PL EN


Preferences help
enabled [disable] Abstract
Number of results
Journal
2011 | 9 | 1 | 13-44
Article title

On the analytic properties of the S-matrix for the unknown interactions surrounded by centrifugal and rapidly decreasing potentials

Content
Title variants
Languages of publication
EN
Abstracts
EN
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.
Publisher

Journal
Year
Volume
9
Issue
1
Pages
13-44
Physical description
Dates
published
1 - 2 - 2011
online
24 - 9 - 2010
Contributors
  • Institute for Nuclear Research of NASU, prospekt Nauki, 47, Kiev, 03028, Ukraine, Olkhovsky@mail.ru
References
  • [1] W. Heisenberg, Z. Phys. A-Hadron Nucl. 120, 513 (1943)
  • [2] W. Heisenberg, Z. Phys. A-Hadron Nucl. 120, 673 (1943)
  • [3] W. Heisenberg, Z. Naturforsch. Pt A 1, 608 (1946)
  • [4] C. Moeller, Mat. Fys. Medd. Dan. Vid. 23, N1 (1945)
  • [5] C. Moeller, Mat. Fys. Medd. Dan. Vid. 22, N19 (1946)
  • [6] N. Hu, Phys. Rev. 74, 131 (1948) http://dx.doi.org/10.1103/PhysRev.74.131[Crossref]
  • [7] N. Van Kampen, Phys. Rev. 89, 1072 (1953) http://dx.doi.org/10.1103/PhysRev.89.1072[Crossref]
  • [8] N. Van Kampen, Phys. Rev. 91, 1267 (1953) http://dx.doi.org/10.1103/PhysRev.91.1267[Crossref]
  • [9] V.S. Olkhovsky, Yu.V. Tsekhmistrenko, Ukrainian Physical Journal 6, 149 (1961) (in Ukrainian, abstract in English; partially in English)
  • [10] V.S. Olkhovsky, Theor. Math. Phys.+ 20, 211 (1974)
  • [11] V.S. Olkhovsky, Ukrainian Physical Journal 22, 752 (1977) (in Ukrainian, abstract in English)
  • [12] M.V. Nikolayev, V.S. Olkhovsky, Theor. Math. Phys.+ 31, 214 (1977)
  • [13] M.V. Nikolayev, V.S. Olkhovsky, Lett. Nuovo Cimento 8, 703 (1973) http://dx.doi.org/10.1007/BF02725307[Crossref]
  • [14] V.S. Olkhovsky, A.K. Zaichenko, Nuovo Cimento A63, 155 (1981)
  • [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)
  • [16] M. Baldo, V.S. Olkhovsky, Theor. Math. Phys.+ 147, 539 (2006)
  • [17] I. Saavedra, Nucl. Phys. 29, 137 (1962) http://dx.doi.org/10.1016/0029-5582(62)90172-4[Crossref]
  • [18] I. Saavedra, Nucl. Phys. 87, 267 (1966) http://dx.doi.org/10.1016/0029-5582(66)90286-0[Crossref]
  • [19] R. Newton, Scattering Theory of Waves and Particles (McGraw-Hill Book Company, New York-San Francisco-St.Louis-Toronto-London-Sydney, 1969)
  • [20] M.G. Gasymov, Dokl. Akad. Nauk SSSR+ 165, 261 (1965)
  • [21] M. Bertero, G. Dillon, Nuovo Cimento A2, 1024 (1971)
  • [22] V. De Alfaro, T. Redge, Potential scattering (North-Holland Publish. Company, Amsterdam, 1965)
  • [23] E.C. Titchmarsh, The Theory of Functions (Oxford University Press, Oxford, 1939)
  • [24] R. Jost, Helv. Phys. Acta 20, 256 (1947)
  • [25] S. Ma, Phys. Rev. 71, 195 (1947) http://dx.doi.org/10.1103/PhysRev.71.195[Crossref]
  • [26] I.S. Gradstein, I.M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Acad. Press, New York, 1965)
  • [27] A.S. Davydov, Theory of atomic nucleus (Fizmatgiz, Moscow, 1958) (in Russian)
  • [28] Yu.V. Tsekhmistrenko, ZhETPh 38, 1237 (1960)
  • [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)
  • [30] Yu.V. Tsekhmistrenko, Ukt. Fiz. Zh.+ 13, 1192 (1968)
  • [31] P.A. Moldauer, Phys. Rev. B135, 642 (1964) http://dx.doi.org/10.1103/PhysRev.135.B642[Crossref]
  • [32] P.A. Moldauer, Phys. Rev. B136, 957 (1964)
  • [33] P.A. Moldauer, Phys. Rev. C11, 426 (1975)
  • [34] C. Mahaux, H.A. Weidenmueller, Annu. Rev. Nucl. Part. S. 29, 1 (1979) http://dx.doi.org/10.1146/annurev.ns.29.120179.000245[Crossref]
  • [35] T. Brody et al., Rev. Mod. Phys. 53, 385 (1981) http://dx.doi.org/10.1103/RevModPhys.53.385[Crossref]
  • [36] A.M. Lane R.G. Thomas, Rev. Mod. Phys. 30, 257 (1958) http://dx.doi.org/10.1103/RevModPhys.30.257[Crossref]
  • [37] C. Mahaux, H.A. Weidenmueller, Shell-model approach to nuclear reactions (North-Holland Publish. Company, Asterdam-London, 1969)
  • [38] J. Richert, M.H. Simbel, H.A. Weidenmueller, Z. Phys. A273, 195 (1975)
  • [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)90005-6[Crossref]
  • [40] M. Simonius, Nucl. Phys. A218, 53 (1974)
  • [41] V.L. Lyuboshitz, Phys. Lett. B72, 41 (1977)
  • [42] V.S. Olkhovsky, Sov. J. Nucl. Phys.+ 37, 350 (1983)
  • [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/S0218301393000352[Crossref]
  • [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-z[Crossref]
  • [45] V.S. Olkhovsky, Nucl. Phys. A425, 445 (1984)
  • [46] V.S. Olkhovsky, Nuovo Cimento A4, 605 (1971)
  • [47] V.S. Olkhovsky, Sov. J. Part. Nucl. 15, 130 (1984)
  • [48] V.S. Olkhovsky, E. Recami, Int. J. Mod. Phys. A 15, 5063 (2007) http://dx.doi.org/10.1142/S0217751X0703724X[Crossref]
  • [49] H.M. Nussenzweig, Causality and dispersion relations (Academic Press, New York and London, 1972)
  • [50] V.S. Olkhovsky, N.L. Doroshko, Europhys. Lett. 18, 483 (1992) http://dx.doi.org/10.1209/0295-5075/18/6/002[Crossref]
  • [51] A. D’Arrigo et al., Nucl. Phys. A 549, 375 (1992)
  • [52] A. D’Arrigo et al., Nucl. Phys. A 564, 217 (1993) http://dx.doi.org/10.1016/0375-9474(93)90518-3[Crossref]
  • [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/S0217732394002690[Crossref]
  • [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)
  • [55] N.N. Bogolyubov, B.V. Medvedev, M.K. Polivanov, Problems of Modern Physics 2, 3 (1957)
  • [56] N.N. Bogolyubov, B.V. Medvedev, M.K. Polivanov, Problems of theory of dispersion relations (Fizmatgiz, Moscow, 1958) (in Russian)
  • [57] D.V. Shirkov, V.V. Serebryakov, V.A. Meshchereryakov, Dispersive theories of strong interactions at low energies (Nauka, Moscow, 1967)
  • [58] J.G. Taylor, Lectures on Dispersion Relations in Quantum Field Theory and Related Topics (Univ.of Maryland, New Issue, 1959)
  • [59] T.-Y. Wu, T. Ohmura, Quantum Theory of Scattering (Prentice-Hall Inc., New York, 1962)
  • [60] I.E. Kashuba, V.S. Olkhovsky, Izv. An. SSSR Fiz.+ 53, 134 (1989) (in Russian)
  • [61] I.E. Kashuba, V.S. Olkhovsky, Ukr. Fiz. Zh.+ 36, 651 (1991)
  • [62] I.E. Kashuba et al., Sov. J. Nucl. Phys.+ 55, 68 (1992)
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-010-0030-z
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.