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Electronic energy transfer processes in collisions of metastable argon with Nâ‚‚ and Hâ‚‚

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Title:
Electronic energy transfer processes in collisions of metastable argon with Nâ‚‚ and Hâ‚‚
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Lishawa, C. Randal ( Charles Randal ), 1951-
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vi, 82 leaves : ill. ; 28 cm.

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Subjects / Keywords:
Electronics ( jstor )
Molecular beams ( jstor )
Molecules ( jstor )
Nozzles ( jstor )
Photons ( jstor )
Potential energy ( jstor )
Rotational spectra ( jstor )
Signals ( jstor )
Velocity ( jstor )
Wavelengths ( jstor )
Argon ( lcsh )
Collisional excitation ( lcsh )
Energy transfer ( lcsh )
Hydrogen ( lcsh )
Molecular beams ( lcsh )
Nitrogen ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1981.
Bibliography:
Includes bibliographical references (leaves 79-81).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by C. Randal Lishawa.

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University of Florida
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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.
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ELECTRONIC ENERGY TRANSFER PROCESSES IN COLLISIONS OF
METASTABLE ARGON WITH N2 AND H2










By

C. RANDAL LISHAWA


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


1981















ACKNOWLEDGMENTS


The author wishes to thank the many people who have contributed

to this study. First and foremost is Professor E. E. Muschlitz, Jr.,

who provided experience, patience, and funding for this work. Also

Professor T. L. Bailey has unselfishly provided experimental equipment,

helping to overcome the various shortages in time and money. A major

contributor to the development of the experimental devices fabricated

for this experiment, as well as many hours of private discussions, was

Dr. W. Allison. The author would also like to thank his son, Adam, for

the many hours of relaxation which often led to a break in thought pat-

terns and the resolution of a difficult problem.















TABLE OF CONTENTS


Page


ACKNOWLEDGEMENTS

ABSTRACT

CHAPTER

I INTRODUCTION
A. Molecular Beams
B. Supersonic Nozzle Beams
C. Capillary Array Beams
D. Reaction Cross Sections
E. The Franck-Condon Principle
F. Energy Distributions in Product States
G. Electronic Energy Transfer Processes
H. Purpose and Scope of Present Study

II DESCRIPTION OF THE APPARATUS
A. Introduction
B. Gas-Handling System
C. Metastable Beam Production
D. Velocity Analysis
E. Optical System
F. Data Collection System
G. Mass Spectrometer Calibration System

III EXPERIMENTAL PROCEDURE
A. Optical Considerations for Ar*/N2
B. Optical Considerations for Ar*/H2
C. Experimental Procedure

IV DATA ANALYSIS AND RESULTS
A. N2 Band Profiles and Rotational Distributions
B. H2 + Ar* Cross Sections and Spectral Distributions

V DISCUSSION
A. Collisions Involving Ar*/N2
B. Collisions Involving Ar*/H2
B.1 Radiation from H2(a 3Hn, v' = 0)
8.2 Radiation from ArH*
B.3 Conclusion










TABLE OF CONTENTS (Continued)


APPENDIX I MCA/STEPPING MOTOR SCHEMATICS

APPENDIX II SPECTRAL SIMULATION PROGRAM

REFERENCES

BIOGRAPHICAL SKETCH


Page

62

65














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


ELECTRONIC ENERGY TRANSFER PROCESSES IN COLLISIONS OF
METASTABLE ARGON WITH N2 AND H2

By
C. Randal Lishawa

December 1981

Chairman: E. E. Muschlitz, Jr.
Major Department: Chemistry

Estimates of the rotational distributions in the N2(C 3Tu, v'

0,1) product of the reaction

Ar*(3P2,0) + N2(X 1 )-- Ar(1S) + N2(C 3 1

have been made on the band profiles of the N2(C 31u, v' = 0.1) -*-

N2(B 31g, v" = 0) fluorescence. These measurements were made at relative

energies of 0.074 eV, 0.089 eV, and 0.161 eV. The N2(C 31u, v' = 0) band

was found to be well represented by Boltzmann distributions with charac-

teristic temperatures of 1700 + 100 K, 1600 + 100 K, and 2200 + 100 K,
respectively. The N2(C 3Iu, v' = 1) data could not be fit by Boltzmann
distributions, but did fit "Golden Rule" distributions within the experi-

mental error. The reaction involving metastable argon and ground state

hydrogen molecules was examined by observing a continuum emission. The

cross section for fluorescence was measured and seen to rise rapidly from

v









an onset at 0.080 eV and reach a maximum around 0.125 eV. The spectral

distributions were seen to peak at lower energies than that calculated

by James and Coolidge, leading to speculation that at least some of

the photon emission may arise from an excited state of ArH rather than

the excited H2.















CHAPTER I
INTRODUCTION


A. Molecular Beams

The first detection of a molecular beam was Fleming's discovery

of a shadow on the glass walls of incandescent lamps with copper fila-

ments [1]. At the time, this was considered a confirmation of the kinetic

theory which predicted that a molecule would travel in a straight path

in the absence of collisions or applied fields. This phenomenon was

previously observed for ions and electrons, but this was the first

discovery involving neutral species.

The first deliberately designed experiments utilizing molecular

beams were the experiments of Dunoyer [2], which again verified the idea

that a molecule which is not disturbed by collisions will continue to

travel in a straight line.

The next significant work involving the use of molecular beams

was the work of Stern which ultimately led to the famous Stern-Gerlach

experiments verifying the existence of space quantization and electron

spin [3]. This work led to techniques for the measurement of the mag-

netic moment of various molecules by the magnetic resonance techniques

of Rabi [4], and the further refinements in molecular beam techniques

by Ramsey [5].

During this time, the study of chemical reactions was moving from

the field of bulk reaction studies toward attempts to understand the

1










dynamics of such reactions in terms of individual collisions between

molecules. It has been in this field that the molecular beam has found

its most significant uses. The pioneering experiments in this field were

conducted with effusive or oven beams, which provided only thermal

averages of the quantities being measured, or else were velocity selected,

greatly reducing the beam intensity. The first major improvement in

this condition was the development in the 1950s of the multiparallel canal

sources. In 1953, King and Zacharias 16] used a bundle of hypodermic

needle tubing and sheets of foil to produce a beam of high intensity.

This was followed rapidly, in 1955, by the production of intense beams

of ammonia by the multiparallel canal source for the study of masers 17].
At the same time the first nozzle beam sources were being devel-

oped for use in studies of chemical interest. In 1954 Becker and Bier

[8] first achieved the high pumping rates required for a successful nozzle

beam. Because of the higher intensities and narrower velocity distri-

butions of this type of beam, the nozzle beam has shown a marked increase

in use as high-speed vacuum systems have come into more common use.

B. Supersonic Nozzle Beams

The supersonic nozzle beam is a source of highly collimated, high-

intensity, and nearly monoenergetic particles. The beam is created by

applying a high pressure behind a small orifice and allowing the gas to
expand into a vacuum. The expansion jet is shown in Figure I-1.

The major feature of interest is the central region terminated by

the Mach disk. Within this region is the supersonic portion of the expan-

sion. By the interception of this portion of the gas, a supersonic beam






3


















O -
.J

0 \



Z w


z X


I 0
z C
/- o
CA I

I I

a





z
01





I-



Chi





za
I ^ / 0 '-*
\ 'i Y 3










produced. This interception is accomplished by means of an appropriately
positioned device called a skimmer. The skimmer penetrates into the
Mach disk, and shields the supersonic flow from collisions with the
background gas. These collisions would, if not prevented, destroy the
desired beam characteristics. Beyond the skimmer is a low-pressure
region in which the beam may propagate without this interference.
As the beam is essentially formed at the mouth of the skimmer, the
properties of the gas at this point, the gas pressure and velocity distri-
bution, determine the ultimate characteristics of the beam. These condi-
tions are described by [9]

dn = n(m/2 Kt)3/2exp -(m/2kT)(c-u)2 d3c (1)

where n, T, and u are the density, translational temperature, and mean
gas velocity. The mass of the molecule in the beam (m) and the Boltzmann
constant (k) are the remaining parameters in this equation. From inte-
gration of Equation (1), several important relationships are derived.
These are given as Equations (2) through (7).

Xm/d* = O.67(P/P1)1/2 (2)

u = ((2/(y 1))(kTo m)112 (3)

M = u/(ykT/m)1/2 (4)

S = u/(2kT/m)1/2 = (y/2)1/2M (5)

I(6=0) = (Alnlao/27t2)M(3 + yM2)[l + (y )M2/2]-1/2 (6)










G = A*(my/kTo)1/2 P (2/(y+l))(Y+1)/2(Y-1) (7)

In the above equations the symbols are M = Mach number = the ratio of

the flow velocity to the local speed of sound, u = the bulk stream veloc-

ity, k = the Boltzmann constant, d* = orifice diameter of the nozzle,

y = specific heat ratio (C /C ), T = temperature, m = mass, p = pressure,
S = speed ratio = the ratio of velocity of the beam to that of a thermal

beam, n = number density, A = area, Z = distance downstream from the

skimmer, G = mass flow through the nozzle in grams/second, a = speed

of sound =(ykT/m)1/2, x = distance. The subscripts are 0 = stagnation

(source) conditions, 1 = nozzle exhaust chamber, skimmer orifice, 2 =

collimation chamber, collimator slit. The above equations are quite use-

ful in design considerations for such a source.

Another key feature of the supersonic beam is a "cooling" of the

internal degrees of freedom providing additional translational energy to

the beam. This follows from the thermodynamics of an ideal gas under-

going isentropic expansion. The total amount of energy available to the

gas is given by

E = CpT (8)


where C is the heat capacity at constant pressure of the gas and TO is

the temperature of the gas behind the nozzle (stagnation temperature).
Recalling that C = y/(y-l), (y = C /C ). If not all of this energy is
converted to translational energy the beam is characterized by a

"temperature" T and the energy converted is given by


E (y/(y-l))(TO-T) = mu2/2 (9)










where u is the velocity of the beam. The ratio of the stagnation
temperature to the final beam temperature is given as

TO/T = 1 + ((y l)/y)M2 (10)

where the Mach number (M) is defined as u/(ykT/M)1/2

This temperature may be broken down into components relating to
random translational motions, vibrational energies, and rotational ener-
gies. By assuming most of the rotational energy relaxation occurs in the
high-pressure portion of the expansion where collisions between beam
members predominate, it is possible to calculate a rotational temperature
for.a given expansion [10]. This assumes the collision process is
described by a van der Waals type of interaction potential (V = -C6/r6).
The results are given as


TO/Tr = T(YS)-1( 0Z )6(Y-1)/(Y+2) (11)

where T(y,E) is a tabulated constant, a measure of the strength of the
rotational to translational energy coupling, y is the ratio Cp/Cv,

X0 = (3/2)2/3(3 C6/kTo)1/3 (5/3) (n /2)(32/27) sin2 6 (3/2)M

(12)

and


Z2 = r2 K[{(y l)/(y + 1)}1/2 (2/y +1)1/Y-1] (13)
0 0










where k is the Boltzmann constant, no is the number density of the gas

at the nozzle, the geometric term, sin2 6, is calculated to be 0.0812,

r0 is the nozzle aperture radius, and K is a peaking factor related to y.


C. Capillary Array Beams

Another type of molecular beam source which has become popular

is the multichannel or capillary array source. Although its centerline

intensity is not as great as a nozzle beam source, the capillary array

beam is a high-intensity directional molecular beam source when compared

with the conventional oven source. The capillary array source has the

advantages over a nozzle source of a much lower gas flow rate and operat-

ing conditions which may be accurately recreated, allowing for greater

day-to-day reproducibility of the beam.

Pauly and Toennies [11] have calculated a theoretical centerline

intensity for a conventional oven source operating under Knudsen flow

conditions, that is, the mean free path of the particle in the source

is on the order of the exit hole diameter. This relationship is


I(0=0) = 1.12 x 1022 P0FO/(MT)1/2 (14)


where PO is the source pressure in torr, F0 is the orifice area in cm ,

T is the temperature in degrees Kelvin, and M is the molecular weight

of the gas.

When this is compared to a multichannel array in which the length

of the channel is much larger than the diameter of the channel and which

is operated under conditions such that the mean free path is on the order










of the channel length, a relationship between the centerline intensities

of the two sources may be obtained as


I( =0)Array/I(B = O)ven = 0.32 v1/2(FTm)1/4 /(I1/4N) (15)


where v is the average velocity in the source, N is the total gas flow

rate, a is the scattering cross section, F is the total area of the

source, T is the transparency of the array, and m is the total number of
holes in the array. Becker and Houkes [12] have demonstrated that for

a given beam intensity the gas flow from a capillary array source is

approximately 100 times less than the flow from a conventional oven

source, thereby reducing the stress placed on the vacuum-pumping system

and conserving what may be an expensive quantity of gas.

D. Reaction Cross Sections

At a particular reaction energy, an expression for the reaction

rate (R), as determined for crossed molecular beam experiments, may be
written as

V
R = o(vr)v fnA(x,y,z)n (x,y,z) dxd (16)


where o(v ) is the reaction cross section, vr is the relative velocity of

the collision partners, nA(x,y,z) and nB(x,y,z) are the coordinate
dependent beam densities of the two beams, and V is the interaction vol-

ume. The primary experimental difficulty in using this equation is the
measurement of the quantities nA and nB. Assuming these are at most

slowly varying quantities within the interaction region, the reaction

rate may be written as










R = o(vr)VrnAnB (17)


where the beam densities are no longer spatially dependent. In experi-

ments such as the one to be described, one of the direct products of a
collision is a photon which is later detected. This photon flux is then
proportional to the reaction rate.

Sp = KR = Ko(Vr)vrnAB (18)


where S is the photon flux and K is the proportionality constant. The

metastable beam detector measures the intensity (IA = VA/nA). From this
an expression for the reaction cross section may be obtained:


S(vr) K-1SpyA/IAnBv (19)


Upon integration over all collision energies with a Maxwell-Boltzmann
weighting factor this quantity may be related to the more familiar rate

constant, which is determined in most kinetics experiments.

E. The Franck-Condon Principle

In 1925 Franck [13] proposed a method for explaining the band

spectrum observed in diatomic molecules. His basic postulate was that
the electron transition directly affects neither the position nor the

momentum of the nuclei. That is, during an electronic transition, the
electron will jump from one potential surface to another more rapidly
than the nuclei can respond to the impetus imparted.
In 1927 Condon [14] made the first attempts to connect this pos-

tulate with quantum mechanics. In 1928 Condon [15] made a more elaborate










proposal on this relationship. Using the notation of this paper, the
mathematical formulation takes the following form.
Beginning with the Born-Oppenheimer approximation, it is possible
to write the energy of a state E(e,n) characterized by e, an ensemble of
all the electronic quantum numbers, and by n, the vibrational quantum
number (for the purposes of this study, rotational motions are neglected).

E(e,n) = Ee + En (20)

Also the total wave function may be written as


Wen(r,x) = pe(X)4n(r) (21)

Any given transition (e', n') -(e",n") may now be given in terms

of pen(x,r) and the electronic moment M(e',e",n',n"). This transition
moment may be resolved into components depending only on the individual
coordinates as Me + M.n The transition moment R may now be calculated as

R = IMet *,'_,v dT+ fM *~1P'" dT (22)

As Mn does not depend on the electronic coordinates, the second integral

may be written as

fM d 'T*" dTe (23)
nvv dn/e e

Because of orthogonality of the electronic states the integral reduces
to zero. Thus the transition moment reduces to


vR = drT Me e* dTe
v n eII, 1eI


(24)










The latter portion of this integral is the electronic transition moment

(R ) and in the Franck-Condon limit is assumed to vary only very slowly

with nuclear distance and as such may be replaced by an average value

of the electronic transition moment (R). The transition moment may

then be written

R = Re fv' dr


and the intensity of a given transition may be written

in'II" 4 4 -2 I 2
I (64/3)r4 cNv,v R I v dr 2(26)


The key result of this manipulation is that the intensity of the

transition is proportional to the square of the overlap integral between

the vibrational states involved. Therefore, the maximum will be found

for a transition for which this factor is maximized, rather than for a

straightforward vertical transition.

F. Energy Distributions in Product States

The most familiar distribution of energy in a product is observed

in bulk reactions. The energy in this process has had time to randomize

into the well-known thermal or Boltzmann distribution. This distribution

is characterized by a well-defined temperature.

A second way of dividing the energy in the product states is given

by the Fermi Golden Rule [161. In this case, the relative transition

probabilities for the formation of a given final state is given by

first-order perturbation theory as










Wif_ = (2Tr/)Ii2 pf(e) (27)


where V is the interaction potential connecting the initial (li>) and
final ( dependent on the available energy (e) [17]. In the limit of a highly
impulsive or sudden collision, the matrix elements in Equation 27 become
the Franck-Condon factors connecting the initial and final states

I 2 lIl2 (28)

For a vibrating rotor, the density of states function is given by
(18)


pf(E)(l fv)3/2 ~ ( f')3/2 (29)


where f v is the fraction of the mean available energy channeled into
a particular vibronic state.
Kinsey [191 has calculated a density of states function for a
variety of conditions including the partial resolution of product and
rotational states. For the case in which the translational energy (E ),
total energy (E), vibrational state (v), and rotational state (J) are
known, the density function is given by

Pf.(E',v',J') = (2J'+1)pT[E' -E (v',J')] (30)

where the density of translational states (p ) is given by


(E) 5/2 3/2E/23 A E/2 (31)
pT(ET) T =T T










where p is the reduced mass of the colliding molecules. For the purpose

of calculating the internal energy of the product states the rigid-rotor-

harmonic-oscillator model has been used with first-order correction for

anharmonicity. This gives an internal energy of

E1(v,J) = (v + 1/2)e + (v + 1/2)2eXe + BeJ(J+)

+ ae(v+ 1/2)J(J+1) (32)

G. Electronic Energy Transfer Processes

Electronic energy transfer processes are observed both in nature

and in man-made laboratory experiments. In the rarefied gases of the

upper atmosphere, electronically excited species play an important role

in the chemistry of this region. Because of the low pressures, and cor-

responding long path lengths, energy carriers must be very efficient at

transferring energy; that is, the transfer must be accomplished in a very

few collisions. It has been shown that vibrational energy often requires

tens of thousands of collisions to transfer energy [20], while energy

stored in electronic energy levels is transferred after only a very few

collisions [21].

In the laboratory one of the more notable successes of the study
of electronic excitation processes is found in various laser systems,

such as the He-Ne laser [22], CO2 laser [23], and the various eximer
lasers [24]. Although these studies have led to many practical benefits,

the study of electronic energy transfer has also led to greater under-

standing of the interactions of atoms and molecules.










Electronic energy transfer takes place in a variety of processes,

depending upon the energy.available and the dynamics of the collisions.

Some of the more common processes are listed in Equations (33) through

(37) below.

A* + XY A + XY+ + e- (33)
(Penning Ionization)

A* + XY -- AXY+ + e- (34)
(Associative Ionization)

A* + XY -- A + X + Y+ + e- (35)
(Dissociative Ionization)

A* + XY -* A + X + Y* (36)

A* + XY -+ A + XY* (37)

In all of these reactions, the asterisk indicates the location of the

electronic excitation. In the last two equations, (35) and (36), the

excited product will relax to lower states by the emission of a photon if

the optical transition is allowed.
The most prolific experimental technique in the study of neutral

products has been the flowing afterglow technique used by Setser, Stedman

and Coxon [25]. This method has been used to study many reaction systems,

obtaining total cross sections as well as relative cross sections for

energy transfer into various rotational, vibrational, and electronic

states. However, this type of experiment yields only thermal averages of

the measured quantities. For the energy dependence of the processes,










molecular beams have played an important role. The technique of molecu-

lar beams has been used to study this type of process in time-of-flight

crossed beam measurements [26], angular scattering measurements [27],

and crossed beams in which photon emission is used as the detection

process [28]. It is the latter of these techniques which is employed in

this study.

H. Purpose and Scope of Present Study

The reaction


Ar*(3p2,0) + N2(X1E ) -+ Ar(S) + N2(C3u)


has been studied by the detection of fluorescence from the process


N2(C3)u) --+ N2(B3" ) + hv


by Sanders, Schweid, Weiss and Muschlitz [29] who determined the cross-

section response to collision energy for the total radiation emitted.

This process has also been investigated by Lee and Martin [30], using

time-of-flight, with differing results for the onset energy for the

process. Cutshall and Muschlitz [31] have studied the energy dependence

of the distribution of the energy into the various vibrational levels of

the N2(C) manifold. The results of those experiments have been explained

theoretically by Gislason, Kleyn and Lus [32] using a model in which, as

the reactants approach a critical distance, the N2(X) potential surface is

disturbed by the close lying N2 + Ar- potential energy surface. This

causes the N2 molecule to begin to vibrate. Several vibrational periods










later, the collision partners reach a second critical distance of approach

and jump from the N2(X) + Ar* surface to the N2(C) + Ar( S) potential sur-

face. It is this time interval prior to the final surface jump that then

influences the final distribution of vibrational states. The first por-

tion of this work consists of an investigation of the rotational distri-

bution of the energy within specific vibrational levels.

Investigations of the radiation from the hydrogen continuum have

been carried out theoretically [33,34,35,36] and experimentally by

Coolidge [37] as well as by Smith [38] and by Finkelnburg and Weitzel

[39]. The potential energy for the H2 molecule has been recalculated

recently by Kolos and Wolniewicz [40]. The second portion of this work

consists of measurement of the Ar*/H2 cross section for the observed

continuum radiation.

Chapter II is a description of the apparatus, the vacuum system,

and the data collection system. Chapter III presents a description of

the general experimental procedures as well as details of the specific

systems studied. Chapter IV presents the measured spectra and cross

sections as well as a discussion of the errors in the data. Chapter V

is a discussion of the results of this study. Previous measurements

are discussed when available, and possible mechanisms for these processes

are presented.















CHAPTER II
DESCRIPTION OF THE APPARATUS

A. Introduction

The experimental apparatus is a crossed supersonic molecular beam

device. This device is housed under a high vacuum within an aluminum

cylinder four feet in diameter and two feet high. This cylinder is

divided into three distinct chambers as shown in Figure II-1. The first,

and the largest, is the main chamber. In this chamber the beams intersect,

the fluorescence is detected, and both beams are velocity analyzed. The

second and third chambers are virtually identical in construction, the

only differences arising in the additional equipment used in the prepara-

tion of metastable species. Within the first of these two chambers, the

target chamber, is a nozzle which may be heated by a resistive element

to provide variation in the beam velocity. The second, and last of the

internal chambers, contains a nozzle within a jacket through which a

coolant liquid may be passed to provide for velocity variation of this

beam. Also in this chamber is an electron gun used in the excitation

of the ground state argon atoms to their metastable states. These cham-

bers are each differentially pumped by oil diffusion pumps with typical

pressures attainable listed in Table II-1.

The gas-handling system has been extensively described by Sanders

[41] and Cutshall [42] and so will not be detailed in this paper. The

data acquisition system and the calibration system for the target beam
17





































-J:










are new elements to the experiment and as such will be extensively

discussed.


Table II-1. Typical Vacuum Pressures in Experimental Apparatus


Chamber Pressure before Experiment During Experiment

Main 5 x 10-7 torr 1 x 10-6 torr

Metastable 1 x 10-6 torr 5 x 10-4 torr

Target 1 x 10- torr 5 x 10- torr



B. Gas-Handling System

The purpose of the gas-handling system is to provide a means of

admitting high-purity gases into the vacuum system in a controlled

manner. By means of a series of valves, shown in Figure 11-2, the gases

are reduced in pressure from several hundred atmospheres in a standard

high-pressure cylinder to approximately one atmosphere behind the nozzle

orifice. This pressure is monitored by a Wallace and Tiernan model

FA160 absolute pressure gauge to guarantee beam operation under constant

conditions. The gas then expands through the orifice as described in

Chapter I and is ultimately pumped out of the system and vented to the

atmosphere.

C. Metastable Beam Production

The production of the metastable beam involves conventional use

of the methods of supersonic nozzle beams as described in Chapter I but

with a novel source for exciting the metastable states in the beam gas.
































C1 >
E +3r-
3 3 to























CO,
>)

ca


c.

1-
I.-- o


r- OU
N >
N -
00o
Z>


0>
4-)
.U>










This source was developed by Cutshall [43] for previous investigations

of the Ar*/N2 reaction system. The source is detailed in Figure 11-3,

and consists of a tungsten filament cathode located to the side of the

nozzle cap and the skimmer opening. The electrons are boiled off the

filament by a 15-ampere current passing through the filament. The

electrons are accelerated across the beam at right angles to the direc-

tion of the beam path and collected by a nickel plate anode. This anode

is maintained at approximately +30 volts relative to the filament by a

constant current power supply and regulates the discharge current at

150 milliamperes. This source is capable of exciting the ground state

argon atoms into a variety of excited states as well as ionizing the

atoms. However, because of the length of the flight path most of the

excited states decay prior to leaving the metastable chamber, and the

charged particles are swept out of the beam by a 100-volt potential

applied between a pair of sweep plates located just downstream of the

skimmer exit. In the case of the work with N2 as the target gas, the

beam then proceeds through the interaction region, is detected on a

Bendix model 306 magnetic electron multiplier, and time-of-flight analyzed

to determine the velocity distribution of the beam. In the work involving

the H2 target, the electron multiplier is run as a simple surface detec-

tor from which electrons are ejected by the metastable atoms. These

electrons are then detected by placing a 10 0-ohm resistor in the path

to ground and measuring the voltage drop across the resistor by an elec-

trometer. In this work the velocity of the argon metastable atoms was

a minor contribution to the relative energy. The metastable argon beam










4
-a


a


4


r











was generated at the same source conditions used in the room temperature

N2 experiments, and the velocity distribution was assumed to be the same

as in those experiments.

D. Velocity Analysis

The velocity analysis of both beams is carried out in an identical

manner with only the particular detection method varying. For the pur-

poses of this discussion, the specific method of detection is irrelevant

and will be considered as a black box from which emerges a signal pro-

portional to the number of particles reaching the detector per second.

It should be mentioned that for the calculation of cross sections, the

quadrupole measures a number density while the electron multiplier

measures an intensity.

The beam under analysis is periodically interrupted by a slotted

disk, shown in Figure 11-4. This disk is driven at 50 Hz by a wide band

amplifier which is in turn driven by an oscillator. This disk is so

constructed as to allow four pulses to pass the chopper in every cycle,

two long pulses and two short pulses. The long pulses are used in the

photon counting portion of the experiment and are not used in the velocity

analysis. Only the short pulses are used to prevent a smearing out of

the distribution due to the large bandwidth introduced by the long

pulse.

As the beam is chopped, so too is a light path between a light

emitting diode (Texas Instruments TI-351) and a phototransistor (Texas

Instruments LS-400). As in the case of the beam, the light signal is

also divided into two separate pulses, an optical long and an optical







24








-o




>-






S-
a
s-







0




I/II
*-r



4./
ca














L-
4.-






0
~0













*r,




0 -
|-30 1--= id










short pulse. These pulses are separated by electronic circuitry and

used independently. The relationship between the optical pulses and
the beam pulses is shown in Figure 11-5. The signals are then fed into

a Princeton Applied Research model 121 phase-locked amplifier with the

optical short signal being used as the reference signal. Signal averaging

is accomplished in a Princeton Applied Research model TDH-8 wave-form

eductor and then displayed on an oscilloscope triggered by a delayed

optical short pulse. This allows the intensity to be measured on the

lock-in amplifier during the velocity analysis portion of the experiment.


E. Optical System

The photon collection system is composed of a mirror, two lenses,

a monochromator, a third lens, and a photomultiplier positioned as shown

in Figure II-6. The mirror is a 20-mm (Rolyn Optics 61.2200) focal-length

mirror with an aluminum overlay coating. This mirror is located one

focal length below the interaction region. This mirror collects all

photons emitted in the downward direction and reflects them back through

the interaction region. Located approximately 11 cm above the inter-

action region is a 100-mm (Rolyn Optics 11.2300) focal-length lens which

collimates the photons into parallel rays and directs them up the 2.5 in.

o.d. aluminum tube which serves as a mounting structure for the optical

system. Before the photons reach the monochromator the photons pass

through a second lens with a focal length of 200 mm (Rolyn Optics 11.2650),

which serves to focus the light on the entrance slit to the monochromator.

The photons then leave the vacuum system through a 1.37 in. diameter

window (Ceramaseal #94784901-1). The monochramator is a Spex 1670






















































.r-
0





*1-


-.-







S SU










L00.



o.-


*r






,r- -- --.-















0
5--































S0O 0 0 0.J 0 0-J 00





















PHOTOMULTIPLIER








MONOCHROMATOR





Z WINDOW





ARGON BEAM


NITROGEN BEAM


CONCAVE
MIkROR


Photon Collection System


LENS


LENS 2


LENS 1


Figure II-6.










Minimate monochromator with a grating ruled at 1200 grooves per inch

and blazed at 300 nm. This spectrometer has replaceable slits. A 1.0-

nm resolution was used for the N2 work and 10.0-nm resolution for the

H2 experiments. The light from the exit slit is then defocused by

lens 3, a 25-mm (Rolyn Optics 11.2050) lens. This defocusing allows

the fullest use of the photocathode surface. All lenses, as well as the

window, are of Herasil grade quartz. The detector is an EMI photomulti-

plier with an S-20 extended photocathode. The photomultiplier is cooled

to -250C by a Products for Research 104-TE-RF thermoelectric refrigera-

tor. This reduces the dark current which would otherwise be the major

source of noise in the system.

F. Data Collection System

After a photon has been detected by the photomultiplier, the

pulse must be analyzed in terms of the chopped beam phases. This is

accomplished by the digital electronics referred to in Figure 11-8 as

the MCA/Stepping Motor Interface. This figure also traces the path of

the photon signal from the photomultiplier to the storage or rejection

of the pulse. The pulse is first amplified by a Tennelec TC-145 pre-

amplifier, further amplified by a Tennelac TC-202 linear amplifier,

filtered and converted to a square pulse by a Tennelac TC-440 single

channel analyzer, and finally put out to the interface circuitry where

the signal is compared to the signal generated by the chopper mechanism

as the target beam is periodically interrupted.

This signal, the optical long, is first delayed in a simple delay

circuit, shown in Figure 11-7:













In Q Out
+5VOu












Figure 11-7. Pulse Delay Circuit


This circuit takes advantage of the intrinsic delay times through the

exclusive-or gates to provide an output pulse of short duration (50 nsec)

on each change of state of the input signal corresponding to the opening

and closing of the chopper. This signal then triggers a monostable

vibrator (TTL-74123) which outputs a pulse after a time delay controlled

by a ten-turn potentiometer adjustable from the front panel. This pulse

then triggers a D-type flip-flop (TTL-7474) which outputs a signal

dependent upon the current state of the chopper.

This circuit puts out two complementary signals which are

delayed by a given time interval from the opening of the chopper to

allow the target beam to reach a steady state within the interaction

region prior to beginning data counting. The signal which takes on the

same state as the original optical long then serves a triple function.

This signal feeds the interface to provide a signal which is used to

synchronize all of the timing within the interface, triggers an










Elscint CBC-N-1 crystal clock which opens a window in the interface

during a set time interval in which the beam is actually in the

interaction region, and finally triggers a Tennelec TC-551 preset

scalar which monitors the stepping function of the system.

The complementary signal is fed directly to the data storage

device, a Nuclear Data series 1100 multichannel analyzer (MCA), as a

reference signal determining whether a given photon is to be added into

the memory as a signal + noise pulse or subtracted from memory as a

noise pulse.

The remaining input into this interface is the output of a free-

running BNC-8010 pulse generator which controls the stepping rate of

the Slo-Syn translator and stepping motor.

The outputs from this interface are the photon pulses which

arrive in the predefined time intervals (DATA OUT), a pulse which tells

the MCA to advance a channel (MCS XTL CLK), an output which keeps

track of the number of channels stepped to allow for reset of the sys-

tem (SCALER), a pulse train telling the stepping system to act (UP/DN),

and a pulse which informs a second MCA (Tracor Northern TN-1710) which

was used in some experiments to gather signal-to-noise data. The

complete schematic diagram for the interface, as well as the timing

diagrams for the input and output signals, are included in Appendix I.

After the experiment has been concluded the output from the Nuclear

Data MCA may be read out on either an oscilloscope or as hard copy on

a Teletype ASR-33. These signal trains are shown in Figure 11.8.























w
W&

wU)


n T-


x5 o u
000 W
-<- 0
4,-
0



UZ


31
































I-
o

r_
0








r-
0
O
u-

c.




'U
0



C)





I-










G. Mass Spectrometer Calibration System

As seen in Chapter I, a capillary array molecular beam is

primarily dependent only upon the pressure of the gas behind the

array. This guarantees, if the applied pressure is accurately known,

that the beam will be reproducible on a day-to-day basis. This prop-

erty makes the capillary array source ideal for use as a calibration

source for the quadrupole mass spectrometer used in these experiments.

The source, shown in Figure 11-9, is composed of three major

components, the gas introduction lines, the pressure measuring device,

and the capillary array itself. The gas introduction system is simply

a 1/4 in. copper line tapped into the target gas line and terminated

by a leak valve. This leak valve is used to control the pressure be-

hind the capillary array. For the H2/Ar* cross section measurements

this pressure was regulated at 0.500 torr relative to the main chamber

pressure (' 1 x 10-6 torr). This pressure was measured by an MKS

Instruments, Inc. Baratron Model 90 capacitive manometer. One end of

the device was attached to the high pressure region behind the cap-

illary array and the other end opened into the main vacuum chamber.

These two sides were connected by a valve which allowed for rapid

pump out of the high pressure region.

The beam source itself was located in a small block of aluminum

and contained the capillary array, a chopping mechanism, and an LED-

phototransisotr system identical to that used with the supersonic

sources. The capillary array maintained the pressure difference be-

tween the source and the main chamber. It also provided the


















IL
a














U
o



































-\ It I-
0



>1

S.-



LI
U-

\ o ; \.
________ ____ \
\ \ \ ^________{
V ^ it-n----





34



collimation required for high beam intensities. As with the super-

sonic nozzles, this beam was chopped providing short pulses of gas

which were detected by the quadrupole mass spectrometer. The design

of the chopper mechanism and associated electronics was such that the

detection procedures were identical to those discussed in the time-of-

flight measurements.














CHAPTER III
EXPERIMENTAL PROCEDURE


A. Optical Considerations for Ar*/N2

The flowing afterglow experiments of Setser and Stedman [44] and

Setser, Stedman and Coxon [45] have shown three emission bands for the

Ar*/N2 system. These bands correspond to the transitions

C 3H -- B 3Rg
u g 2nd Positive


B 31 ---A 1 + 1st Positive
9 u

A 3E+ --X 1E+ Vegard-Kaplan
u 9

Figure III-1 shows the relevant potential energy curves for N and N2.

Interference with the desired C+B transitions are not important in this

work as the A-X transition is metastable, transitions occurring several

milliseconds downstream. This time lag causes all A-X fluorescence to

occur outside of the detection region. The B-A transition is short

lived; however, this radiation occurs in the infrared region of the spec-

trum and does not pass the monochromator.

Of primary importance to this experiment are the 0-0 band and

the 1-0 band of the C-+B electronic transition. These are found to lie

in the near ultraviolet in the ranges 330-339 nm and 310-318 nm,












IA2 nu


N (SO) + N ('D0)


A'3IU


N,


Xg


0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6


INTERNUCLEAR


DISTANCE


Figure III-1. N2 Potential Energy Curves


24

22

20

18

16


12

I0

8










respectively. These regions were repetitively scanned, using 1 nm

spectrometer resolution, until the peak channel contained in excess of

2,000 counts. This value gave a modest signal-to-noise ratio, approxi-

mately 2:1, within a reasonable data collection time.

B. Optical Considerations for Ar*/H2

James and Coolidge [46] have calculated the anticipated H2 con-

tinuum spectra. For the v' = 0 vibrational state, the emission is

expected to lie between 220 nm and approximately 500 nm, with a maxi-

mum emission at 260 nm. The appropriate potential energy curves for

the H2 molecule [47] are given in Figure III-2.

An alternative source of photons is the continuum emission from

an excited bound state of an ArH molecule to the unbound ground state.

Figure III-3 shows the potential energy curves for this molecule as

calculated by Olson [48]. It can be seen that the emission would cover

approximately the same region of the spectrum, although a lower energy

maximum may be expected.

Regardless of the product, the region to be explored ranged

from 220 nm to 500 nm. This region was scanned only one time, but with

a 10 nm bandwidth and a 10 second dwell time per step.

C. Experimental Procedure

The first step in the experimental procedure was the evacuation

of the vacuum chambers. The entire system was rough pumped by the

main chamber backing pump through the master valve and three Veeco

valves located directly beneath each internal chamber. During this
































w
6J


z
w
0
2-



0 0.4

INTERNUCLEAR


DISTANCE (A)


Figure III-2. H2 Potential Energy Diagram





39








10.0
Bel

9.0 n -


8.0


7.0


6.0-

S\Ar+H
z 5.0

-j
< 4.0
l--\
z
LJ
3.0


2.0-


1.0-
X2

0.4 0.8 1.2 1.6 2.0 2.4 2.8
INTERNUCLEAR DISTANCE (1)


Figure 111-3. ArH Potential Energy Diagram










time the diffusion pumps were isolated from their respective backing

pumps. After the pressure in the chambers fell below 750 microns, the

refrigerator to the main chamber baffle was turned on. After at least

15 minutes and after the pressure in the system had fallen below 100

microns, the cooling water to the three diffusion pumps and the baffle

to the metastable chamber was turned on and the backing lines to the

metastable chamber and target chamber were evacuated. At this point

the diffusion pumps were connected with the backing lines by opening the

isolation valves. The diffusion pumps were turned on and the Veeco

valves and master valve closed. The system was allowed to pump,

usually overnight, until the static pressures noted in Chapter II were

attained.

After the system had been evacuated, it was necessary to

establish the beams, prepare the electronics, and ready the photon

counting system. Adequate warmup time (several hours) for the electronics

to stabilize was necessary. The critical electronics include the power

supplies for the metastable discharge, the oscillators driving the

choppers, the high-voltage power supplies for the quadrupole mass

spectrometer, electron multiplier, and the photomultipler, the electrome-

ter, lock-in amplifier, and wave-form eductor. All other electronic

elements did not require extended warmups, although they were normally

turned on at the same time as the critical devices.

The establishment of the beams required the same procedure for

either beam, although generation of the metastable beam required the

additional step of generating the electrical discharge between the nozzle










and skimmer. The first step in setting up the beams was the evacuation

of the nozzle lines. After the line pressure fell below 50 microns the

vacuum pumps were isolated from the system. With the valve connecting

the nozzle to the gas line open and the leak valve and leak-valve bypass

valve closed the gas was allowed to enter the line at 20 psig through a

regulator attached to a high-pressure gas cylinder. The leak valve was

then slowly opened, allowing the gas to flow to the nozzle. The pressure

behind the nozzle was stabilized at 15 psia by adjusting the leak valve

setting. If the experiment required the heating or cooling of the

nozzle, the procedure was begun at this time. The target beam was now

allowed to stabilize, a process requiring about two hours, prior to the

beginning of data collection. As the pressure in the metastable chamber

rose to approximately 1 x 10-4 torr, the electron gun was turned on and

the power supplies adjusted to provide 150 milliamperes discharge cur-

rent. The metastable beam was then allowed several hours to stabilize.

Stabilization of the beams was detected by a steady backing pressure to

the nozzle, a steady output from the associated detection device, and

most importantly by constant measurements of the beam velocity.

While the beams were stabilizing, the photon collection system

was prepared. This required the refrigeration of the photomultiplier,

the heating of the photomultiplier window to prevent condensation on

the window, the setting of the monochromator to its initial position,

and the clearing of the memory of the MCA. Just prior to the photon

counting portion of the experiment liquid nitrogen was added to a cryo-

pump, thereby reducing the background due to condensibles in the vacuum

system.










Photon counting was initiated by opening the shutter to the

photomultiplier, chopping the target beam, and pressing the start but-

ton on the MCA/Stepping Motor Interface panel. After sufficient data

were collected, the process was terminated by pressing the stop button

on the same panel. The photon-counting portion of the experiment then

ceased to be operative at the end of the current scan.

At the end of a run, a measurement of the velocity of the beams

by means of the time-of-flight technique was made. The short burst of

particles passing through the small slot in the chopper was detached

by the quadrupole in the case of the target beam, or the electron mul-

tiplier for the metastable beam. This signal was amplified by the lock-

in amplifier and signal averaged by the wave form eductor. The signal

was then compared for timing purposes with the optical short signal and

a simple distance-over-time calculation provided the most probable

velocity of the beam. For cross-section measurements, an analog signal

from the lock-in amplifier, which was proportional to the target beam

intensity was measured. The proportionality constant, which depended

on daily operating conditions, was determined by producing a known

pressure, as measured by the capacitance manometer, behind the capillary

array. The resulting beam was then monitored in the same fashion as the

target beam had been monitored.

Other correction factors are given in Figures III-4 and III-5.

Figure III-4 is a wavelength calibration of the spectrometer system

determined using a mercury vapor lamp. Figure III-9 is an intensity

calibration based on a comparison with a deuterium standard lamp.










_ I I I I I I I I I I


MERCURY


VAPOR


o



10 O H
SLIT WIDTH


3400


3600


WAVELENGTH


SI I I


3800
(A")


4000


Figure 111-4. Experimentally Observed Hg Vapor Spectrum


LINES


201-


10
9
8
7
6
5

4

3


2


3000


IL.J'~ .1J


3200


I I I


40-

30-






44


0
o
1111111| I I I





Sn








0a
ro

__- 0
E
CCA
II









4-
-J
O 0


L .I





O L







0 0n

A11SNJNI 3All 7 13














CHAPTER IV
DATA ANALYSIS AND RESULTS

A. N2 Band Profiles and Rotational Distributions

The profiles of the N2(C33u (v' = 0)) to N2(B3g (v" = 0) band

were measured at the relative collision energies of 0.076 eV, 0.080 eV,

and 0.161 eV. These profiles are given in Figure IV-1 as the vertical

slash marks, the size of these marks being determined by the estimated

errors on the particular data point. Figure IV-2 shows the profiles for

the N2(C3 u(v' = 1) to N2(B3g (v" = 0)) transitions obtained at the same

relative energies as the 0-0 bands.

The smooth curves through the data points on the two sets of

spectra represent the best fit to the data based on known spectroscopic

constants and various trial rotational distributions. The procedure for

obtaining these fits was to assume a particular rotational distribution,

feed this into a computer program [49] along with the spectroscopic

constants for the relevant states, broaden the spectra to allow for the

spectrometer bandwidth, and finally generate a least-squares fit to the

original data. This procedure was then repeated with a new trial distri-

bution of rotational states until a minimum was obtained in the least-

squares fit. The resultant spectrum was then compared visually to the

data and a decision was made as to the advisability of attempting the

fitting procedure with a different type of distribution. A listing of


















0.5




I I


>-
S1.0-
o) Er = 0.089 eV
z
w



I.



0:


1.0-
Er= 0.076 eV



0.5




3310 3330

WAVELENGTH


N2 (0-0) Band Profiles


(4)


Figure IV-1.





47



N2 (C-"B) 1-0 BAND


Er = 0.161 eV
1.0



0.5






Er= 0.0089 eV
S1.0-
C,)
Z
w
I-
z 0.5

w



w
. 10
Er 0.076 eV




Im II
.5-






3120 3140 3160 3180
WAVELENGTH (A)
Figure IV-2. N2 (1-0) Band Profiles










the computer program used to generate these spectra is included in

Appendix II.

For the 0-0 band it was found that the data could be adequately

fit by a thermal, i.e., Boltzmann, distribution. As this entailed only

the fitting of a "temperature" to the data the routines for the fitting

were quite easily accomplished. The results of this procedure are given

in Figure IV-3.

For the 1-0 band a simple thermal distribution was not found to

adequately fit the data and more complex procedures were required. The

most successful procedure involved calculating the spectra using the

first several Chebyshev polynomials [50] with arbitrary coefficients to

represent the rotational distribution, and then performing a correlation

of the results to determine the best coefficients to be used. Upon

visual inspection a second distribution suggested itself. This is the

so-called "Golden Rule" distribution discussed in the Introduction,

Equations (30) and (31). These distributions are both plotted in Figure

IV-4.

Summarizing these results given in Figure IV-3, the 0-0 band is

in all cases characterized by a rotational "temperature." These "tem-

peratures" are 2400 K, 1600 K, and 1700 K, and have an estimated error of

100 K. The 1-0 band may be represented by either a series of Hermite

polynomials or by a "Golden Rule" distribution. In the case of the

Chebyshev polynomials the distribution is given by


P(J) = Ax TO + B x T1 + C x T2


where the Chebyshev polynomials on the interval 0-1 are





49









v'= 0O
0.050
0.161ev
"T"= 2200K

0.025



1 0.0



0 .025
n 0.089 ev
"T" = 1600K










0.025 -




0 10 20 30 40
ROTATIONAL QUANTUM NUMBER, J
Figure IV-3. Rotation Distributions N2 (0-0)
-Best Fit with Thermal Distribution
---"Golden Rule" Distribution










0.050


0.025



0.0



0.025



0.0



0.025




0


' = I


10 20 30


ROTATIONAL QUANTUM NUMBER, J
Figure IV-4. Rotation Distributions N2 (1-0)
-Best Fit with Chebyshev Polynomials
---"Golden Rule" Distribution


a-



I-
0
oa
a-










TO = 1

T1 = 2X 1

T2 = 4X2 2X

The series was cut off based on the statistics which indicated that

no further information was gained with additional terms.

B. H2 + Ar* Cross Sections

and Spectral Distributions

The behavior of the cross section as a function of the relative

translational energy of the collision partners is quite typical of any

endoergic process in that there is no contribution to the cross section

until a certain minimum energy is obtained, after which there occurs a

rapid rise to a maximum and then a slow tapering off. Figure IV-5 is

the experimentally determined energy dependence of the cross section

for the process involving the collision of H2(Xlog) + Ar*(3P2,0). The

error bars for the energy determination represent the full width half-

maximum distribution of the beam velocities and the error bars on the

value of the cross section represent 95% confidence intervals. All data

points have been calculated according to Equation (19) in Chapter I.

The major characteristic of this curve is the rapid rise in the

cross section beginning at the onset at 0.08 eV and the apparent maximum

at 0.170 eV. Because of limitations in the design of the experiment,

higher energies were not attainable and the behavior at higher energies

could not be ascertained.













































0.050 0.075 0.100 0125 0.150 0.175 0200


RELATIVE


Figure IV-5.


ENERGY


(eV)


Energy Dependent Cross Section for Ar* + H2 Collisions










Figures IV-6 and IV-7 are spectral distributions of the process

taken at the lowest (0.067 eV) and highest (0.165 eV) relative energies,

respectively. These distributions have been smoothed by a three-point

smoothing routine [51] and corrected for spectral response of the

photon-gathering system. An estimate of the errors on the individual

data points near the peak of the distributions was obtained by position-

ing the spectrometer on the peak and running the experiment without

stepping the spectrometer. These data were then run through the same

smoothing procedure and the errors estimated from the variation observed

in these data. It was found that the errors on the data points are

approximately the same as the apparent oscillations in the distribution.

The results of the photon distribution experiment indicate that

the maximum, regardless of collision energy, lies at approximately 290

5 nm and that the distributions of photons are nearly identical over all

observed wavelengths independent of collision energy.

















,, .." x ,


;I o

S- 0


E *
+ c








S0** S
/ ,. o jS



* *- 0 8
* 0


-00 ,



L/ \
* *
I C '
00O
.0C
0( 0
O Q)CO I rC)~t r) 0
*0 zodd
(sl~n qo) ~ISN3N I NI0*

























I:

*


*

'..






*
S:


O On o q- D iO OO rO Oc -
-d dd ddddd

(sliun "qiO) AIISN31NI NOLOHd


CI



0

0
O -
-o
*-






0
E -
o Co



S 0
e C
w-


o

0





10 -E
-- l










L
ii (














CHAPTER V
DISCUSSION

A. Collisions Involving Ar*/N2

The rotational distributions observed for the N2(C 3n, v' = 0)

product of the Ar*/N2 collision system may be represented well by

Boltzmann distributions over the range of collision energies of 0.078 eV

to 0.161 eV. The Boltzmann temperatures for these distributions vary

from 1600 K to 2200 K. For these collisions there is sufficient energy

to populate rotational levels up to the 45th to 50th quantum level. The

distributions, as shown in Figure IV-3, rise rapidly to maximum popula-

tions in the range J = 18-20, and then slowly taper off until the

maximum allowed J-value is reached.

In contrast to the v' = 0 levels, the N2(C 3H, v' = 1) product

shows a marked difference in the distribution. In fact the spectra

could not be fit by a Boltzmann-type distribution. Instead, the spectra

were found to be reproduced within the experimental error by the

"Golden Rule" distributions shown in Figure IV-4. These distributions,

because of the additional energy required to enter the v' = 1 vibrational

level, do not have sufficient energy to populate higher rotational levels

and the distributions cut off at approximately J = 35. The character-

istics of these distributions are a more gentle rise to the maximum

population levels of J = 25-30 and then slowly begin to taper off. Be-

cause the cut-off occurs so quickly after the maximum is reached, the










relative population levels are still quite high at the maximum allowable

value for J.

No good explanation as to why the v' = 0 vibrational level

appears to be represented by a Boltzmann distribution is currently avail-

able. Although such a distribution would be expected in the case in

which the product was in thermal equilibrium, in the single-collision

processes examined in the molecular beam experiment no such equilibra-
tion occurs.

B. Collisions Involving Ar*/H2

The photon energy distribution data and the collisional energy

dependence of the cross section for the Ar*/H2 system do not unambigu-

ously define the process being observed. Two possible processes may be

responsible, either singly or in tandem, for the observed results.

These processes are the transfer of electronic energy to the H2 diatomic

with the observed continuum radiation corresponding to the H2(a 31u,

v' = 0) -* H2(b 311) transition or an exchange process resulting in a

bound excited state of ArH* which then fluoresces to the unbound ground

state, again with a broad-band emission of photons. Each of these

processes will be discussed with respect to the consequences of the

particular assumption.

B.1 Radiation from H2(a 31u, v' = 0)

The process of exciting the ground state molecule to the excited
"a" state requires 11.788 eV of energy. The Ar*(3po) metastable stores

11.723 eV resulting in a deficit of 0.065 eV which must be the minimum










amount of energy provided by the translational motion of the system for

the process to occur. The Ar*(3p2) metastable provides only 11.548 eV

to the system with a resulting deficit of 0.240 eV. As the maximum

energy available from translational motion in the experiment is 0.161 eV,

the 32 component cannot contribute to the process. Also the v' = 1

vibrational level of the "a" state lies approximately 0.243 eV above the
v' = 0 level, making this level energetically unattainable by any species

in the system. Although the H2(c 3g, v' = 0) is attainable energetically,

the state is metastable and does not decay in the detection zone.

From the above results, it is possible to predict the behavior

of the energy-dependent cross sections for the Ar*/H2 system. The cross

section should be zero until the relative translational energy reaches

0.065 eV, after which the cross section should rise rapidly to a

maximum and then slowly taper off. This does assume that no activation

energy is required, in which case the onset would occur at a still higher

relative energy. Examination of Figure IV-5 reveals this type of a

behavior with the onset occurring at approximately 0.080 eV implying

an activation energy of 0.015 eV.

Serious questions about this interpretation arise when the

spectral distributions are examined. As seen in Figure IV-6 the ob-

served distributions are significantly different than those predicted

by James and Coolidge [51]. The potential energy curves calculated in

this work compare quite well with the later work of Kolos and Wolniewicz

[52], therefore the theoretical prediction must be considered reliable.
The observed spectral distributions might arise from potential energy

curves perturbed by the presence of the heavy argon atom. This










hypothesis runs into trouble when the observed distributions at differ-

ent relative energies are compared. At the higher relative energies,

it would be expected that the argon atom would be further away from

the hydrogen molecule at the time of the radiation. The perturbation

would thus be smaller and the distribution of photons would be differ-

ent. This does not agree with the spectra observed in Figure IV-6 and

Figure IV-7, which show nearly identical distributions.

One further piece of evidence damaging to this model is found

in the work of Feldstein [53]. He found that the onset for radiation

in the Ar*/D2 system lies at 0.075 eV, 0.023 eV below the expected onset

of 0.098 eV, a situation in which the "a" state of the D2 molecule

cannot possibly be populated.

B.2 Radiation from ArH*

The ArH* molecule has been observed in the visible region of

the spectrum by Johns [54]. The potential energy curves have been

calculated by Olson [55] using SCF-CI methods (see Figure IV-8). Using

the potential energy parameters derived from these sources, it is

possible to calculate the endoergicity for the formation of the

ArH*(A 2, v' = 0) molecule. For the 3P0 metastable the endoergicity

is -0.72 eV, and for the 3P2 metastable the endoergicity is -0.55 eV.

In all cases the process should occur at all relative energies, if no

activation energies are involved. The cross section data previously

mentioned can then be explained by an activation energy on the order of

0.70 eV. By being exoergic, the results of Feldstein for the Ar*/D2

system are no longer in conflict with the anticipated results. A










comparison of the energy differences between the excited bound states

and the lower energy unbound states at the equilibrium positions of

the bound states

H2(a-b) re = 0.9888 A AE = 4.02 eV

ArH(A-X) re = 1.2686 A AE = 3.58 eV

indicate that the spectral distribution would be expected to peak at a

higher wavelength for the ArH transitions. The exact position of this

maximum cannot be predicted without the calculation of the overlap

integrals between the ArH(A) and the unbound ArH(X) states.

B.3 Conclusion

The current data tend to support the premise that the process
being observed is

Ar*(3p20) + H2(X 1I ) -+ ArH*(A 2 ) + Ar(1S)


although the production of H2(a 3 u) cannot be ruled out as contributing

to the total radiation observed. This conclusion may be further tested

experimentally by observing the process in which the H2 molecule is

excited to the "a" state by electron impact and comparing the observed

fluorescence from this process with that observed in this study. A

calculation of the three-body potential energy surfaces for the (Ar/H2)*

system may also yield information making the interpretation a more

definite one.

The surfaces of interest would include the Ar*-H-H surface. This

surface represents the incoming channels of the collision process on






61



which the two hydrogen atoms would be closely associated with one

another and the Ar* atom would be approaching the pair. This surface

then must cross the Ar-H(2s)*-H surface as this surface contains the

two primary exit channels for the process. Along one path the three-body

collision complex would exit as a normal Ar atom and an excited hydrogen

pair, which would have a normal hydrogen atom and an excited (2s) hydro-

gen atom in its dissociation limit. The other path would have as its

dissociate limit a ground state ArH.















APPENDIX I


MCA/STEPPING MOTOR SCHEMATICS






63
















I-













a I II ...
I I-










I I
x*,
1-


3 x I 5



o I ~

! *i
Ao gi "j-y -n










INTEGRATED CIRCUIT CHIP LOCATION AND IDENTIFICATION CHART


CHIP INTEGRATED C
#* # (TTL)

1 7405

2 7404

3 7410

4 7400

5 7450

6 7420

7 7402

8 7474

9 7404

10 7474

11 7405

12 7474

13 7410

14 74122

15 74123

16 74190

17 74190

18 74190

19 74190

*Chips are numbered top

observed with the edge

observer.


:IRCUIT


FUNCTION


Hex Inverter (Open Collector)

Hex Inverter

3-Input NAND Gate

Quad 2-Input NAND Gate

And-Or-Invert Gate

Dual 4-Input NAND Gate

Quad 2-Input NDR Gate

Dual D Flip-Flop

Hex Inverter

Dual D Flip-Flop

Hex Inverter (Open Collector)

Dual D Flip-Flop

3-Input NAND Gate

Monostable Multivibrator

Monostable Multivibrator

Decade Up/Down Counter

Decade Up/Down Counter

Decade Up/Down Counter

Decade Up/Down Counter

to bottom, left to right when the board is

connector up and the chips facing toward the















APPENDIX II


SPECTRAL SIMULATION PROGRAM










MAIN

C***********************************
C THIS PROGRAM WILL CALCULATE THE SPECTRUM FOR A TRANSITION FROM A
C 3-PI-U STATE TO A 3-PI-G STATE SUCH AS IN THE CASE OF THE
C N2(C-B) TRANSITIONS. FOR TRANSITIONS INVOLVING OTHER TYPES
C OF SYMMETRY STATES, THE HONL-LONDON FACTORS MUST BE ALTERED.
C THIS SECTION OF THE PROGRAM IS MARKED IN THE BODY OF THE TEXT.
C THE PROGRAM FIRST CALCULATES A STICK SPECTRUM FROM THE SPEC-
C TROSCOPIC DATA SUPPLIED AND GIVEN ROTATIONAL DISTRIBUTIONS.
C THE RESULTS ARE THEN CORRECTED FOR SPECTROMETER SENSITIVITY
C AND SPECTRAL RESOLUTION. THE RESULTS ARE THEN PRINTED OUT
C AND IF DESIRED PLOTTED USING THE GOULD PLOT ROUTINES.
C
C REFERENCE: THE SPECTRA OF DIATOMIC MOLECULES BY G. HERZBERG.
C
C THE DATA IS INPUT TO THE PROGRAM IN THE FORM OF A SERIES OF NAME-
C LIST READS. THE NAMELIST NAME, DATA NAME, AND A DESCRIPTION
C OF THE DATUM INCLUDING THE DEFAULT VALUES ARE GIVEN IN THE
C TABLE BELOW.
C
C NAMELIST VARIABLE DESCRIPTION
C
C UPPER..........OMEGA..........THIS IS AN ARRAY OF DIMENSION 12,
C AND CONTAINS THE FIRST 12 VIBRA-
C TIONAL CONSTANTS AS DETERMINED BY
C SPECTROSCOPIC ANALYSIS. THE CON-
C STANTS ARE TO THE SERIES OF THE FORM
C OMEGA(L)*(V+O.5)**L
C WHERE L IS THE SUMMATION VARIABLE
C WHICH RUNS FROM 1 TO 12. V IS THE
C VIBRATIONAL QUANTUM NUMBER OF THE
C STATE UNDER CONSIDERATION. (DEFAULT=O)
C
C ALPHA..........THIS IS AN ARRAY OF DIMENSION 12,
C AND CONTAINS THE FIRST 12 ROTATIONAL
C CONSTANTS TO THE SERIES
C ALPHA(L)*(V+0.5)**L
C WHERE L IS THE SUMMATION VARIABLE
C WHICH RUNS FROM 1 TO 12. V IS THE
C VIBRATIONAL CONSIDERATION. (DEFAULT=O)
C
C BE.............THIS IS THE ROTATIONAL CONSTANT AT
C EQUILLIBRIUM AND IS ASSOCIATED WITH
C THE ROTATIONAL ENERGY OF THE MOLECULE
C BE*J*(J+1)
C WHERE J IS THE ROTATIONAL QUANTUM
C NUMBER. (DEFAULT=O)
C
C DE............THIS IS THE ROTATIONAL CONSTANT AT
C EQUILLIBRIUM AND IS ASSOCIATED WITH











THE SECOND ORDER CORRECTION TO THE
ROTATIONAL ENERGY
DE*J*J*(J+1)**2
WHERE J IS THE ROTATIONAL QUANTUM
NUMBER. (DEFAULT=O)

BETA...........THIS IS THE ROTATIONAL CONSTANT DUE
TO THE CENTRIFUGAL DISTORTION AND
FITS THE FIRST TERM OF THE SERIES
BETA*(V+0.5)
(DEFAULT=O)

HV.............THIS IS THE ROTATIONAL CONSTANT
ASSOCIATED WITH THE THIRD ORDER
CORRECTION TO THE ROTATIONAL ENERGY
HV*(J*(J+1))**3
WHERE J IS THE ROTATIONAL QUANTUM
NUMBER. (DEFAULT=O)


AR............


LOWER.........


SPEC..........


.THIS IS THE SPIN COUPLING CONSTANT
AND AS SUCH IS IMPORTANT ONLY IN
HIGH RESOLUTION SPECTRA. TO INCLUDE
THE FUNCTION ROUTINE F MUST BE
ALTERED. (DEFAULT=O)


.OOMEGA.........THE SAME AS OMEGA, EXCEPT FOR THE
LOWER STATE. (DEFAULT=O)

AALPHA.........THE SAME AS ALPHA, EXCEPT FOR THE
LOWER STATE. (DEFAULT=O)

BBE...........THE SAME AS BE, EXCEPT FOR THE
LOWER STATE. (DEFAULT=O)

BBETA..........THE SAME AS BETA, EXCEPT FOR THE
LOWER STATE. (DEFAULT=O)

DDE...........THE SAME AS DE EXCEPT FOR THE
LOWER STATE. (DEFAULT=O)


.TE.............THIS IS THE ENERGY BETWEEN THE MIN-
IMA IN THE POTENTIAL ENERGY CURVES
OF THE STATES OF INTEREST. (MUST
BE SUPPLIED)

DNUL...........THIS IS THE DISSOCIATION ENERGY

VMIN...........THE LOWEST VIBRATIONAL STATE OF
INTEREST. (DEFAULT=O)

VMAX...........THE HIGHEST VIBRATIONAL STATE OF










INTEREST. (DEFAULT=O)

VVMIN..........THE SAME AS VMIN EXCEPT FOR LOWER
STATE. (DEFAULT=O)


VVMAX.........THE SAME AS VMAX EXCEPT
STATE. (DEFAULT=O)


JMIN......


JMAX......


TYPE...........VERTLG....


.....LOWEST ROTATIONAL STATE
(DEFAULT=1)


FOR LOWER


OF INTEREST.


.....HIGHEST ROTATIONAL STATE OF INTEREST.
(DEFAULT=99)

.....THIS CONSTANT DECIDES THE TYPE OF
ROTATIONAL DISTRIBUTION TO BE USED
VERTLG=O GAUSSIAN WITH VAR
GIVING THE WIDTH OF
THE DISTRIBUTION.
VERTLG>O ARBITRARY DISTRIBUTION
STORED IN PMOD.
VERTLG TEMPERATURE IS GIVEN
BY TEMV.


ROTMAX.........GIVES THE MAXIMUM ROTATIONAL VALUE TO
BE USED IN THE DISTRIBUTIONS.

VAR............AS DEFINED ABOVE

JTR............VALUE OF J AT WHICH TRUNCATION BEGINS


JCUT........


TABH........


...VALUE OF J AT WHICH DISTRIBUTION IS
SET TO 0

...THIS DECIDES THE TYPE OF VIBRATIONAL
DISTRIBUTION TO BE USED.
TABH = 0 SET OF ENERGIES ALONE
DETERMINE DISTRIBUTION
TABH<>O TEMPERATURE TEMP (V)
DETERMINES THE ENERGIES


TEMP...........TEMPERATURE OF A GIVEN VIBRATIONAL LEVEL

VIN............STARTING VIBRATIONAL LEVEL OF UPPER
STATE

VVIN...........STARTING VIBRATIONAL LEVEL OF LOWER
STATE











COLL...........ECM............CENTER-OF-MASS COLLISION ENERGY

EXOTH..........EXOTHERMICITY OF THE REACTION

TEMPV..........TEMPERATURE OF MOLECULE PRIOR TO
COLLISION

DISTR..........FCFFAK ........FRANCK-CONDON FACTORS

PMOD...........SUPPLIED ROTATIONAL DISTRIBUTIONS

SWITCH.........USED TO CALCULATE ROTATIONAL DIS-
TRIBUTIONS ONLY ONE TIME PER PASS

IV.............PROGRAMMER SUPPLIED VIBRATIONAL
DISTRIBUTION

PIV............PROGRAMMER SUPPLIED VIBRATIONAL
DISTRIBUTION

PSCHW..........ALTERNATIVE DISTRIBUTION

PLOT...........LMIN...........MINIMUM WAVELENGTH OF INTEREST

LMAX...........MAXIMUM WAVELENGTH OF INTEREST

KAN............NUMBER OF STEPS BETWEEN LMIN AND
LMAX

FL.............AREA OF EXPERIMENTAL SPECTRUM TO
WHICH CALCULATION IS TO BE NORMAL-
IZED

LX.............THIS IS THE DESIRED LENGTH OF THE
SPECTRA

MSKY............THIS IS THE NUMBER OF EVENTS/CHANNEL
ANALYZER

AVFLG..........THIS IS THE RESOLUTION OF SPECTRO-
METER IN ANGSTROMS

ITOT..........THE NUMBER OF SUPPORTING POINTS IN
THE SENSITIVITY CALCULATION

KL.............THE LOWER CALIBRATION WAVELENGTH

KH.............THE HIGHER CALIBRATION WAVELENGTH











C EKL............LOWER WAVELENGTH LIMIT
C
C EKH............HIGHER WAVELENGTH LIMIT
C
C ASC............LENGTH OF SCALE IN WAVELENGTHS
C
C DLAMD..........DISTANCE OF SCALE IN WAVELENGTHS
C
C ALI............WAVELENGTH OF CALIBRATION POINTS
C
C SI.............CALIBRATION POINTS
C
C IPLOT..........DECISION WHETHER TO PLOT ON GOULD
C PLOTTER
C IPLOT=O PLOT WILL BE DRAWN
C****** *******************************
**** ******************************.^J.^J.J.lJ.^il.J.>^***************************^4"44"^4"f'lp******


C-


DIMENSION PR(200),CTG(1024),CT(1024),FCFFAK(35,35),
PMOD(4,100),ALI(100),SI(100),PSCHW(30),
IV(4),PIV(4),T(27),AI(27),AINT(27),
WL(27),OMEGA(12),OOMEGA(12),ALPHA(6),
AALPHA(6),TEMP(3),PV(30)
DOUBLE PRECISION OMEGA,OOMEGA,TE
INTEGER VMIN,VMAX,VVMIN,VVMAX,VIN,VVIN,V,VV
REAL JSKY,LA,LX,LMIN,LMAX
DATA PR,FCFFAK,IV,PIV/200*0.,1225*0.,4*0,4*0./,
PMOD,ALI,SI,PSCHW/400*0.,100*1.,100*1.,30*0./,
PV,OMEGA,OOMEGA/30*0.,12*0.,12*0./,
ALPHA,AALPHA,ITEST,CTU,CTC,CTL/6*0.,6*0.,0,0.,0.,0./,
BE,BETA,DE,HV,AR/O.,O.,O.,O.,O./,
IPLOT,SWITCH/O.O./
NAMELIST /UPPER/OMEGA,ALPHA,BE,BETA,DE,HV,AR
/LOWER/OOMEGA,AALPHA,BBE,BBETA,DDE
/SPEC/TE,DNULL,VMIN,VMAX,VVMIN,VVMAX,JMIN,JMAX
/TYPE/VERTLG,ROTHMAX,VAR,JTR,JCUT,TABH,TEMP,VIN,VVIN
/COLL/ECM,EXDTH,TEMPV
S/DISTR/FCFFAK,PMOD,SWITCH,IV,PIV,PSCHW
/PLOT/LMIN,LMAX,KAN,ITOT,ALI,SI,ALMIN,ALMAX,
MSKY,LX,AUFLG,FL,KH,EKH,ASC,SLAMD,IPLOT


READ(5,UPPER)
READ(5,LOWER)
READ(5,SPEC)
READ(5,TYPE)
READ(5,COLL)
READ(5,DISTR)
READ(5,PLOT)
CALL PVIB(PV,VMAX,OMEGA,IV,PIV,TEMPV,SWITCH,PSCHW)
CHAN=FLOAT(KAN)


nnnnn


L, .....


i











DEL=(LMAX-LMIN)/CHAN
VMIN=VMIN+1
VMAX=VMAX+1
VVMIN=VVMIN+1
VVMAX=VVMAX+1
DO 10 I=VVMIN,VVMAX
VV=I-1
GVV=O.
DO 20 L=1,12
20 GVV=GVV+OOMEGA(L)*(VV+0.5)**L
BVV=BBE
DO 30 L=1,6
30 BVV=BVV+AALPHA(L)*(VV+0.5)**L
DO 10 I1=VMIN,VMAX
V=I 1-1
GV=0
DO 40 L=1,12
40 GV=GV+OMEGA(L)*(V+0.5)**L
EE=(ECH+EXOTH)*8064.5
IF (EE.GT.O.) GOTO 50
WRITE(6,9000) V
GOTO 9999
50 IF (TABH.GE.O) GOTO 60
TEMV=TEMP(1)*(EE-GV)/EE
GOTO 70
60 TEMV=TEMP(V)
70 TV=TE+GV-GVV
BV=BE
DO 80 L=1,6
80 BV=BV+ALPHA(L)*(V+0.5)**L
DV=DE+BETA*(V+0.5)
DVV=DDE+0.5*BBETA*(V+0.5)
IF (EE,GT,DNULL) GOTO 90
AJMAX=SORT ((EE-GV)/BV)
JJMAX=IFIX(AJMAX)
GOTO 110
90 DO 100 J=JMIN,JMAX
GI=F(J,BV,DV,HV,Y)
IF (DNULL+0.5*OMEGA(1)-GV-G1.LE.O.) GOTO 100
JJMAX=J
100 CONTINUE
110 IF (JJMAX.GE.JMAX) JJMAX=JMAX
CALL PROT(PR.ROTMAX,VAR,JJMAX,TEMV,BV,V,VERTLG)
WRITE(6,9010) ECM,JJMAX
DO 10 J=JMIN,JJMAX
JPL1=J+1
JMI1=J-1
Y=AR/BV










T(1)=TV+X-FF(JPL1,BVV,DVV,HVV)
T(2)=TV+X-FF(J,BVV,DVV,HVV)
T(3)=TV+X-FF(JMI1,BVV,DVV,HVV)
DO 115 M=1,3
115 WL(M)=1.E8/T(M)
WRITE(6,9020) (WL(N),N=1,3)
C*********************************************************************
C*********************************************************************
C THE AI(I)'S WHICH FOLLOW ARE THE HONL-LONDON FACTORS FOR THE 3-PI-U
C TO 3-PI-G TRANSITIONS. THESE MUST BE REPLACED FOR ANY OTHER TYPE
C SYMMETRY TRANSITIONS.
C*********************************************************************
AI(1)=(J+2.)*J/(J+1.)
AI(2)=(2.*J+1.)/(J*(J+1.))
AI(3)=(J+1.)*(J-1.)/J
r********************************************************************


FCF=FCFFAK(V+1,VV+1)
DO 10 M=1,3
IF (T(M).LE.O.) GOTO 10
AINT(M)=FCF*T(M)**3*AI(M)*PV(V+1)*PR(J+1)/(J*J+1)
LA=1.E8/T(M)
X=(LA-LMIN)/DEL
IF (X.LE.CHAN) GOTO 120
CTU=CTU+AINT(M)
GOTO 10
120 IF (X.GT.O.) GOTO 130
CTL=CTL+AINT(M)
130 CTC=CTC+AINT(M)
N=IFIX(X)+1
CALL SENS(LA,LMIN,LMAX,S,I TEST,ALMIN,ALMAX,ITOT,.
CT(N)=CT(N)+AINT(M)*S
10 CONTINUE
ANGPK=(LMAX-LMIN)/KAN
BETA=AUFLG/ANGPK
IBETA=IFIX(BETA)
IBETA1=IBETA-1
L=KAN-IBETA
DO 140 I=IBETA,L
SUM=1.
CTG(I)=CT(I)
DO 150 J=1,IBETA1


SI)


J1=I-J
J2=I+J
CTG(CTG(I=CT )+(IBETA-J)*CT(J1)/IBETA+(IBETA-J)*CT(J2)/IBETA
150 SUM=SUM+2.*(IBETA-J)/IBETA
140 CTG(I)=CTG(I)/SUM
SCTG=O.
DO 160 N=1, KAN










160 SCTG=SCTG+CTG(N)
DO 170 N=1,KAN
170 CTG(N)=CTG(N)*FL/SCTG
IF (IPLOT.NE.O.) GOTO 9900
CALL PLOTS(12.,18.,0,1,1.,2.)
CALL AXIS(0.,9.,'WAVELENGTH(A)',-13,12.,O.,ASC,DLAMD)
DO 180 I=1,KAN
Y=CTG(I)/MSKY
X=LX*I/KAN
180 CALL PLOT(X,Y,2,2)
CALL PLOT(O.,0.,999)
9900 WRITE (6,UPPER)
WRITE(6,LOWER)
WRITE(6,SPEC)
WRITE(6,TYPE)
WRITE(6,TYPE)
WRITE(6,COLL)
WRITE(6,DISTR)
WRITE(6,PLOT)
9000 FORMAT (1X,'INSUFFICIENT ENERGY AT V = ',15)
9010 FORMAT (1X,'THE CENTER-OF-MASS ENERGY IS ',E12.5./.
#'THE MAXIMUM ALLOWED J IS ', 15)
9020 FORMAT (1X,3E12.5)
9999 STOP
END










PVIB


SUBROUTINE PVIB(PV,VMAX,OMEGA,IV,PIV,TEMPV,SWITCH,PSCHW)
INTEGER V,VMAX,V1,VMAX1,VSAVE,SWITCH,A
DIMENSION PV(1),OMEGA(1),IV(1),PIV(1),PSCHW(1),
# A(50),G(30)
DATA IBLANK/' '/,ISTAR/'*'/
VMAX1=VMAX+1
PPV=O.
IF (SWITCH.GT.O) GOTO 100
DO 10 V1=1,VMAX1
10 PV(V1)=PSCHW(V1)
GOTO 1000
100 IF (SWITCH.NE.1) GOTO 200
DO 110 V1=1,VMAX1
G(V1)=0.
DO 105 L=1,12
105 G(V1)=G(V1)+OMEGA(L)*(V1-0.5)**L
110 PV(VI)=EXP(-G1(V1)/TEMPV)
GOTO 1000
200 IF (IV(1).GE.VMAX) WRITE(6,2000)
N=IV(1)+1
DO 290 V1=1,N
290 PV(V1)=PIV(1)
DO 300 1=1,3
ILO=IV(I)+1
IHI=IV(I+1)+1
DO 300 V1=ILO,IHI
300 PV(V1)=(PIV(I+1)-PIV(I))*(VI-(IV(I)+1))/(IV(I+1)-IV(I))+PIV(I)
IV41=IV(4)+1
DO 310 V=IV41,VMAX1
V1=V+1
310 PV(V1)=0.
1000 DO 1100 V1=1,VMAX1
1100 PPV=PPV+PV(V1)
DO 1200 V1=1,VMAX1
1200 PV(V1)=PV(V1)/PPV
VSAVE=1
DO 1300 V1=1,VMAX1
IF (PV(V1).LT.PV(VSAVE)) GOTO 1300
VSAVE=V1
1300 CONTINUE
DO 1400 V1=1,VMAX1
V=V1-1
PL=60*PV(V1)/PV(VSAVE)
KK=IFIX(PL)
KK1=KK-1
DO 1350 K-1,KK1






75




1350 A(K)=IBLANK
1400 A(KK)=ISTAR
2000 FORMAT(1X,'IV(V) IS GREATER THAN VMAX')
RETURN
END











PROT

SUBROUTINE PROT(PR,ROTMAX,VAR,JTR,JCUT,TEMV,BV,V,BERTLG,PMOD)
DIMENSION PR(100),PMOD(3,100)
INTERGER V
REAL MJ
SMJ=O.
SUMG=O.
N1=JCUT+1
IF (VERTLG) 110,10,210
C********************************************************************
C VERTLG=O YIELDS GAUSSIAN DISTRIBUTION OF THE ROTATIONAL STATES
C WITH VAR (THE VARIANCE) GIVING THE WIDTH OF THE
C DISTRIBUTION
C*******************************************************************
10 DO 60 L=1,N1
K=L-1
IF (K-JTR) 40,40,50
40 PR(K+1)=(2*K+1)*EXP(VAR*K)
GOTO 60
50 IF (K=JCUT) 55,55,56
55 PR(K+1)=PR(JTR+1)*(JCUT-K)/(JCUT-JTR)
GOTO 60
56 PR(K+1)=O.
60 SUNG=SUMG+PR(K+1)
GOTO 1000
C********************************************************************
C VERTLG C OF THE DISTRIBUTION GIVEN BY TEMV
C********************************************************************
110 DO 160 L=1,N1
K=L-1
IF (K-JTR) 140,140,150
140 PR(K+1)=(2*K+1)*EXP(-BV*K*(K+1)/(0.695*TEMV))*BV/TEMV
GOTO 160
150 IF (K-JCUT) 155,155,156
155 PR(K+1)=PR(JTR+1)*(JCUT K)/(JCUT-JTR)
GOTO 160
156 PR(K+1)=0.
160 SUMG=SUMG+PR(K+1)
GOTO 1000
C***************************************************
C VERTLG>0 YIELDS A DISTRIBUTION SET ARBITRARILY BY THE
C PROGRAMMER. THESE DISTRIBUTIONS ARE DEPENDENT UPON
C THE PARTICULAR VIBRATIONAL STATE BEING CONSIDERED
C AND ARE PROVIDED IN THE PMOD ARRAY
***210 DO 220 L,N*********************************
210 DO 220 L=1,N1





77





K=L-1
PR(K+1)=(K+1)*PMOD(V+1,K+1)
220 SUMG=SUMG+PR(K+1)
C**************************************
C THE ROTATIONAL DISTRIBUTION IS NOW NORMALIZED TO A UNIT AREA
C******************************************* ****************
1000 DO 1010 L=1,N1
K=L-1
1010 PR(K+1)=PR(K+1)/SUMG
RETURN
END










SENS

SUBROUTINE SENS(LA,LMIN,LMAX,S,ITEST,ALMIN,ALMAX,ITOT,ALI,SI)
REAL LA,LMIN,LMAX
C********************************************************************
C ALMIN AND ALMAX ARE THE WAVELENGTHS (IN ANGSTROMS) FOR WHICH
C THE SENSITIVITY CALIBRATION IS AVAILABLE
C*******t***********************************************************


IF (ALMIN-LMIN) 20,20,30
IF (ALMAX-LMAX) 40,22,22
ITEST=1
DO 25 I=1,ITOT
IF (LA-ALI(I)) 26,26,25
CONTINUE
NX=II-1
NXI=NX+1
S=SI(NX)+(SI(NX1)=SI(NX))*(LA-ALI(NX)


GOTO 999
30 PRINT 2100
GOTO 999
40 PRINT 2110
2100 FORMAT (IX,'WAVELENGTH
2110 FORMAT (1X,'WAVELENGTH
999 RETURN
END


)/(ALI(NX1)-ALI(NX))


OUT OF RANGE LOW')
OUT OF RANGE HIGH')


F

FUNCTION F(J,BV,DV,HV,Y)
F=BV*(J*(J+1)-DV*(J*(J+1))**2+HV*(J*(J+1))**3
RETURN
END




FF

FUNCTION FF(J,BVV,DVV,HVV)
FF=BVV*J*(J+1)-DVV*(J*(J+1))**2+HVV*(J*(J+1))**3
RETURN
END










REFERENCES


1. J.A. Fleming, The Electrician, 11, 65, 1883.

2. L. Dunoyer, Le Radian, 8, 142, 1911.

3. W. Gerlach and 0. Stern, Z. Phys. 8, 110, 1921.

4. I.I. Rabi, Nature, 123, 163, 1929.

5. N.F. Ramsey, "Molecular Beams," Oxford University Press, London,
1956, p. 397.

6. J.G. King and J.R. Zacharias, Advan. Electron. Electron Phys.,
8, 1, 1956.

7. J.P. Gordon, Phys. Rev., 99, 1264, 1955.

8. E.W. Becker and K. Bier, Z. Naturforsch, 9A, 975, 1954.

9. J.B. Anderson, "Molecular Beams and Low Density Gas Dynamics,"
R.P. Wegener, Ed., Marcel Decker, Inc., New York, 1974, p. 16.

10. C.E. Klots, J. Chem. Phys., 72, 192, 1980.

11. H. Pauly and J.P. Tonnies, "Methods of Experimental Physics,"
B. Bederson and W.L. Fite, Ed., Academic Press, New York, 1968,
p. 236.

12. E.W. Becker and W. Houkes, Z. Physik, 146, 320, 1956.

13. J. Franck, Trans. Faraday Soc., 1925.

14. E.V. Condon, Proc. Nat. Acad. Sci., 13, 466, 1927.

15. E.V. Condon, Phys. Rev., 32, 858, 1928.

16. J. Krenos and J. Bel Bruno, Chem. Phys. Letters, 49, 447, 1977.

17. M.J. Berry, Chem. Phys. Letters, 29, 329, 1974.

18. A. Messiah, "Quantum Mechanics," Wiley, New York, 1961, 737.

19. J.L. Kinsey, J. Chem. Phys., 54, 1206, 1971.










20. R.D. Levine and R.B. Bernstein, "Molecular Reaction Dynamics,"
Oxford University Press, New York, 1974, p. 129.

21. R.D. Levine and R.B. Bernstein, "Molecular Reaction Dynamics,"
Oxford University Press, New York, 1974, p. 168.

22. A. Javan, W.R. Bennet, Jr., and D.R. Herriot, Phys. Rev. Letters,
8, 106, 1961.

23. C.K.N. Patel, Phys. Rev., 136, 1187, 1964.

24. W.M. Hughs, J. Shannon, A. Kulb, E. Nult and M. Bhaumik, App.
Phys. Lett., 23, 385, 1973.

25. D.W. Setser, D.H. Stedman and J.A. Coxon, J. Chem. Phys., 53, 1004,
1970.

26. R. Martin, T. Fukuyoma, R.W. Gregor, R.M. Jordan and P.F. Sisko,
J. Chem. Phys., 65, 3720, 1976.

27. H.V. Hochstettler and R.B. Bernstein, Rev. Sci. Instr., 31, 872,
1960.

28. A.N. Schweid, M.A.D. Fluendy and E.E. Muschlitz, Jr., Chem. Phys.
Letters, 42, 103, 1976.

29. R.E. Sanders, A.N. Schweid, M. Weiss and E.E. Muschlitz, Jr.,
J. Chem. Phys., 65, 2700, 1976.

30. W. Lee, and R.M. Martin, J. Chem. Phys., 63, 962, 1975.

31. E.R. Cutshall and E.E. Muschlitz, Jr., J. Chem. Phys., 79, 3171, 1979.

32. E.A. Gislason, A.W. Kleyn and J. Los, Chem. Phys. Letters, 67, 252,
1979.

33. H.M. James and A.S. Coolidge, J. Chem. Phys., 1, 825, 1933.


34. A.S. Coolidge, H.M. James and R.D. Present, J. Chem. Phys., 4, 193,
1936.

35. A.S. Coolidge and H.M. James, J. Chem. Phys., 6, 730, 1938.

36. H.M. James and A.S. Coolidge, Phys. Rev., 55, 184, 1939.
37. A.S. Coolidge, Phys. Rev., 65, 236, 1944.










38. N.D. Smith, Phys. Rev., 49, 345, 1936.

39. W. Finkelnburg, and W.B. Weitzel, Z. Physik, 68, 577, 1931.

40. W. Kolos and L. Wolniewicz, J. Chem. Phys., 48, 3672, 1968.

41. R.E. Sanders, Ph.D. Dissertation, University of Florida (1976).

42. E.R. Cutshall, Ph.D. Dissertation, University of Florida (1976).

43. E.R. Cutshall and E.E. Muschlitz, Jr., J. Chem. Phys, 70, 3172,
1979.

44. D.W. Setser and D.H. Stedman, J. Chem. Phys., 53, 1004, 1970.

45. D.W. Setser, D.H. Stedman and J.A. Coxon, J. Chem. Phys., 52,
3957, 1970.

46. H.M. James and A.S. Coolidge, Phys. Rev,, 55, 184, 1939.

47. A.S. Coolidge and H.M. James, J. Chem. Phys., 6, 730, 1938.

48. Personal communication with E.E. Muschlitz, Jr. from R.E. Olson.

49. Personal communication with E.E. Muschlitz, Jr. from P. Toennies.

50. R. Carnahan, H.A. Luther and J.O. Wilkes, "Applied Numerical
Methods," John Wiley & Sons, Inc., New York, 1969, p. 115.

51. H.M. James and A.S. Coolidge, Phys. Rev., 55, 184, 1939.

52. W. Kolos and L. Wolniewicz, J. Chem. Phys., 48, 3672, 1968.

53. J.W. Feldstein, M.S. Thesis, University of Florida (1980).

54. J.W.C. Johns, J. Mol. Spec., 36, 488, 1970.

55. Private communication with E.E. Muschlitz, Jr. from R.E. Olson.















BIOGRAPHICAL SKETCH


C. Randal Lishawa was born February 14, 1951, in Lancaster,

Pennsylvania. He graduated from Findlay High School in Findlay, Ohio,

in 1969. He graduated from Bowling Green State University in Bowling

Green, Ohio, in 1976, with a Master of Science degree in physics, having

earned his Bachelor in Science in physics from Bowling Green State

University in 1974. From 1976 to the present he has pursued studies

leading to the degree of Doctor of Philosophy in chemistry at the Uni-

versity of Florida at Gainesville, Florida.










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.



E. E, Musch/itz, Jr.,, aitPan
Professor df Chemistry




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.



T. L. Bailey
Professor of Phys cs




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.



D. A. Micha -
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. B. Person
Professor of Chemistry






This dissertation was submitted to the Graduate Faculty of the Department
of Chemistry in the College of Liberal Arts and Sciences and to the
Graduate Council, and was accepted as partial fulfillment of the require-
ments for the degree of Doctor of Philosophy.

December 1981


Dean for Graduate Studies and Research





































UNIVERSITY OF FLORIDA
11I II I I II Il 1 11111 lilli ll I
3 1262 08553 9590




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