Atoms III — Molecules I / Atome III — Moleküle I

444 Pages·1959·20.059 MB·English

by  S. Flügge (auth.)

ENCYCLOPEDIA OF PHYSICS
EDITED BY
S. FLUGGE
VOLUME XXXVII/l
ATOMS III - MOLECULES I
WITH 215 FIGURES
S P RI N G E R-VE R LA G
BERLIN· GOTTINGEN . HEIDELBERG
1959
HANDBUCH DER PHYSIK
HERAUSGEGEBEN VON
S. FLOGGE
BAND XXXVII!l
ATOME III - MOLEKULE I
MIT 215 FIGUREN
S PRIN G E R-VERLAG
BERLIN. GOTTINGEN . HEIDELBERG
1959
TSBN-13: 978-3-642-45919-1 e-TSBN-13: 978-3-642-45917-7
DOT: 10.1007/978-3-642-45917-7
AlIe Rechte, insbesondere das der Obersetzung in fremde Sprachen, vorbehalten.
Ohne ausdriickliche Genehmigung des Verlages ist es auch nicht gestattet, dieses
Buch oder Teile daraus auf photomechanischem Wege (Photokopie, Mikrokopie)
zu vervieliaItigen.
© by Springer-Verlag OHG. Berlin' G6ttingen' Heidelberg 1959
Softcover reprint of the hardcover 1st 1959
Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw.
in diesem Werk berechtigt auch ohne besondere Kennzeichnung nicht zu der
Annahme, daB solche Namen im Sinn der Warenzeichen- und Markenschutz
Gesetzgebung als frei zu betrachten waren und daher von jedermann benutzt
werden diirften.
Contents.
Page
Atomic and Molecular Beam Spectroscopy. By Dr. POLYKARP KUSCH, Professor of
Physics, Department of Physics, Columbia University, New York/N.Y. (USA), and
Dr. VERNON W. HUGHES, Associate Professor of Physics, Physics Department, Yale
University, New Haven/Connecticut (USA). (With 110 Figures)
A. Methodology. . 2
I. The beam . 3
a) Sources 3
b) Beam characteristics . 18
c) Detectors. . . 25
II. Beam deflection . . 35
a) General theory . 35
b) Deflecting fields. 41
III. The transition process 54
B. Atomic spectroscopy 80
I. Hyperfine structure 81
a) General theory . 81
b) Methods of measurement and results. 89
II. Atomic magnetism and fine structure. 112
C. Molecular spectroscopy . . . . . . . . . 123
I. Unresolved molecular spectra by magnetic resonance method 126
a) High field case . . . . . . . . . . . . . . . . . 126
b) Intermediate and low field cases. . . . . . . . . . . 134
II. Resolved molecular spectra by electric resonance method . 138
III. Resolved molecular spectra by magnetic resonance method 152
Acknowledgment. . . 1 55
General references 155
References to original papers 156
The Vibration-rotation Energies of Molecules and their Spectra in the Infra-red. By
Dr. HARALD H. NIELSEN, Professor of Physics and Chairman, Department of Phy
sics and Astronomy, The Ohio State University, Columbus/Ohio (USA). (With
29 Figures) . . . . . . . 173
Symbols and notation used . . . . . . . . . . . . . . . 173
I. Introduction. . . . . . . . . . . . . . . . . . 174
II. The general formulation of the quantum mechanics. 177
III. The quantum mechanical Hamiltonian for a polyatomic molecule. 191
IV. The energies of a polyatomic molecule . . . . . . . 209
V. The improved energies of a polyatomic molecule . . . 240
VI. The interpretation of the infrared spectra of molecules 251
VII. Anomalies in the infrared spectra of molecules. 273
Acknowledgments 311
Bibliography . 311
VI Contents.
Page
The Collisions of Electrons with Molecules. By JOHN DRUMMOND CRAGGS, MSc., PhD.,
F.Inst.P., Professor of Electronic Engineering, The University of Liverpool, Liver
pool (Great Britain). and Dr. HARRIE STEWART WILSON MASSEY, Quain Professor of
Physics and Head of Department, Department of Physics, University College, London
(Great Britain). (With 76 Figures) 314
Introduction 314
A. General theoretical considerations. 315
B. The elastic scattering of electrons by molecules 320
C. Inelastic collisions of electrons with molecules 332
D. Electronic excitation 334
E. Excitation of molecular vibration and rotation 344
F. Ionization of molecules . . . . . . . . . . 357
G. Experimental data for ionization of diatomic molecules 363
H. Experimental data for ionization of polyatomic molecules 372
Acknowledgments . . . . . . . 415
Sachverzeichnis (Deutsch/Englisch) . 416
Subject Index (English/German) . . 428
Atomic and Molecular Beam Spectroscopy.
By
P. KUSCH and V. W. HUGHES.
With 110 Figures.
1. Introduction. Experimental procedures in which the generation and obser
vation of an atomic or molecular beam is an important part have been applied
to a large range of problems. The older work [7J to [9J, [25J included studies
of gas kinetics, molecular scattering cross sections in gases, the interaction of
molecules with solid surfaces, and the diffraction of molecular beams. Space
quantization of magnetic moments was demonstrated, and the magnetic and
electric properties of molecules, atoms, and nuclei were determined by studies
of the deflection of neutral atoms or molecules in magnetic and electric fields.
High resolution optical spectroscopy utilizes a beam of particles in order to
avoid Doppler line broadeningl.
In most of the recent and present applications of molecular and atomic beams
in physics, the apparatus is used as a spectrometer of extremely high resolution
to measure directly the frequency of transition between energy levels. The range
of frequencies over which the spectrometer operates extends substantially from
zero as a lower limit to an upper limit determined by the upper frequency limit
of available generators of electromagnetic radiation, which corresponds at present
to a wavelength of about 1 mm. The frequency range within which the beam
spectrometer operates leads to the investigation of a range of phenomena which
is not generally open to investigation by the methods of optical spectroscopy,
but which does overlap the phenomena observed by the methods of microwave
absorption spectroscopy and nuclear resonance spectroscopy.
The purpose of any spectrometer is to detect and measure the emission and ab
sorption lines which occur in the transition of an atom or molecule from one er.ergy
level to another. In classical optical spectrometers this is achieved in familiar
ways by the use of the light-dispersing properties of optical media or the diffrac
tion properties of light in gratings and interferometers. In all these methods an
analysis is made of the light itself. Further, in certain recently developed methods
of spectroscopy, as microwave absorption methods or the methods used in the
observation of nuclear resonance phenomena, an observation is made of the
absorbed or emitted radiation. The method of atomic and molecular beams is
unique as a spectroscopic device in that an observation is made of the changed
properties of the atoms or molecules consequent to a transition, and not, directly,
of the absorbed or emitted radiation.
The emphasis in much of modern beam spectroscopy has been on the study
of the properties of nuclei and of the electron. Nuclear magnetic moments and
hyperfine structure separations in atoms and molecules due to the nuclear mo
ments-magnetic dipole, electric quadrupole, and magnetic octupole-have been
1 S. TOLANSKY: High Resolution Spectroscopy. New York and Chicago: Methuen and Co.,
Ltd. London 1947.
Handbuch der Physik, Bd. XXXVII/I.
2 P. KUSCH and V.W. HUGHES: Atomic and Molecular Beam Spectroscopy. Sect. 2.
measured. Nuclear masses have been determined from the study of rotational
state transitions of diatomic molecules. The Lamb shift and the anomalous
magnetic moment of the electron were discovered by the method of atomic beam
spectroscopy, and extensive work has been done on these subjects. In addition,
much information on detailed atomic and molecular properties has been obtained.
The present article deals primarily with atomic and molecular beam spectro
scopy. The first chapter on methodology includes discussions of the production,
characteristics, detection, and deflection of beams of neutral particles, and of the
theory and experimental technique associated with the transition process. The
second and third chapters deal with atomic and molecular spectroscopy respecti
vely. They include a summary of the theory of the energy levels studied, a dis
cussion of the type of measurements that have been made and of the present
limitations to the accuracy of the experiments, and a compilation of the more
important data obtained.
A. Methodology.
2. General principles and characteristics of spectrometer operation. The opera
tion of an atomic or molecular beam apparatus as a spectrometer depends essen
tially on the existence of some observable differential property of the particle
in the two states a and b between which a transition is to be observed. Usually
this property is the magnetic or the electric dipole moment, and the change in
the moment associated with the transition is observed through a change in tra
jectory of the particle. Trajectories which depend on the magnetic or electric
dipole moment of a particle are achieved by allowing the particle to pass through
inhomogeneous magnetic or electric fields in which its deflection depends on the
value of the moment. In the Lamb shift and related experiments on hydrogen
and ionized helium in the 22S~, 22P~, and 22P~ states, detection of transitions
is achieved by use of the differential metastability of the magnetic sublevels of
the 22S~ state in certain magnetic fields.
A schematic diagram of the usual beam spectrometer is shown in Fig. 1. The
source of an atomic or molecular beam is an enclosure containing gas or vapor
which is allowed to effuse through a slit. An additional collimating slit defines
the beam, which ordinarily has a thin ribbon-like cross sect jon. Inhomogeneous
magnetic or electric fields occur in the regions A and B in which the particles
are deflected in a direction perpendicular to the plane of the beam. The C-region
contains the oscillating electromagnetic field, which may cause the transition
of the particle from one state to another. Some appropriate detector of neutral
particles is placed beyond the end of the B-region. If a particle emerges from the
source in a state a and if no transition to another state b occurs in the C-region,
the particle may follow a trajectory as shown and finally strike the detector.
If, on the other hand, the oscillating field in the C-region is near the Bohr fre
quency v = (H;; - ~)/h and if the amplitude and polarization of the field are
suitable, then the particle may undergo a transition to state b because of the
absorption or stimulated emission of radiation. In the state b the particle will
experience a different deflection in the B-region, provided that the moment is
different than in the state a, and hence will not strike the detector. Thus the
transition is observed as a decrease in beam intensity at the detector. A transition
from the state b to the state a may in general be observed in a similar manner.
In addition to the oscillating electromagnetic field, the C-region usually contains
a constant and homogeneous magnetic or electric field, which may be required
to develop a splitting of the energy levels of interest and to maintain the particle
in a definite quantum state throughout the apparatus in the absence of an in-
Sect. 3. Introduction. Gas kinetics. 3
duced transition. Many variations of this classic beam spectrometer have been
used and will be discussed in this article.
The usual forms of microwave spectroscopy and nuclear resonance spectro
scopy, in which the effect of the particles on the radiation is observed, depend for
their signal on an excess number of particles in the low energy state at thermal
equilibrium, because the probability for spontaneous emission is negligible for the
transitions studied and the probabilities for absorption and stimulated emission
are equal. In beam spectroscopy, on the other hand, transitions both from state a
to state b and from state b to state a result in a decrease in the number of par
ticles reaching the detector. Thus the signal depends on the total number of
particles in which the change in state has occurred, regardless of the net ab
sorption or emission of energy. Since the difference in population of the two
!!!l
1
Dz
s
Fig. 1. Schematic diagram of beam spectrometer. s is the source chamber with source slit. c is the collimator slit. The
A and B regions are regions with inhomogeneous magnetic or electric fields. The C region contains the oscillating electro·
magnetic field and, in addition, a constant, homogeneous magnetic or electric field. (Magnetic fields are indicated in the
diagram.) d is the detector. The dashed curve (-- -) is the trajectory of a particle which remains in state a throughout
the apparatus. The dot-dash curve (-. - . -) is the trajectory of a particle which undergoes a transition from state
a to state b in the C-region.
states is ordinarily very small, this characteristic of beam spectroscopy is a
distinct advantage.
The line widths in beam spectroscopy are generally determined by the natural
width associated with the HEISENBERG uncertainty principle or by inhomo
geneity of the constant magnetic or electric field in the C-region. Collision broaden
ing due to other particles or due to the walls is completely negligible, and Doppler
broadening can usually be avoided because of the unidirectional character of the
beam trajectory. Thus beam spectroscopy has yielded many of the highest
precision measurements of transition frequencies.
1. The beam.
a) Sources.
3. Introduction. Gas kinetics. In general the range of problems which have
been investigated by the methods of atomic and molecular beams has been
much more limited by the restrictions imposed by the detector than by the
difficulty of constructing adequate sources of beams of molecules and atoms.
Recently, however, particularly in work with radioactive substances where the
amount of material available is usually small, the source problem has been se
vere. Further, the number of sources that are required has been greatly extended
by recent developments in detectors.
The source of an atomic or molecular beam is an enclosure filled with gas or
vapor and provided with a slit through which a sheam of particles effuses. Some
of the gas kinetic considerations will be presented in this section. The following
sections will deal with evaporation of solids, gas sources, sources of atoms in
metastable and in optically excited states, and sources of radioactive atoms.
1*
4 P. KUSCH and V. W. HUGHES: Atomic and Molecular Beam Spectroscopy. Sect. 3.
If a gas is in thermal equilibrium with its surroundings, then the number of
particles per unit volume which lie within the velocity interval between v and
v +dv is given by the Maxwell distribution law:
f(v) dv = -_4n- v2e-V'OI t'dv (3·1 )
Vn0l:3
where f(v) is the velocity distribution function, n is the number of particles per
unit volume, and rJ.= V2kTjm in which k is BOLTZMANN'S constant (k=1.38X
10-16 erg deg-1 K), T is the absolute temperature, and m is the mass of the par
ticle. The quantity rJ. is the velocity for which f(v) is a maximum, i.a., the most
probable velocity. The average velocity, V, is given by: v=2ocjVn=1.13rJ..
Suppose that the gas is contained in an oven, essentially an isothermal ca
vity, which has a small aperture of area As' The aperture is in a wall of infinitesi
mal thickness and its area is so small that the Maxwellian velocity distribution
within the oven is not affected by effusion from the aperture. For this condition
of ideal effusion the number of particles, N, which escape from the oven into a
vacuum per unit time is:
N=tnvAs· (3.2)
The expression for N may be rewritten:
pAs
N= --- (3·3)
VZnkTm
where No is AVOGADRO'S number (No=6.02X1023), R is the gas constant per
mole (R=8.32X107ergsdeg-1K), T is the source temperature in OK, M is the
molecular weight, and P is the pressure in dynesjcm2. In a typical case the
quantities may have the approximate values p = 103 dynesjcm2, M = 40 (LiCl,
NaF, K), T=1000oK, As=10-3cm2; hence N will be 1.3X1017particlesjsec.
Particles leave the oven according to the cosine law and the number of par
ticles emitted at an angle {} from the normal to the aperture and within a solid
angle dQ is:
N({}) dQ = nvAs cos{}dQ. (3.4)
4n
For the ovens used in atomic and molecular beams, the angle {} is approximately
zero.
The above formulae are strictly applicable only for ideal effusion. If the
source involves evaporation of a solid, then the surface area from which evapora
tion occurs must be large compared to the aperture area in order that ideal
effusion shall occur. If the source is a gas, the effusion rate must be small com
pared to the rate at which the gas attains thermal equilibrium with its containing
vessel. In practice these conditions are ordinarily fulfilled. A not-unrelated
requirement for ideal effusion is that the mean free path of the particles in the
enclosure be large compared to the slit width. If this were not so, particles
emerging from the slit in the direction to constitute the beam would suffer
collisions in the neighborhood of the slit and a particle cloud formation exterior
to the enclosure would result!. The width of the beam would then be increased
and not determined simply by the source slit width. It has been found satis
factory in customary practice to have the mean free path of the order of the slit
width, and a typical order of magnitude figure for the mean free path-appli
cable to potassium, for example-is 0.1 mm at a source pressure of 1 mm Hg.
1 F. KNAUER and O. STERN: Z. Physik 39, 764 (1926).
Sect. 4. Evaporation of solids. 5
Source slits with a finite thickness (canals) are unavoidable in practice and
have found useful application because of the more directional beams they pro
duce. Provided the canal length is small compared to the mean free path of
particles in the source, which is the condition of practical interest, the charac
teristics of the forward beam remain unchanged by the thickness of the source
slit. However, effusion from a canal does not occur according to the cosine
law as for the ideal thin aperture, but rather is preferentially in the forward
direction. Hence for the same forward intensity the total number of particles
emitted from an ideal aperture is greater than the number of particles emitted
from a canal. If G is defined as the ratio
!(I
of these numbers, then G is given by: (\
(3.5) 6( Theu!)') J8
0
a8 6(fxfl!.)oS8
1
where l is the length and w is the
width of a canal with square cross sec a7
tion. Measurements as indicated in
Fig. 2 have shown this expression to
be roughly correct provided that the
pressure in the oven is sufficiently low
(less than 3 X 10-3 mm Hg for the oven
in question) so that the mean free path
is larger than the length of the canal!. aJ
The intensity and angular distribution ! \
u
of effusion from a canal are reviewed
by FRASER [8J and RAMSEY [25J. ,/1 . \,
a/
If the distribution in the source is
Maxwellian at a temperature T, then (I?--O-r--o--,0 .......0 """-I- 0
-J(I -2(1 -1(1 (} /(1
the number of particles effusing from
!lf7s/e if7 o'fSrel!s
an ideal aperture per unit time within
the velocity interval from v to v + d v is: Fig. 2. Relative beam intensity as a function of angle of
beam with respect to axis of source canal. The canal dimen
sions are length = 6.3 mm, width = 0.12 mm, and height =
0.12 mm. The quantity G is a measure of the directivity of
(3.6) the beam.
Hence the v2 factor multiplying the exponential in the Maxwellian distribution
which describes the velocity distribution among all the particles in the cavity
is altered to v3 for describing the number of particles that effuse per unit time
and lie in the velocity interval dv. The most probable velocity for a particle in
the beam is VI ex = 1.22 ex and the mean velocity is (-!) Vn ex = 1.33 ex.
4. Evaporation of solids. Ovens to evaporate a material which is a solid of
low vapor pressure at room temperature have been the most common source
of molecular and atomic beams. The oven must have a well which holds the
material from which evaporation is to occur and which is sealed from the sur
rounding vacuum except for a slit. Heaters must be supplied to maintain the oven
at an appropriate temperature, and it is convenient to have a thermocouple or
other device for the measurement and control of temperature. The oven material
must be such that no significant reaction or alloying between the oven and its
load occurs, since a reaction may lead to an excessive rate of loss of material,
an excessive rate of evolution of gas, or a destruction of essential geometrical
detail such as slits.
1 DAVIS, NAGLE and ZACHARIAS: Phys. Rev. 76,1068 (1949).