A method has been developed for calculating rotationally inelastic cross sections of atom‐diatom collisions in a semiclassical approximation (classical path, quantum internal states). An analysis of the relations among the intermolecular potential, the cross sections, and the experimental quantities indicates that many experiments related to inelastic scattering give significant information about the intermolecular potential. A computer program embodying this method of calculation has been developed and tested. Quantities related to experimental measurements have been calculated to within experimental accuracy in a reasonable computing time, which suggests that the information about the intermolecular potential contained in various experimental results can be extracted by a semiclassical calculation.

1.
(a)
R. G.
Gordon
,
Adv. Magn. Reson.
3
,
1
(
1968
).
(b)
R. G.
Gordon
,
W.
Klemperer
, and
J.
Steinfeld
,
Annu. Rev. Phys. Chem.
19
,
215
(
1968
).
2.
A. O. Cohen (private communication).
3.
A. Messiah, Quantum Mechanics (Wiley, New York, 1958), Chap. 7.
4.
A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, N.J., 1957), Chap. 4.
5.
E. Isaacson and H. B. Keller, Analysis of Numerical Methods (Wiley, New York, 1966), Chap. 1.
6.
W.
Magnus
,
Commun. Pure Appl. Math.
7
,
649
(
1954
).
7.
P.
Pechukas
and
J. C.
Light
,
J. Chem. Phys.
44
,
3897
(
1966
).
8.
K. P.
Lawley
and
J.
Ross
,
J. Chem. Phys.
43
,
2930
(
1965
).
9.
R. P.
McGinnis
and
R. G.
Gordon
,
J. Chem. Phys.
55
,
4898
(
1971
).
10.
A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, N.J., 1957), Chap. 5.
11.
The factor (2j′+1)1/2 is inserted in Eq. (27) so that the reduced matrix elements (j′|T|j) correspond to the line amplitudes d defined in the classical limit by
R. G.
Gordon
,
J. Chem. Phys.
45
,
1649
(
1966
);
R. G.
Gordon
,
J. Chem. Phys.
46
,
448
(
1967
).
12.
The factors (2jα′+1)1/2(2jα+1)−1/2 in the sigma matrix (B‐10) make it consistent with the convention for the reduced matrix elements adopted in Eq. (27). This form of the sigma matrix thus corresponds to the classical definitions in Ref. 11. In Ref. 1(b) the quantity q, which is the projection of the tensor onto the z axis, was inadvertently given a different value in the two three‐j coefficients. Our thanks to Dr. Hershel Rabitz for pointing out this error.
13.
M.
Baranger
,
Phys. Rev.
111
,
494
(
1958
),
U.
Fano
,
Phys. Rev.
131
,
259
(
1963
),
A.
Ben‐Reuven
,
Adv. At. Mol. Phys.
5
,
201
(
1969
).
14.
A. H. Stroud and D. Secrest, Gaussian Quadrature Formulas (Prentice‐Hall, Englewood Cliffs, N.J., 1966).
15.
L.
Spitzer
,
Phys. Rev.
58
,
348
(
1940
);
M.
Baranger
,
Phys. Rev.
111
,
494
(
1958
);
R. G.
Gordon
,
J. Chem. Phys.
45
,
1649
(
1966
).
16.
R.
Herman
and
R. F.
Wallis
,
J. Chem. Phys.
23
,
637
(
1955
).
17.
R. G.
Gordon
,
J. Chem. Phys.
44
,
3083
(
1966
).
18.
M. E.
Van Krefeld
and
J.
Van der Elsken
,
Chem. Phys. Lett.
1
,
532
(
1968
).
See also
M. E.
Van Krefeld
,
R. M.
Van Aalst
, and
J.
Van der Elsken
,
Chem. Phys. Lett.
4
,
580
(
1970
).
19.
J. H.
Van Vleck
and
V. F.
Weisskopf
,
Rev. Mod. Phys.
17
,
227
(
1945
).
20.
A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, N.J., 1957), Chap. 3.
21.
See Eq. (5.1) in Ref. 17.
22.
A.
Ben‐Reuven
,
Adv. At. Mol. Phys.
5
,
201
(
1969
).
23.
R. G.
Gordon
,
J. Chem. Phys.
45
,
1649
(
1966
).
24.
Equations (12) and (13) in Ref. 23.
25.
A. Abragam, Principles of Nuclear Magnetism (Oxford U.P., London, 1961).
26.
Reference 25, Chap. 8.
27.
Reference 25, Chap. 3.
28.
R. G.
Gordon
,
J. Chem. Phys.
44
,
228
(
1966
).
29.
R. G.
Gordon
,
J. Chem. Phys.
42
,
3658
(
1965
).
30.
G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand, Princeton, N.J., 1950), Vol. 1, p. 128.
31.
K. F. Herzfeld and T. A. Litovitz, Absorption and Dispersion of Ultrasonic Waves (Academic, New York, 1959).
32.
R. G.
Gordon
,
Physica (The Hague)
34
,
398
(
1967
).
33.
R. G.
Gordon
,
J. Chem. Phys.
51
,
14
(
1971
).
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