Abstract
We apply the quasipotential approach of quantum field theory to solve the inverse scattering problem in the relativistic quasiclassical approximation. We obtain expressions for reconstructing the quasipotential from the phase shifts and consider both nonrelativistic and ultrarelativistic cases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
A. I. Baz', V. F. Demin, and M. V. Zhukov, Fiz. Élem. Chastits At. Yadra,6, 515 (1975).
R. Newton, Scattering Theory of Waves and Particles, McGraw-Hill, New York (1966).
K. Chadan and P. Sabatier, Inverse Problem in Quantum Scattering Theory, Springer-Verlag, New York (1977).
B. N. Zakhar'ev et al., Yad., Fiz.20, No. 6, 1273 (1974); Fiz. Élem. Chastits At. Yadra,8, Np. 2, 290 (1977); Fiz. Élem. Chastits At. Yadra,13, No. 6, 1284 (1982); V. V. Malyarov et al., Zh. Éksp. Teor. Fiz.,68, 432 (1975); Yad. Fiz.,21, No. 5, 987 (1975); Yad. Fiz.,22, No. 4, 1125 (1975); Yad. Fiz.,25, No. 1, 72 (1977); L. S. Vasilevskii and N. I. Zhirnov, Yad. Fiz.,27, No. 1, 1122 (1978); K. V. Varsimashvili et al., Yad. Fiz.,31, No. 3, 816 (1980); M. N. Adamyan, Teor. Mat. Fiz.,48, No. 1, 70 (1981).
H. B. Thaker, C. Quigg, and J. L. Rosner, Phys. Rev.,D18, 274, 287 (1978); C. Quigg and J. L. Rosner, Phys. Rev.,D23, 2625 (1981); P. Moxhay and J. L. Rosner, Phys. Rev.D23, 2638 (1981).
A. A. Logunov and A. N. Tovkhelidze, Nuovo Cim.,29, 380 (1963).
I. T. Todorov, Schrödinger Equation for the Relativistic Two-Body Problem, Lectures at the Dubna-CERN School, Varna, Bulgaria, JINR E2-5813, Dubna (1971), pp. 7–35; I. T. Todorov, Prop. Fundam. Interact.,9C, 952 (1973); V. A. Rizov and I. T. Todorov, Fiz. Élem. Chastits At. Yadra,6, 669 (1975).
V. V. Malyarov et al., Yad. Fiz.,30, No. 4 (10), 1126 (1979).
I. V. Amirkhanov, G. V. Grusha, and R. M. Mir-Kasimov, Fiz. Elem. Chastits At. Yadra,12, No. 3, 651 (1981).
V. G. Kadyshevskii, Nucl. Phys.,B6, 125 (1968).
V. G. Kadyshevskii, Zh. Éksp. Teor. Fiz.,46, 654 (1964).
V. G. Kadyshevskii, R. M. Mir-Kasimov, and N. B. Skachkov, Nuovo Cim.,55A, 233 (1968); Fiz. Elem. Chastits At. Yadra,2, No. 3, 635 (1972).
M. Freeman, M. D. Mateev, and R. M. Mir-Kasimov, Nucl. Phys.,B12, 197 (1969).
N. B. Skachkov and I. L. Solovtsov, Teor. Mat. Fiz.,41, No. 2, 205 (1979).
A. D. Donkov et al., International Conference on High-Energy Hadron Interactions, Collected Abstracts, Baku (1971); Proceedings of IVth International Symposium on Non-local Quantum Field Theory, JINR D2–9788, Dubna (1976).
N. B. Skachkov and I. L. Solovstov, Pis'ma Zh. Éksp. Teor. Fiz.,28, 326 (1978); Yad. Fiz.,31, No. 5, 1332 (1980).
I. L. Solovtsov, Izv. Akad. Nauk SSR, Ser. Fiz.-Mat. Nauk, No. 1, 109 (1982).
I. L. Solovtsov and Yu. D. Chernichenko, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 63 (1984).
M. Abramovits and I. Stigan, Handbook of Special Functions [in Russian], Nauka, Moscow (1979).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No-5, pp. 11–17, May, 1987.
The authors are deeply grateful to Yu. S. Vernov and N. B. Skachkov for their interest and helpful discussion of the results.
Rights and permissions
About this article
Cite this article
Solovtsov, I.L., Chernichenko, Y.D. Inverse scattering problem in the relativistic quasiclassical approximation. Soviet Physics Journal 30, 366–371 (1987). https://doi.org/10.1007/BF00900082
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00900082