Quasispotential equations for the scattering states of two relativistic particles are considered. A representation of the relativistic partial waves in terms of the associated Legendre functions with integer subscript and hyperbolic cotangent of the rapidity as their argument is found. An explicit form of the partial Green’s functions is found in the relativistic configuration representation for three versions of the quasipotential equations. An algorithm for numerical solution of the partial equations for scattering states of the particles with nonzero orbital angular momentum is presented.
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References
Logunov A. A. and Tavkhelidze A. N., Il Nuovo Cimento, 29, No. 2, 380–399 (1963).
R. Blankenbecler and R. Sugar, Phys. Rev., 142, No. 4, 1051–1059 (1966).
V. G. Kadyshevsky, Nucl. Phys. B., 6, No. 2, 125–148 (1968).
F. Gross, Phys. Rev., 186, No. 5, 1448–1462 (1969).
V. G. Kadyshevsky, R. M. Mir-Kasimov, and N. B. Skachkov, Il Nuovo Cimento A, 55, No. 2, 233–257 (1968).
M. Freeman, M. D. Mateev, and R. M. Mir-Kasimov, Nucl. Phys. B, 12, No. 1, 197–215 (1969).
V. G. Kadyshevsky, R. M. Mir-Kasimov, and N. B. Skachkov, Elem. Chast. At. Yad., 2, No. 3, 635–690 (1972).
M. Bawin, Ann. Phys., 77, No. 1–2, 431–451 (1973).
I. V. Amirkhanov, G. V. Grusha, and R. M. Mir-Kasimov, Teor. Mat. Fiz., 40, No. 3, 384–393 (1979).
V. N. Kapshai and N. B. Skachkov, Teor. Mat. Fiz., 55, No. 1, 26–38 (1983).
V. N. Kapshai and T. A. Alferova, J. Phys. A, 32, No. 28, 5329–5342 (1999).
V. N. Kapshai, K. P. Shilyaeva, and Y. A. Grishechkin, Probl. Fiz. Mat. Tekh., 9, No. 4, 33–37 (2011).
Yu. A. Grishechkin and V. N. Kapshai, Russ. Phys. J., 56, No. 4, 435–443 (2013).
V. N. Kapshai, M. S. Danil’chenko, and Yu. A. Grishechkin, Probl. Fiz. Mat. Tekh., 22, No. 1, 11–15 (2015).
R. J. Yaes, Phys. Rev. D, 3, No. 12, 3086–3090 (1971).
R. M. Woloshyn and A. D. Jackson, Nucl. Phys. B, 64, 269–288 (1973).
R. G. Newton, Scattering Theory of Waves and Particles, Dover Publications, Mineola; New York (2013).
G. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 1, McGraw-Hill Book Company, New York (1953).
Yu. D. Chernichenko, Russ. Phys. J., 53, No. 11, 1179–1195 (2011).
J. M. Howie, Complex Analysis, Springer Verlag, London (2003).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 44–50, October, 2017.
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Kapshai, V.N., Fialka, S.I. Partial Quasipotential Equations in the Relativistic Configuration Representation. Russ Phys J 60, 1696–1704 (2018). https://doi.org/10.1007/s11182-018-1271-3
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DOI: https://doi.org/10.1007/s11182-018-1271-3