of the radiative lifetimes of the v=1 and v=2 levels of the A state of carbon monoxide
Creator:
Burnham, Ralph Laurence, 1944-
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
1972
Language:
English
Physical Description:
viii, 95 leaves. : illus. ; 28 cm.

## Subjects

Subjects / Keywords:
Absorption spectra ( jstor )
Lamps ( jstor )
Magnetic fields ( jstor )
Molecular rotation ( jstor )
Molecular spectra ( jstor )
Rotational spectra ( jstor )
Rotational states ( jstor )
Signals ( jstor )
Spectral bands ( jstor )
Visible spectrum ( jstor )
Carbon monoxide ( lcsh )
Dissertations, Academic -- Physics -- UF
Physics thesis Ph. D
Spectrum analysis ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

## Notes

Thesis:
Thesis -- University of Florida.
Bibliography:
Bibliography: leaves 93-95.
Also available on World Wide Web
General Note:
Typescript.
General Note:
Vita.

## Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
022777240 ( AlephBibNum )
14082361 ( OCLC )

Full Text

v = 1 AND v = 2 LEVELS OF THE A STATE
OF CARBON MONOXIDE

BY

RALPH LAURENCE BURNH-LAM

A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY'

UNIVERSITY OF FLORIDA
1972

ACK .NU' LEDG:,IENT S

The author w.'ishesr to thaniik the members of his supervi sory

committee for th.iir assist L :cc throughout his graduate program.

In part icul, ar be wishes to thank the chairman of his superviscry

committee, Dr. Ralph C. Isler, for his guidclnce during the course

of this research.

The author also v.'jishes to thank Dr. William W','ells for his

assistance during the earl\ sta iges of this research.

ACK NO LEDGENTS . . . . . . . . .

LIST OF TA L.S . . . . . . . . .

LIST OF FIGU;ES . . . . . . . . .

ABSTRACT . . . . . . . . . . .

CHAPTER

I.

I NTRODLUC I ON

II. THF.ORLTICAL CONSIDERATIONS . . . .

Semiclassical Analog to the Level-Crossing
Phenomenon . . . . . . . .

Quantum Mechanical Calculation of the Hlanle
Effect Signal for the A State of CO . .

Rotational Line Contributions to the
Molecular Level-Crossing Signal . . .

Rotational Intensity Distribution in
a Molecular Discharge . . . . .

Rotational Intensities in Resonance
Fluorescence . . . . . . .

The Effect of Rotational Perturbations
on the Level-Crossing Signal . . . .

and r-Centroids of Molecular Transitions .

III. EXPERIMENTAL APPARATUS . . . . .

Molecular Discharge Lamp Design . . .

Optical System . . . . . . .

Detection Apparatus . . . . . .

Magnetic Field Control Circuitry . . .

. . . 7

. . . 7

. . . 12

. . . 20

. . . 20

. . . 25

es,

. . . 30

. . . 33

. . . 40

. . . 143

. . . 49

. . . 53

. . . 57

Page

. . . ii

. . . v

. . . v i

. . . v i i

TABLE OF CONTfNTS (Con.tinued)

CHAPTER Pr gc.

IVX. EXPERIMENTAL PROCEDURE . . . . . . . . 61

Lanrp Spectra . . . . . . . . ..... . 62

Spectra of Scattered Light . . . . . . . 66

Anrilysis of theic Hnnle Effect Signals . . . . 71

V. RESULTS . . . . . . . . . . . . 78

v = 1 . . . . . . . . . . . . 78

Results for Unperturbed Levels . . . . . 81

Results for Perturbed Levels . . . . . 82

v 2 . . . . . . . . . . . . 33

VI. CONCLUSIONS . . . . . . . . . . 87

LIST OF REFERENCES . . . . . . . . . . . 93

LIST OF TABLES

Tab] e Page

I. Rc-sults of the Qi:- Lum M.echanic:1l Calculation of the
lianle EffecL Signal for trli A State of CO . . . 22

II. Contributions to the Hanle Effect Signal from
Excited Rotational Stal--s . . . . . . . 73

III. Experimental Resul ts for PCrturbed lotationzal Levels 85

IV. Lifetimes of \'ibrutional Levels of the A State of CO 89

LIST OF FIGURES

Figure

I. Semiclassical Analog to the Level-Crossing
Phenomenon . . . . . . . . .

II. a. Coordinate System for the Molecular Level-
Crossing Experiment
b. Partial Energy Level Diagram for a T- F
Molecular Transition . . . . . . .

III. Coordinate System for the Scattering Region

IV. E:.xperimental Apparatus . . . . . .

V. Molecular Discharge Lamp . . . . . .

VI. Scattering Cell . . . . . . .

VII. Control Circuitry for the Flectromvingnet . .

VIII. Lamp Spectrum of the (1,0) Band . . . .

IX. Fluorescent Spectrum of the (1,0) Band . .

X. Fluorescent Spectrum of the (2,0) Band . .

XI. Experimental Hanle Effect Signal with Fitted
Lineshape . . . . . . . . .

XII. Experimental Results for the v= 1 and v= 2
Vibrational Levels . . . . . . .

Page

. . 15
.... 529

. . 29

. . 42

. . 48

. . 52

. . 59

. . 64-1

. . 68

. . 70

77
. . 77

. . 80

Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy

NTEASURREMFNT OF THE RADIATIVE LIFETI1.IES OF THE
v = 1 AND v= 2 LEVELS OF THE A STATE
OF CARBON MONOXIDE

By

Ralph Laurence Durnham

March, 1972

Chairman: Dr. Ralph C. Isler
Major Departmcnt: Physics

The technique of zero-field level-crossing spectroscopy was

employed to obtain the radiative lifetimes of the v= 1 and v= 2

vibrational levels of the Al T state of carbon monoxide. Level-crossing

signals %ere obtained for eight individually resolved rotational fea-

tures in the (1,0) vibrational band and for four individually resolved

rotational features in the (2,0) vibrational band. The signals were

found to consist of level-crossing lineshapes from only three rota-

tional transitions, and were analyzed to yield values of g T the

product of the Landc g factor and the lifetime. Narrowing of the

lineshapes of several of the rotational levels was observed in the

v = 1 state. This effect was attributable to a perturbation caused

by the a state. The values of the coupling constants for the

perturbed rotational levels were obtained from analysis of the level-

crossing data. The experimental lifetimes of the v = 2 level and of

the unperturbed states of the v= 1 level were obtained by calculating

the Lande g factor for the ITT state from Hund's case (n) coupling

scheme. The lifetimes of individual rotational states within a level

were averaged to yield the lifetime of the level. For the v= 1 level

the result w.a T = 10. -11 0.8 nsec. For the v = 2 level the

result v.as T1 = 5.-!1 1.0 nsec.

Sj i i

CIlAPTl;ER I

I NTRODUC f IONT

T'I] h.nrfi r.f thro frit 'th podi j i .', FvsFTmni nf c rhbon monoxide

..'nhch ari.e from. transitions betv-een vibrational levels of the A lT

state and thle X1 I state of the molecule have historically been of

fundamenta'-l research interest. Original spectroscopic work was

stimulated I;y the presence of intense fourth positive bands as a

contaminant i:n spnctra taken in the ultraviolet and vacuum-

ultraviolet regions of the spectrum. Early wv.orkers investigated

the structure of b.rnd. seen in botl, emission and absorption, and by

1940 vibrational and rotational analysis of all known bands was essen-

tially complete [1].

Percent research has been devoted to the investigation of the

lifetime, oscillator strengths, and perturbations of the A 1i state.

Simunons et al. [2] have made accurate assignments of perturbations

due to six: kno'..n states in the region of the A llT state. Their work

was based on the analysis by Ilerzberg and others [3,4,5] of bands

arising from forbidden transitions to the ground state. It is the

upper states of these transitions which interact with the A IT state

giving rise to the observed perturbations.

Discovery of carbon monoxide bands in both the infrared and

ultraviolet regions of the solar spectrum [6], as well as the predic-

tion of the existence of the gas in interstellar space [7] has

emphasized the astrophysical importance of the molecule. Quite *

recently Mariners VI and VIT have detected rnc!di ation from carbon mon-

oxide bands produced in the upper lawyers of the Martian atmosphere

[8,9]. Surprisingly, the observed Cimeron baInds which arise from a

forbidden 13 +- 1 transition were more intense than those of the

fourth positive system. James [c101] has derived expressions for the

oscillator strengths of the Cameron bands by assuming a coupling

between the a3 T and the A lf states. An accurate knowledge of the

fundamental properties of the A 1V state is thus becoming important

for several aspects of astrophysical research.

Considerable contro''ersy has developed over attempts to relate

measured values of the lifetimesto oscillator strengths of the bands

of the A-X transition. Hesser [13] obtained the lifetimes of several

vibrational levels using the phase shift technique. These values were

then used in conjunction with his measurement of the relative inten-

sities of the bands to obtain a value of .094 for the absorption oscil-

lator strength of the transition. The result was in conspicuous dis-

agreement with the value, f = .24, obtained by Meyer et al. [12] from

e'cetron scattering data. In order to determine the source of the

discrepancy, Wells and Isler [13] measured the lifetime of the A(v =2)

state using level-crossing spectroscopy. Their result %as in substan-

tial agreement with that of Hesser. The controversy was partially

resolved by Mumma et al. [1-1] who remeasured the relative intensities

of the vibrational bands using a system which had a calibrated spectral

response. These measurements were normalized to the average of the

lifetime measurements and yielded a value of 15 for the integrated

oscillator strength. Lawrence [15] also reanalyzed Hlesser's data and

obtained an f value of .17. These results may be coI)ipared to the

value, f = .195.012, obtained by Lassettre and Sherbele [16] through

the comparison of elastically and inclastically scattered electrons.

Me,,er's meastiremeni s havr-e n -e hn-n rrn.fi nd [17] and the results are

now consistent with thosc of Lassettre and SI.erbele. The agreement

between the values of the oscillator strength calculated from lifetime

measurements and those obtained from electron impact experiments is

thus considerably improved, but not perfect.

Mumma's intensity measurements also revealed a strong depen-

dence of the electronic transition moment on the internuclear separa-

tion in the carbon monoxide molecule. This dependence produces: a varia-

tion of the transition moment over the bands of the fourth positive

system, and must be considered when calculating f values from radiative

lifetimes. Numma assumed a linear relation between the transition

moment and the r-centroid of the vibrational transition, and analysis

of his intensity data gave

R a (1 .60r /, ,) (1)

where R is the transition moment and r / .. is the r-centroid of the
e v V

(v'v') vibrational band. This relation was in good agreement with

'.r tata of Lassettre and Skerbele. Some doubt has been cast upon the

relationship of equation 1 by the recent lifetime measurements of Imhof

and Read [18]. Their data, obtained for v' = 0 through v' = 6 levels

by W,!e dcl .d, coincidence technique, indicate a quadratic or higl4cr

rcpendc rin.-a of the trinnsition nioment on the r-centroid. Chervennk and

Ande,.on [19] hnve alao calculated a quadrntic dependence from life-

lim. information obinined from an experimcnt employing a pulsed :inver-

tr n. The vn'.idjty of thcir data is, ho'..ever, open to question.

The v.or'i described in this dissertation was undertaken in order

of thle A lf st-ate of carbon monoxide. The experimental results con-

tAineId ],crein will most certainly prove useful in determining the oscil-

n ;tor stLrcnths and transition moments of bands of the fourth positive

rV.. istLm.

The level-crossing phenomenon which was employed to obtain the

lifetime measurements reported in this work was first discovered by

H-ipl'l, [20] in 1924. Level-crossing signals are produced when two or

more a.ignetic sublevels of an excited atomic or molecular state become

degenerate at a particular magnetic field. The degenerate sublevels

arc e;:cited coherently. Re-emitted radiation from the sublevels suffers

interference, giving rise to an alteration in the polarization and

angular distribution of the observed light. When the signal arises

from the degeneracy in the Zeeman levels at zero magnetic field, the

level-crossing phenomenon is known as the Hanle effect. The phenom-

enon was explained by Breit [21] in 1933, but lay unexploited until

accidentally rediscovered by Colgrove et al. [22] in 1959. Since then,

level-crossing spectroscopy has proved to be an excellent technique for

measuring a variety of fundamental properties of excited states of

atomic systems.

Quite recently level-crossing spectroscopy has begun to be

applied to the measurement of properties of diatomic molecules.

iThe technique is quite similar to that used with atoms but in general

exper nientnl procedure is complicated by the vibrtional and rotational

structure of the molecular electronic states. The effects of level

crossings in diatomic molecules were derived from Breit's original

formula by Zarc [23] .,who also suggested several systems as possible

subjects for investigation. The first molecular level-crossing Fignals

were reported for NO by Crosley and Zare [2-1]. Unfortunately their

results v.ere later found to be spurious and due to mercury contamination

of their experiment [25]. Several molecular systems have no'. been

successfully treated. Silvers et al. [26] have observed signals from

individual rotational levels of CS excited by overlapping atomic lines

from Mln II. DeZafra et al. [25] have used molecular resonance radia-

tion to excite individual rotational levels in the OH and OD radicals,

and have combined level-crossing and optical double resonance data to

determine lifetimes and g factors for excited states of these species.

In a slightly different approach, Wells and Isler [13] used radiation

from an entire vibrational band to excite the v'= 2 level of the A T

state of carbon monoxide. Contributions to the level-crossing signal

from each rotational line present in the scattered radiation were then

assessed in the analysis of their data.

In the experiment described in this dissertation resonance

radiation produced in a molecular discharge lamp was used to excite

high rotational levels in the v' = 1 and v' = 2 vibrational levels of

the AIT state of carbon monoxide. The level-crossing signals obtained

weic sho.'.it to consist of contributions from on] y three unresolved rota-

tional liner, and proved to be amenable to analysis by curve-fitting

techniques. The basic experimental quantity obtained from the data

analysis was the product of the lifetime and the Landc g factor for

the vibration.l-rotational state under investigation. A theoretical

value for the g factor was obtained by assuming a case (a) coupling

scheme for thc A IT state. The experimental value of the radiative life-

time was thus obtained. Narrowing of the observed lineshapes .-.'as quite

evident for several of the levels in the v = I state. This distortion

of the Hanle effect signals was attributed to a rotational perturbation

in the A IT state. Data from the perturbed levels were analyzed to

obtain value= for the parameters characteristic of the perturbation.

CHAPTER II

THEORETICAL CONSIDERATIONS

In this section the theoretical linei-hapes for lInnle effect

signal'; arising from A T X + transitions in carbon monoxide will

i.'.s e.'perinient consisted of a superposition of three unresolved

rotntiona] lines, a mathemirtical model will be constructed which will

allow tlhe contribution to the level-crossing signal from transitions

from z-iach excited rotational level within a vibrational state to be

assessed. Finally, the effects of a rotation'.l perturbation in the

A IT upper state upon the level-crossing line shape will be developed

using basic perturbation theory.

Semiclassical Analog to the
Level-Crossing Phenomenon

Some of the basic features of the zero-field level-crossing

phenomenon (Hanle effect) may be easily understood if one considers

the following semiclassical analog to the exact quantum system.

An electronic transition in an atom or molecule may be repre-

sented classically as an electric dipole with components p, p and

p z The upper state of the transition has a magnetic moment, 1o, as

shown in figure 1. In an ideal experimental arrangement exciting

tl

Cr

C-1
U
'01

C,
I-I

C,-

-I

wC-
F-

c0
0

u
F-
UJ

I-

N
w

u
CU

F-
u

-j
uJ

LU

radiation with polarization vectors, E. and Ez, is incident along the

x axis. Light scattered by the atom is detected along the z axis.

A magnetic field, H, may be applied along the y axis.

If initially the magnetic field is zero, only light associated

with the y component of the electric dipole will reach the detector.

If now a magnetic field is applied as shown in figure I, the magnetic

moment will process about the y axis with the Larmor frequency,

WL = H (2)

The radiated intensity observed along the z axis v.ill then be given by

r> -t,/T 2
It = c e sin wLt dt (3)

Integration yields

c r1
I -t L1 -- .(4)
t L 1+(2g pjoTH 'h)

2
In the above integral sin Lt gives the intensity of radiation asso-

ciated %\ith the processing dipole, and the danping term, e is

included to account for the decay of the dipole associated '..ith the

crossing signal, a constant background due to radiation from the y

component of the electric dipole will also be observed unless the

polarization of the incident radiation is chosen to exclude excita-

tion of this component.

The level-crossing signal has the form of an inverted

Lori'ntizian lineshape having I = 0 at I = 0. if HIi is the magnetic
t
1
field necessary to produce 1 maximum intensity, then T, the lifetime

of the state is given by

T= (5)
g2t H2
02

Thus if the g factor of the radiating state is known, the lifetime is

given by a simple measurement of the halfwidth of the experimentally

obtained Lorentzian lineshape.

The semiclassical analog is also useful for understanding the

effects on the level-crossing signal of departures from the ideal exper-

imental geometry given in figure I. Suppose that scattered light is

detected in the x-z plane at an angle, e, to the 7 axis. Then the

sin2 w Lt term in equation 3 must be replaced by sin (ut + t ). Making

this substitution, the intensity of light scattered into the detector

will be given by

t = c e sin (w t + O)dt

CO
c 1 (cos 2w t cos 29 + sin 2wu t sin 29) dt. (6)
2 L L L

Integration of equation 6 yields

2
t = c- cos 20 sin 29 R (7)
1+R 1+R

where
2pog jHT
R = ((8)
h

The level-crossing signal given by equation 7 no.' contain ^

terms of both even and odd functional dependence on the magnetic field.

The dependence on the detector angle, 6, must be taken into account

under actual e p.erimental conditions when the finite volume of the

scattering region and the solid angle of the detector are considered.

Quantum Mechanical Calculation of the Hanle
Effect Sir1nal for the A State of CO

The rate at which radiation is absorbed, exciting an individual

molecular rotational level, and subsequently re-emitted into a single

rotational branch is given by the Breit [21] formula,

i- ,J J'') t I rf .Jm,/.Jml .rIj <'..J. 4r n'I' .J m "j' m"|g-rK .j'
[1- i(p.-4 )ogoTj H h]

The vectors, f and g, are the polarizations of the exciting and

re-emitted radiation, respectively. J and J m and m are the quantum

numbers related to the total angular moment of the ground states and

their projections on the space-fixed z axis, and J and u' are the

corresponding quantum numbers for the excited state. In the denom-

inator, g and T / denote the Lande g factor and the lifetime of the

excited state, and H is the magnetic field strength. The level-

crossing signal is calculated by inserting the proper v.avefunctions

for the If excited state and the + ground state into equation 9 and

summing over all possible combinations of magnetic quantum numbers.

The wavefunction for the ground state may be expressed as the

product of electronic and rotational functions

+ r 0-
( ) = (r )(2n) [2(2J + 1) ]- / (aQ y) (10)

The coordinates, r and 0 are defined with respect to a coordinate

system in which z corresponds to the internuclenr vxis of the mole-

cule. The quantities c*, -, and y, are the Euler angles associated

with the transformation which takes the space-fixcd axes into the

molecule-fixed coordinate system. (See figure IIa.) The elements of

the rotation rwatrix, .0's, may be shown to be the rotational eigen-

functions for the,- symmetric top molecule when multiplied by the normal-

izing factor,[l(2J + 1 [27]. The wave functions for the A doubled -I

upper state are constructed in a similar fashion:

,( )j -2 1 ily -ih
,() = .(r'0')(4n) 2(2J' + 1)]2[ e1 + eI]

where C denotes either the c or d component of the doublet. The

electronic parts of the wavefunctions for the upper state are either

symmetric or antisymmetric under reflection in a plane which contains

the internuclear axis of the molecule. This may be seen by making the

substitution 'p -p' in equation 11. The + state is symmetric

under this reflection.

h2 0

3)

*H

I 0o
a;- ci

CE w

* t2
rr4

,. *** O aS
4 0 t
04 N CJ -
U-l UV urnr

CiJ

S1+

1 1+

0
UZJ
cC 0

0<

I

n le n CM C- 0
C4 Cli N CY CJ CMj

I I
+ I

"+ I +

_nil

(- t- )d

+1 1 -4- H-

1--

-(PZ)d --

-(Ze)u -

The .'.'avefunctions in equations 10 and 11 may also be seen'to

possess definite symmetry (parity) under an inversion, R, of the

space-fi :ed coordinates through, the origin. Under such as t.r:nsfor-

mat ion

a-TT+ a-, I - s, y-' ',

and

S(nT+ n-B, --) = (- )J-2m (, ) (12

Application of the transformation, R. to the wavcfunctions yields

the follo'.,.ing results:

RY( ) = (-1) Iv(C) (13a)

c c
RY(l d)j = (-1) j Y(1 d) (13b)

Thus the parity alternates as a function of even and odd values of J.

The operators such as f r which appear in the Breit formula

(equation 9) may be expanded as the scalar product of t\,.o spherical

tensors with the components of r expressed in terms of the rotating

coordinate system

.r( l)^(1 (1) (_) o(1) (1) (o ..)r(1) (1 )
f r = (-I) "f (-I) f .0) )r (14)
=I -X +% =L -) %,v v
X Xv

The dipole matrix elements appearing in the Breit formula are most

readily evaluated by employing the relationship

(Jl) (J2) (J3)
2n nr 2n 1 2 3
I o m I (0y) (Y) ds sin -d dY
o o o 1 1 2 2 3 3

S 2 (1 2 1 2 3) ,(15)
1 2 3 1 2 3

where the terms appearing on the right side of the equation are Wigner

3-j symbols. Integration over the molecule-fixed coordinates is

facilitated by the use of orthogonality relationship,

oo0 T 2r ,
SJ' J' S *X(r e X.(r e )e r dr sin G de' d
0o o 0

= R 6 (16)

where the integration over cp has been carried out, and the integra-

tion over r and 6 is contained in R.

Using equations 10 and 11 the matrix elements may be written as

(J
= Xv

N2 I(1) (1)
(2J+1)(2J +1)(-1) f f
4TTi
(17)
Cto
F (J)* (J)
r* {[l o) ( -Alr 'v I710)S]Sf f(lD + ]-)

0n 1 r-n ,-A)

+ 110

( (1) (J)d dJ
A + mOL A

Employing equations 15 and 16 and the property that

f (J)* 1 ( 1)0+ f J)
C,0 = ( 1"o,-0

equation 17 becomes

(j'pf17. Jm) (JmT7 7.J' ')

= (2J+1)(2J +l)(-l) .+o+ p+m-A

,'

(1)
f

(1)
f
-ci

i J 1 i .I J 0 1 J J 1 J J J

* J J' 0' 1 -
L -m p c $J A J -A 0 0 -J m c .I The symmetry properties of the 3-j symbols may be used to write the matrix elements in their final form ', lT.T'X C, m+ 1 W pJf- .rJm) jm fy-rj.jp" ) =' 16(2J+1) (2J '+1) (-1) X.c (1) ) 2 J+J +l 'J J 1 J 1' f f R (.1_m:) ' [.(&1 '+) ( f .0 -v The matrix elements for emission may be obtained in a similar manner. The final form of the Breit formula then becomes (18) (19) R 2(Sn)) 19 , ,, 4, R2J'+J+J++ +'+m+ "+%+a+6+ I(J,J',J ) 16a -- (-1) i. I mm 4p Ko l, i) 2 (1 ) 9(1 (1) (1) [ 4 J+J 4+1 2 J J 1)2 J +J'+12 'J J )2 IJ J' 1) 'J J, 1) 'J" J 1, J J 1j -p X ym -, m -/ -e r n"1 1+i(-)'.4oJTJH'h 20 -1 + io (20) The terms 1 + (-1) +' +1 and 1 + (-1) +J+1J in equation 20 arise from the selection rule which requires a parity change in absorption and emission of radiation. The terms indicate that excitation from a lov.er level, J, to an upper level, J' takesplace to a c state if J' = J- 1 and to a d state if J' = J, and that re-emission takes place in a similar fashion. A consequence of the parity selection rule is the prohibition of excitation through a Q branch followed by re-emission in a P or R branch and vice versa, as may be seen by examining the partial energy level diagram for 1TT Z transitions (figure lib). The summation indicated in equation 20 is performed by first grouping terms for which |L-P'| = 0,1, or 2 and then summing over all possible sets of the indices X, a, 6, c. The process is facil- itated through the use of the sums, n=.J 0 n = odd V- n (2J+1) n = 0 L ~(2J+1)J(J.1),- 3 n = 2 rli=J (?.J+1)J(J+1) (3.J +3,.T-1)/15 n= 4 or, inl certain cases, through the use of the defining relationship bctwecii 3-j and 6-j symbols. Table I gives the result of the calculation for the IT - transition in carbon monoxide. Undc-r the e:-pcrimental coiLditions of unpolarizccd c:-:citing and scatter-ed radiation, ternuis for v which |-j = 1 cancel and tihe sign-.l consists of a field-independent background v.lhich arises from terms for .'.hicl, I -"i = 0 and a field-dependent pnrt Ii.hich arises frol.i t ermt:l: for v hicl I --p'I = 2. Rot :t ional Line Contriljutions to the lol-cCul ar Lev-el-Crossing Signal In the follo..'ing paragraphs a mathematical model '.'ill be developed wl'ich will allo'. the contributions of unresolved rotational lines to the l-vc-1-crossing signal to be calculated. The calculation will be carried out by first determining the contributions of individ- ual rotation.il lines to the intensity of a molecular discharge and then deriving the rate of resonance fluorescence from a scattering gas. Rotational Intensity Distrilbution in a Molecular Discharge The relative intensities of isolated rotational lines produced under conditions of thermal equilibrium may be expressed as the product U Cf CIO c 0 ::) 44- C 0 4-j V) C) C)j L~ 0 0 f- I + + In t- - ++ LLJ co C -E -i 00 + + -- I- f - -( N 1 N - II 0 0 II II + + 1 e4-, -- ++ . + r i : S-------- -- C+) + + -li 4- * 4--.( 4. CT Ltl ) T-,r [ (b) r I (d) 1+.r ,,f uoTadaosqV of the line strength of the transition and the temperature dependent Boltzmanmfanctor divided by the rotational partition function i(J ,J")exp [-B'J'(J'+l)hc.kT L I(J',J") = (21) Q rot Here B is the rotational constant for the upper state, TL is the effective rotational temperature for the discharge, and the rotational partition function is given by kT /'hcB for all but very low temper- aturces. The line strength is given by the lionl-London factor for the transition. For a TT transition in a symmetric top molecule these factors are i(J ,J ) = (2j'+1),'2 i(J' ,J'-1) = (J',l)/2 (22) i(J',J'+l) = J,/2 for the Q, R, and P branches, respectively. The relative intensity and shape of a Doppler broadened rota- tional line produced in a layer of gas of thickness dx in a discharge lamp of uniform cross section is given by e 2v -(2 d4(v,J ,J") = I(J ,J )oex-p 9- D- j dx (23) The parameter, k is the absorption coefficient of the gas and the Doppler breadth of the line, AMD, may be written as 22k 2 /2 2- 24) D c Vm The distance in v.avenumber from the center of the line is given by . The contribution to the output intensity at the front of the 1 lmp (x= 0) from the element dx is ds(v,J ,J ) = I(J' ,J )1: exp -.r D exp -1; 1 (J ,J )x exp - 2) dx (25) o -D d. v.here the second term accounts for absorption present in the lai.p. It is assumed here that once a photon has been absorbed it is lost to the output of the lamp. The relative absorptioii from molecules in the lower state is given by i(J ,J") e:x- -D"J (J"+1)hc. kTL I (J ,J") = (26) Qrot where B is the rotational constant of the lov.er state. Integration over the length of the lamp gives the contribution to the intensity from a frequency band dv: s(,J, J ')d% = LI( J ,J') L I ,(J J ) exp L- cI 2(J ,J") exp D- T2 J du . (27) The effective absorption coefficient for the discharge has been defined as a'L = 1: L. The total intensity from an isolated rotational line is found by integrating over the Doppler profile of the line CO S(J' ,J") = J s(v),.J',J )d' (28) 0 The simulated spectrum for an entire molecular band is generated by forming a sum of the rotational line intensities over the wavelength region of the band: max (,(X) = ) T( )S( (J' ,J")) (29) I 1 1 X.=X I min The parameters, min. and ?, m give the lower and upper wavelength limits of the band, A. is the wavelength of a particular rotational 1 line characterized by the upper and lower quantum numbers (J ,J ), and T(X-X.) is the triangular bandpnss function of the monochromator 1 used to resolve the spectrum. The bandpass function is defined as T(X) = |l- |/AXI | JVt| ^ 1 (30) 0 I X/AXi where AX is the resolution of the monochromator and is assumed to be much larger than the width of the rotational lines. Rotational Intensities in Resonance Fluorescence Calculation of the intensity of radiation absorbed and re-emitted by the scattering gas proceeds in a fashion similar to the calculation of the lamp intensity. For a particular mode of absorption followed by re-emission characterized by the rotational quantum numbers, J' -J -J, the intensity of light scattered into a detector at approximately right angles to the incident beam is given by D 4TT co i(-s ,J, ,J') cc dz IJ cQ F S(J' ,J)A(a ,J' ,J ")I(J,J ,J )du (31) 5 n 0 0 0 S(v,J ,J ) is the incident radiation intensity. The intensity of radiation absorbed and re-emitted by the scattering gas is given by the product, A(o- ,J ,J" ) (J,J ,J ), where A(C ,J',.J )dz = oe M(T ,J') exp (- -- Sexp s (T ,J,J )z exp -- ., 2 dz (32) The parameters, o' and T are the absorption coefficient and s s temperature of the scattering gas, and exp B J (J +l)hic kT M(T ,J ) = (33) Qrot gives the relative populations of the ground state rotational levels. The rate at which radiation is absorbed and re-emitted by the scatter- ing gas is given by T(J,J ,J ). This is the term which w.as calculated above from the molecular Breit formula, and contains the dependence on the magnetic field and scattering angle. Integration over z, the length of the scattering region, and 0, the solid angle subtended by the detector at the point of scattering, accounts for departures from the ideal right angle scattering geometry. The geometry of the scattering region is show.-n in figure III. If y represents the distance along the detector face, the differential area element on the detector face may be written as dA(y) = 2(2ay-y2") dy (34) The solid angle subtended by dA(y) is then 3 d: = (2ay-y) L (z-y) + a dy, (35) ,.here "a" gives the distance from the center of the exciting beam to the detector. Equation 35 holds only approximately if the detector is not sufficiently removed from the scattering region. However, the error introduced by this approximation is small compared to other uncertainties present in this analysis. In addition, it has been assumed that the exciting radiation is confined to a narrow beam along the central axis of the scattering region. 'V.hile this is not strictly the case under actual experimental conditions, it may be seen that scattering angles from above and below the center line tend to average to the scattering angle, 9. The integral in equation 31 is readily evaluated with a digital computer, using the Conroy [28] routine for multiple integrals. 0a ca ch Ur. a$
La

1-4

F-4

bLi

-I:,

LU
0~

-J

Ca,

_____1

I
I

I'
!
!
I^ -
-l 1

I-o-

The Effect of Rotational Perturbations on the
Molecular Level-,Crossing Signal

The A I state of carbon monoxide is characterized by the many
1
perturbations v.hich result from the mixing of the A^ i state .i.ith

another staic of the molecule. The coupling of tv.o states of nearly

equal energy arises from terms omitted from the Hamil tonian and pro-

duces shifts from the expected rotational energy progressions v.ithin

a vibrational level. In addition, if the coupling is sufficiently

strong, additional lines will appear in the spectrum of the vibrational

band. To see the effect of a perturbation of a rotational level upon

the level-crossing signal let the v.avefunction of the A I1 state be

represented by [A,J) and that of the perturbing state by IB,J).

A selection rule (see Herzberg [29, p. 285]) prohibits the mixing of

states of different rotational quantum number. It will be assumed that

m1 remains a good quantum number for the range of the magnetic field

encountered in the level-crossing experiment. This assumption is

justified for the types of terms being considered in the perturbation

calculation.

A perturbation which couples tv.o molecular states, IA,J' and

IB,J), gives rise to the two mixed states with wavefunctions,

Y = c'A,J) &|B,J) (36)

and

Y2 = IA,J) + 'IB,J) (37)

where

9 + = .
0' + =1.

(38)

If the unperturbed energies of the states are designated by EA

and E then the pcrturbcd energies will be given by

(.A'E B + B/(EA-E B +
E = 2 (39)

where A is the matrix element of the perturbation term, P, between

the two states:

6 = (A,JJP B,J) (.10)

The coupling coefficients, en and may be written as

2
(EA-E ) + .I- + (E A- B)
cA = ) (41)

2,/( -EB) + 4A2

and

2,/( 2+ .*IA

Using equations 39, 411 and '12, it can be shown that A may be written

as2 2 9
Sc (E -E ) (1--)
A = 9 ) (43)
(2 1)-

The Zeeman energy for the mixed state, T may be obtained

through the following considerations. The Zeeman energy is written as

E = (,.:1-\(1B)w.I(ol|A -1, (44)

or

E I. < A ( .\ I 1| + I| 1 < _1 P (45)

Th us

E = zo2g1 (A)HmJ + o J'() }m

= [1 c,-2g (A) + I, gj (B) m (46)

where g (A) and g (B) are the molecular g factors for the states

A and B, respectively. The Zeenman energy may now be 'written as

E = 'LgJ 1mj (47)

if the effective g factor for the mixed state is defined as

g, = [ g (A) + P-g (B)] (48)

From equation 5, the relationship between the product, gT ,
J J
for the perturbed state and the experimental halfwidth of the level-

crossing signal becomes

gT = h (49)
J J 24 Hz

If the lifetime of state B is long compared to that of state A, the

lifetime of the perturbed level '.'ill be given by

Tj = T A."c (50)
J A

where T is the lifetime of the pure A state. Then using equatLiols -IS
A
and 50, equation 49 may be written as

= (o2gj((A) 2gj r (f)) (!)i,
2 2 = 2. ,1
J J \ J J 2H III

or

(1-c ) (b2)
g (A) + 2 g (B) = 2 T (52)
C oA A

Thus, if the g factors and approximate lifetimes for the two

states participating in the perturbation are knoi'n, the coupling

constants may be obtained from the experimental level-crossinrg data.

If, in addition, the term values for the perturbing states are kno'.,n

from spectroscopic analysis, equation -13 may be employed to obtain I,

the strength of the perturbation.

and r-Centroids of Molecular Transitions

The discrepancy between the results of certain experiments

involving measurements of the fundamental properties of the A IT state

of carbon monoxide has been discussed in Chapter I. These discrepan-

cies arose, in part, from attempts to relate absorption oscillator

directly in electron impact experiments. In the following paragraphs

a discussion is given of the theory which may be used to relate some

of the fundamental quantities obtained in experiments involving

electronic transitions in simple molecules. The discussion is based

on the treatment of molecular quantum mechanics outlined by Herzberg

r29] and the discussion :l transition probabilities given by James [10].

The Schrocingwr equation of a diatomic molecule may be

written as

1 -, 1 2' Sn2
m- + ? + (E-V)'r = 0 (53)
i k

where i refers to the c..rdinaLes of the electrons (mass m) and k

refers to those of the nuclei (mass MV). An approximate solution to

equation 53 may be written as -'i = i (ri )'i (r ) where and vi are
e yr k e Vr

solutions of the equations

V72. + ( -V )( = 0 (54)
L i e 2 e e
i

and

1 2 -2 ,el- 0 (55)
L k vr 1 2 n vr

respectively. The first of these equations is the Schrodinger equation

for electrons moving in the field of fixed nuclei and having a poten-

tial energy, V For different internuclear distances V is different
e e
el
and therefore the eigenfunctions, 'i and the eigenvalues, E of this
e
equation depend on the internuclear distance as a parameter. The second

equation is the Schrodinger equation of the nuclei moving under the

el
action of the potential energy, E + V where V is the Coulomb
n n

potential energy of the nuclei. It may be shovn that the expression

given above for the total eigenfunction is a solution to equation 53

only if the variation of er with the internuclear distance may be

el
neglected. This condition is fulfilled for most diatomic molecules

and is known as the Dorn-Oppenheimer approximation. The use of E + V
11
as the potential energy for the motion of the nuclei and the resolution

of 41 into the product of \re and V is therefore usually justified.

The intensity of an electronic transition from an upper state,

a, to a lower state, b, is determined by the transition probability,

Aab. The transition probability is in turn determined by the square of

the dipole matrix element between the upper and lover states. Under the

assumption that the Born-OppenJheimer approximation holds, the matrix

element may be written as

R = aR(r) b ) (56)

The matrix element. R(r), is the electronic transition moment given by

R(r) ( ( | (57)

i

If the variation of R(r) with the internuclear distance is slow, R(r)

may be replaced by its average for the vibrational transition.

Equation 56 then becomes

R = R (* ) b (58)

Further, the vibrational-rotationnl overlap integral may be written

as

V,,I > 1 <(' 'v") .o ,t (59)

v.here the first term is the square root of the Franck-Condon factor

for the vibrational transition, and the second term is the overlap

integral for the rotational transition.

The transition probability for emission, A /, ,,, is
ab ,v ,J J
given by

4 3
64n T ,, ,
A = R" I (60)
ab,v v ,J J 3hd _L '
a / a
m m

where the sum is over all values of the magnetic quantum numbers,

m and m The parameter, d the degeneracy of the upper state, is

equal to 2J 1 for 2 states. States for which A> 1 are A doubled and

therefore the degeneracy is 2(2,J +1). Summing over all possible rota-

tional transitions from the upper state gives

4 3
64n V ,
v %, In e 'I <,1'Iv > (61)
A = I v")2 (61)
ab,v v 3h e

on account of the sum rule,

IRZ Io' 2 = (2J +1) (62)
J ,mm

The transition probability is therefore independent of the rotational

quantum number.

The transition probability for emission from a particular

electronic-vibrational state may be written as

A a / I "I)ir I % (62)
V V
v v

It should be noted that equation 63 applies to states for which only

one route of decay to the lov.er state is allowed. For states which h

exhibit electronic branching, the sum in equation 63 must be taken

over all states to which transitions occur. The electronic transition

moment appearing in equation 63 has been written as a function of the

average internuclear separation for the (v ,v ) transition. The

parameter, r ./, is known as the r-centroid of the transition, and
V V

gives a measure of the separation. The r-centroid is defined as

(vIrv")
,., = (64)
V V 4 %'

The lifetime of the electronic-vibrational state is given by

1
T -(65)
v A ,
v

The transition moment, R may be taken to be constant for

some molecules and removed from the sum in equation 63. In other cases

the variation of v over the vibrational band system may be neglected.

Under these approximations, and in view of the sum rule, |(v v ) = 1,
V

1 64n7v -2
3h R (66)
V

In this apprcximintion the lifetimes of all vibrational levels become
3
equal. A more correct formula could le obtained by replacing '3 by
,3 I ,,, I 2
the mean cubed w.avenumber, \V = (v v For the case where
V
3
the variation of v.-iLth v can be neglected but r is not constant,
C

equation 63 yields

6-1n T 2 I 2
A 3; v Je(r) '"' (67)

heree use I'ris been made: of the completeness relationship,
V-

V. v),v = 1. Thus .%ien 'v does not vary strongly with v lifetime

measurements may be used to obtain information about the dependence

R on the internuclear distance provided that Franck-Condon factors for
e

the vibrational transitions are known.

The oscillator strength or f-value gives the degree to which

a transition resembles a classical oscillating dipole in the absorp-

tion or re-emission of radiation. The f-value is given by

f 1.199 (9 ) A f (68)
v v 2 v v

where the degeneracy factors, G's, are given by (2S+1) for Z states

and 2(2S+I) for states for uhich A 1 1. The absorption oscillator

strength or integrated f-value may be defined as

fo= f o (69)

The absorption oscillator strength may, in principle, be related to

the radiative lifetime through the use of equations 63, 65 and 68.

The bjand(.- of the fourth positive system of carbon monoxide

extend over such a large ,.'av'el ength region that the variation of 'V

may not be neglected. In addition, the strong dependence of the

electronic transition moment on the internuclear distance has been

uell established. lice assumptions which simplify the expTression for

the transition probability are therefore not appropriate to the bands

of the A-X transition in carbon monoxide.

The f-values of the A-Y transitions may be related to the

lifetimes of the vibrational levels by employing equation 63 in con-

junction with a model for the dependence of the electronic transition

moment on the r-centroids of the vibrational transitions. It is

usually assumed that R is a simple function of r-centroid. The
e

parameters characteristic of the functional dependence are varied in

equation 63 to obtain the best fit to the set of radiative lifetimes

of the vibrational levels. Using the values of R the absorption

oscillator strength may be calculated from equations 68 and 69. The

use of this particular technique of analysis has produced the reason-

able agreement between oscillator strengths calculated from lifetime

values and those measured directly in electron scattering experiments.

CHAPTER I 1

EX'PER MENTAL APPARATUS

A diagram of the apparatus used for the molecular Hanle effect

experiment is shown in figure I\'. Radiation for the excitation of the

scattering gas was produced in a molecular discharge lamp. A one-

meter vacuum monochromator '.'as used to select bands of the fourth

positive system of carbon monoxide. A beam of resonance radiation

passed from the monochromator into the scattering cell where the proper

geometry for the entrance bean, detector, and magnetic field was main-

tained. The scattering cell was mounted between the pole-pieces of an

electromagnet capable of providing fields up to 10,000 Gauss. Reson-

ance fluorescence from the scattering gas was shifted to a wavelength
0
of about -1000 A by a coating of sodium salycilate on the lover end of

a lucite light pipe. The light was detected by a photomultiplier

tube mounted in a field-free chamber. After amplification and time-

constant smoothing, the signal, proportional to the photon counting

rate for scattered resonance radiation, was stored in the memory of

a signal average as a function of the magnetic field in the scatter-

ing region. The stored signal could be obtained from a digital printer

and from an X-Y plotter.

cli

In.
in.

-I.

-4

1a)

I-4

UJ

Co
V)

42

w
> Zc
> 0-
< -
o mz
N
w m

< < o
00
Lu aN.~I I----c'
0 '' -^-.

0 0 w

Oi-
I---

O,

0

0
z
0
I.- O z-
Ino

"I
C)

Molecular Dischbirge Lamp Design

In the molecular Hanle effect experiment, one of the most

difficult of experimental problems proved to be the development of

a satisfactory source of radiation for the excitation of the scatter-

ing gas. The need for relatively large intensities in the bands of

the fourth positive system suggested the -use of a molecular disch:rge

source. In addition to the need for high intensity, t'.,.o other factors

v.ere present for consideration in the design of the discharge lamp.

The first consideration was the reductic.n of self-reversal of the

resonance radiation emitted by the lamp. Self-reversal occurs ,.hen

a layer of unexcited gas lies betvecn the emitting layer and the exit

port of the lamp. Under this condition tihe line profile for the

emitted radiation may exhibit a minimuin at the center of the line.

Self-reversed radiation is, of course, very ineffective in the excita-

tion of the scattering gas. Fortunately, the absorption line strengths

v.ere relatively small for the high rotational levels investigated in

this experiment, and most discharges were found to be optically thin,

thus minimizing the problem of self-reversal.

The second and most important concern was the minimization of

fluctuations in the intensity of the lamp. Since the level-crossing

signal amounted to only a fev percent of the total scattered light,

nonstatistical fluctuations in intensity had to be kept low for the

signal to be seen at all. It was found that the most stable radiation

sources were those excited by radio frequency power.

The first type of lamp tried was a McPherson Model 630 ultra-

violet light source as modified by Wells [30]. This source was

basically a flow lamp in v.Ihich the discharge took place in a mixture

of helium and carbon dioxide in a water cooled capillary tube between

aluminum electrodes. Helium flo..ced in a reverse direction through the

lamp to help prevent self-reversal. The discharge was excited by a

diathermy machine capable of producing up to 500 watts of R. F. power

at 27 AUiz. Impedance matching bet,..een the lamp and the H. F. generator

produced low standing wave ratios into the lamp under operating condi-

tions. As an aid to reducing fluctuations in intensity, large ballast

bottles were employed between the lamp and the gas supply tanks. The

lamp was found to produce resonance radiation which was relatively free

from self-reversal; however, the high R.F. power necessary for the

operation of the lamp caused severe interference with the electronic

apparatus used throughout the experiment. Serious attempts .,.ere made

to shield against the spurious radiation before the use of the lamp was

finally abandoned.

Extensive use of lamps excited by microwave energy in atomic

level-crossing [31] and optical pumping [32] work suggested that a

lamp of this type might prove equally useful in the molecular HanLe

effect experiment. In a microwave discharge the power is usually

coupled into the gas through a resonant cavity, permitting the use of

electrodeless lamps which are less susceptible to deterioration due to

contamination. In addition, higher output intensities may be obtained

with an expenditure of less excitation energy than with lower frequency

discharges due to the close coupling between the discharge and the

power source. Bearing these factors in mind, several Inmps were

designed to be used with a Raytheon microwave power generator which

produced up to 80 watts output at 2-150 M z. These lamps were all con-

structed in such a way that the output radiation was eu.iitted through

a differential pumping port located at the front of the lamp. This

design was choscin because LiF and MgF2, the only materials suitable
o
for windows in the wavelength region of interest (around 1500 A),

exhibit rapid deterioration in transmission upon exposure to intense

ultraviolet radiation [33,34]. Several investigators [30,35,36] have

reported useful lifetimes of only a few hours for discharge lamps with

LiF windows. Differentially pumped lamps, on the other hand, were

found to run indefinitely with no diminution of output intensity.

In the first source constructed, the discharge was carried in

a 1/2-inch-diameter vicor ignition tube which was situated along the

axis of a cylindrical TM0,1,0 [37] cavity. Gasses were admitted at the

back of the tube through a side arm. The lamp produced adequate inten-

sity in the ultraviolet region but exhibited serious instability under

certain operating conditions. This behavior was judged to be due to

the limited number of modes available to the exciting radiation in the

cavity. At certain pressures the lamp was seen to oscillate between

two modes of excitation with an accompanying oscillation in inten-

sity. In addition, the vicor tube was found to dissipate a siz-

able part of the microwave energy as heat. In order to overcome

these difficulties, a second design was developed, utilizing a more

sophisticated Evans [38] type microwave cavity. This lamp is shdoi in

detail in figure IV and in figure V. The Evans cavity was machined

from brass stoc-. and included both tuning and coupling adjustments.

The low..er portion of the cavity contained the discharge lamp itself

which was machined from grade HP boron nitride. This material,

a practically lossless dielectric in the microwave region, proved to

be ideal for the confinement of the discharge. The discharge was

carried within a 1/,'4-inch-diameter blind hole drilled along the axis

of the boron nitride piece. Differential pumping took place across

a 1.'4-inch x. 1 mm counter bore at the front of the lamp. This slit

also served as an exit port for the vacuum ultraviolet radiation.

Gas was admitted through a Sv.agelock fitting v.hich was scre.'.ed into

the central bore at the back of the lamp. The entire apparatus, lamp

and cavity, 'as designed to be mounted on the slit housing of the

monochromator as close to the entrance slits as possible. Differential

pumping was accomplished by a large diffusion pump contained within the

monochromator. The flow.. of gas into the back of the lamp, and conse-

quently the gas pressure within the lamp, was regulated by two needle

valves.

In operation, helium and carbon dioxide flowed into the back

of the lamp, and the pressures of the two gasses were adjusted to pro-

duce the maximum output intensity in the molecular band of interest.

Helium was found to produce a stable discharge in which the dissocia-

tion of the carbon dioxide and the excitation of the resulting carbon

monoxide could take place. The use of carbon dioxide proved to be

Figure V: Molecular Discharge Lamp

TUNING

TRIDE

COUPLING

CO IN-

tion. The Evans microwave cavity allowed very lowv standing wave ratios

to be obtained under almost all pressure conditions in the lamp. It

was found that a pressure differential of about 10 could be maintained

across the differential pumping slit, so that during operation the
--4
pressure in the monochromator was kept below 10 Torr. It was esti-

mated from absorption in the spectrum of radiation emitted by the lamp

that the partial pressure of carbon monoxide in the monochromator was

-7
not more than 10 Torr.

Optical Systemn

For the purpose of description in this paper, that part of the

experimental apparatus following the exit port of the discharge lamp

and preceding the photomultiplier tube shall be designated as the

optical system. Included in the optical system are the monochromator,

the scattering cell, and the fluorescent detector and light pipe.

The bands of the fourth positive system of carbon monoxide

were selected, using a McPherson Model 225 one-meter vacuum monochro-

mator. This instrument w.'as equipped with a large oil diffusion pump

and could be evacuated to a pressure of less than 10-7 Torr. The mono-

chromator was of normal incidence geometry and employed a cylindrical

grating measured 56 mm x 96 mm and was ruled with 600 lines per mm.

With this grating the monochromator had a first-order reciprocal

dispersion of 16.6 A.nLm. With the entrance and exit slits set at*

10 microns a typical setting for the level-crossing experiment the
a
monor'hronmator had a resolution of .166 A. Light impinging upon the

entrance slit .'.as focused on the exit slit by the grating, and from

there a diverging benam entered the scattering cell by the w.ay of a

hollow pipe of about on'.-iall-meter length. The scattering cell was

separated from thi. monochromator by a one-half-inch-diameter x 1-mm-

thick LiF w.iiidov..

The scattering cell wa.ns machined from aluminum in the form of

nn octagonal cylinder. A diagram of the scattering cell is given in

figure VI. The cylinder was 2 inches thick, and the distance between

the faces of the octagon was 6 inches. The scattering region v.as

a two-inch-diameter ;: 5 S-inch-thick cylinder machined into the center

of the scattering cell. Ports led from the scattering region to seven

of the eight faces of the cell. Admission and removal of the scatter-

ing gas, as well as the entrance and exit of radiation, was through

these ports. Gas .was exhausted from the scattering region by a mechan-
-4
icnl vacuum pump, and a base pressure of 5 ;10 Torr could be attained.

Admission of carbon monoxide, the scattering gas, w.as through a micro-

metering valve. Under typical experimental conditions the pressure of

the scattering gas was maintained at about 50 microns as measured by

a Teledyne Model 2A thermocouple vacuum gauge.

A light pipe made of one-half-inch-diameter lucite rod extended

into the scattering region to a position directly above, and adjacent

to the entrance window. The lower tip of the light pipe v.as coated

-4
r-4
C)
u-

to

-'r4

z
-0
CC Z

ciFO

E< Go
Q-U <

a.

OL

.r
.J
-j
0-

4--

0
I-

I-
Q.
0

with a thin deposit of sodium salycilate which fluorescod at about
D
4000 A when struck by the scattered ultraviolet radiation. The

fluorescent emission was propagated up the light pipe by internal

reflection.

The scattering region was positioned between thi: 2-inch-

diameter faces of the tapered pole pieces of the electromagnet.

Spacing of the pole pieces was 3,/4 inch.

Detection Apparatus

Light emitted by the sodium salycilate was detuctcd by an

LEIl Model 6256S photomultiplier tube. The 1-cm-di meter photocathode

of the tube was positioned directly above the polished upper tfip of

the light pipe. The response curve of the CsSb photocathode of thi

photomultiplier exhibited a maximum sensitivity at a wavelength which

matched the output wavelength of the sodium salycilate. Overall effi-

ciency of the detection system, scintillator, lightpipe, and photo-

cathode, was judged to be some,.hat less than 10 percent at an input
0
wavelength of 1500 A.

The photomultiplier along with its voltage-divider chain

was mounted in a thermoelectrically cooled light-tight housing. Within

the housing the photomultiplier tube was cooled to around 0C. The

dark counting rate for the tube at this temperature was between

10 sec and 20 sec This rate was a factor of 50 below the counting

rate for scattered light encountered in the level-crossing ex-periment.

The housing also contained several concentric layers of "nctic" and

"conetic" magnetic shielding material. In addition, the photomnitti-

plier tube itself .wais surrounded by a mu-r.,etal shield. Extensive

magnetic shielding of the photomultiplier tube was necessary to assure

that the sensitivity of the tube remained constant as thc magnetic

field .was swept through its full range. With all of the shielding in

place, the field at the location of the tube v.as found to vary by less

than .2 Gauss as the field on the outside of and perpendicular to the

cylinder axis of the housing was changed from 0 to 1000 Gauss. The

sensitivity of the tube was found to change by less than .1 percent

under these same circumstances. Systematic error introduced by the

sensitivity of the photomultiplier tube to magnetic fields was necgli -

gible since the field-dependent component of the level-crossing signal

always amounted to more than 2 percent of the intensity of the scat-

tered light.

A potential of 1000 volts was maintained across the dynode

chain of the photomultiplier tube. The voltage was supplied by

stabilized high voltage power supply. The anode of the photoriultiplier

was maintained at ground potential. Output pulses from the tube were

coupled to a wideband preamplifier through a 500 pfd capacitor. This

capacitor in combination with the output load resistor of the photo-

multiplier tube formed a filter which yielded pulses with a width of

about 5 psec. The preamplifier was run at unity gain and served to

drive several feet of 53 ohm coaxial cable. Output pulses from the

preamplifier were transmitted along the coaxial cable to a linear ampli-

fier. The gain of this amplifier could be varied from 60 to -100 and

was set so that the largest input pulses just drove the amplifier to

full output. The pulses passed from the linear amplifier into a

single channel analyzer. This device generated a pulse of precise

shape each time it received a pulse whose height exceeded a certain

threshold which could be set manually. In practice, the threshold

was set to just exclude those noise pulses generated in the pre-

amplifier.

In order to reduce noise fluctuations in the level-crossing

signal, the output pulses from the single channel analyzer were fed

into a ratemeter. In this instrument the series of input pulses was

converted into a more slowly fluctuating analog voltage proportional

to the counting rate. The conversion was accomplished by electron-

ically integrating the input signal. The ratemeter contained a

simple RC filter circuit which converted the input voltage, V.(t),
1
into an output voltage given by

t
V (t) = k J e-(t-s)/RC V(s)ds (70)
-CO

where RC was the time constant of the filter-. The time constant was

set so that only a small distortion was introduced into the shape of

the level-crossing signal. The setting depended upon the rate at which

the magnetic field was swept through its range, but time constants of

a few tenths of a second were usually employed.

The output of the ratemeter was amplified to a level of a few

volts and passed into the digitizer of the Fabri-Tek Model 1062 instru-

ment computer whichh was used as a signal average. In order to accom-

plish this amplification, the output of the ratemeter, which was only

10 millivolts, full scale, was boosted to a level of a few volts by

a General Radio Type 1230-A electrometer. In the digitizer the analog

signal was converted to digital form which allowed it to be stored in

the memory of the instrument computer.

The use of the instrument computer as a signal average proved

to be essential to the detection of the level-crossing signal; under

ordinary operating conditions the field-dependent part of the scattered

light intensity v.as never found to exceed the statistical fluctuation
-1
in the total intensity. With counting rates of 1000 sec and an

integrating time constant of .5 second, the field-dependent signal and

the statistical fluctuation both amounted to about 3 percent. With

signal averaging, the signal to noise ratio could be increased to a

more useful level. This was possible, since, as counts were collected

in the memory of the instrument computer, the field-dependent signal'was

accumulated in direct proportion to N, the number of counts; whereas

the statistical noise increased as V/J. Thus the signal to noise ratio

was proportional to l. The memory of the signal average consisted
18
of 1024 channels, each of which could retain up to 2 counts. In

practice, only one-fourth of the memory or 256 channels was utilized

during an experimental run. The channels were addressed sequentially,

and the number of counts stored in each was proportional to the voltage

level appearing at the input of the digitizer at the time the channel

the scattering region was stepped through its range. Thus the level-

crossing signal was stored as a function of the independent variable,

the magnnc-tic field. The rate at which the field was swept depended on

the d.rjcll time for each channel utilized in the memory. D.,.ell tim-es

of .05 and .02 seconds per channel were most c.ften used. The tiiip-

constant of the counting system 'as adjusted to be equal to approx-

imately 10 channels (i.e. .2 and .5 second, respectively, for the

dw.'ell times given above). For a dwell time of .05 second per channel,

a sweep of the complete range of the field took. place in .05 x 25G

or 12.8 seconds. The signal stored in the memory was monitored on an

oscilloscope and readout was accomplished with a Farbi-Tel: digital

printer. Data could also be plotted as a function of channel nuliber

on an X-Y plotter.

Magnetic Field Control Circuitry

The magnetic field in the scattering region was produced by

an Alpha Model 1800 electromagnet. A diagram of the control rnd power

circuitry for the electromagnet is given in figure VII. The basic

control voltage for the experiment w.'as supplied by the instrument

computer. This voltage, which varied between 0 and 4 volts, was

proportional to the number of the channel being addressed, and was

used to drive two bipolar operational amplifiers. The amplifiers

served as buffers for isolating the two legs of the circuit. Two

Kepco Model JQE 36-30 power supplies were used to drive the electro-

magnet. These supplies could be voltage programmed and could supply

up to 30 amperes at 40 volts. Programming voltagesfor the supplies

4-1

01

C:

0
u-

4-i

i

7
-z

m

v.ci- taken from the output of the operational amplifiers. The waveforms

of the programnniiing voltages in figure VII show that as one supply w.'as

stepped from its minimum to its maximum outpui voltage, the other *-as

stepped in thec opposite direction. The voltage across the electro-

magnet therefore passed through zero at the middle of each sweep.

Use of the circuit in figure VII resulted in the dissipation in -he

one-ohm resistors of over one-half of the power generated by the

supplies, Lut the ability to sweep smoothly through zero field madc

tlhe power waste tolerable. At the end of each sv.eep a transient was

introduced as the energy stored in the magnetic field *.'as fed back into

the circuit. The capacitors and series and p:irallel diodes v.ere placed

in the circuit to help protect the power supplies from overvoltages and

reverse polari ties. A delay after each sweep allo.:ed the circuit to

come to equilibrium before a new sweep was started.

The field in the scattering region v.as monitored by a Hall

effect probe. It was found that the field sweep was reproducible and

had a maximum range of from 10,000 Gauss to -10,000 Gauss. The effects

of hysteresis in the magnet were small. Corrections for nonlinearity

in the field sweep were included in the analysis of the level-crossing

signal. The Hall effect probe was calibrated periodically in a proton

magnetic resonance spectrometer. The field within the scattering

region was found to be homogeneous to within 1 percent.

CHAPTER IV

EXPERI MENTAL PROCEDURE

Molecular Hannlo effect experiments v.ere initj cited v.ith the

recording of the spectrum of the (1,0) band of the fourth positive

system of carbon monoxide from the molecular discharge lanp. The

spectrum was tahen in order to determine the characteristic temper-

ature and absorption coefficient of the discharge, and the (1,0) bannd

was chosen because it is relatively free from overl.ipping bands of

the fourth positive system. Although spectra were not taken before

each experimental run, they ..'re recorded periodical ly and the condi-

tions in the lamp were found to be reproducible. A spectrum of the

light scattered by the carbon monoxide gas sample was next recorded

for the molecular band under investigation. From this spectrum the

effective absorption coefficient of the scattering gas as well as

the relative contributions to the Hanle effect signal from excited

rotational levels were determined. The Hanlc effect experiment itself

was begun by centering the bandpass of the monochromator on a partic-

ular rotational feature of the band under investigation, and by

adjusting the range of the magnetic field to be swept. Ordinarily

the sweep was set to cover a range of about 14,000 Gauss centered on

zero magnetic field. A plot of the magnetic field versus the channel

number in the memory of the signal average was taken in order to

determine the linearity and range of the sweep. The collection of

level-crossing data in the memiio'ry,' thlen commrenccd and was continued

until the quality of the ex-pel inental line shape reached the desired

level. Generally, an experimental run lasted from two to four hours.

At the end of the run the spectrum of scattered light was again recorded

to assure that experimental conditions had not changed drastically.

The level-crossing data were then fitted to theoretical line shapes

with the aid of a digital computer.

Lamp Spectra

Ideally, molecular lifetime determinations using level-crossing

spectroscopy would be performed on isolated rotational levels within

a vibrational state. In experiments on the fourth positive system of

carbon monoxide, this ideal could not be realized, since, for the bands

investigated, the higher rotational lines tended to be arranged in

closely spaced triplets. The components of these triplets could not

be individually resolved by the monociromator. It was therefore neces-

sary to assess the contribution to the level-crossing signal from each

rotational state of the scattering molecules excited by a component of

the unresolved triplet.

An example of a spectrum of the (1,0) band obtained from the

discharge lamp is given in figure VIII. In obtaining the spectrum the

detector was mounted directly on the exit slit housing of the monochro-

mator. The discharge in the lamp was begun and allowed to stabilize.

Helium pressure in the lamp was then adjusted until the partial pressure

Figure VIII: Lamp Spectrum of the (1,0) Band

(1.0) BAND
* TL-300K, aL=5.0
A TL-3500K, OL:4.5
O TL=4000K. OL=4.0

(4.2)

P(16)- Q(20)

1510

1514 1512
WAVELENGTH (A)

1516

of helium in the monochromator was 5 X 10 Tory as indicated by a cold

cathode vacuum gauge. CO2 h.'as then admitted into the lamp until the
-5
tol a] pressure in the monochromator was S or P' x 10 Torr. The powtr

input to the lamp was set at 80 wv'atts, rind the SvrI into the microv.'wve

cavity wus minimizc-d. Tihe ,ri-n c;:'2na-to' slits were adjusted so that

the rotational feature of interest was well resolved. it was found

that when this procedure was followed reproducible spectra could be

obt ai ned.

The basic features of the (1,0) band are apparent in the spec-

trum in figure VIII. For J >12 rotational features which consist of

one line each from the P, Q, and R rotational branches are resolved.

The components of the triplets are of the form P(J), Q(J+4) R(J.-9).

There are also coILtributions to the spectrum from two overlapping bands
o
of the fourth positive system. The (4,2) band has a maximum at 1510.4' A,
0
and the (7,4) band has a maximum at 1515.7 A. However, both of these

bands fall outside of the region of interest for rotational lines

investigated in this experiment.

The plotted points in figure VIII are local maxima of the

simulated spectra generated by the application of equation 29 to the

(1,0) band. The spectra were generated for three different combinations

of lamp temperature and absorption coefficient. From the analysis the

temperature and absorption coefficient for the discharge were found to

be 3500K and 4.5, respectively. The other sets of values were taken

to give the experimental limits for these quantities. The simulated

spectra were normalized to the experimental spectrum at the P(16),

Q(20), R(25) spectral feature. Once the two lamp parameters were.,

determined the intensities of rotational lines in the exciting radia-

tion were found through the application of equation 28.

Spectra of Scattered Light

A spectrum of scattered resonance radiation was recorded

before each run of the level-crossing experiment. Figures IX and X

are typical of the spectra obtained for the (1,0) band and (2,0) band,

respectively. The plotted points are local maxima of the simulated

spectra of scattered light calculated from equation 31. Numerical

integration of equation 31 was implemented through the use of an

IBM 360 digital computer and a program for computation developed by

Wells [30] and Isler [13]. In fitting the simulated spectra to the

experimental data, the temperature of the scattering gas was assumed

to be 3500K and the absorption coefficient, os, was varied to obtain

the points plotted in figures IX and X. For the (1,0) band the best

fit was judged to be for a = 2.0. For the (2,0) band the best fit was
s

for s = 3.0. Both experimental spectra were produced with a scatter-

ing gas pressure of 50 microns. As the pressure of the scattering gas

was varied from run to run it was of course found that different

values of c' produced better fits to the experimental spectra.

The Hanle effect signal produced from excitation by the

incompletely resolved rotational features of the v = 1 and v'= 2

vibrational bands consisted of a superposition of line shapes arising

from each excited rotational state of the scattering molecules.

Figure IX: Fluorescent Spectrum of the (1,0)

Band

(1.0) BAND
TL 350 K, aOL-.5
0 as'1.0

x as= 3.0

0
o >H
0 Az
LuJ
HI-2
X z

0

x
P(16)-Q(20)
x

__. I I ILI I

1516 1514 1512 1510
WAVELENGTH (A)

Figure X: Fluorescent Spectrum of the (2,0)

Band

70

(2.0) BAND
TL 3500 K. aL=4.5
A as,2.0
x as'3.0 /
o aS 4.0

gX
x

F-
o _L)
0 U)
z

0

x
0

P(16) -0(20)
0
A

A

1484 1482 1480 1478
WAVELENGTH (A)

The contributions to the Hannc effect signal were calculated from

equation 31 and are listed in Table II. The tabulated figures give

the relative contribution to the signal from rotational states

excited by a particular branch line. For ex:citation by a Q branch

line, Table I shows that re-radiation from the excited state may be

only through a Q branch. For excitation by a P or R branch line,

there will be a contribution from re-radiation in both the P and R

branches. For the latter case, Table II gives the total contribution

from both modes of decay. The contributions to the HanIc effect

signal have been tabulated for three values of ca for each rotational

line of interest. The figures calculated for the bracketing values of

the absorption coefficient were taken to give the limits of error in

the intermediate value. It may be seen that the contributions to the

signal from levels excited by R branch lines are almost negligible.

Analysis of the lian1e Effect Signals

Analysis of the experimental Han16 effect lineshapes was

carried out on the IBM 360 computer, using a nonlinear least-squares

(NLLS) curve fitting program. The theoretical lineshapes to which

the signals were fitted consisted of a superposition of a Lorentzian

and a dispersion curve for each of the excited rotational states, and

a term proportional to the amplitude of the field-independent back-

ground. Six parameters were varied simultaneously in the NLLS program

to produce the best fit to the experimental data. The rotational

levels were assumed to have the same lifetime, and this value was

Table II: Contributions to the Hanle Effect

Signal from Excited Rotational States

Table 11

(1,0) Band

TL=3500 K.
LJ

Resolution =0.32 A

J /s P(J) Q(J+41) R(J+9)

1.0 21.2 77.6 1.2
15 2.0 19.8 78.3 1.9
3.0 19.1 78.6 2.4

1.0 22.8 76.2 0.9
16 2.0 21.2 78.0 0.9
3.0 20.4 78.4 1.3

1.0 25.3 74.2 0.5
17 2.0 23.4 75.9 0.7
3.0 22.0 77.2 O.8

1.0 27.7 72.3 0.0
18 2.0 25.9 73.7 0.4
3.0 24.5 75.0 0.5

1.0 31.0 69.0
19 2.0 29.6 70.4 0.0
3.0 28.4 71.6

1.0 34.8 65.2
20 2.0 33.1 66.9 0.0
3.0 31.9 68.1

1.0 40.0 60.0
21 2.0 38.1 61.9 0.0
3.0 36.9 63.0

1.0 44.4 55.6
22 2.0 43.6 56.4 0.0
3.0 42.6 57.4

Table II continued

(2,0) Band

-'=4.S

*T =3500 K.
L

Resolution =0.32 A

J s r(J) Q(J+4) R(J+9)

2.0 19.7 7S.3 1.8
15 3.0 18.8 78.9 2.2
4.0 18.1 79.4 2.5

2.0 21.2 77.6 1.2
16 3.0 20.1 78.4 1.5
4.0 18.5 79.8 1.7

2.0 23.3 76.1 0.6
17 3.0 21.8 77.5 0.8
4.0 20.3 78.8 0.9

2.0 25.9 74.6 0.0
18 3.0 24.4 75.4 0.2
4.0 23.0 76.4 0.6

varied to adjust the "halfwidth" of the theoretical curve. In add t :on,

the dispersion curve conLributions, the amplitude of the signal, and

the ratio of the field-dependent to field-independent terms were

adjusted until the experimental and theoretical cur.ecs conve.'ged.

Convergence ,,was judged l'y monitoring6 the PRMIS deviation bet'.~oen the

t%%o curves. Deviations of less than 5 percent per point could usually

be obtained after eight iterations of the curve fitting program.

Data sets were generally analyzed over intervals of 75 percent

and 100 percent of the range of the independent variable, the magnetic

field. If the lifetime values predicted by the two fits differed by

more than 20 percent, the data were rejected as unreliItbl e. The exper-

caused by the timru constant present in the detection system. A time

constant of 4 percent of the sweep period (a typical value) produced

less than 2 percent decrease in the experimental lifetime. The result

of an experimental run has been plotted in figure XI along with the

fitted curve produced by the :.'LLS computer program.

-0

s-I

rSi

0
C

?-----5s

0

0
LL

z
-o
uc)

10
LC)
O
\ l

So -

^f^^ -C) U)
o(/2
()

?0
LA ..J
w
LL

CO
0
C\ W
Z
0

o
U')

10
0
Cv)
O

LO
ID

0

co

(S.ILl Nn8uv) Ail SN31Nl

CHAPTER V

RESULTS

Hanlc effect data ..ere taken on eight resolved rotationc-.l

features in the (1,0) vibrational band and on four in the (2,0) hand.

For the (1,0) band,lineshapes from several lines showed pronounced

narrov.'ing of their hal fwidths due to a perturbation in the A 17 upper

state. These data were analyzed separately from those for %..hich the

effects of the perturbation were not apparent. For the unperturbed

rotational levels the lifetimes derived from the data w.'ere averaged

to yield the lifetime of the vibrational state. For the (2,0) band,

no evidence of narrowing due to perturbations was found for the levels

values of the pressure of the scattering gas for both the v = 1 and

v = 2 vibrational levels. No dependence of the measured lifetimes

on the scattering gas pressure was detected for either vibrational

level for pressures between 50 and 300 microns.

S= 1

Figure XII shows the results of lifetime measurements carried

out on the v = 1 vibrational level of the A IT state. In this figure

the product of the lifetime and the Lande g factor, g T is plotted

(NJ
II

0-

.0

,-4
U

4.

-I4

(C
0 C

-i 0

9--
R 4 -
Lz 1-

---1-T

H-

S0N

I-
Z

S0

.-
<

0
,- I-
I-
0
cr

o
c'J

(su) (e)r6/ r.r6

Ps a function of the rotational quantum number of the Q branch comipo-

neut of each spectral feature investigated. Since analysis of the

Hanle effect ] inesliip)es yielded the product, g it ,''as necessary

to know the Lande g factor in order to ascertain the lifetime of the

rotlational state. For a 1T molecular state the g factor is found by the

application of Ilund's case (a) coupling scher.me. For case (a) coupling,
-1
g = J(.(+1) The data plotted in figure XII have been normalized to

these values.

Results ior Unperturbed Levels

The measured lifetimes of rotational features characterized by

Q branch lines for which J' = 19, 20, 21, and 2G were averaged to yield

the lifetime of the v' = 1 vibrational state. The result \\as

T = 10.41 0.8 nanoseconds.
v = 1

The lifetimes plotted in figure XII represent averages of two

or three runs, each between two and four hours long. The error bars

plotted represent the deviation from the mean of the averaged values.

In all cases deviations of about 10 percent %.ere obtained. The error

quoted for the experimental lifetime is the square root of the sum of

the squares of the estimated random errors incurred in the experiment.

Contributions to this figure were from the three following sources:

(1) Uncertainty in the range of the magnetic field sweep. This

error was estimated to be, at most, 4 percent of the total range

of the field. (2) Variation among measured lifetimes derived from

individuiAl runs. For the v = 1 measurement this error was tal-erdto

be the mean deviation from the Meann of the measured lifetimes and

amounted to 5 percent of the average value. (3) Uncertainty inherent

in the analys-i : of the contributions to the level-crossing signal

from unresolved rotational levels. This error may be estimated from

Table II. The maximum deviation from the estimated value for any Ot

the contributions tabulated is less than 5 perccr.t. Further, it may

be shown that a 5 percent deviation in the contribution to the level-

crossing signal from one of the unresolved rotational levels will cause-

only a 2 percent deviation in the ex-perimental lifetime. The exper-

imentnl error, 1E, may therefore be written as

2 2 2 1
S [(4) + (5) + (2) ] 6= 6.7, .

Results for Perturbed Levels

The pronounced increase in the product, gT1 for levels

adjacent to J = 23 is believed to result from a perturbation which

couples the A TT, v = 1 state to another state of the molecule.

Simmons et al. [2] have attributed a perturbation which has a max-

imum in the Q branch at J = 23 to the a L Fl(v = 10) state. The

notation, F71, designates the component of the triplet for which

J = N+ 1, %here N is the quantum number for the total angular momentum

apart from spin. This state perturbes the ITT state by a spin-orbit

interaction for which the selection rule, AJ= 0, holds [27,39].

The theory outlined above for the analysis of level-crossing signals

from perturbed states %as applied to lineshapes from those rotational

features containing Q branch lines for which J' = 22, 23, 24, and 25.

In fitting lineshapes from perturbed rotational features o-.ly the

product, g T for the perturbed Q bri-nclh upper state was varied to

obtain the fit. The lifetime of the other two components v.'as ta.len

to be that of the v' = 1 state (10.11 nanoseconds). The Lande g factor
3-+
for the L perturbing state is given by Hund's case (b) coupling
3 +
scheme e. For the F component of the Z state, gj = 2/J. The result ts
1 J

of the analysis of the perturbed levels are given in Table III.

The coupling coefficients, ce and z., were first calculated from equn-

tion 52 using the e:qperimental value of 11 Employing the value of

o, the lifetime and effective g factor for the perturbed level were

calculated from equations 50 and *18, respectively. The values of t,

the matrix element of the perturbation between the IT and 3 states,

were obtained by application of equation 43.

v = 2

The measured lifetimes of rotational features containing Q

branch lines for whichh J' = 19, 20, 21, and 22 were averaged to yield

the lifetime of the v' = 2 vibrational state. The result was

T ,=2 = 8.49 1.0 nanoseconds.

Results of the lifetime measurements on the v' =2 state have

been plotted in figure XII. The error bars give the uncertainty in

i:.c results for the individual rotational levels. The uncertainty

amounts to about 12 percent of the experimental values. No functional

dependence of the lifetime on the rotational quantum number is apparent

4-J

$4 .Li r4- :$ U

U) r-4
Q) 0)
C4 >
0)
r-4 ,-J

C13

~4 r4

Ei 0

Li 4

'-4

r- cn i) cn
ot o 0 0n

C'4 CM, r-l r-

M-I r-4 r-I r-4

%0 L0 r0 0
Cl) U') r4) 00

0 C-% C4 0

co r C co
0 Vm L o

* r co
CT> co cc cr>
0' 0 00 0"
m *

C cn -T In
C4 04 CMi C1

I-D

-4
E
u

b

86

.for the levels inv.es tigated. Sinrmnons et al. [2], in fact, report

no perturbations in either the Q or P branches for 'alues iof J between

10 and 25. The uncertainty in the ex.Terinienl al lifetime is due almost

entirely to statistical fluctuation in the measured results frui, the

individclnl rotrtioniA l levels.

CHAPTER VI

CONCLUSIONS

Level-crossing spectroscopy has been showv.n to be a useful

technique for the investigation of certain fundamental properties

of excited molecular states. The measured lifetimes obtained in this

experiment were found to be in very good agreement with those obtained

by other investigators as may be seen from Table IV. The agreement

with the results of Wells and Isler [13] is particularly interesting.

The Hanle effect signals produced in their investigation resulted

from transitions from the first eight rotational levels of the v' = 2

vibrational state. In both experiments, however, the technique of

analysis of the observed lineshapes was similar and the agreement

between the lifetime values obtained for small and large rotational

quantum numbers affords credibility to the technique.

Hesser's [11] lifetime values were obtained by the direct

observation of the decay of upper states of the four positive system

excited by electron impact of carbon monoxide. The results seem con-

sistently large, however, and may contain systematic error introduced

by undetected cascading transitions from higher excited states.

the use of the delayed coincidence technique. In monitoring the

decay of the excited states, no photon was counted which was not

,l.
oj

Q)
.C
4-i

0

U,
-1

0
--4
4-1

.Q
04
F-4

r-4

89

<:

0

aJ
< C

(0i

**J
1..

oc
C.

-a -
u

I '
IV C

-00

r_--
) 13

Ca

.0 0

EC' 0

n-' I n

L I- C)

-H4 I
I
a w
a C)

1-1 C) C W

c^ 0i ^ ^ '

-4 C"J C'3 .0 U *~

1-4 C1J

correlated to a particular scattered electron responsible for their*

excitation of tle state.

'The lic-time results of Chervenak and Ander-son [19] were

obtained by using a pulsed invertron [-10] excitation source and a

delayed coinci dence measurement technique [41]. The large discrcpancy

between their results and those of the other investigators may be

atLributnble to one or more of the following e'ox-lnations: (1) Carcad-

ing. The C1 state of carbon monoxide lies above the A Tl state nnd

the B Z+ state would d be difficult to detect and could cause an increr.as.e

in the apparent lifetime of the A IT state. (2) Radiation trapping.

The invertron v.as operated with carbon monoxide pressures of from 50

to 500 microns and at a temperature of about 900"E. Ulider these con-

ditions it is probable that resonance trapping of the escaping radin-

tion occurred. The trapping process could produce a marked increase

in the apparent lifetimes of states participating in resonance transi-

tions. (3) Slov.. system response. The pulsed invertron technique has

not been applied to the measurement of lifetimes in the 10 nanosecond

range. It is possible that the system is limited to a response time

of around 15 nanoseconds and therefore could not "follow" the decay of

the A T state

level found in this work and that of Imhof and Read is significant.

These results indicate a dependence of the electronic transition

moment on the internuclear separation in the carbon monoxide molecule.

Unfortunately, the observed decrease in the lifetime from v' = 1 to

v = 2 is not consistent with the dependence of the transition moment

on the r-centroid bound by Mumma et al. [14] given in equation 1.

This relation produces a slight increase in the lifetime with the vibra-

tional level. Theoretically, the trend in the lifetimes is very sensi-

tive to the slope of the transition moment versus the r-centroid curve

so that a slight adjustment of equation 1 might produce agreement with

the lifetime results. It is also possible that the transition moment

has a higher than linear dependence on the r-centroid, although this

dependence cannot be inferred from the results of the present experiment.

The sensitivity of the level-crossing technique is demonstrated

by the results for the perturbed levels of the v = 1 vibrational level.

The experimental values of the coefficients, and p, show the coupling

between the 1T and 3 + states to be rather small even at the maximum

of the perturbation. Additional lines in the spectrum of the (1,0)

band were reported by Simmons et al. [2] only for J'= 23 and J' = 24,

but the effect of the perturbation was clearly evident in the level-

crossing data for four different rotational levels. The sensitivity

of the lHanle effect lineshapes to the perturbation may be accounted

for by the fact that the halfwidth of the signal is proportional to

(gT )-1. While the perturbation left the lifetimes of the affected

levels unchanged, the effective g values we.'ere found to increase by

as much as a factor of two over the values predicted for the IT state

by case (a) coupling. The values of A listed in Table III show a

dependence on the rotational quantun numbers of the perturbed levels,

92

but this variation is almost certainly introduced by statistical

uncertainty in the data. The moan for these values was

-1
A = 2.7 cm

and is in agreement ".'ith values v.which may be obtained from conven-

tional spectroscopic analysis.

Full Text

PAGE 1

MEASUREMENT OF THE RADIATIVE LIFETIMES OF THE V = 1 AND V = 2 LEVELS OF THE A STATE OF CARBON MONOXIDE BY RALPH LAURENCE BURNHAM A DISSERTATION PRESENTED TO THE GRADUATE COL-NCI L OF THE UNIVERSm' OF FLORIDA IN PARTIAI, FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPH\' UNIVERSITY OF FLORIDA 1972

PAGE 2

ACKNOIVLEUGMENTS The author wishes to thank the members of his supervisory committee for their assistance throughout his graduate program. In particular he wishes to thank tJie chairman of his supervisory committee, Dr. Ralph C. Isler, for his guidance during the course of this research. The author also wishes to thank Dr. William Wells for his assistance during the early stages of this research. 11

PAGE 3

TABLE OF CONTENTS Page ACKNOWLEDGMENTS Â• Â• Â• ^^ LIST OF TABLES "^ LIST OF FIGURES "^^ ABSTRACT ^^^ CHAPTER I. INTRODUCTION ^ II. THEORETICAL CONSIDERATIONS 7 Semiclassical Analog to the Level -Crossing Phenomenon Â• Quantum Mechanical Calculation of the Hanle Effect Signal for the A State of CO 12 Rotational Line Contributions to the Molecular Level -Crossing Signal 20 Rotational Intensity Distribution in a Molecular Discharge 20 Rotational Intensities in Resonance Fluorescence ^^ The Effect of Rotational Perturbations on the Level-Crossing Signal 30 Lifetimes, Transition Probabilities, f -Values , and r-Centroids of Molecular Transitions 33 III. EXPERIMENTAL APPARATUS 40 Molecular Discharge Lamp Design 43 Optical System 49 Detection Apparatus 53 Magnetic Field Control Circuitry 57 111

PAGE 4

TABLE OF CONTENTS (Continued) CHAPTER Page IV. EXPERIMENTAL PROCEDURE 61 Lamp Spectra 62 Spectra of Scattered Light 66 Analysis of the Hanle Effect Signals 71 V. RESULTS 78 v' = 1 78 Results for Unperturbed Levels 81 Results for Perturbed Levels 82 v' =2 83 VI. CONCLUSIONS 87 LIST OF REFERENCES > 93 IV

PAGE 5

LIST OF TABLES Table Page I. Results of the Quantum Mechanical Calculation of the Hanle Effect Signal for the A State of CO 22 II. Contributions to the Hanlo Effect Signal from Excited Rotational States 73 III. Experimental Results for Perturbed Rotational Levels . 85 IV. Lifetimes of Vibrationnl Levels of the A State of CO . 89

PAGE 6

LIST OF FIGURES Figure Page I. Semiclassical Analog to the Level-Crossing Phenomenon 9 II. a. Coordinate System for the Molecular LevelCrossing Experiment ^ b. Partial Energy Level Diagram for a iTS Molecular Transition 15 III. Coordinate System for the Scattering Region 29 IV. Experimental Apparatus 42 V. Molecular Discharge Lamp 48 VI. Scattering Cell 52 VII. Control Circuitry for the Electromagnet 59 VIII. Lamp Spectrum of the (1,0) Band 64 IX. Fluorescent Spectrum of the (1,0) Band 68 X. Fluorescent Spectrum of the (2,0) Band 70 XI. Experimental Hanle Effect Signal with Fitted Lineshape 77 XII, Experimental Results for the v=l and v = 2 Vibrational Levels , 80 VI

PAGE 7

Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MEASUREMENT OF THE RADIATIVE LIFETIMES OF THE V = 1 AND V = 2 LEVELS OF THE A STATE OF CARBON MONOXIDE By Ralph Laurence Burnham March, 1972 Chairman: Dr. Ralph C. Isler Major Department; Physics The technique of zero-field level-crossing spectroscopy was employed to obtain the radiative lifetimes of the v=l and v=2 vibrational levels of the A Tl state of carbon monoxide. Level-crossing signals were obtained for eight individually resolved rotational fea-' tures in the (1,0) vibrational band and for four individually resolved rotational features in the (2,0) vibrational band. The signals were found to consist of level -crossing lineshapes from only three rotational transitions, and were analyzed to yield values of g T , the product of tlie Lande g factor and the lifetime. Narrowing of the lineshapes of several of the rotational levels was observed in the v=l state. This effect was attributable to a perturbation caused by the a E state. The values of the coupling constants for the perturbed rotational levels were obtained from analysis of the levelcrossing data. The experimental lifetimes of the v=2 level and of the unperturbed states of the v=l level were obtained by calculating Vll

PAGE 8

1 the Lande g factor for the TT state from Hund' s case (a) coupling scheme. The lifetimes of individual rotational states within a level were averaged to yield the lifetime of the level. For the v=l level the result was T = 10.41 Â±0.8 nsec. For the v=2 level the result was T Â„= 8.49 Â± 1.0 nsec. v=2 Vlll

PAGE 9

CHAPTER I INTRODUCTION Thp hr>nd'=; of fhr' frn-'^th poPi^ivp pvPt.prn of carbon monoxide which arise from transitions between vibrational levels of the A Tf 1 + state and the X E state of the molecule have historically been of fundamental research interest. Original spectroscopic work was stimulated by the presence of intense fourth positive bands as a contaminant in spectra taken in the ultraviolet and vacuumultraviolet regions of the spectrum. Early workers investigated the structure of barids seen in botli eiaission and absorption, and by 1940 vibrational and rotational analysis of all known bands was essentially complete [1]. Recent research has been devoted to the investigation of the lifetime, oscillator strengths, and perturbations of the A TT state. Simmons e t al . [2] have made accurate assignments of perturbations due to six known states in the region of the A TT state. Their work was based on the analysis by Herzberg and others [3,4,5] of bands arising from forbidden transitions to the ground state. It is the upper states of these transitions which interact with the A TT state giving rise to the observed perturbations. Discovery of carbon monoxide bands in both the infrared and ultraviolet regions of the solar spectrum [6] , as well as the prediction of the existence of the gas in interstellar space [7] has

PAGE 10

emphasized the astrophysical importance of tlie molecule. Quite recently Mariners VI and VII have detected radiation from carbon monoxide bands produced in the upper layers of the Martian atmosphere [8,9]. Surprisingly, the observed Cameron bands which arise from a forbidden TT E transition were more intense than those of the fourth positive system. James [W] has derived expressions for the oscillator strengths of the Cameron bands by assuming a coiipling between the a TT and the A Ti states. An accurate knowledge of the fundamental properties of the A TT state is thus becoming important for several aspects of astrophysical research. Considerable controversy has developed over attempts to relate measured values of the lifetimesto oscillator strengths of the bands of the A-X transition. Hesser [11] obtained the lifetimes of several vibrational levels using the phase shift technique. These values were then used in conjunction with his measurement of the relative intensities of the bands to obtain a value of .094 for the absorption oscillator strength of the transition. The result was in conspicuous disagreement with the value, f = .24, obtained by Meyer et al. [12] from electron scattering data. In order to determine the source of the discrepancy. Wells and Isler [13] measured the lifetime of the A(v' = 2) state using level-crossing spectroscopy. Their result was in substantial agreement with that of Hesser. The controversy was partially resolved by Mumma et al. [14] who remeasured the relative intensities of the vibrational bands using a system which had a calibrated spectral response. These measurements were normalized to the average of the

PAGE 11

lifetime measurements and yiolded a value of .15 for the integrated oscillator strength. Lawrence [15] also reanalyzed Hesser' s data and obtained an f value of .17. These results may be compared to the value, f = .195 Â±.012, obtained by Lassettre and Skerbele [16] through the comparison of elastically and inclastically scattered electrons. Meyer's measurements have aJ "^o hrp-n refined [17] and tlic results are now consistent with those of Lassettre and Skerbele. The agreement between the values of the oscillator strength calculated from lifetime measurements and those obtained from electron impact experiments is thus considerably improved, but not perfect. Mumma's intensity measurements also revealed a strong dependence of the electronic transition moment on the internuclear separation in the carbon monoxide molecule. This dependence produces a variation of the transition moment over the bands of the fourth positive system, and must be considered when calculating f values from radiative lifetimes. Mumma assumed a linear relation between the transition moment and the r-centroid of the vibrational transition, and analysis of his intensity data gave R cc (1 .60r / //) (1) e v V where R is the transition moment and r / Â« is the r-centroid of the e V V (v v'^ vibrational band. This relation was in good agreement with *:,Â« data of Lassettre and Skerbele. Some doubt has been cast upon the relationship of equation 1 by the recent lifetime measurements of Imhof and Read [18]. Their data, obtained for v =0 through v =6 levels

PAGE 12

by the delayed coincidence technique, indicate a quadratic oihigher dependence of the transition moment on the r-centroid. Cliervenak and Anderson [19] have also calculated a quadratic dependence from lifetime information obtained from an experiment employing a pulsed jnvertron. The va'idity of their data is, however, open to question. The woj'k described in this dissertation was undertaken in order to olitain accurate radiative lifetimes of individual vibrational levels of the A Tf state of carbon monoxide. The experimental results contained ]iorein will most certainly prove useful in determining the oscillator strengths and transition moments of bands of the fourth positive system. Tiie level-crossing phenomenon which was employed to obtain the Â• lifetime measurements reported in this work was first discovered by Hanle [20] in 1924. Level-crossing signals are produced when two or more magnetic sublevels of an excited atomic or molecular state become degenerate at a particular magnetic field. The degenerate sublevels are excited coherently. Re-emitted radiation from the sublevels suffers interference, giving rise to an alteration in the polarization and angular distribution of the observed light. When the signal arises from the degeneracy in the Zeeman levels at zero magnetic field, the level-crossing phenomenon is known as the Hanle effect. The phenomenon was explained by Breit [21] in 1933, but lay unexploited until accidentally ji ediscovered by Colgrove et al . [22] in 1959. Since then, level-crossing spectroscopy has proved to be an excellent technique for measuring a variety of fundamental properties of excited states of atomic systems.

PAGE 13

Quite recentlj' level-crossing spectroscopy has begun to be applied to the measurement of properties of diatomic molecules. The technique is quite similar to that used with atoms but in general experimental procedure is complicated by the vibrational and rotational structure of the molecular electronic states. The effects of level crossings in diatomic molecules were derived from Brett's original formula by Zare [23] who also suggested several systems as possible subjects for investigation. The first molecular level-crossing signals were reported for NO by Crosley and Zare [24] . Unfortxmately their results were later found to be spurious and due to mercury contamination of t]ieir experiment [25]. Several molecular systems have now been successfully treated. Silvers et al . [26] have observed signals from individual rotational levels of CS excited by overlapping atomic lines from ]\In II. DeZafra et al. [25] have used molecular resonance radiation to excite individual rotational levels in the OH and OD radicals, and have combined level-crossing and optical double resonance data to determine lifetimes and g factors for excited states of these species. In a slightly different approach, Wells and Isler [13] used radiation from an entire vibrational band to excite the v = 2 level of the A TT state of cai'bon monoxide. Contributions to the level-crossing signal from each rotational line present in the scattered radiation were then assessed in the analysis of their data. In the experiment described in this dissertation resonance radiation produced in a molecular discharge lamp was used to excite high rotational levels in the v = 1 and v = 2 vibrational levels of

PAGE 14

the A "TT state of carbon monoxide. The level-crossing signals obtained were shown to consist of contributions from only three unresolved rotational liner, ard proved to be amenable to analysis bj' curve-fitting teclmiques. The basic ex]Derimental quantity obtained from the data analysis was the product of the lifetime and the Lande g factoi* for the vibrational -rotational state under investigation. A theoretical value for the g factor was obtained by assuming a case (a) coupling scheme for the A TT state. The experimental value of the radiative lifetime was thus obtained. Narrowing of the observed lineshapes was quite evident for several of the levels in the v = 1 state. This distortion of the Hanle effect signals was attributed to a rotational perturbation in the A TT state. Data from the perturbed levels were analyzed to obtain values for the parameters characteristic of the perturbation.

PAGE 15

CHAPTER II THEORETICAL CONSIDERATIONS In this section the theoretical lineshapes for Hnnle effect signals arising from A IT X E transitions in carbon monoxide will be developed. In addition, since tlie exciting radiation employed in t'lis experiment consisted of a superposition of three unresolved rotational lines, a mathematical model will be constructed which will allow the contribution to the level-crossing signal from transitions from each excited rotational level within a vibrational state to be assessed. Finally, the effects of a rotation.il perturbation in the A Tf upper state upon the level-crossing line shape will be developed using basic perturbation theory. Semiclassical Analog to the Level -Crossing Plienomenon Some of the basic features of the zero-field level -crossing phenomenon (Hanle effect) may be easily understood if one considers the following semiclassical analog to the exact quantum system. An electronic transition in an atom or molecule may be represented classically as an electric dipole with components p , p , and p . The upper state of the transition has a magnetic moment, \i , as shown in figure I. In an ideal experimental arrangement exciting

PAGE 16

bfl C Â•H m m O U O 1 fH 0) > o Â•p bD f-l a < a V Â•H m w ca S o o o S o c a> fcD Â•H

PAGE 17

o GC O Io LU hLU Q
PAGE 18

10 radiation with polarization vectors, G and Â€ , is incident along the y 2 X axis. Light scattered by the atom is detected along the z axis. Â— A magnetic field, H, may be applied along the y axis. If initially the magnetic field is zero, only light associated with the y component of the electric dipole will reach the detector. If now a magnetic field is applied as shown in figure I, the magnetic moment will precess about the y axis with the Larmor frequency. -L = (tT' Â« Â• <=> The radiated intensity observed along the z axis will then be given by 03 -t/T . 2 _ n -t/T Z I = c J e sin uj t dt . (3) o Integration yields h-Vl'--Â—^-Â—2'\ (4) l+(2g IX TH/h)' J O 2 In the above integral sin u) t gives the intensity of radiation asso^ L -t/T ciated with the precessing dipole, and the damping terra, e , is included to account for the decay of the dipole associated with the emission of radiation. In addition to the field-dependent levelcrossing signal, a constant background due to radiation from the y component of the electric dipole will also be observed unless the polarization of the incident radiation is chosen to exclude excitation of this component.

PAGE 19

11 The level-crossing signal has the form of an inverted Lorentizian lineshape having I = at H = 0. If H^^ is the magnetic field necessary to produce Â— maximum intensity, then T, the lifetime of the state is given by g T = -i^ . (5) Thus if the g factor of the radiating state is known, the lifetime is given by a simple measurement of the halfwidth of the experimentally obtained Lorentzian lineshape. The semiclassical analog is also useful for understanding the effects on the level-crossing signal of departures from the ideal experimental geometry given in figure I. Suppose that scattered light is detected in the x-z plane at an angle, 0, to the z axis. Then the sin^ cu t term in equation 3 must be replaced by sin (uu^^t + 6) . Making this substitution, the intensity of light scattered into the detector will be given by T = c r e"*^^ sin^(uj t + e)dt t " L = J e'^'^'^jl (cos 2u; t cos 29 + sin 2a)^t sin 29) Jdt . o (6) Integration of equation 6 yields T = ^ Tl cos 29 -^ sin 29 -^ | where (7) 2u g HT R = Â°J . (8)

PAGE 20

12 The level-crossing signal given by equation 7 now contains terms of both even and odd functional dependence on the magnetic field. The dependence en the detector angle, G, must be taken into account under actual experimental conditions when the finite volume of the scattering region and the solid angle of the detector are considei'ed. Quantum Mechanical Calculation of the Hanlc Effect Signal for the A State of~CO The rate at which radiation is absorbed, exciting an individual molecular rotational level, and subsequently re-emitted into a single rotational branch is given by the Breit [21] formula, I(J j' j") cc y (j'\i\i-r\jra)(jm\f-r\j'^'){j'[i'\g-v\j":n")(j"m"\g-r\j'^) ^ ^-. [l+i(^-^')^.^g^.Tj,H/h] mm' (g^ Â— Â• -^ The vectors, f and g, are the polarizations of the exciting and // // re-emitted radiation, respectively. J and J , m and m are the quantum numbers related to the total angular momenta of the ground states and their projections on the space-fixed z axis, and J , jj, and ji are the corresponding quantum numbers for the excited state. In the denorainator, g / and T / denote the Lande g factor and the lifetime of the J tJ excited state, and H is the magnetic field strength. The levelcrossing signal is calculated by inserting the proper wavefunctions for the TT excited state and the E ground state into equation 9 and summing over all possible combinations of magnetic quantum numbers.

PAGE 21

13 The v/avefunction for the ground state may be expressed as the product of electronic and rotational functions 4. , , , -^ 1 p^^"^^ i'iYT') = X-nd' ,e )(2tT) [2(2J+1)]2 V , (Qpy) . (10) 'j ^Tl' m ,o The coordinates, r and 6 , are defined with respect to a coordinate system in which z corresponds to the internuclear axis of the molecule, Tlie quantities a, 3, and y, are the Euler angles associated with the transformation which takes the space-fixed axes into the molecule-fixed coordinate system. (See figure Ila.) The elements of the rotation matrix, fj' s , may be shown to be the rotational eigenfunctions for the symmetric top molecule when multiplied by the norma] i 1 izing factor , [l(2J + Ij^ [27]. The wave functions for the A doubled "IT upper state are constructed in a similar fashion: [ZS^^;>(.Sv)*^<^;j^(cBv)J. <11) where Q denotes either the c or d component of the doublet. The electronic parts of the wavefunctions for the upper state are either symmetric or antisymmetric under reflection in a plane which contains the internuclear axis of the molecule. This may be seen by making the substitution cp -Â• -cp in equation 11. The E state is symmetric under this reflection.

PAGE 22

(U

PAGE 23

15 "5 Â•< CO

PAGE 24

16 The wavefunctions in equations 10 and 11 may also be seen to possess definite symmetry (parity) under an inversion, R, of the space-fixed coordinates through the origin. Under such a transformation a-'TT+cv, p-'TT-.B, Y~*~Y> and &'\ (TT+a, n-P. -Y) = (-l)-""'" jby\ (CP.Y) . (12) Application of the transformation, R, to the wavefunctions yields the following results: RY(E'^)j = (-l)'^Y(E"*")j (13a) c c RY(V)^ = Â±(-l)'^Y(V)^ . (13b) Thus the parity alternates as a function of even and odd values of J. The operators such as f Â• r which appear in the Breit formula (equation 9) may be expanded as the scalar product of two spherical tensors with the components of r expressed in terms of the rotating coordinate system X XV The dipole matrix elements appearing in the Breit formula are most readily evaluated by employing the relationship

PAGE 25

17 2n TT 2TT^<^1^ .^V ^^V \m. inÂ„ mÂ„/Mn, m^ inÂ„/ where the terms appearing on the right side of the equation are Wigner 3-j symbols. Integration over the molecule-fixed coordinates is facilitated by the use of orthogonality relationship, r f f\^-'^^ X:(r'e')e-^^-^' r^^>'dr'sine'de'dcp' o o o where the integration over cp has been carried out, and the integration over r and 9 is contained in ^^r>Using equations 10 and 11 the matrix elements may be written as = 2^ XV 2 ,.. (1) (1) = y (-^) (2j+i)(2j'+i)(-i)^+Â°' f f ''^ (17) Â• {[ . J[;//(JD^'\;)^';)

PAGE 26

18 Employing equations 15 and 16 and the propei'ty that a,p 0!,-p equation 17 becomes (j'tll? Â• rljm) =^ 16(2J+1) (2j'4.1) (-1) ^+Â°^+^^'^+^ \a .(1)^(1) I |2, ^,J+j'+l /J j' 1\ (J j' 1 !x ^-cv I\tiI ^-^> L -^. xJ Vm -^.' a. Â• [(lid)^-^^'^^) (^ f _J)]' . (19) The matrix elements for emission may be obtained in a similar manner. The final form of the Breit formula then becomes

PAGE 27

19 KJ.J ,J ) <:2, ^^'V|' ^"^ nun y.)J. Xa6e (2J.1)(2j".1)(2jM,= f<Â» f<Â» g<Â» .!Â» 2 ..// cx^<-)-^'^v(^ r .ir[-(.>^'-"-]^(r r .d // Vm -(J, Xy Vm -p, -a/ Vm -p, d / Vm -p, -e -1 [ 1 + i ( p,-p.' ) p^gj / T J / H/hJ (20) The terms Tl + (-1)'^ ^"^ "^M and I 1 + (-1)*^ +J+1 J ^n equation 20 arise from the selection rule which requires a parity change in absorption and emission of radiation. The terms indicate that excitation from a lower level, J, to an upper level, J , takesplace to a c state if j' = J = l and to a d state if J = J, and that re-emission takes place in a similar fashion. A consequence of the parity selection rule is the prohibition of excitation through a Q branch followed by re-emission in a P or R branch and vice versa, as may be seen by examining the partial energy level diagram for IT E transitions (figure lib). The summation indicated in equation 20 is performed by first grouping terms for which | p |i' [ = 0,1, or 2 and then summing over all possible sets of the indices X, a, 6, e. Tlie process is facilitated through the use of the sums,

PAGE 28

20 mJ n = odd Y ^^n _ (2J+1) n:rO L ~ (2j+l)J(J+l)/3 2 n=2 rfcJ (2j+l)J(Jt-l) (3J +3J-1)/15 n=4 or, in certain cases, through the use of the defining relationship between 3-j and 6-j symbols. 1 1 -Â»Table I gives the result of the calculation for the TT E' transition in carbon monoxide. Under the experimental conditions of unpolarized exciting and scattered radiation, terms for which [ p,-ij,' [ =1 cancel and the signal consists of a field-independent background which arises from terms for which | p,-ij, j = and a field-dependent part which arises from terms for which j p,-(i' j -2.. Rotat ional Line Contributions to the Molecular Level -Crossing Signal In the follov.'ing paragraphs a mathematical model will be developed which will allow the contributions of unresolved rotational lines to the level-crossing signal to be calculated. The calculation will be carried out by first determining the contributions of individual rotational lines to the intensity of a molecular discharge and then deriving the rate of resonance fluorescence from a scattering gas. Rotational Intensity Distribution in a Molecular Discharge The relative intensities of isolated rotational lines produced under conditions of thermal equilibrium may be expressed as the product

PAGE 29

d

PAGE 30

22 o i-H Â•-5 Â•-5 I C o Â•H Â•iH E IX]

PAGE 31

23 of the line strength of the transition and the temperature dependent Boltzmann factor divided by the rotational partition function i(j' ,j")cxp [-B'j'(j'+l)hc/kT ] I(j',j") = ^. (21) S-ot Here b' is the rotational constant for the upper state, T is the Li effective rotational temperature for the discharge, and the rotational partition function is given by kT /hcfi' for all but very low temperatures. Tlie line strength is given by the Honl-London factor for the transition. For a TT I^ transition in a symmetric top molecule these factors are i(j',j') = (2j'+l)/2 i(j',j'-l) = (j'+l)/2 (22) i(j',j'+l) = jV2 for the Q, R, and P branches, respectively. The relative intensity and shape of a Doppler broadened rotational line produced in a layer of gas of thickness dx in a discharge lamp of uniform cross section is given by d^(v,j',j") = I(j',j")k^exp I -l^y^^rTj dx . (23) The parameter, k , is the absorption coefficient of the gas and the Doppler breadth of the line, Av , may be written as ^MLMvo/T. (24) D c a/ m

PAGE 32

24 The distance in wavenumber from the center of the line is given by V . The contribution to the output intensity at the front of the lamp (x = 0) from the element dx is ,2 ds(V,j',j") = I(j',j")k^ exp ^^ 2v I D ^/l7^2 r . _ ,. ,,,. I 2V r^-^\^~! exp I -k I .(j',j")x exp (Jl/n. 2J I dx , (25) D where the second term accounts for absorption present in the lamp. It is assumed here that once a photon has been absorbed it is lost to the output of the lajnp. Tlie relative absorption from molecules in the lower state is given by r-B"j"(j"+l)hc/kT^ j i(j',j") exp I -B"J" (J"+l)hc/kT I, (J ,J ) = i^^ (26) Q ^rot where B is the rotational constant of the lower state. Integration over the length of the lamp gives the contribution to the intensity from a frequency band dV: s(v,j',j")dv = LKJ'.J") r^^Llj^^j' 'J'M 2 Â• {l exp cy^I_^(j',j") exp (^ ^^JiT^) J } ^^ Â• (27) The effective absorption coefficient for the discharge has been defined as cy = k L. The total intensity from an isolated rotational L o line is found by integrating over the Doppler profile of the line

PAGE 33

25 S(j',j") = J s(v,j',j")clv . (28) o The simulated spectrum for an entire molecular band is generated by forming a sum of the rotational line intensities over the wavelength region of the band: X max JiX) = Y^ T(X-X.)S(X.(j'',j")) . (29) X. = X . 1 mm The parameters, X . and X .give the lower and upper wavelength mm max' limits of the band, X. is the wavelength of a particular rotational line characterized by the upper and lower quantum numbers (J ,J ) , and T(X-X.) is the triangular bandpass function of the monochromator used to resolve the spectrum. The bandpass function is defined as T(X) |l |X/AX| I |X/AX| < 1 I 1 ^^Â°^ X/AX where AX is the resolution of the monochromator and is assumed to be mucli larger than the width of the rotational lines. Rotational Intensities in Resonance Fluorescence Calculation of the intensity of radiation absorbed and re-emitted by the scattering gas proceeds in a fashion similar to the calculation of the lamp intensity. For a particular mode of absorption followed by re-emission characterized by the rotational

PAGE 34

26 quantum numbers, J -"J -"J, the intensity of light scattered into a detector at approximately right angles to the incident beam is given by D 4T-f CO Kff ,J,j',j") Â°=Jdz I
PAGE 35

27 accounts for departures from the ideal right angle scattering geometry. The geometry of the scattering region is shov/n in figure III. If y represents the distance along the detector face, the differential area element on the detector face may be written as 2 dA(y) = 2(2ay-y )^ dy . (34) The solid angle subtended by dA(y) is then 3 1 rÂ„ Â„-i2 (35) P 1 r o o~i2 dn = (2ay-y^)2 |^(z-y)'' + a^J dy, where "a" gives the distance from the center of the exciting beam to the detector. Equation 35 holds only approximately if the detector is not sufficiently removed from the scattering region. However, the error introduced by this approximation is small compared to other uncertainties present in this analysis. In addition, it has been assumed that the exciting radiation is confined to a narrow beam along the central axis of the scattering region. While this is not strictly the case under actual experimental conditions, it may be seen that scattering angles from above and below the center line tend to average to the scattering angle, 6. The integral in equation 31 is readily evaluated with a digital computer, using the Conroy [28] routine for multiple integrals.

PAGE 36

o Â•H 00 d bO c Â•H (U p n) u w o M-l (0 CO 0) 4J CO o o o 0) >^ bO Â•rl

PAGE 37

>29

PAGE 38

30 The Effect of Rotational P erturbations on the Molecular Level -Crossing Signal The A TT state of carbon monoxide is characterized by the many perturbations which result from the mixing of the A'TT state with another state of the molecule. The coupling of two states of nearly equal energy arises from terms omitted from the Hamiltonian and produces shifts from the expected rotational energy progressions within a vibrational level. In addition, if the coupling is sufficiently strong, additional lines will appear in the spectrum of the vibrational band. To see the effect of a perturbation of a rotational level upon the level -crossing signal let the wavef unction of the A TT state be represented by (a.j) and that of the perturbing state by |b,J>. A selection rule (see Herzberg [29, p. 285]) prohibits the mixing of states of different rotational quantum number. It will be assumed that m remains a good quantum number for the range of the magnetic field cJ encountered in the level-crossing experiment. This assumption is justified for the types of terms being considered in the perturbation calculation. A perturbation which couples two molecular states, |a,j) and |b,J), gives rise to the two mixed states with wavef unctions , Y^ = a|A,J> 3Ib,J> , (36) and Y^ = P|a,J) + a\B,j) , (37) where cv^ + P^ = 1 . (38)

PAGE 39

31 If the unperturbed energies of the states are designated by E and E_, then the perturbed energies will be given by B (E^..E ) Â± JiE^-E)\4A^ E^ = , (39) where A is the matrix element of the perturbation term, P, between the two states: A = . (40) Tlie coupling coefficients, oand P, may be written as . s Â»=l Â— I (41) a/(E^-E3)^ + 4A^ / and /(-.2 ..23.1 ''v v -" -"a :V| . 2y(E^-Eg)^ + 4A^ Using equations 39, 41 and 42, it can be shown that A may be written as 2 "^ ^""a-V ^^-^^) A 2 2 (43) (2a^-l)^ The Zeeman energy for the mixed state, Y may be obtained through the following considerations. The Zeeman energy is written as

PAGE 40

32 or Thus E^ = [^(a* -P|b))j! , (44) E^ = |a|^ < a|^-h|a>+ |p| (BiJ-lj|B). (45) E = \a\ n g^(A)Hm + |3| p, g fB)Hm = ^^^Ja\^Sj(A) + |3pgj(B)Jmj , (46) where g (A) and g (B) are the molecular g factors for the states J J A and B, respectively. The Zeernan energy may now be written as E = n g^ Hm , (47) z o J J if the effective g factor for the mixed state is defined as ij = [cv^gjCA) + p\j(B)] . (48) From equation 5, the relationship between the product, g\T for the perturbed state and the experimental halfwidth of the levelcrossing signal becomes g T = Â— ^ . (49) If the lifetime of state B is long compared to that of state A, the lifetime of the perturbed level will be given by T^ = T/a^ , (50) J A

PAGE 41

33 where T is the lifetime of the pure A state. Then usinp equations 48 A and 50, equation 49 may be written as a 'o Â§ or a o A i Thus, if the g factors and approximate lifetimes for the two states participating in the perturbation are knov/n, the coupling constants may be obtained from the experimental level-crossing data. If, in addition, the term values for the perturbing states are knovm from spectroscopic analysis, equation 43 may be employed to obtain A, the strength of the perturbation. Lifetimes

PAGE 42

34 electronic transitions in simjDle molecules. Tlie discussion is based on the treatment of molecular quantum mechanics outlined by Herzberg [29], and the discussion of transition probabilities given by James [10] The Schrodinger equation of a diatomic molecule may be written as 2 i k where i refers to the coordinates of the electrons (mass m) and k refers to those of the nuclei (mass M, ) Â• An approximate solution to Â— Â» Â— Â» equation 53 may be v/rittcn as ^ = ii (r.)* (r, ) where A and iIi are ^ ^e 1 ^vr k ^e ^vr solutions of the equations Vv^t ^Â—^ (i:"'-V )* = (54) Z_j 1 e , -i e e \ and 2 y W-'^l^ + ^ (E-E^^-V )^ =0, (55) Z_i M k vr 2 n ^vr k respectively. The first of these equations is the Schrodinger equation for electrons moving in the field of fixed nuclei and having a potential energy, V . For different internuclear distances V is different e e el and therefore the eigenfunctions , ijr , and the eigenvalues, E , of this equation depend on the internuclear distance as a parameter. The second equation is the Schrodinger equation of the nuclei moving under the el action of the potential energy, E +V , where V is the Coulomb n n

PAGE 43

35 potential energy of the nuclei. It may be shown that the expression given above for the total eigenfunction is a solution to equation 53 only if the variation of ij/ with the internuclear distance may be neglected. This condition is fulfilled for most diatomic molecules el and is known as the Born-Oppenlieimer approximation. The use of E +V n as the potential energy for the motion of the nuclei and the resolution of i(r into the product of ij; and jf is therefore usually justified. The intensity of an electronic transition from an upper state, a, to a lower state, b, is determined by the transition probability, A . The transition probability is in turn determined by the square of the dipole matrix element between the upper and lower states. Under the assumption that the Born-Oppenheimer approximation holds, the matrix element may be written as The matrix element, R(r) , is the electronic transition moment given by R(r) Â°^ ('i/l I X^'*e^ Â• i If the variation of R(r) with the internuclear distance is slow, R(r) may be replaced by its average for the vibrational transition. Equation 56 then becomes R = R . (58)

PAGE 44

36 Further, the vibrational-rotnticnal overlap integral may be written as ' " (f UM = (v'W')ll' ' , (59) vr ' 'vi' rot where the first term is the square root of the Franck-Condon factor for the vibrational transition, and the second term is the overlap integral for the rotational transition. The transition probability for emission, A , ///,/,//, is ab,v V ,J ,J given by ^^4 3 64tt V / // ^ A , / // / // = Â„ y ^ ) |r| , (60) ab,v V ,J J 3hd L, ' ' a / // m m where the sura is over all values of the magnetic quantum numbers, m and m . The parameter, d , the degeneracy of the upper state, is equal to 2J +1 for E states. States for which A^l are A doubled and therefore the degeneracy is 2(2J +1). Summing over all possible rotational transitions from the upper state gives ^^4 3 64tt V / // Â„ ^ A^ , . = -f^ |r |2||' (61) ab,v V 3h ' e' ' ' ' on account of the sum rule, // // ' J ,nun The transition probability is therefore independent of the rotational quantum number.

PAGE 45

37 The transition probability for emission from a particular electronic-vibrational state may be written as A,.yA,. = ^y V^ .|r (1. .)|^| The lifetime of the electronic-vibrational state is given by T / = -r^ . (65) V A / V The transition moment, R , may be taken to be constant for e some molecules and removed from the sum in equation 63. In other cases the variation of V over the vibrational band system may be neglected. Under these approximations, and in view of the sum rule, ) |(v |v )| = 1, // V the lifetime becomes ^ ^^"'^' r2 . (66) T / 3h e

PAGE 46

38 In this approximation the lifetimes of all vibrational levels become 3 equal. A more correct formula could be obtained by replacing v by the mean cubed wavenumber , ( v) = ) v // 1 , (67) V 3h e where use has been made of the completeness i-elationship , L |v">1. The absorption oscillator strength or integrated f-value may be defined as f =y f , . (69) o Z_i V o V The absorption oscillator strength may, in principle, be related to the radiative lifetime through the use of equations 63, 65 and 68.

PAGE 47

39 The bands of the fourth positive system of carbon monoxide extend over such a large wavelength region that the variation of v may not be neglected. In addition, the strong dependence of the electronic transition moment on the jnternuclear distance has been well established. ITie assumptions which simplify tlie expression for the transition probability are therefore not appropriate to the bands of the A-X transition in carbon monoxide. The f -values of the A-X transitions may be related to the lifetimes of the vibrational levels by employing equation 63 in conjunction with a model for the dependence of the electronic transition moment on the r-centroids of the vibrational transitions. It is \asually assumed that R is a simple function of r-centroid. The e parameters characteristic of the functional dependence are varied in equation 63 to obtain the best fit to the set of radiative lifetimes of the vibrational levels. Using the values of R , the absorption e oscillator strength may be calculated from equations 68 and 69. The use of this particular technique of analysis has produced the reasonable agreement between oscillator strengths calculated from lifetime values and those measured directly in electron scattering experiments.

PAGE 48

CHAPTER III EXPERIMENTAL APPARATUS A diagram of the apparatus used for the molecular Hanle effect experiment is shown in figure IV. Radiation for the excitation of the scattering gas was produced in a moleculai' discharge lamp. A onemeter vacuum monochromator was used to select bands of the fourth positive system of caibon monoxide, A beam of resonance radiation passed from the monochromator into the scattering cell where the proper geometry for the entrance beam, detector, and magnetic field was maintained. The scattering cell was mounted between the pole-pieces of an electromagnet capable of providing fields up to 10,000 Gauss. Resonance fluorescence from the scattering gas was shifted to a wavelength o of about 4000 A by a coating of sodium salycilate on the lower end of a Incite light pipe. The light was detected by a photomultiplier tube mounted in a field-free chamber. After amplification and timeconstant smoothing, the signal, proportional to the photon counting rate for scattered resonance radiation, was stored in the memory of a signal averager as a function of the magnetic field in the scattering region. The stored signal could be obtained from a digital printer and from an X-Y plotter. 40

PAGE 49

m n) u (0 p. cd 4-1 > H 00

PAGE 50

42
PAGE 51

43 Molecular Discharge Lamp D esign In the molecular Hanle effect experiment, one of the most difficult of experimental pj'oblems proved tc be the development of a satisfactory source of radiation for the excitation of the scattering gas. The need for relatively large intensities in the bands of the fourth positive system suggested the use of a moleculaidischarge source. In addition to the need for high intensity, two other factors were present for consideration in the design of the discharge lamp. The first consideration was the reduction of self-reversal of the resonance radiation emitted by the lamp. Self -reversal occurs when a layer of unexcited gas lies between the emitting layer and the exit port of the lamp. Under this condition the line profile for the emitted radiation may exhibit a minimum at the center of the line. Self-reversed radiation is, of course, very ineffective in the excitation of the scattering gas. Fortunately, the absorption line strengths were relatively small for the high rotational levels investigated in this experiment, and most discharges were found to be optically thin, thus minimizing the problem of self-reversal. The second and most important concern was the minimization of fluctuations in the intensity of the lamp. Since the level-crossing signal amounted to only a few percent of the total scattered light, nonstatistical fluctuations in intensity had to be kept low for the signal to be seen at all. It was found that the most stable radiation sources were those excited by radio frequency power.

PAGE 52

44 Tlie first type of lamp tried was a McPherson Model 630 ultraviolet light source as modified by Wells [30]. This source was basically a flow lamp in which the discharge took place in a mixture of helium and carbon dioxide in a water cooled capillary tube between aluminum electrodes. Helium flowed in a reverse direction through the lamp to help prevent self -reversal. The discharge was excited by a diathermy machine capable of producing up to 500 watts of R. F. power at 27 Miz. Impedance matching between the lamp and the R. F. generator produced low standing wave ratios into the lamp under operating conditions. As an aid to reducing fluctuations in intensity, large ballast bottles were employed between the lamp and the gas supply tanks. The lamp was found to produce resonance radiation which was relatively free from self-reversal; however, the high R.F. power necessaiy for the operation of the lamp caused severe interference with the electronic apparatus used throughout the experiment. Serious attempts were made to shield against the spurious radiation before the use of the lamp was finally abandoned. Extensive use of lamps excited by microwave energy in atomic level-crossing [31] and optical pumping [32] work suggested that a lamp of this type might prove equally useful in the molecular Hanle effect experiment. In a microwave discharge the power is usually coupled into the gas through a resonant cavity, permitting the use of electrodeless lamps which are less susceptible to deterioration due to contamination. In addition, higher output intensities may be obtained with an expenditure of less excitation energy than with lower frequency

PAGE 53

45 discharges due to the close coupling between the discharge and the power source. Bearing these factors in mind, several lamps were designed to be used with a Raytheon microwave power generator which produced up to 80 watts output at 2450 Hhz. These lamps were all constructed in such a way that the output radiation was emitted througli a differential pumping port located at the front of the lamp. This design was chosen because LiF and RfeFg' ^^^Â® Â°^^^ materials suitable o for windows in the v/avelength region of interest (around 1500 A) , exliibit rapid deterioration in transmission upon exposure to intense ultraviolet radiation [33,34]. Several investigators [30,35,36] have reported useful lifetimes of only a few hours for discharge lamps with LiF windows. Differentially pumped lamps, on the other hand, were found to run indefinitely with no diminution of output intensity. In the first source constructed, the discharge was carried in a 1/2-inch-diameter vicor ignition tube which was situated along the axis of a cylindrical TM [37] cavity. Gasses were admitted at the back of the tube through a side arm. The lamp produced adequate intensity in the ultraviolet region but exhibited serious instability under certain operating conditions. This behavior was judged to be due to the limited number of modes available to the exciting radiation in the cavity. At certain pressures the lamp was seen to oscillate between two modes of excitation with an accompanying oscillation in intensity. In addition, the vicor tube was found to dissipate a sizable part of the microwave energy as heat. In order to overcome these difficulties, a second design was developed, utilizing a more

PAGE 54

46 sophisticated Evans [38] type microwave cavity. This lamp is shown in detail in figure IV and in figure V. The Evans cavity was machined from brass stocl; and included both tuning and coupling adjustments. The lower portion of the cavity contained the discharge lamp itself which was machined from grade HP boron nitride. This material, a practically lossless dielectric in the microwave region, proved to be ideal for the confinement of the discharge. The discharge was carried within a 1/4-inch -diameter blind hole drilled along the axis of the boron nitride piece. Differential pumping took place across a 1/4-inch x 1 mm counter bore at the front of the lamp. This slit also served as an exit port for the vacuum ultraviolet radiation. Gas was admitted through a Swagelock fitting which was screwed into the central bore at the back of the lamp. The entire apparatus, lamp and cavity, was designed to be mounted on the slit housing of the monochromator as close to the entrance slits as possible. Differential pumping was accomplised by a large diffusion pump contained within the monochromator. The flow of gas into the back of the lamp, and consequently the gas pressure within the lamp; was regulated by two needle valves. In operation, helium and carbon dioxide flowed into the back of the lamp, and the pressures of the two gasses were adjusted to produce the maximum output intensity in the molecular band of interest. Helium was found to produce a stable discharge in which the dissociation of the carbon dioxide and the excitation of the resulting carbon monoxide could take place. The use of carbon dioxide proved to be

PAGE 55

Figure V: Molecular Discharge Lamp

PAGE 56

48 TUNING MICROWAVE RADIATION BORON NITRIDE He IN CO IN

PAGE 57

49 helpful in preventing self-reversal of the molecular resonance radiation. The Evans microwave cavity allowed very low standing wave ratios to be obtained under almost all pressure conditions in the lamp. It 4 was found that a pressure differential of about 10 could be maintained across the differential pumping slit, so that during operation the -4 pressure in the monochromator was kept below 10 Torr. It was estimated from absorption in the spectrum of radiation emitted by t)ie lamp that the partial pressure of carbon monoxide in the monochromator was -7 not more than 10 Torr. Optical System For the purpose of description in this paper, that part of the experimental apparatus following the exit port of the discharge lamp and preceding the photomultiplier tube shall be designated as the optical system. Included in the optical system are the monochi'omator , the scattering cell, and the fluorescent detector and light pipe. The bands of the fourth positive system of carbon monoxide were selected, using a McPherson Model 225 one-meter vacuum monochromator. This instrvuiient was equipped with a large oil diffusion pump and could be evacuated to a pressure of less than 10 Torr. The monochromator was of normal incidence geometry and employed a cylindrical replica grating of one-meter radius to disperse the radiation. The grating measured 56 mm x 96 mm and was ruled with 600 lines per mm. With this grating the monochromator had a first-order reciprocal

PAGE 58

50 o dispersion of 16,6 A/mm. With the entrance and exit slits set at* 10 microns a typical setting lor the level-crossing experiment the o monochromator had a resolution of . 166 A. Light impinging upon the entrance slit was focused on the exit slit by the grating, and from there a diverging beam entered ihe scattering cell by the way of a hollow pipe of about onc-nalf-meter length. The scattering cell was separated from the monochromator by a one-half-inch-diameter x 1-mmthick LiF window. The scattering cell was machined from aluminum in the form of an octagonal cylinder. A diagram of the scattering cell is given in figure VI. The cylinder was 2 inches thick, and the distance between the faces of the octagon was 6 inches. The scattering region was a two-inch-diametei' x 5/8-inch-thick cylinder machined into the center of the scattering cell. Ports led from the scattering region to seven of the eight faces of the cell. Admission and removal of the scattering gas, as well as the enti'ance and exit of radiation, was through these ports. Gas was exiiausted from the scattering region by a mechan-4 leal vacuum pump, and a base pressure of 5 x 10 Torr could be attained. Adjnission of carbon monoxide, the scattering gas, was through a micrometering valve. Under typical experimental conditions the pressure of the scattering gas was maintained at about 50 microns as measured by a Teledyne Model 2A thermocouple vacuum gauge. A light pipe made of one-half -inch -diameter Incite rod extended into the scattering region to a position directly above, and adjacent to the entrance window. The lower tip of the light pipe was coated

PAGE 59

0) 00 a Â•H 0) U CO V 0) Â•H

PAGE 60

52 tO IL. < X ai fii o a: a. 111 :e o H O X a. -L HI tc COUJ a:< z Â»o

PAGE 61

53 with a thin deposit of sodium salycilate which fluoresced at about o ! 4000 A when struck by the scattered ultraviolet radiation. The fluorescent emission was propagated up the ligJit pipe by internal reflection. Tlie scattering region was positioned between tho 2-inchdiameter faces of the tapered pole pieces of the electromagnet. Spacing of the pole pieces was 3/4 inch. Detection Appar atus Light emitted by the sodium salycilate was detected by an EMI Model 6256S photomultiplier tube. The 1-cm-diameter photocathode of the tube was positioned directly above the polished upper tip of the light pipe. The response curve of the CsSb photocathode of the photomultiplier exhibited a maximum sensitivity at a wavelength which matched the output wavelength of the sodium salycilate. Overall efficiency of the detection system, scintillator, lightpipe, and photocathode, was judged to be somewhat less than 10 percent at an input o wavelength of 1500 A. The photomultiplier along with its voltage-divider chain was mounted in a thermoelectrically cooled light-tight housing. Within the housing the photomultiplier tube was cooled to around 0Â°C. The dark counting rate for the tube at this temperature was between 10 sec and 20 sec . This rate was a factor of 50 below the counting rate for scattered light encountered in the level -crossing experiment. The housing also contained several concentric layers of "netic" and

PAGE 62

54 "conetic" magnetic shielding matei^ial. In addition, the photormiltiplier tube itself was surrounded by a mu-metal shield. Extensive magnetic shielding of the photomultiplier tube was necessary to assure that the sensitivity of the tube remained constant as tlie magnetic field was swept through its full range. With all of the shielding in place, the field at the location of the tube was found to vary by less than .2 Gauss as the field on the outside of and perpendicular to the cj'linder axis of the housing was changed from to 1000 Gauss. The sensitivity of the tube was found to change by less than .1 percent under these sa:ne circumstances. Systematic error introduced by the sensitivity of the photomultiplier tube to magnetic fields was negligible since the fielddependent component of the level-crossing signal always amounted to more than 2 percent of the intensity of the scattered light. A potential of 1000 volts was maintained across the dynode chain of the photomultiplier tube. The voltage was supplied by stabilized high voltage power supply. The anode of the photomultiplier was maintained at ground potential. Output pulses from the tube were coupled to a wideband preamplifier through a 500 pfd capacitor. This capacitor in combination with the output load resistor of the photomultiplier tube formed a filter which yielded pulses with a width of about 5 (i3ec. The preamplifier was run at unity gain and served to drive several feet of 53 ohm coaxial cable. Output pulses from the preamplifier were transmitted along the coaxial cable to a linear amplifier. The gain of this amplifier could be varied from 60 to 400 and was set so that the largest input pulses just drove the amplifier to

PAGE 63

55 full output. The pulses passed from the linear amplifier into a single channel analyzer. This device generated a pulse of precise shape each time it received a pulse whose height exceeded a certain threshold which could be set manually. In practice, the threshold was set to just exclude those noise pulses generated in the preamplifier. In order to reduce noise fluctuations in the level-crossing signal, the output pulses from the single channel analyzer were fed into a ratemeter. In this instrument the series of input pulses was converted into a more slowly fluctuating analog voltage proportional to the counting rate. Thfe conversion was accomplished by electronically integrating the input signal. The ratemeter contained a simple RC filter circuit which converted the input voltage, V (t) , into an output voltage given by t V^(t) = k / e~^*"^^/^*^ V.(s)ds (70) where RC was the time constant of the filter-. The time constant was set so that only a small distortion was introduced into the shape of the level-crossing signal. The setting depended upon the rate at which the magnetic field was swept through its range, but time constants of a few tenths of a second were usually employed. The output of the ratemeter was amplified to a level of a few volts and passed into the digitizer of the Fabri-Tek Model 1062 instrument computer which was used as a signal averager. In order to accomplish this amplification, the output of the ratemeter, which was only

PAGE 64

56 10 millivolts, full scale, was boosted to a level of a few volts by a General Radio Type 1230-A electrometer. In the digitizer the analog signal was converted to digital form which allowed it to be stored in the memory of the instrument computer. The use of the instrument computer as a signal averager proved to be essential to the detection of the level-crossing signal; under ordinary operating conditions the field-dependent part of the scattered light intensity was never found to exceed the statistical fluctuation in the total intensity. With counting rates of 1000 sec , and an integrating time constant of .5 second, the field-dependent signal and the statistical fluctuation both amounted to about 3 percent. With signal averaging, the signal to noise ratio could be increased to a more useful level. This was possible, since, as counts were collected in the memory of the instrument computer, the field-dependent signal' was accumulated in direct proportion to N, the number of counts; whereas the statistical noise increased as a/^. Thus the signal to noise ratio was proportional to V^. The memory of the signal averager consisted 18 of 1024 channels, each of which could retain up to 2 counts. In practice, only one-fourth of the memory or 256 channels was utilized during an experimental run. The channels were addressed sequentially, and the number of counts stored in each was proportional to the voltage level appearing at the input of the digitizer at the time the channel was addressed. As the channels were addressed, the magnetic field in the scattering region was stepped through its range. Thus the levelcrossing signal was stored as a function of the independent variable.

PAGE 65

57 the magnetic field. The rate at which the field was swept depended on the dwell time for each channel utilized in the memory. Dwell times of ,05 and .02 seconds per channel were most cften used. The time constant of the counting system was adjusted to be equal to approximately 10 channels (i.e., ,2 and .5 second, respectively, for the dwell times given above). For a dwell time of ,05 second per channel, a sweep of the complete range of the field took place in .05 x 256 oi' 12.8 seconds. The signal stored in the memory was monitored on an oscilloscope and readout was accomplished with a Farbi-Tek digital printer. Data could also be plotted as a function of channel nuinber on an X-Y plotter. Magnetic Field Conti'ol Circuitry The magnetic field in the scattering region was produced by an Alpha Model 4800 electromagnet. A diagram of the control and power circuitry for the electromagnet is given in figure VII. The basic control voltage for the experiment was supplied by the instrument computer. This voltage, which varied between and 4 volts, was proportional to the number of the channel being addressed, and was used to drive two bipolar operational amplifiers. The amplifiers served as buffers for isolating the two legs of the circuit. Two Kepco Model JQE 36-30 power supplies were used to drive the electromagnet. These supplies could be voltage programmed and could supply up to 30 amperes at 40 volts. Programming voltagesfor the supplies

PAGE 66

4J s, e o u 4J U (U iH W
PAGE 67

59 o O CO O Q. UJ CO UJ o

PAGE 68

60 \\ieiX3 taken from the output of the operational amplifiers. The v.'aveforms of the programming voltages in figure VII shov/ that as one supply was stepped from its minimiim to its maximum outpui voltage, the other was stepped in tlie opposite direction. Tlie voltage across the electromagnet therefore passed through zero at the middle of each sweep. Use of the circuit in figure VII resulted in the dissipation in the one-ohm resistors of over one-half of the power generated by the supplies, but the ability to sweep smoothly through zero field made the power waste tolerable. At the end of each sweep a transient was inti'oduced as the energy stored in the magnetic field was fed back into the circuit. The capacitors and series and parallel diodes were placed in the circuit to help protect the power supplies from overvoltages and reverse polarities. A delay after each sweep allowed the circuit to come to equilibrium before a new sweep was started. The field in the scattering region was monitored by a Hall effect probe. It was found that the field sweep was reproducible and had a maximum range of from 10,000 Gauss to -10,000 Gauss. Tlie effects of hysteresis in the magnet were small. Corrections for nonlinearity in the field sweep were included in the analysis of the level-crossing signal. The Hall effect probe was calibrated periodically in a proton magnetic resonance spectrometer. The field within the scattering region was found to be homogeneous to within 1 percent.

PAGE 69

CHAPTER IV EXPERIMENTAL PROCEDURE Molecular Ilanle effect experiments were initiated with the recording of the spectrum of the (1,0) band of the fourth positive system of carbon monoxide from the molecular discharge lamp. The spectrum was taken in order to determine the characteristic temperature and absorption coefficient of the discharge, and the (1,0) band was chosen because it is relatively free from overlapping bands of the fourth positive system. Although spectra were not taken before each experimental run, they wore recorded periodically and the conditions in the lamp were found to be reproducible. A spectrum of the light scattered by the carbon monoxide gas sample was next recorded for the molecular band under investigation. From this spectrum the effective absorption coefficient of the scattering gas as well as the relative contributions to the Hanle effect signal from excited rotational levels were determined. The Hanle effect experiment itself was begun by centering the bandpass of the monochromator on a particular rotational feature of the band under investigation, and by adjusting the range of the magnetic field to be swept. Ordinarily the sweep was set to cover a range of about 14,000 Gauss centered on zero magnetic field. A plot of the magnetic field versus the channel number in the memory of the signal averager was taken in order to 61

PAGE 70

62 determine the linearity and ranjre of the sweep. The collection of level-crossing data in the memorj' then commenced and was continued until the quality of tlie e:-q3erimental line shape reached the desired level. Generally, an exi^erimental run lasted from two to four hours. At the end of the run the spectrum of scattered light was again recorded to assure that experimental conditions had not changed drastically. The level-crossing data were then fitted to theoretical line shapes with the aid of a digital computer. Lamp Spectra Ideally, molecular lifetime determinations using level-crossing spectroscopy would be performed on isolated rotational levels within a vibrational state. In exiDcriments on the fourth positive system of carbon monoxide, this ideal could not be realized, since, for the bands investigated, the higher rotational lines tended to be arranged in closely spaced triplets. The components of these triplets could not be individually resolved by the monochromator. It was therefore necessary to assess the contribution to the level-crossing signal from each rotational state of the scattering molecules excited by a component of the unresolved triplet. An example of a spectrum of the (1,0) band obtained from the discharge lamp is given in figure VIII. In obtaining the spectrum the detector was mounted directly on the exit slit housing of the monochromator. The discharge in the lamp was begun and allowed to stabilize. Helium pressure in the lamp was then adjusted until the partial pressure

PAGE 71

Figure VIII: Lamp Spectrum of the (1,0) Band \.

PAGE 72

64 (1.0) BAND Tl = 300Â°K. 0^=5.0 A Tl:350Â°K, aL:4.5 O Tl=400Â°K. aL:4.0 IÂ— CO z LJJ IÂ— P(16)-Q(20) Â± 1516 1514 1512 WAVELENGTH (A) 1510

PAGE 73

65 -5 of heiium in the monochromator was 5 X 10~ Torr as indicated by a cold cathode vacuum gauge. CO^ was then admitted into the lamp until the total pressure in the monochromator was 8 or y X 10~ Torr. The power input to the lamp was set at 80 watts, and the SV.Tv into the microwave cavity was minimized. The monochromator slits wore adjusted so that the rotational feature of interest was well resolved. It was found that when this procedure was followed reproducible spectra could be obtained. The basic features of the (1,0) band are apparent in the spectrum in figiire VIII. For J > 12 rotational features which consist of one line each from the P, Q, and R rotational branches are resolved. The components of the triplets are of the form P(J) , Q(J+4) , R(J+9). There are also contributions to the spectrum from two overlapping bands o of the fourth positive system. The (4,2) band has a maximum at 1510.4 A, o and the (7,4) band has a maximum at 1515.7 A. However, both of these bands fall outside of the region of interest for rotational lines investigated in this experiment. The plotted points in figure VIII are local maxima of the simulated spectra generated by the application of equation 29 to the (1,0) band. The spectra were generated for three different combinations of lamp temperature and absorption coefficient. From the analysis the temperature and absorption coefficient for the discharge were found to be 350Â°K and 4.5, respectively. The other sets of values were taken to give the experimental limits for these quantities. The simulated spectra were normalized to the experimental spectrum at the P(16),

PAGE 74

66 Q(20) , R(25) spectral feature. Once the two lamp parameters were determined the intensities of rotational lines in the exciting radiation were found through the application of equation 28. Spectra of Scattered Light A spectrum of scattered resonance radiation was recorded before each run of the level-crossing experiment. Figures IX and X are typical of the spectra obtained for the (1,0) band and (2,0) band,, respectively. The plotted points are local maxima of the simvilated spectra of scattered light calculated from equation 31. Numerical integration of equation 31 was implemented through the use of an IBM 360 digital computer and a program for computation developed by Wells [30] and Isler [13]. In fitting the simulated spectra to the experimental data, the temperature of the scattering gas was assumed to be 350Â°K and the absorption coefficient, a , was varied to obtain the points plotted in figures IX and X. For the (1,0) band the best fit was judged to be for a =2.0. For the (2,0) band the best fit was for a =3.0. Both experimental spectra were produced with a scattering gas pressure of 50 microns. As the pressure of the scattering gas was varied from run to run it was of course found that different values of a produced better fits to the experimental spectra. The Hanle effect signal produced from excitation by the incompletely resolved rotational features of the v = 1 and v = 2 vibrational bands consisted of a superposition of line shapes arising from each excited rotational state of the scatterinsr molecules.

PAGE 75

Figure IX: Fluorescent Spectrum of the (1,0) Band

PAGE 76

68 (1,0) BAND 1^-350Â° K. aLÂ«4.5 o asÂ»io A as* 2.0 X as'3.0 1516 1514 1512 WAVELENGTH (A) 1510

PAGE 77

Figure X: Fluorescent Spectrum of the (2,0) Band \.

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70 (2.0) BAND K, aL--4.5 A as'2.0 X asÂ«3.0 o as=4.0 IÂ— CO z LU P(16)-Q(20) Â± Â± I 1484 1482 1480 WAVELENGTH (A) 1478

PAGE 79

71 The contribiitions to the Hanle effect signal were calculated from equation 31 and are listed in Table II, The tabulated figures give the relative contribution to the signal from rotational states excited by a particular branch line. For excitation by a Q branch line, Table I shows that re-radiation from tlie excited state may be only through a Q branch. For excitation by a P or R branch line, there will be a contribution from re-radiation in both the P and R branches. For the latter case. Table II gives the total contribution from both modes of decay. The contributions to the Hanle effect signal have been tabulated for three values of a for each rotational s line of interest. The figures calculated for the bracketing values of the absorption coefficient were taken to give the limits of error in the intermediate value. It may be seen that the contributions to the signal from levels excited by R branch lines are almost negligible. Analysis of the Hanle Effect Signals Analysis of the experimental Hanle effect lineshapes was carried out on the IBM 360 computer, using a nonlinear least-squares (NLLS) curve fitting program. The theoretical lineshapes to which the signals were fitted consisted of a superposition of a Lorentzian and a dispersion curve for each of the excited rotational states, and a term proportional to the amplitude of the field-independent background. Six parameters were varied simultaneously in the NLLS program to produce the best fit to the experimental data. The rotational levels were assumed to have the same lifetime, and this value was

PAGE 80

Table II: Contributions to the Hanle Effect Signal from Excited Rotational States

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Table II 73 (1,0) Band aL=4.5 Tj^=350Â° K. Resolution =0.32 A a, P(J) Q(J+4) R(J+9) 15 1.0 2.0 3.0 21.2 19.8 19.1 77.6 78.3 78.6 1.2 1.9 2.4 16 1.0 2.0 3.0 22.8 21.2 20.4 76.2 78.0 78.4 0.9 0.9 1.3 17 1.0 2.0 3.0 25.3 23.4 22.0 74.2 75.9 77.2 0.5 0.7 0.8 18 1.0 2.0 3.0 27.7 25.9 24.5 72.3 73.7 75.0 0.0 0.4 0.5 19 1.0 2.0 3.0 31.0 29.6 28.4 69.0 70.4 71.6 0.0 20 ,0 .0 ,0 34.8 33.1 31.9 65.2 66.9 68.1 0.0 21 22 ,0 ,0 ,0 1.0 2.0 3.0 40.0 38.1 36.9 44.4 43.6 42.6 60.0 61.9 63.0 55.6 56.4 57.4 0.0 0.0

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74 Table 11 continued (2,0) Band o? =4.5 T =350Â° K, Resolution =0.32 A L L J as P(J) Q(J+4) R(J+9) 2.0 19.7 78.3 1.8 15 3.0 18.8 78.9 2.2 4.0 18.1 79.4 2.5

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75 varied to adjiist the "halfwidth" of the theoretical curve. In addition, the dispersion curve contributions, the amplitude of the signal, and the ratio of the field-dependent to field-independent terms were adjusted until the experimental and theoretical curves converged. Convergence was judged by monitoring the RMS deviation between the two curves. Deviations of less than 5 percent per point could usually be obtained after eight iterations of the curve fitting program. Data sets were generally analyzed over intervals of 75 percent and 100 percent of the range of the independent variable, the magnetic field. If the lifetime values predicted by the two fits differed by more than 20 percent, the data were rejected as unreliable. The experimental lifetime values were adjusted to compensate for broadening caused by the time constant present in tlie detection system. A time constant of 4 percent of the sweep period (a typical value) produced less than 2 percent decrease in the experimental lifetime. The result of an exi^erimental run has been plotted in figure XI along with the fitted curve produced by the NLLS computer program.

PAGE 84

Id 0) Â•H 4J ca 00 Â•H CO o m Fx3 ^(U r-H d W H C8 4J d
PAGE 85

77 (siiNn aav) aiisn3ini

PAGE 86

CHAPTER V RESULTS Hanle effect data were taken on eight resolved rotational features in the (1,0) vibrational band and on four in the (2,0) band. For the (1,0) band, lineshapes from several lines showed pronounced narrowing of their half widths due to a perturbation in the A IT upper state. These data were analyzed separately from those for which the effects of the perturbation were not apparent. For the unperturbed rotational levels the lifetimes derived from the data were averaged to yield the lifetime of the vibrational state. For the (2,0) band, no evidence of narrowing due to perturbations was found for the levels investigated. Measurements of the lifetimes were made for several values of the pressure of the scattering gas for both the v = 1 and V -2 vibrational levels. No dependence of the measured lifetimes on the scattering gas pressure was detected for either vibrational level for pressures between 50 and 300 microns. v^ = l Figure XII shows the results of lifetime measurements carried out on the v = 1 vibrational level of the A TT state. In this figure the product of the lifetime and the Lande g factor, g T , is plotted 78

PAGE 87

CM

PAGE 88

80 I Â« I |-Â«IÂ— Â®H l-oH h-Â»-H-oÂ— I h-Â«l-K>-H m > > Â• o CM If) 04 CM oo O 2 < CM Q < Z g TH CM < o O CM O) CO in CM o CM to in Pc /r.r. (su) (e)'6/'x'6

PAGE 89

81 as a fonrtion of the rotational quantum number of the Q branch component of each spectral feature investigated. Since analysis of the Hanle effect lineshapes j'ielded the product, gj-j. it was necessary to know the Lande g factor in order to ascertain the lifetime of the rotational state. For a Tl molecular state the g factor is found by the application of llund's case (a) coupling scheme. For case (a) coupling, g = J(J+1)~ . The data plotted in figure XII have been noi^malized to these values. Results for Unperturbed Levels Tlie measured lifetimes of rotational features characterized by Q branch lines for which j' = 19, 20, 21, and 26 were averaged to yield the lifetime of the v' = 1 vibrational state. The result was T / = 10.41 Â± 0.8 nanoseconds, v = 1 The lifetimes plotted in figure XII represent averages of two or three runs, each between two and four hours long. The error bars plotted represent the deviation from the mean of the averaged values. In all cases deviations of about 10 percent were obtained. The error quoted for the experimental lifetime is the square root of the sum of the squares of the estimated random errors incurred in the experiment. Contributions to this figure were from the three following sources: (1) Uncertainty in the range of the magnetic field sweep. This error was estimated to be, at most, 4 percent of the total range of the field. (2) Variation among measured lifetimes derived from

PAGE 90

82 individual runs. For the v = 1 measurement this error v/as taken to be the mean deviation from the mean of the measured lifetimes and amounted to 5 percent of the average value. (3) Uncertainty inlaerent in the analysis of the contributions to the level-crossing signal from unresolved rotational levels. This error may be estimated from Table II. The maximum deviation from the estimated value for any of the contributions tabulated is less than 5 percent. Further, it may be shown that a 5 percent deviation in the contribution to the levelcrossing signal from one of the unresolved rotational levels will cause only a 2 percent deviation in the experimental lifetime. The experimental error, G, may therefore be written as 6 = [(4)^ + (5)^ + (2)^]^ % = 6.7% . Results for Perturbed Levels The pronounced increase in the product, g^'^^, for levels adjacent to J = 23 is believed to result from a perturbation which couples the A TT, v = 1 state to another state of the molecule. Simmons et al. [2] have attributed a perturbation which has a maximum in the Q branch at J = 23 to the a' E F (v' = 10) state. The notation, T , designates the component of the triplet for which J = N+1, where N is the quantum number for the total angular momentum apart from spin. This state perturbes the TT state by a spin-orbit interaction for which the selection rule, AJ = , holds [27,39]. The theory outlined above for the analysis of level-crossing signals from perturbed states was applied to lineshapes from those rotational

PAGE 91

83 features containing Q branch lines for which J = 22, 23, 24, and 25. In fitting lineshapes from perturbed rotational features only the product, g T , for the perturbed Q branch upper state was varied to obtain the fit. The lifetime of the other two components was taken to be that of the v' = 1 state (10.41 nanoseconds). Tlie Lande g factor for the E perturbing state is given by Hund' s case (b) coupling 3 + scheme. For the F component of tlie E state, g = 2/J. The results X J of the analysis of the perturbed levels are given in Table III. Tlie coupling coefficients, a and 3, were first calculated from equation 52 using the experimental value of H-l . Employing the value of a, the lifetime and effective g factor for the pert\irbed level were calculated from equations 50 and 48, respectively. The values of A, 1^ 3 + the matrix element of the perturbation between the IT and E states, were obtained by application of equation 43. v' = 2 The measured lifetimes of rotational features containing Q branch lines for which j' = 19, 20, 21, and 22 were averaged to yield the lifetime of the v' =2 vibrational state. The result was T /Â„= 8.49 Â± 1.0 nanoseconds, v =2 Results of the lifetime measurements on the v =2 state have been plotted in figure XII. The error bars give the uncertainty in V.'C results for the individual rotational levels. The uncertainty amounts to about 12 percent of the experimental values. No functional dependence of the lifetime on the rotational quantum number is apparent

PAGE 92

(U u 3 4J VI (U P4 O <4-( CO Â•U t-l CO 0) w \. 0) > C o Â•H 4-) o Pi M H M 0) cd H

PAGE 93

85 CO 60 Â•-0 60 St tn CJ o en CM rH ^Â— N

PAGE 94

86 for the levels investigated. Simmons et al . [2], in fact, report no perturbations in either the Q or P branches for values of J between 10 and 25. The uncertainty in the experimental lifetime is due almost entirely to statistical fluctuation in the measured results from the individual rotational levels.

PAGE 95

CHAPTER VI CONCLUSIONS Level -crossing spectroscopy has been shown to be a useful technique for the investigation of certain fundamental properties of excited molecular states. The measured lifetimes obtained in this experiment were found to be in very good agreement with those obtained by other investigators as may be seen from Table IV. The agreement with the results of Wells and Isler [13] is particularly interesting. The Hanle effect signals produced in their investigation resulted from transitions from the first eight rotational levels of the v = 2 vibrational state. In both experiments, however, the technique of analysis of the observed lineshapes was similar and the agreement between the lifetime values obtained for small and large rotational quantum numbers affords credibility to the technique. Hesser's [11] lifetime values were obtained by the direct observation of the decay of upper states of the four positive system excited by electron impact of carbon monoxide. The results seem consistently large, however, and may contain systematic error introduced by undetected cascading transitions from higher excited states. Imhof and Read [18] have eliminated the problem of cascading through the use of the delayed coincidence technique. In monitoring the decay of the excited states, no photon was counted which was not 87

PAGE 96

0) 4J M-l O (0 r-l (U a o Â•H cd .a o n o o Â•H o 0) CO H

PAGE 97

89 > H c

PAGE 98

PAGE 99

91 Unfortunately, the observed decrease in the lifetime from v = 1 to v' = 2 is not consistent with the dependence of the transition moment on the r-centroid bound by Mumma et al . [14] given in equation 1, This relation produces a slight increase in the lifetime with the vibrational level. Theoretically, the trend in the lifetimes is very sensitive to the slope of the transition moment versus the r-centroid curve so that a slight adjustment of equation 1 might produce agreement with the lifetime results. It is also possible that the transition moment has a higher than linear dependence on the r-centroid, although this dependence cannot be inferred from the results of the present experiment. The sensitivity of the level-crossing technique is demonstrated by the results for the perturbed levels of the v' = 1 vibrational level. The experimental values of the coefficients, or and g, show the coupling between the ''"TT and ^E"^ states to be rather small even at the maximum of the perturbation. Additional lines in the spectrum of the (1,0) band were reported by Simmons et al. [2] only for j' = 23 and J =24, but the effect of the perturbation was clearly evident in the levelcrossing data for four different rotational levels. The sensitivity of the Hanle effect lineshapes to the perturbation may be accounted for by the fact that the halfwidth of the signal is proportional to (g T )"'". While the perturbation left the lifetimes of the affected levels unchanged, the effective g values were found to increase by as much as a factor of two over the values predicted for the TT state by case (a) coupling. The values of A listed in Table III show a dependence on the rotational quantum numbers of the perturbed levels.

PAGE 100

92 but this variation is almost certainly introduced by statistical uncertainty in the data. The mean for these values was A = 2.7 cm" and is in agreement with values which may be obtained from conventional spectroscopic analysis. \,

PAGE 101

LIST OF REFERENCES 1. P. H. Krttpenie, The Band Spectrum of Carbon Monoxide , National Standard Reference Data Series (1966). 2. J. D. Sinunons , A. M. Bass, and S. G. Tilford, Astrophys. J. 155 , 345 (1969). 3. G. Herzberg and T. J. Hugo, Canadian J. Phys. 33, 125 (1955). 4. J. D. Sinmons and S. G. Tilford, J. Chem. Phys. 45, 2965 (1966), 5. G. Herzberg, J. D. Simmons, A. M. Bass, and S. G. Tilford, Canadian J. Phys. 44, 3039 (1966). 6. L. Goldberg, W. H. Parkinson, and E. M. Reeves, Astrophys. J. 141 , 1293 (1965). 7. T. P. Stecher and P. A. Williams, Astrophys. J. 146 , 88 (1965). 8. C. Barth, Science 165, 1004 (1969). 9. C. Barth, J. Geophys. Res. 76, 2213 (1971). 10. T. C. James, "Transition Moments, Franck-Condon Factors, and Lifetimes of Forbidden Transitions. Calculation of the Intensity of the Cameron System of CO. ," to be published. 11. J. E. Hcsser, J. Qiem. Phys. 48, 2518 (1968). 12. V. Meyer, A. Skorbele, and E. Lassettre, J. Chem. Phys. 43 , 805 (1965). 13. W. C. Wells and R. C. Isler, Phys. Rev. Letters 24, 705 (1970). 14. M. J. Mumna, E. J. Stone, and E. C. Zipf, J. Chem. Phys. 54, 2627 (1971). 15. G. M. Lawrence, Bull, of the 7\in. Phys. Soc. 16, 204 (1971). 16. E. Lassettre and A. Skerbele, J. Chem. Phys. 54, 1597 (1971). 17. V. Meyer and E. Lassettre, J. Chem. Phys. 54, 1608 (1971). 18. R. E. Imhof and F. H. Re.^d, Oiem. Phys. Letters IJ., 326 (1971). 93

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94 19. J. G. Chervenak and R. A. Anderson, J. Opt, Soc. Am. 61, 952 (1971). 20. W. Hanle, Z. Physik 30 (1924). 21. G. Breit, Rev. Mod. Phys. 5, 91 (1933). 22. F. D. Colgrove, P. A. Franken, R. R. Lewis, and R. N. Sands, Phys. Rev, Letters 3, 420 (1959). 23. R. Zare, J. Cham. Phys. 45, 4510 (1966). 24. P. R. Crosley and R. Zare, Phys. Rev. Letters 18, 942 (1967). 25. R. deZafra, A. Marshall, and H. Metcalf, Phys. Rev. A3, 1557 (1971). 26. S. G. Silvers, T. H. Bergeraan, and W. Klemperer, "Tlie Optical Detection of Zero Field Level Crossing in the A-'-'lT State of CS" (Twenty-Third Symposium on Molecular Structure and Spectroscopy, Columbus, Ohio, Sept. 3-7, 1968). 27. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton, N. J., 1960). 28. H. Conroy , "Molecular Schrodinger Equation VIII. A New Method . for the Evaluation of Multidimensional Integrals" (Mellon Institute, Theoretical Chemistry Preprint No. 24, July 10, 1967), 29. G. Herzberg, Molectilar Spectra and Molecular Structxire I . Spectra of Diatomic Molecules (D. Van Nostrand Co. , Inc. , Princeton, N. J., 1950), 2nd ed . 30. Vi. C, Wells, "Level -Crossing Spectroscopy of Diatomic Molecules: Application to an Excited State of Carbon Monoxide," Ph.D. dissertation. University of Florida (1969). 31. D. K. Anderson, Phys. Rev. A 137, 21 (1965). 32. n. Okabe, J. Opt. Soc. Am. 54, 478 (1964), 33. R. G. Taylor, T. A. Chubb, and R. W. Kriplin, J. Opt. Soc. A:ii. 55, 1078 (1965). 34. D. F. Heath and P. A, Sacher , Appl . Optics 5, 937 (1966). 35. P. V/arneck, J. Opt. Soc. Am. 55, 921 (1965). 36. R. A. Young, G. Black, and T. G. Slangcr, J. Chem. Phys. 48, 2067 (1968).

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95 37. J. D. Jackson, Classical Electrodynamics (John Wiley and Sons, Inc., New York, 1962), p. 254. 38. F. C. Fehsenfeld, K. M. Evenson, H. P. Broida, Rev. Sci. Instr 36, 294 (1965). 39. I. Kovacs, Canadian J. Phys. 36 (1958). 40. T. M. Holzberlein, Rev. Sci. Instr. 35, 1041 (1964). 41. J. Z. Klose, Phys. Rev. 141, 181 (1966).

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BIOGRAPHICAL SKETCH Ralph Laurence. Burnham was born April 16, 1944, in Jacksonville, Florida. In June, 1962, he was graduated from Terry Parker High School. In June, 1966, he received the degree of Bachelor of Science with a major in Physics from the Georgia Institute of Technology. In 1966 he enrolled in the Graduate School of the University of Florida. He worked as a graduate assistant in the Department of Physics until March, 1972. From September, 1966, until the present time, he has pursued his work toward the degree of Doctor of Philosophy. Ralph Laurence Burnham is a member of the Tau Beta Pi Society.

PAGE 105

I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Ralph C: Isler, Chairman Associate Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Charges F. Hooier, Jr. Associate Professor of Phys I certify that I have read this study and that in my opinion It conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. las A. Scott ^^ Thomas Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and Is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. W^ Thomas L. Bailey Professor of Physics

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T certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosopliy. Uilliara W. Weltncr, Jr. Professor of Chemistry This dissertation v/as submitted to the Department of Physics & Astronomy in the College of Arts and Sciences and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. March, 1972 Dean, Graduate School

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.Mi^ \.' 6^^-*"' , fi^