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Inverse problem in the complex λ-plane in the case of a coulomb interaction

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Abstract

In view of the large body of experimental information available, there is intense interest in the problem of reconstructing the nuclear potential from data on the scattering of charged particles. The inverse problem of scattering theory is solved in the complex λ-plane in the case of a nuclear-Coulomb potential by a method similar to that used by Burget et al. A generalized Yukawa potential is used as nuclear potential. It is shown that the nuclear potential can be reconstructed unambiguously from the spectral function given in the λ-plane. The solution of the problem reduces to one of solving an integral equation of the Gel'fand-Levitan type in which the kernel is expressed in terms of the Jost solutions of the radial Schrödinger equation with a Coulomb potential and in terms of the spectral function.

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Literature cited

  1. G. Burget, M. Giffon, and E. Predazzi, Nuovo Cimento,36, 1337 (1965).

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  2. I. V. Poplavskii, Izv. VUZ, Fizika, This issue, p. 1212.

  3. I. V. Poplavskii, Izv. VUZ, Fizika, No. 2, 23 (1970).

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 116–120, September, 1970.

The author thanks Professor V. V. Malyarov for useful discussion.

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Poplavskii, I.V. Inverse problem in the complex λ-plane in the case of a coulomb interaction. Soviet Physics Journal 13, 1216–1219 (1970). https://doi.org/10.1007/BF01100557

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  • DOI: https://doi.org/10.1007/BF01100557

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