Table Of ContentEXPERIMENTAL METHODS IN
THE PHYSICAL SCIENCES
Robert Celotta and Thomas Lucatorto, Editors in Chief
Founding Editors
L. MARTON
C. MARTON
Volume 29B
Atomic, Molecul ar, and
Optical Physics:
Atoms and Molecules
Edited by
F. B. Dunning
Department of Physics
Rice University, Houston, Texas
and
Randall G. Hulet
Department of Physics
Rice University, Houston, Texas
ACADEMIC PRESS
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CONTRIBUTORS
Numbers in parentheses indicate the pages on which the authors' contributions begin.
ANNE M. ANDREWS(2 73), National Institute of Standards and Technology,
Molecular Physics Division, Gaithersburg, Maryland 20899
JAMESC . BERGQUIS(T2 55), National Institute of Standards and Technology,
Boulder; Colorado 80303
J. BLAND-HAWTHO(R3N63 ); Department of Space Physics and Astronomy, Rice
University, Houston, Texas 77251
CURTISC . BRADLEY(1 29), Department of Physics and Rice Quantum Institute,
Rice University, Houston, Texas 77251
J. M. BROWN(8 5), Department of Physical Chetnistry, Oxford OX1 3QZs England
OLIVIEHR. CARNA(L3 4 I), Holtronic Technologies S.A., Murin, Switzerland
G. CECIL( 363), Department of Physics and Astronomy, University of North
Carolina, Chapel Hill, North Carolina 27599
A. CHUTJIA(N49 ), Jet Propulsion Laboratory, California Institute of Technology,
Pasadena, Calijiornia 91109
K. M. EVENSON(8 5), Nutional Institute of Standards and Technology, Boulder;
Colorado 80303
T. F. GALLAGHE(R1 1 5, 325), Department of Physics, University of Virginia,
Churlottesville, Virginia 22503
TIMOTHJY. G AY (93, Behlen Laboratory of Physics, University of Nebraska,
Lincoln, Nebraska 68588
H. HOTOP ( 19 1 ), Fachbereich Physik, Universitat Kaiserslautern, 0-67653
Kaiserslautern, Germany
RANDALGL . HULET( 1 29), Department of Physics and Rice Quantum Institute,
Rice University, Houston, Texas 77251
G. SAMUEHLU RST( 17 I), Institute of Resonance Ionization Spectroscopy, The
University of Tennessee, Knoxville, Tennessee 37932
'Current address: Anglo-Australian Observatory, P.O. Box 296, Epping, NSW 2 12 1.
...
Xlll
xiv CONTRIBUTORS
CARTERK ITTRELL( 393), Department of Chemistry and Rice Quantum Institute
Rice University, Houston, Texas 77251
J. E. LAWLE(R2 17), Department of Physics, University of Wisconsin-Madison,
Madison, Wisconsin 53706
JABEZ J. MCCLELLAN(D1 43, Electron Physics Group, National Institute of
Standards and Technology, Gaithersburg, Maryland 20899
JURGEN MLYNEK(3 4 I). Fakultat fur Physik, Universitat Konstanz, 0-7750
Konstanz, Germany
MICHAEDL. MORSE(2 1), Department ($Chemistry, University of Utah, Salt Lake
City, Utah 84112
T. R. O'BRIAN( 2 17), Radiometric Physics Division, National Institute of
Standards and Technology, Gaithersburg, Maryland 20899
0. J. ORIEN(T4 9), Jet Propulsion Laboratory, California Institute of Technology,
Pasadena, California 91109
JAMES E. PARKS( 17 l), Institute of Resonance Ionization Spectroscopy, The
University of Tennessee, Knoxville, Tennessee 37932
NORMANF. RAMSEY (l), Lyman Physics Luboratory, Harvard University,
Cambridge, Massachusetts 02138
R. D. SUENRAM(2 73), National Institute of Standards and Technology,
Molecular Physics Division, Gaithersburg, Maryland 20899
C. R. VIDAL( 67), Max Planck Institute fur Extraterrestriche Physik, 0-8046
Garching bei Miinchen, Germany
LINDAY OUNG(3 01 ) , Argonne National Laboratory, Argonne, Illinois 60439, and
Joint Institute for Laboratory Astrophysics, University of Colorado, Boulder;
Colorado 80309
PREFACE
Since the publication in 1967 of “Atomic Sources and Detectors,”
Volumes 4A and 4B of this series, the field of atomic, molecular, and
optical physics has seen exciting and explosive growth. Much of this
expansion has been tied to the development of new sources, such as the
laser, which have revolutionized many aspects of science, technology,
and everyday life. This growth can be seen in the dramatic difference
in content between the present volumes and the 1967 volumes. Not all
techniques have changed however, and for those such as conventional
electron sources, the earlier volumes still provide a useful resource to the
research community. By carefully selecting the topics for the present
volumes, Barry Dunning and Randy Hulet have provided us with a coher-
ent description of the methods by which atomic, molecular, and optical
physics is practiced today. We congratulate them on the completion of
an important contribution to the scientific literature.
Beginning with Volume 29A, the series is known as Experimental
Methods in the Physical Sciences instead of Methods of Experimental
Physics. The change recognizes the increasing multidisciplinary nature of
science and technology. It permits us, for example, to extend the series
into interesting areas of applied physics and technology. In that case, we
hope such a volume can serve as an important resource to someone
embarking on a program of applied research by clearly outlining the
experimental methodology employed. We expect that such a volume
would appear to researchers in industry, as well as scientists who have
traditionally pursued more academic problems but wish to extend their
research program into an applied area. We welcome the challenge of pro-
viding an important and useful series of volumes for all of those involved
in today’s broad research spectrum.
Robert J. Celotta
Thomas B. Lucatorto
xv
1. THERMAL BEAM SOURCES
Norman F. Ramsey
Lyman Physics Laboratory, Harvard University
Cambridge, Massachusetts
1 .I Introduction
The different kinds of sources for beams of neutral atoms and molecules
include thermal sources for slow beams, jet sources for supersonic beams, and
fast beam sources formed by neutralization of ion beams. Since the last two are
discussed in later chapters, this chapter concentrates on the many varieties of
thermal sources. In discussions of thermal sources, the words atomic and
molecular are often used interchangeably because the basic design principles are
similar for atomic and molecular sources.
The earliest atomic beam sources were simple containers with narrow aper-
tures, which were either rectangular or circular. Gases that are noncondensable at
ordinary temperatures pass at the correct source pressure to the source through
tubes. Typically the source pressures are a few torr (millimeters of Hg or
133.32 Pa) for apertures whose smallest linear dimension are a few hundredths of
a millimeter. Such sources are often cryogenically cooled to obtain slower
molecules or lower rotational states. For the study of atoms, such as hydrogen
which normally occur in polyatomic form, it is often necessary to have an electric
discharge in the source to dissociate the molecules [I]. If elevated temperatures
are required to obtain the desired vapor pressures, the sources are usually heated
ovens with suitable exit apertures.
It is often necessary to diminish the emission of unused source material to
conserve the material, to provide long uninterrupted operating times, or to
diminish pumping or contamination problems in the source region. The on-axis
flux with atomic beam thermal sources depends primarily on the source vapor
pressure. To decrease the loss of source material from wrongly directed source
molecules, different techniques are used. These are called dark wall, bright wall,
or recirculating, depending on whether the beam intercepted by the wall is not
reemitted, is reemitted, or is recirculated [2-61.
All thermal sources depend on principles of kinetic theory summarized in the
next section.
1
EXPERIMENTAL METHODS FN THE PHYSICAL SCIENCES Copyright 8 1996 by Academic Press, Inc.
Val. 298 All rights of reproduction in any form reserved.
2 THERMAL BEAM SOURCES
1.2 Theoretical Principles
1.2.1 Effusion from Thin-Walled Apertures
The sources of molecules in many molecular-beam experiments consist of
small chambers which contain the molecules in a gas or vapor at a few torr
pressure and which have small circular apertures or narrow slits about 0.02 mm
wide and 1 cm high. Except where otherwise indicated, the equations in this
section apply to apertures of any shape provided the width, w,i s taken as the
smallest cross-sectional dimension of the aperture. The width of the slit and the
pressure are such that there is molecular effusion [I, 71 as contrasted to hydro-
dynamic flow. Under such conditions, the number, dQ, of molecules which will
emerge per second from the source slit traveling in solid angle do at angle 8
relative to a normal to the plane containing the slit jaws is, by elementary kinetic
theory arguments [ 1,7],
dQ = (dwl4n)nii cos BAS, (1.1)
where n is the number of molecules per unit volume, 6 is the mean molecular
velocity inside the source, and A, is the area of the source slit. For an ideal gas
of pressure p and absolute temperature T,
p = nkT. (1.2)
The total number Q of molecules that should emerge from the source in all
directions can be found by integrating Eq. (1.1) over the 277 solid angle of the
forward direction. In this case, and with dw taken as 271 sin Ode so that the
integration goes from 8 equals 0 to $71, one immediately obtains from the
integration that
Two assumptions are inherent in Eqs. (1.1 ) and (1.3) One of these is that
every molecule which strikes the aperture passes through it and does not have its
direction changed. This assumption is valid only if the thickness of the slit jaws
is as discussed later in this section. The other assumption is that the spatial and
velocity distributions of the molecules inside the source are not affected by the
effusion of the molecules. The strict requirement for this condition is that
w % AM,, (1.4)
where w is the slit width and AM, the mean free collision path inside the source.
By the usual kinetic theory demonstration,
THEORETICAL PRINCIPLES 3
where o is the molecular collision cross section. For air at room temperature,
AMs = 300 meters at torr. For the small collision angles that are often
significant with well-defined molecular beams, the effective mean free paths are
usually considerably smaller than the above.
In actual practice it is found that for most purposes, effusive sources are
effective when
-
(1.6)
AMs,
If Eq. (1.4) or (1.6) is not satisfied, a partial hydrodynamic flow results with the
creation of a jet instead of free molecular flow. This may create turbulence and
a widened beam, or it may provide a cooled jet beam with the advantages
discussed later in the chapter on supersonic beams. It is significant that the
restrictions in Eqs. (1.4) or (1.6) depend only on the width and not on the height
of the slit or with circular apertures on the radius of the aperture. Consequently,
approximately the same source pressure can be used with a slit whose width
equals the radius of a circular aperture. On the other hand, if the slit is a high one,
it will have a greater area and produce a correspondingly greater beam
intensity.
1.2.2 Effusion from Long Channels
The cosine law of molecular effusion that is implied by Eq. (1.1) was
established by the pioneer work of Knudsen [I]. However, if the thin-walled
aperture assumed above is replaced by a canal-like aperture of appreciable
length, the molecules which enter the canal at a considerable angle will strike the
canal wall and have a smaller chance of escaping. In this way the angular
distribution of the emergent beam is changed considerably [ 11.
One consequence of the change is that the total amount of gas which emerges
from the source is diminished, but that which emerges in the direction of the
canal is undiminished, provided the pressure is sufficiently low for collisions
inside the canal to be negligible-that is, provided AM^ 2 e, where C is the canal
length. This improvement of beam intensity per amount of source material
consumed is of great value in many molecular beam experiments such as those
with radioactive isotopes. The effectiveness of the canal in reducing the total
number of emerging molecules is expressed in terms of a factor 1/~w,h ich is
such that Eq. (1.3) with a canal-like aperture is replaced by
Q = (l/~)$zL4~. (1.7)
Claussing and others [l] have calculated the values of 1 / f~or apertures of a
number of different shapes making the bright wall assumption mentioned in
Section 1.1 Their results for slits of various shapes are as follows, if w is the
e
aperture width, h the height, Y the radius, and the canal length:
4 THERMAL BEAM SOURCES
e
(a) Any shape aperture of very short length or with = 0:
1/K = 1.
e
(b) Long circular cylindrical tube with % r:
8 r
I/u=--. (1.9)
3 e
e,
(c) Long rectangular slit with h B C % w:
w e
1 /=~ -e In -w (1.10)
(d) If the aperture is of a shape different from any of the above, a poorer
e
approximation to 1 /c~an often be obtained for large from the expression of
Knudsen [ 11:
(1.11)
where o is the periphery and A the area of a normal cross section at position 6
along the length of the canal. A, is present just to cancel that in Eq. (1.7).
(e) If the cross section of the canal remains unaltered along its length, Eq. ( 1.1 1)
reduces to
1/K = (1 6/3)Aleo. (1.12)
It should be noted that Eq. (1.9) is a special case of Eq. (1.12).
Although the preceding calculations apply to single channels, they can also
be applied to a large number of parallel channels, provided that they do not
significantly interfere with each other. Successful sources have been made from
arrays of small-diameter tubes and from multichanneled glass. All of the
foregoing channel results are based on the bright wall assumption. With the same
geometry, but with dark walls or with recirculating ovens, the effective K factor
can be much larger.
1.2.3 Molecular Beam Intensities
If the pressure in the molecular-beam apparatus is sufficiently low that no
appreciable amount of the beam is scattered out, and if no collimating slit or
similar obstruction intercepts the beam on its way to the detector, the theoretical
