Advances in Chemical Physics: Molecular Beams, Volume 10

418 Pages·1966·15.317 MB·English

MOLECULAR BEAMS
ADVANCES IN CHEMICAL PHYSICS
VOLUME X
ADVANCES IN CHEMICAL PHYSICS
EDITOR: I. Prigogine
Facultk des Sciences, Universitk Libre de Bruxelles, Brussels, Belgium
EDITORIAL BOARD
THORA . BAK,U niversitetets Fysik Kemiske Institut, Copenhagen, Denmark
J. DUCHESNUEni,v ersity of Lihge, Li&ge, Belgium
H. C. LONGUEIT-HIGGINTSh,e University Chemical Laboratory, Cambridge,
England
M. MANDELU, niversity of Leiden, Leiden, Holland
V. MATHOTU, niversite Libre de Bruxelles, Brussels, Belgium
P. MAZURI, nstitut Lorentz, Leiden, Holland
A. MONSTERL, aboratoire de Chimie Physique, Universite de Paris, Paris,
France
S. ONO,I nstitute of Physics, College of General Education, Tokyo, Japan
B. PULLMANL,a boratoire de Chimie Theorique, Universitk de Paris, Paris,
France
S. RICE,I nstitute for the Study of Metals, University of Chicago, Chicago,
Illinois
J. W. STOUTI,n stitute for the Study of Metals, University of
Chicago,
Chicago, Illinois
G. SZASZG, eneral Electric Company, Zurich, Switzerland
M. VOLKENSTEIINn,s titute of Macromolecular Chemistry, Leningrad,
V.
U.S.S.R.
B. H. ZIMMS, chool of Science and Engineering, University of California at
San Diego, La Jolla, California
MOLECULAR BEAMS
Edited by JOHN ROSS
Brown University, Providence, lulode Island
INTERSCIENCE PUBLISHERS
a division of John Wiley & Sons, New York - London - Sydney
COPYRIGH0T 1966 JOHN WILEY& SONS, INC.
BY
ALL RIGHTS RESERVED
LIBRARY CONGRESS CATALOCGA RDN UMBE58R-9 935
OF
PRINTED IN THE UNITED STATES OF AMERICA
AUTHORS
I. AMDURD,e partment of Chemistry, Massachusetts Institute of Technology,
Cambridge, Massachusetts
JAMES B. ANDERSONM,e chanical Engineering Department, Princeton Univer-
sity, Princeton, New Jersey
RONALDP. ANDRESM, echanical Engineering Department, Princeton Univer-
sity, Princeton, New Jersey
BENJAMIBNE DERSONPh, ysics Department, New York University, New York,
New York
RICHARD B. BERNSTEINT, heoretical Chemistry Institute and Chemistry
Department, University of Wisconsin, Madison, Wisconsin
JOHNB . FENNM, echanical Engineering Department, Princeton University,
Princeton, New Jersey
CLAYTONG ~ESED,e partment of Physics, The University of Chicago, Chicago,
Illinois
E. F. GREENEM, etcalf Chemical Laboratories, Brown University, Providence,
Rhode Island
DUDLEYH ERSCHBACHD,e partment of Chemistry, University of California,
Berkeley, California
J. E. JORDADNe,p artment of Chemistry, Massachusetts Institute of Technol-
ogy, Cambridge, Massachusetts
A. L. MOURSUNDM, etcalf Chemical Laboratories, Brown University,
Providence, Rhode Island
E. E. MUSCHLITZJ,r ., Department of Chemistry, University of Florida,
Gainesville, Florida
EDWARDJ. ROBINSONPh, ysics Department, New York University, New York,
New York
JOHNR oss, Department of Chemistry, Brown University, Providence, Rhode
Island
R. F. STEBBINGSG, eneral Atomic Division of General Dynamics Corpora-
tion, San Diego, California
PREFACE
Studies of molecules in nearly collision-free and unidirectional
motion, that is, in molecular beams, have been made for over fifty years.
The technique has long been recognized as particularly suitable for the
determination of the interaction of a single molecule with another
molecule, with a photon, with external fields, or with surfaces. (See
the Appendix for some general references.) In principle. at least,
molecular beam experiments provide the means for direct measure-
ments of molecular properties. Of course, the properties of macroscopic
systems are related to those of their molecular constituents by the
theories of statistical mechanics. These relations are always some
statistical average of molecular properties, an average which obscures
the dependence of the macroscopic measurement on the molecular
properties. In practice the removal of all statistical averages even in
molecular beam experiments presents extreme problems.
The articles in this volume are reviews of some of the current molecu-
lar beam research in the general area of chemical physics. Interest in
such experiments has increased sharply in the last ten years, especially
among chemical kineticists. The predominant, common theme through-
out the volume is molecular interactions.
Elastic scattering is discussed in two articles, one reviewing high-
energy scattering and repulsive forces, the other low-energy scattering
and a number of quantum-mechanical effects for which both attractive
and repulsive forms are of importance. Reactive scattering is the topic
of four articles, two on neutral reactions and two on ionic reactions.
Information on chemical reactions may be obtained by molecular beam
measurements on the scattered chemical product or from the study of
elastic scattering in reactive systems. Both methods are reviewed.
Ion-molecule and charge-transfer reactions are also discussed in sep-
arate articles. The remaining sections of the volume are devoted to
inelastic scattering of metastable atoms, the determination of atomic
polarizabilities, and the technique of hypersonic beams.
The articles are representative of current molecular beam research in
chemical physics, but the selection is by no means complete. For
vii
viii
PREFACE
instance, reviews on nonreactive inelastic scattering, on the use of beams
as a technique for molecular resonance spectroscopy, and on the inter-
actions of molecules with surfaces are among the omissions.
I wish to thank my colleague Professor F. Greene for much help
E.
and advice in editing this volume and Dr. G. P. Flynn for compiling
the subject index.
JOHN Ross
CONTENTS
1. Beam Measurements of Atomic Polarizabilities
.
By Benjamin Bederson and Edward J. Robinson 1
2. Elastic Scattering of High-Energy Beams: Repulsive Forces
.
By I. Amdur and J. E. Jordan 29
3. Quantum Effects in Elastic Molecular Scattering
By Richard B. Bernstein . . 75
4. Elastic Scattering in Chemically Reactive Systems
.
By E. F. Greene, A. L. Moursund, and J. Ross 135
5. Collisions of Electronically Excited Atoms and Molecules
By E. E. Muschlitz, Jr. . . 171
6. Charge Transfer
By R. F. Stebbings . . 195
7. Ion-Neutral Reactions
By C. F. Giese . . 247
8. Supersonic Nozzle Beams
. . .
By J. B. Anderson, R. P. Andres, and J. B. Fenn 275
9. Reactive Scattering in Molecular Beams
.
By D. R. Herschbach . 319
. .
Appendix. Selected References on Molecular Beam Research 395
. .
Author Index 397
Subject Index . . 411
Advance in Chemical Physics, VolunzeX
Edited by John Ross
Copyright © 1966 by John Wiley & Sons. Inc.
1. BEAM MEASUREMENTS
OF ATOMIC POLARIZABILITIES"
BENJAMIN BEDERSON and EDWARD J. ROBINSON
Physics Department, New York University, New York
CONTENTS
I. Introduction .................................. ................. 1
11. Theory ....................................... ................. 2
111. Methods of Calculating Polarizabilities ............ ................ 6
IV. Atomic Beam Experiments ..................... ................. 9
A. Alkali Measurements ....................... ................. 9
B. Measurements of Metastable 3 PA~r gon ....... ................ 20
V. Conclusion ................................... .................. 25
References ......................................... ................. 26
I. INTRODUCTION
Polarizability is a seemingly ubiquitous atomic property which
appears as a parameter in the description of many important atomic
processes. The calculation of the van der Waals interaction, the des-
cription of charge transfer and other ion-atom and electron-atom
collision processes, of optical lifetimes, and of optical dispersion all
directly involve or are related to the static polarizabilities of ground
and excited states of neutral atoms and molecules. In a general sense
one can expect that the atomic polarizability will be a useful para-
meter when dealing with any atomic process in which the outer part
of the electronic wave function plays an important role. Direct experi-
mental determinations of atomic polarizabilities provide a very sensitive
check on the accuracy of electronic wave functions, where these are
* Some of the work described in this article was supported by the Advanced
Research Projects Agency, through the Office of Naval Research, Washington,
D.C., under Contract No. NONR-285(60), and by the Defense Atonlic Support
Agency, through the Army Research Office, Durham, N.C., under Contract No.
DA-ARO-D-3 1-12 4G530.
1
2 BENJAMIN BEDERSON AND EDWARD J. ROBINSON
available. In addition, since the approximation methods used in
calculating quadrupole shielding factors can also be used to calculate
polarizabilities,’ comparison of such calculations with experiment
provides an independent check on these methods, and is therefore
helpful in providing more reliable values of nuclear quadrupole moments.
Atomic beam methods would appear to be eminently suited to
measuring polarizabilities, because of the absence of particleparticle
interactions. Yet, there have been only a few such experiments in recent
years, notably the deflection experiments of Chamberlain and Zorn’
at Yale, and the balance experiment^^-^ by the N.Y.U. group. (The
earlier work of Scheffers and Stark5 is primarily of historic interest.)
Our purpose in this article is to discuss these experiments in some detail,
and also to briefly describe some of the principal methods by which
atomic polarizabilities have been calculated in recent years.
THEORY
II.
The energy of an atom in an external field is readily calculable from
perturbation theory, provided one has means of estimating the relevant
matrix elements. Let an unperturbed atom have a Hamiltonian Ho
with energy go. In the presence of an electric field E, the Hamiltonian
+
becomes So 2’T.h e perturbation 2’= -p;E, where the electric
dipole operator
pe= - C eri
i
with ri the position vector of the ith electron. The first-order pertur-
bation energy is
B1 = (Ol&”lO) = (0Jp;EJO) (1)
where 10) is the unperturbed state vector. Since 2’is an operator of
odd parity, the matrix element in Eq. (1) will vanish if (0) has a definite
parity. That is, states of definite parity have zero permanent dipole
moments.
The second-order perturbation energy g2 is given by a summation
containing matrix elements of p, between 10) and other states Ik) of
the form
c,=- c <Ol Pe’El k)< k Ipe*ElO)
(2)
-
k#O da, 80