The sudden approximation is applied to the computation of rotational transition probabilities and inelastic total cross sections for the scattering of polar and nonpolar diatomic molecules (rigid rotors) by atoms. The calculations are based upon an interaction potential which includes both short‐ and long‐range anisotropies. At thermal energies the long‐range attractive parts of the potential are of principal importance in determining the inelasticity, with a significant contribution arising from the quadrupole interaction term (varying as R−7 cos3Θ). The computations show the rapid onset of ``dominant‐coupling'' behavior (randomization of transition probability among all close‐coupled states) for impact parameters below about (S/π)½, where S is the total inelastic cross section.
REFERENCES
1.
K. H.
Kramer
and R. B.
Bernstein
, J. Chem. Phys.
40
, 200
(1964
); hereafter referred to as I.2.
K.
Alder
and A.
Winther
, Kgl. Danske Videnskab. Selskab. Mat. Fys. Medd.
32
, No. 8 (1960
).3.
R. B.
Bernstein
, A.
Dalgarno
, H. S. W.
Massey
, and I. C.
Percival
, Proc. Roy. Soc. (London)
A274
, 427
(1963
).4.
See, for example, E. Merzbacher, Quantum Mechanics (John Wiley & Sons, Inc., New York, 1961), Chap. 19;
A. Messiah, Quantum Mechanics (John Wiley & Sons, Inc., New York, 1962), Chap. 17.
5.
6.
Thus, if represents the total angular momentum (conserved in the collision), then for low j and the usually large and
7.
J. P.
Toennies
, Z. Physik
182
, 257
(1965
) has shown the need for the Anderson anisotropy term.8.
J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (John Wiley & Sons, Inc., New York, 1964), 2nd printing, Chaps. 13 and 14.
9.
Notation is that of A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, N.J., 1957), Chap. 2.
10.
See Ref. 8, Chap. 1, and Appendix.
11.
These integrals may be of interest in connection with pressure‐broadening theory. For early work, see
P. W.
Anderson
, Phys. Rev.
76
, 647
(1949
);more recently, e.g., see
Krishnaji
and S. L.
Srivastava
, J. Chem. Phys.
42
, 1546
(1965
);12.
Recently, H. G. Bennewitz (private communication) has carried out certain elastic scattering experiments involving polarized beams of TlF which have bearing on the repulsive anisotropy. Earlier work by
H. G.
Bennewitz
, K. H.
Kramer
, W.
Paul
, and J. P.
Toennies
, Z. Physik
177
, 84
(1964
), has led to a fairly reliable value of the coefficient for TlF‐rare gas.13.
These tables have been deposited as Document No. 8857 with the ADI Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington, D.C. A copy may be secured by citing the Document number and by remitting $1.25 for photoprints, or $1.25 for 35‐mm microfilm. Advance payment is required. Make checks or money orders payable to: Chief, Photoduplication Service, Library of Congress.
14.
This conclusion is based on extensive checking with different sets of integration intervals for widely different integrand cases. For any given entry the penultimate digit listed can be considered accurate. By way of confirmation, it is noted that for a large number of cases the sum of the computed transition probabilities (even for the limited number of transitions considered) totals as much as 0.999, yet in no case does it exceed unity.
15.
These results are, of course, somewhat too small due to the neglect of the contribution from low impact parameters.
16.
However, the contribution to the total inelastic total cross section from any individual transition is small, and is dominated by the one or two small peaks in its partial total cross section curve (i.e., angular distribution).
17.
This question has been considered in some detail by J. L. J. Rosenfeld (private communication, June 1965),
and by P. Pechukas and J. C. Light (preprint, December 1965).
An alternate approximation scheme has been proposed by
K. P.
Lawley
and J.
Ross
[J. Chem. Phys.
43
, 2930
(1965
)].See also the recent paper on the classical scattering of an atom by a rotor, by
R. J.
Cross
, Jr. and D. R.
Herschbach
[J. Chem. Phys.
43
, 3530
(1965
)].
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