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Classical and Quantal Scattering. I. The Classical Action
1.N. F. Mott and H. S. Massey, The Theory of Atomic Collisions (Clarendon Press, Oxford, England, 1949), 2nd edition.
2.K. W. Ford and J. A. Wheeler, Ann. Phys. (N.Y.) 7, 259 (1959).
3.See, for instance, B. L. Moiseiwitsch, in Lectures in Theoretical Physics, edited by W. E. Brittin, B. W. Downs, and J. Downs (Interscience Publishers, Inc., New York, 1961), Vol. 4, pp. 157–159;
3.compare C. L. Critchfield, Am. J. Phys. 32, 542 (1964).
4.F. T. Smith, “Classical and Quantal Scattering. II. The Scattering Amplitude” (to be published) referred to hereafter as II.
5.E. A. Mason, J. T. Vanderslice, and C. J. G. Raw, J. Chem. Phys. 40, 2153 (1964), have approached this problem by using the theory of asymptotic expansions.
6.To alleviate the embarrassing duplicity here of well‐established meanings for “S,” boldface S is always used for the scattering matrix even in a nonmatrix form as Eq. (13), and italic S always represents an action.
7.R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948).
8.L. Motz, Phys. Rev. 126, 378 (1962);
8.L. Motz, 133, B1622 (1964)., Phys. Rev.
9.R. P. Marchi and F. T. Smith (to be published);
9.see also F. T. Smith, Bull. Am. Phys. Soc. 9, 411 (1964).
10.F. J. Smith, Phys. Letters (Netherlands) 10, 290 (1964), has treated scattering in the same way.
11.H. Payne, Phys. Rev. 132, 2544 (1963).
12.K. W. Ford, D. L. Hill, M. Wakano, and J. A. Wheeler, Ann. Phys. (N.Y.) 7, 239 (1959);
12.F. T. Smith, Bull. Am. Phys. Soc. 9, 254 (1964).
13.C. F. Curtiss and R. S. Powers, Jr., J. Chem. Phys. 40, 2145 (1964);
13.H. T. Wood and C. F. Curtiss, J. Chem. Phys. 41, 1167 (1964)., J. Chem. Phys.
14.S. Choi and J. Ross, J. Chem. Phys. 40, 2151 (1964).
15.R. B. Bernstein, J. Chem. Phys. 36, 1403 (1962).
16.R. B. Bernstein and K. H. Kramer, J. Chem. Phys. 38, 2507 (1963).
17.O. B. Firsov, Zh. Eksperim. i Teor. Phys. 24, 279 (1953);
17.see also G. H. Lane and E. Everhart, Phys. Rev. 120, 2064 (1960), especially Eq. (7).
18.Yu. N. Demkov, Variational Principles in the Theory of Collisions (translated by N. Kemmer, The Macmillan Company, New York, 1963).
19.E. Everhart, Phys. Rev. 132, 2083 (1963),
20.E. M. Baroody, Phys. Fluids 5, 925 (1962).
21.D. R. Bates and A. H. Boyd, Proc. Phys. Soc. (London) 80, 1301 (1962).
22.H. S. W. Massey and C. B. O. Mohr, Proc. Roy. Soc. (London) A144, 188 (1934).
23.J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (John Wiley & Sons, Inc., New York, 1954), Table III, p. 1155.
24.F. J. Smith, Physica 30, 497 (1964).
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