EXPERIMENTAL 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 San Diego New York Boston London Sydney Tokyo Toronto This book is printed 011 acid-free paper. @ Copyright 0 1996 by ACADEMIC PRESS, INC. All Rights Reserved. No part ofthis publication may he reproduced or transmitted in any form or by an! means, electronic or mechanical. including photocop>, recording, or any information storage and retrieval system, without permission in writing fioni the publisher. Academic Press, Inc. A Division of Harcourt Brace & Company 525 B Street. Suite 1900, San Diego, California 92101 -4395 United King~ioniE di/ion piibli.vhed h), Academic Press Limited 24-28 Oval Road. London NW 1 7DX International Standard Serial Number: 1079-4042 International Standard Book Number: 0- 12-475976-9 PRINTED IN TtIE UNITED STATTS OF AMtRlCA 96 97 98 99 00 01 BC 9 8 7 6 5 4 3 3 I 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