Abstract
The analytic structure of the non-relativistic unitary and non-unitary S-matrix is investigated for the cases of the unknown interactions with the unknown motion equations inside a sphere of radius a, surrounded by the centrifugal and rapidly decreasing (exponentially or by the Yukawian law or by the more rapidly decreasing) potentials. The one-channel case and special examples of many-channel cases are considered. Some kinds of symmetry conditions are imposed. The Schroedinger equation for r > a for the particle motion and the condition of the completeness of the correspondent wave functions are assumed. The connection of the obtained results with the usual (temporal) causality is examined. Finally a scientific program is presented as a clear continuation and extension of the obtained results.
[1] W. Heisenberg, Z. Phys. A-Hadron Nucl. 120, 513 (1943) 10.1007/BF01329800Search in Google Scholar
[2] W. Heisenberg, Z. Phys. A-Hadron Nucl. 120, 673 (1943) 10.1007/BF01336936Search in Google Scholar
[3] W. Heisenberg, Z. Naturforsch. Pt A 1, 608 (1946) 10.1515/zna-1946-11-1202Search in Google Scholar
[4] C. Moeller, Mat. Fys. Medd. Dan. Vid. 23, N1 (1945) Search in Google Scholar
[5] C. Moeller, Mat. Fys. Medd. Dan. Vid. 22, N19 (1946) Search in Google Scholar
[6] N. Hu, Phys. Rev. 74, 131 (1948) http://dx.doi.org/10.1103/PhysRev.74.13110.1103/PhysRev.74.131Search in Google Scholar
[7] N. Van Kampen, Phys. Rev. 89, 1072 (1953) http://dx.doi.org/10.1103/PhysRev.89.107210.1103/PhysRev.89.1072Search in Google Scholar
[8] N. Van Kampen, Phys. Rev. 91, 1267 (1953) http://dx.doi.org/10.1103/PhysRev.91.126710.1103/PhysRev.91.1267Search in Google Scholar
[9] V.S. Olkhovsky, Yu.V. Tsekhmistrenko, Ukrainian Physical Journal 6, 149 (1961) (in Ukrainian, abstract in English; partially in English) Search in Google Scholar
[10] V.S. Olkhovsky, Theor. Math. Phys.+ 20, 211 (1974) Search in Google Scholar
[11] V.S. Olkhovsky, Ukrainian Physical Journal 22, 752 (1977) (in Ukrainian, abstract in English) Search in Google Scholar
[12] M.V. Nikolayev, V.S. Olkhovsky, Theor. Math. Phys.+ 31, 214 (1977) Search in Google Scholar
[13] M.V. Nikolayev, V.S. Olkhovsky, Lett. Nuovo Cimento 8, 703 (1973) http://dx.doi.org/10.1007/BF0272530710.1007/BF02725307Search in Google Scholar
[14] V.S. Olkhovsky, A.K. Zaichenko, Nuovo Cimento A63, 155 (1981) 10.1007/BF02902667Search in Google Scholar
[15] V.S. Olkhovsky, DSc thesis, defended in Kiev Institute of Nuclear Research (National Academy of Sciences of the Ukraine) and confirmed in the Highest Attestation Committee for the Scientific Degree of the USSR in Moscow (Kiev-Moscow, Ukraine-USSR, 1989) Search in Google Scholar
[16] M. Baldo, V.S. Olkhovsky, Theor. Math. Phys.+ 147, 539 (2006) 10.1007/s11232-006-0061-1Search in Google Scholar
[17] I. Saavedra, Nucl. Phys. 29, 137 (1962) http://dx.doi.org/10.1016/0029-5582(62)90172-410.1016/0029-5582(62)90172-4Search in Google Scholar
[18] I. Saavedra, Nucl. Phys. 87, 267 (1966) http://dx.doi.org/10.1016/0029-5582(66)90286-010.1016/0029-5582(66)90286-0Search in Google Scholar
[19] R. Newton, Scattering Theory of Waves and Particles (McGraw-Hill Book Company, New York-San Francisco-St.Louis-Toronto-London-Sydney, 1969) Search in Google Scholar
[20] M.G. Gasymov, Dokl. Akad. Nauk SSSR+ 165, 261 (1965) Search in Google Scholar
[21] M. Bertero, G. Dillon, Nuovo Cimento A2, 1024 (1971) 10.1007/BF02826490Search in Google Scholar
[22] V. De Alfaro, T. Redge, Potential scattering (North-Holland Publish. Company, Amsterdam, 1965) Search in Google Scholar
[23] E.C. Titchmarsh, The Theory of Functions (Oxford University Press, Oxford, 1939) Search in Google Scholar
[24] R. Jost, Helv. Phys. Acta 20, 256 (1947) Search in Google Scholar
[25] S. Ma, Phys. Rev. 71, 195 (1947) http://dx.doi.org/10.1103/PhysRev.71.19510.1103/PhysRev.71.195Search in Google Scholar
[26] I.S. Gradstein, I.M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Acad. Press, New York, 1965) Search in Google Scholar
[27] A.S. Davydov, Theory of atomic nucleus (Fizmatgiz, Moscow, 1958) (in Russian) Search in Google Scholar
[28] Yu.V. Tsekhmistrenko, ZhETPh 38, 1237 (1960) 10.1139/v60-175Search in Google Scholar
[29] A.I. Baz’, A.M. Perelomov, Ya.B. Zel’dovich, Scattering, reactions and decays in non-relativistic quantum mechanics (Israel Program for Scientific Translations, Jerusalem, 1969) Search in Google Scholar
[30] Yu.V. Tsekhmistrenko, Ukt. Fiz. Zh.+ 13, 1192 (1968) Search in Google Scholar
[31] P.A. Moldauer, Phys. Rev. B135, 642 (1964) http://dx.doi.org/10.1103/PhysRev.135.B64210.1103/PhysRev.135.B642Search in Google Scholar
[32] P.A. Moldauer, Phys. Rev. B136, 957 (1964) 10.1103/PhysRev.136.B947Search in Google Scholar
[33] P.A. Moldauer, Phys. Rev. C11, 426 (1975) 10.1103/PhysRevC.11.426Search in Google Scholar
[34] C. Mahaux, H.A. Weidenmueller, Annu. Rev. Nucl. Part. S. 29, 1 (1979) http://dx.doi.org/10.1146/annurev.ns.29.120179.00024510.1146/annurev.ns.29.120179.000245Search in Google Scholar
[35] T. Brody et al., Rev. Mod. Phys. 53, 385 (1981) http://dx.doi.org/10.1103/RevModPhys.53.38510.1103/RevModPhys.53.385Search in Google Scholar
[36] A.M. Lane R.G. Thomas, Rev. Mod. Phys. 30, 257 (1958) http://dx.doi.org/10.1103/RevModPhys.30.25710.1103/RevModPhys.30.257Search in Google Scholar
[37] C. Mahaux, H.A. Weidenmueller, Shell-model approach to nuclear reactions (North-Holland Publish. Company, Asterdam-London, 1969) Search in Google Scholar
[38] J. Richert, M.H. Simbel, H.A. Weidenmueller, Z. Phys. A273, 195 (1975) 10.1007/BF01435839Search in Google Scholar
[39] H.M. Hoffmann, J. Richert, J.W. Tepel, H.A. Weidenmueller, Ann. Phys. 90, 403 (1975) http://dx.doi.org/10.1016/0003-4916(75)90005-610.1016/0003-4916(75)90005-6Search in Google Scholar
[40] M. Simonius, Nucl. Phys. A218, 53 (1974) 10.1016/0375-9474(74)90019-0Search in Google Scholar
[41] V.L. Lyuboshitz, Phys. Lett. B72, 41 (1977) 10.1016/0370-2693(77)90058-2Search in Google Scholar
[42] V.S. Olkhovsky, Sov. J. Nucl. Phys.+ 37, 350 (1983) Search in Google Scholar
[43] A. D’Arrigo, G. Giardina, A. Taccone, G. Hassani, V.S. Olkhovsky, Int. J. Mod. Phys. E 2, 809 (1993) http://dx.doi.org/10.1142/S021830139300035210.1142/S0218301393000352Search in Google Scholar
[44] V.S. Olkhovsky, M.D. Dolinska, S.A. Omelchenko, Cent. Eur. J. Phys. 4, 1 (2006) http://dx.doi.org/10.2478/s11534-006-0008-z10.2478/s11534-006-0008-zSearch in Google Scholar
[45] V.S. Olkhovsky, Nucl. Phys. A425, 445 (1984) 10.1016/0375-9474(84)90018-6Search in Google Scholar
[46] V.S. Olkhovsky, Nuovo Cimento A4, 605 (1971) 10.1007/BF02731376Search in Google Scholar
[47] V.S. Olkhovsky, Sov. J. Part. Nucl. 15, 130 (1984) Search in Google Scholar
[48] V.S. Olkhovsky, E. Recami, Int. J. Mod. Phys. A 15, 5063 (2007) http://dx.doi.org/10.1142/S0217751X0703724X10.1142/S0217751X0703724XSearch in Google Scholar
[49] H.M. Nussenzweig, Causality and dispersion relations (Academic Press, New York and London, 1972) Search in Google Scholar
[50] V.S. Olkhovsky, N.L. Doroshko, Europhys. Lett. 18, 483 (1992) http://dx.doi.org/10.1209/0295-5075/18/6/00210.1209/0295-5075/18/6/002Search in Google Scholar
[51] A. D’Arrigo et al., Nucl. Phys. A 549, 375 (1992) Search in Google Scholar
[52] A. D’Arrigo et al., Nucl. Phys. A 564, 217 (1993) http://dx.doi.org/10.1016/0375-9474(93)90518-310.1016/0375-9474(93)90518-3Search in Google Scholar
[53] N.V. Eremin, G. Giardina, V.S. Olkhovsky, S.A. Omelchenko, Mod. Phys. Lett. A 9, 2849 (1994) http://dx.doi.org/10.1142/S021773239400269010.1142/S0217732394002690Search in Google Scholar
[54] V.S. Olkhovsky, M.E. Dolinska, S.A. Omelchenko, M.V. Romanyuk, New developments in the tunneling and time analysis of low-energy nuclear processes, in: Abstracts of the International Conf. Nuclear Reactions on Nucleons and Nuclei, 5–9 October 2009, Messina, Italy (Edition of the Messina University, Messina, 2009) 63 (to be published as a complete text in Proceedings of this conference in a special issue of Int. J. Mod. Phys. E., in 2010) Search in Google Scholar
[55] N.N. Bogolyubov, B.V. Medvedev, M.K. Polivanov, Problems of Modern Physics 2, 3 (1957) Search in Google Scholar
[56] N.N. Bogolyubov, B.V. Medvedev, M.K. Polivanov, Problems of theory of dispersion relations (Fizmatgiz, Moscow, 1958) (in Russian) Search in Google Scholar
[57] D.V. Shirkov, V.V. Serebryakov, V.A. Meshchereryakov, Dispersive theories of strong interactions at low energies (Nauka, Moscow, 1967) Search in Google Scholar
[58] J.G. Taylor, Lectures on Dispersion Relations in Quantum Field Theory and Related Topics (Univ.of Maryland, New Issue, 1959) Search in Google Scholar
[59] T.-Y. Wu, T. Ohmura, Quantum Theory of Scattering (Prentice-Hall Inc., New York, 1962) Search in Google Scholar
[60] I.E. Kashuba, V.S. Olkhovsky, Izv. An. SSSR Fiz.+ 53, 134 (1989) (in Russian) Search in Google Scholar
[61] I.E. Kashuba, V.S. Olkhovsky, Ukr. Fiz. Zh.+ 36, 651 (1991) Search in Google Scholar
[62] I.E. Kashuba et al., Sov. J. Nucl. Phys.+ 55, 68 (1992) Search in Google Scholar
© 2010 Versita Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
