NF SUREt.IENT OF THE RADIATIVE LIFETIMES OF THE
v = 1 AND v = 2 LEVELS OF THE A STATE
OF CARBON MONOXIDE
BY
RALPH LAURENCE BURNHLAM
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.
TABLE OF CONTENTS
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 LevelCrossing
Phenomenon . . . . . . . .
Quantum Mechanical Calculation of the Hlanle
Effect Signal for the A State of CO . .
Rotational Line Contributions to the
Molecular LevelCrossing Signal . . .
Rotational Intensity Distribution in
a Molecular Discharge . . . . .
Rotational Intensities in Resonance
Fluorescence . . . . . . .
The Effect of Rotational Perturbations
on the LevelCrossing Signal . . . .
Lifetimes, Transition Probabilities, fValu
and rCentroids 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. Rcsults 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 Stals . . . . . . . 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 LevelCrossing
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
. . 641
. . 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 zerofield levelcrossing 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. Levelcrossing
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 levelcrossing 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 betveen 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 AX 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 levelcrossing spectroscopy. Their result %as in substan
tial agreement with that of Hesser. The controversy was partially
resolved by Mumma et al. [11] 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 havre n e hnn 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 rcentroid 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 rcentroid 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 rcentroid. 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
t, ..l i an ciorate radiative lifetimes of individual vibrational levels
of thle A lf state 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 levelcrossing phenomenon which was employed to obtain the
lifetime measurements reported in this work was first discovered by
Hipl'l, [20] in 1924. Levelcrossing 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. Reemitted 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
levelcrossing 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,
levelcrossing spectroscopy has proved to be an excellent technique for
measuring a variety of fundamental properties of excited states of
atomic systems.
Quite recently levelcrossing 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 levelcrossing Fignals
were reported for NO by Crosley and Zare [21]. 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 levelcrossing 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 levelcrossing 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 levelcrossing 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 curvefitting
techniques. The basic experimental quantity obtained from the data
analysis was the product of the lifetime and the Landc g factor for
the vibration.lrotational 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 lineihapes for lInnle effect
signal'; arising from A T X + transitions in carbon monoxide will
be developed. In addition, since the exciting radiation employed in
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 levelcrossing signal from transitions
from ziach 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 levelcrossing line shape will be developed
using basic perturbation theory.
Semiclassical Analog to the
LevelCrossing Phenomenon
Some of the basic features of the zerofield levelcrossing
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
C1
U
'01
C,
II
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
emission of radiation. In addition to the fielddependent level
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 levelcrossing 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 levelcrossing signal of departures from the ideal exper
imental geometry given in figure I. Suppose that scattered light is
detected in the xz 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 levelcrossing 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 reemitted 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"grK .j'
[1 i(p.4 )ogoTj H h]
The vectors, f and g, are the polarizations of the exciting and
reemitted 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 spacefixed 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 spacefixcd axes into the
moleculefixed 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 
Ul 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
spacefi :ed coordinates through, the origin. Under such as t.r:nsfor
mat ion
aTT+ a, I  s, y' ',
and
S(nT+ nB, ) = ( )J2m (, ) (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
3j symbols. Integration over the moleculefixed 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 rn ,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+mA
,'
(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 3j symbols may be used to write
the matrix elements in their final form
', lT.T'X C, m+ 1
W pJf .rJm) jm fyrj.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
reemission takes place in a similar fashion. A consequence of the
parity selection rule is the prohibition of excitation through
a Q branch followed by reemission 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 LP' = 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,.T1)/15 n= 4
or, inl certain cases, through the use of the defining relationship
bctwecii 3j and 6j symbols.
Table I gives the result of the calculation for the IT 
transition in carbon monoxide. Undcr the e:pcrimental coiLditions of
unpolarizccd c::citing and scattered radiation, ternuis for v which j = 1
cancel and tihe sign.l consists of a fieldindependent background v.lhich
arises from terms for .'.hicl, I "i = 0 and a fielddependent pnrt Ii.hich
arises frol.i t ermt:l: for v hicl I p'I = 2.
Rot :t ional Line Contriljutions to the
lolcCul ar LevelCrossing Signal
In the follo..'ing paragraphs a mathematical model '.'ill be
developed wl'ich will allo'. the contributions of unresolved rotational
lines to the lvc1crossing 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
4j
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 lionlLondon 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 )oexp 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(XX.) 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
reemitted by the scattering gas proceeds in a fashion similar to
the calculation of the lamp intensity. For a particular mode of
absorption followed by reemission 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 reemitted 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 reemitted 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(2ayy2") dy (34)
The solid angle subtended by dA(y) is then
3
d: = (2ayy) L (zy) + 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
14
F4
bLi
I:,
LU
0~
J
Ca,
_____1
I
I
I'
!
!
I^ 
l 1
Io
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 levelcrossing 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 levelcrossing 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/(EAE 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
(EAE ) + .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(olA 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) + Pg (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
(1c ) (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 levelcrossinrg 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.
Lifetimes, Transition Probabilities, fValues,
and rCentroids 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
strengths calculated from measured radiative lifetimes to those obtained
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 + ? + (EV)'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 DornOppenheimer 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 BornOppenJheimer 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 vibrationalrotationnl overlap integral may be written
as
V,,I > 1 <(' 'v") .o ,t (59)
v.here the first term is the square root of the FranckCondon 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
electronicvibrational 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 rcentroid of the transition, and
V V
gives a measure of the separation. The rcentroid is defined as
(vIrv")
,., = (64)
V V 4 %'
The lifetime of the electronicvibrational 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
the lifetime becomes
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
61n 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 FranckCondon factors for
e
the vibrational transitions are known.
The oscillator strength or fvalue gives the degree to which
a transition resembles a classical oscillating dipole in the absorp
tion or reemission of radiation. The fvalue 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 fvalue 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 AX transition in carbon monoxide.
The fvalues of the AY 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 rcentroids of the vibrational transitions. It is
usually assumed that R is a simple function of rcentroid. 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 polepieces 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 fieldfree 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 XY plotter.
cli
In.
in.
I.
4
1a)
I4
UJ
Co
V)
42
w
> Zc
> 0
< 
o mz
N
w m
< < o
00
Lu aN.~I Ic'
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 selfreversal of the
resonance radiation emitted by the lamp. Selfreversal 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.
Selfreversed 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 selfreversal.
The second and most important concern was the minimization of
fluctuations in the intensity of the lamp. Since the levelcrossing
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 selfreversal. 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 selfreversal; 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
levelcrossing [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 2150 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 1/2inchdiameter 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/,'4inchdiameter blind hole drilled along the axis
of the boron nitride piece. Differential pumping took place across
a 1.'4inch 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
kZ MICROWAVE RADIATION
TRIDE
COUPLING
CO IN
helpful in preventing selfreversal of the molecular resonance radio
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 onemeter vacuum monochro
mator. This instrument w.'as equipped with a large oil diffusion pump
and could be evacuated to a pressure of less than 107 Torr. The mono
chromator was of normal incidence geometry and employed a cylindrical
replica grating of onemeter 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 firstorder reciprocal
dispersion of 16.6 A.nLm. With the entrance and exit slits set at*
10 microns a typical setting for the levelcrossing 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'.iallmeter length. The scattering cell was
separated from thi. monochromator by a onehalfinchdiameter x 1mm
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 twoinchdiameter ;: 5 Sinchthick 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 onehalfinchdiameter 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
r4
C)
u
to
'r4
z
0
CC Z
ciFO
E< Go
QU <
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: 2inch
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 1cmdi 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 voltagedivider chain
was mounted in a thermoelectrically cooled lighttight 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 levelcrossing experiment.
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 mur.,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 fielddependent component of the levelcrossing 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 levelcrossing
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(ts)/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 levelcrossing 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 FabriTek 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 1230A 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 levelcrossing signal; under
ordinary operating conditions the fielddependent 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 fielddependent 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 fielddependent 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 onefourth 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 level
crossing signal was stored as a function of the independent variable,
the magnnctic field. The rate at which the field was swept depended on
the d.rjcll time for each channel utilized in the memory. D.,.ell times
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 FarbiTel: digital
printer. Data could also be plotted as a function of channel nuliber
on an XY 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 3630 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
41
01
C:
0
u
4i
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
oneohm resistors of over onehalf 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 levelcrossing
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
levelcrossing data in the memiio'ry,' thlen commrenccd and was continued
until the quality of the expel 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 levelcrossing data were then fitted to theoretical line shapes
with the aid of a digital computer.
Lamp Spectra
Ideally, molecular lifetime determinations using levelcrossing
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 levelcrossing 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
* TL300K, aL=5.0
A TL3500K, 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 minimizcd. Tihe ,rin c;:'2nato' 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 levelcrossing 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
HI2
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 reradiation 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 reradiation 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 leastsquares
(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 fieldindependent 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 fielddependent to fieldindependent 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
imental lifetime values were adjusted to compensate for broadening
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
sI
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
investigated. Measurements of the lifetimes w.ere 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.
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
1T
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 talerdto
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 analysi : of the contributions to the levelcrossing 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 experimental 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 spinorbit
interaction for which the selection rule, AJ= 0, holds [27,39].
The theory outlined above for the analysis of levelcrossing 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 brinclh 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
4J
$4
.Li
r4
:$ U
U) r4
Q) 0)
C4 >
0)
r4 ,J
C13
~4 r4
Ei 0
Li 4
'4
r cn i) cn
ot o 0 0n
C'4 CM, rl r
MI r4 rI r4
%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
ID
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
Levelcrossing 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.
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
,l.
oj
Q)
.C
4i
0
U,
1
0
4
41
.Q
04
F4
r4
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)
11 C) C W
c^ 0i ^ ^ '
4 C"J C'3 .0 U *~
14 C1J
correlated to a particular scattered electron responsible for their*
excitation of tle state.
'The lictime results of Chervenak and Anderson [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'oxlnations: (1) Carcad
ing. The C1 state of carbon monoxide lies above the A Tl state nnd
has a lifetime of about 24 nanoseconds. Cascading transitions from
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
The variation of the radiative lifetime with the vibrational
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 rcentroid 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 rcentroid 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 rcentroid, although this
dependence cannot be inferred from the results of the present experiment.
The sensitivity of the levelcrossing 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.
