Abstract
In: Transfert d’energie dans les gaz. Douzième conseil de chimie 1962 (R. Stoops., ed.). Interscience Publishers, New York 1963, pp. 211-239, 303-306, 308, 453-457, 515-516. Translated into Hungarian: Áttekintés az ütközések elméletérol. Fizikai Szemle 14, 35-44 (1964)
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References
Professor 1. Prigogine informed me, during the Conference, that he and his collaborators are engaged in the study of this question.
J.A. Wheeler, Phys. Rev., 52, 1107 (1937).
W. Heisenberg, Zeits. f. Physik, 120, 513, 673 (1943).
F. Dyson, Phys. Rev., 75, 486, 1736 (1949).
M. Born, Zeits. f. Physik, 37, 803 (1926).
B.A. Lippmann and J. Schwinger, Phys. Rev., 79, 469 (1950).
The literature of dispersion relations is so large that one hardly can hope to mention even the most important papers. See, however, the reports of M.L. Goldberger and of S. Mandelstam to the Solvay Congress of 1961 (12e Conseil de Physique) or the forthcoming book, “Collision Theory”, by M.L. Goldberger and K.M. Watson.
M. Gell-Mann, Proceedings of the Sixth Annual Rochester Conference (Interscience Publishers, New York, 1956), pages III-30 ff.
N.N. Khuri, Phys. Rev., 107, 1148 (1957).
See the articles of R. Blankenbecler, M.L. Goldberger, N.N. Khuri and S.B. Treiman, Annals of Phys., 10, 60 (1960) and of A. Klein, Jour. Math. Phys., 1, 41 (1960) which actually prove even further-going relations.
The only potential for which it is easy to prove this seems to be c/r 2
See, however, E. Gerjuoy, Rev. Mod. Phys., 33, 544 (1961), particularly page 547; also E. Gerjuoy and N.A. Krall, Phys. Rev., 127, 2105 (1962).
For reviews of this theory see A.M. Lane and R.G. Thomas, Rev. Mod. Phys., 30, 257 (1958) and E. Vogt’s article, “Resonance Reactions, Theoretical” in “Nuclear Reactions” (North Holland Publishing Co., Amsterdam 1959).
For the treatment of the case in which this condition is not met, see T. Teichmann and E.P. Wigner, Phys. Rev., 87, 123 (1952) or the first article of Reference (13).
The meromorphic nature of S as function of the complex k and the position of its poles can easily be established by the methods of R matrix theory, This has been done already by W. Schutzer and J. Tiomno, Phys Rev.,83, 249 (1951); see also E.P. Wigner, Rev. Mexicans de Fis., l, 91 (1952). However, whereas it is known from dispersion theory that, for constant momentum transfer, S goes to a constant value as k→∞ in the upper half plane, no similarly far-reaching statement could be derived so far from R matrix theory.
See e.g., H. Feshbach, Annals of Phys., 5, 357 (1959), R.E. Peierls, Proc. Roy. Soc., A253, 16 (1959), J. Humblet and L. Rosenfeld, Nuclear Physics, 26, 529 (1961).
T. Teichmann, Phys. Rev., 77, 506 (1950); see also Reference (14) or the second article of Reference (13).
T. Regge, Nuovo Cim., 14, 951 (1959), 18, 947 (1960).
N. Levinson, Kgl. Danske Vid. Selskab Mat. Fys. Medd., 25, No. 9 (1949); V. Bargmann, Phys. Rev., 75, 301 (1949); R. Jost and W. Kuhn, Kgl. Danske Vid. Selskab Mat. Fys. Medd., 27, No. 9 (1953). For Yukawa potentials and their superpositions, see A. Martin and G. Targonski, Nuovo Cim. 20, 1182 (1961).
J.A. Wheeler, Phys. Rev., 99, 630 (1955).
T. Regge and G.A. Viano, Nuovo Cim., 25, 709 (1962).
See, for instance, N.F. Mott and H.S.W. Massey, “The Theory of Atomic Collisions” (1st Ed. Oxford University Press, 1933, or 2nd Ed. 1952); H.S.W. Massey and E.H.S. Burhop. “Electronic and Ionic Impact Phenomena” (Oxford University Press, 1952).
E.P. Wigner, Proc. Nat. Acad., 32, 302 (1946). Actually, for pure scattering in the absence of any reaction, the cross section due to a single angular momentum, as function of energy, can and does go through zero. However, the Born approximation shows a similar behavior also in the presence of reactions and not only for a single angular momentum but also for the total scattering cross section in a definite direction.
See P.M. Morse and E.C.G. Stückelberg, Ann. d. Phvs., 9, 579 (1931); H.S.W. Massey and C.B.O. Mohr, Proc. Rov. Soc., 132A, 605 (1931); 140A, 613 (1933). See also H.S.W. Massey, Rev. Mod. Phys., 28, 199 (1956), and the books quoted in Reference (22).
See, for instance, C.A. Levinson and M.K. Banerjee, Ann. of Phys., 2, 471, 499 (1957); 3, 67 (1958). J.R. Lamarsh and H. Feshbach, Phys. Rev., 104, 1633 (1956). The optical model also has a long history which will not be related here. The modern work dates, however, from the paper of H. Feshbach, C.E. Porter and V.F. Weisskopf, Phys. Rev., 96, 448 (1954).
The article of A.M. Lane, R.G. Thomas, and E.P. Wigner, Phys. Rev., 98, 693 (1955) attempts to derive the results, not the equations, of the optical model.
C. Zener, Phys. Rev., 37, 556 (1931); 38, 277 (1931); J.M. Jackson and N.F. Mott, Proc. Roy. Soc, 137A, 703 (1932). Also R.N. Schwartz, Z.I. Slawsky and K.F. Herzfeld, Jour. Chem. Phys., 20, 1591 (1952); R.N. Schwartz and K.F. Herzfeld, ibid., 22, 767 (1954).
F. London, Zeits. f. Phys., 74, 143 (1932).
See, for instance, Proceedings of the Second Conference on Reactions between Complex Nuclei (John Wiley and Sons, New York, 1960), particularly Sessions A, B, D.
See, for instance, J. de Boer and R.B. Bird, Physica, 20, 185 (1954) and J.A. Wheeler and K.W. Ford, Annals of Phys., 7, 259 (1959).
Sang-II Choi and J. Ross, Journ. Chem. Phys., 33,1324 (1960). See, however, also Proc. Nat. Acad., 48, 803 (1962), by the same authors.
See Reference (29), page 309.
See G.N. Watson, “Theory of Bessel Functions” (Cambridge University Press, 1958), page 243 ff.
L. Hulthen, Ark. Mat. Astr. och Fysik, 35A, No. 25 (1948); W. Kohn, Phys. Rev., 74, 1763 (1948).
I. Tamm, J. Exp. Theor. Phys. U.S.S.R., 18, 337 (1948), 19, 74 (1949).
B.A. Lippmann and J. Schwinger, Phys. Rev., 79, 469 (1950); M.L. Gold-berger, ibid., 82, 757 (1951); 84, 929 (1951); M. Kolsrud, ibid., 112, 1436 (1958). This article also contains an example in which the second term of the Born series is very much smaller than the first one (less than 4 %) but this is nevertheless very far from the exact value.
T. Kato, Progr. Theoret. Phys., 6, 295, 394 (1950); L. Spruch and M. Kelly, Phys. Rev., 109, 2144 (1957).
L. Rosenberg, L. Spruch and T.F. O’Malley, Phys. Rev., 118, 184 (1960).
N.W. Bazley, Proc. Nat. Acad., 45, 850 (1959). The method used is due to A. Weinstein, Mémorial des Sci. Math., Paris No. 88, 1937.
G.F. Chew, Phys. Rev., 80, 196 (1950); Y. Fujimoto and Y. Yamaguchi, Progr. Theor. Phys., 6, 166 (1951); G.F. Chew and G.C. Wick, Phys. Rev. 85, 636 (1952); G.F. Chew and M.L. Goldberger, Phys. Rev., 87, 778 (1952).
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Wigner, E.P. (1997). Review of Collision Theory. In: Wightman, A.S. (eds) Part I: Physical Chemistry. Part II: Solid State Physics. The Collected Works of Eugene Paul Wigner, vol A / 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59033-7_24
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