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Description of scattering and of a bound state in the two-nucleon system on the basis of the Bargmann representation of the S matrix

  • Nuclei
  • Theory
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Abstract

For the effective-range function kcotδ, a pole approximation that involves a small number of parameters is derived on the basis of the Bargmann representation of the S matrix. The parameters of this representation, which have a clear physical meaning, are related to the parameters of the Bargmann S matrix by simple equations. By using a polynomial least squares fit to the function kcotδ at low energies, the triplet low-energy parameters of neutron-proton scattering are obtained for the latest experimental data of Arndt’s group on phase shifts. The results are a t = 5.4030 fm, r t = 1.7494 fm, and v 2 = 0.163 fm3. With allowance for the values found for the low-energy parameters and for the pole parameter, the pole approximation of the function kcotδ provides an excellent description of the triplet phase shift for neutron-proton scattering over a wide energy range (T lab ≲ 1000 MeV), substantially improving the description at low energies as well. For the experimental phase shifts of Arndt’s group, the triplet shape parameters v n of the effective-range expansion are obtained by using the pole approximation. It turns out that they are positive and decrease with increasing n. The description of the phase shift by means of the effective-range expansion featuring values found for the low-energy parameters of scattering proves to be fairly accurate over a broad energy region extending to energy values approximately equal to the energy at which this phase shift changes sign, this being indicative of a high accuracy and a considerable value of the effective-range expansion in describing experimental data on nucleon-nucleon scattering. The properties of the deuteron that were calculated by using various approximations of the effective-range function comply well with their experimental values.

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References

  1. A. G. Sitenko, Scattering Theory (Springer-Verlag, Berlin, 1991).

    Google Scholar 

  2. W. Heisenberg, Z. Phys. 120, 513 (1943).

    MATH  MathSciNet  Google Scholar 

  3. R. Jost, Helv. Phys. Acta 20, 256 (1947).

    MathSciNet  Google Scholar 

  4. R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Springer-Verlag, New York, 1982; Mir, Moscow, 1969).

    Google Scholar 

  5. V. A. Babenko and N. M. Petrov, Yad. Fiz. 63, 1798 (2000) [Phys. At. Nucl. 63, 1709 (2000)].

    Google Scholar 

  6. V. V. Malyarov and M. N. Popushoi, Yad. Fiz. 18, 1140 (1973) [Sov. J. Nucl. Phys. 18, 586 (1973)].

    Google Scholar 

  7. B. N. Zakhar’ev, V. N. Pivovarchik, E. B. Plekhanov, and A. A. Suz’ko, Fiz. Élem. Chastits At. Yadra 13, 1284 (1982) [Sov. J. Part. Nucl. 13, 535 (1982)].

    MathSciNet  Google Scholar 

  8. B. N. Zakhar’ev, Yu. P. Nikishov, and E. B. Plekhanov, Yad. Fiz. 38, 95 (1983) [Sov. J. Nucl. Phys. 38, 54 (1983)].

    Google Scholar 

  9. V. Bargmann, Rev. Mod. Phys. 21, 488 (1949).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  10. W. T. H. van Oers and J. D. Seagrave, Phys. Lett. B 24B, 562 (1967).

    ADS  Google Scholar 

  11. G. A. Baker, Jr. and P. Graves-Morris, Padé Approximants (Addison-Wesley, London, 1981).

    Google Scholar 

  12. F. Lambert, O. Corbella, and Z. D. Thome, Nucl. Phys. B 90, 267 (1975).

    Article  ADS  Google Scholar 

  13. K. Hartt, Phys. Rev. C 22, 1377 (1980).

    Article  ADS  Google Scholar 

  14. K. Hartt, Phys. Rev. C 23, 2399 (1981).

    Article  ADS  Google Scholar 

  15. K. Hartt, Bull. Am. Phys. Soc. 23, 630 (1978).

    Google Scholar 

  16. V. G. Neudatchin, I. T. Obukhovsky, V. I. Kukulin, and N. F. Golovanova, Phys. Rev. C 11, 128 (1975).

    Article  ADS  Google Scholar 

  17. V. G. Neudatchin, I. T. Obukhovsky, and Yu. F. Smirnov, Fiz. Élem. Chastits At. Yadra 15, 1165 (1984) [Sov. J. Part. Nucl. 15, 519 (1984)].

    Google Scholar 

  18. V. I. Kukulin, V. M. Krasnopol’skii, V. N. Pomerantsev, and P. B. Sazonov, Yad. Fiz. 43, 559 (1986) [Sov. J. Nucl. Phys. 43, 355 (1986)].

    Google Scholar 

  19. M. Cini, S. Fubini, and A. Stanghellini, Phys. Rev. 114, 1633 (1959).

    Article  ADS  Google Scholar 

  20. R. S. Christian and J. L. Gammel, Phys. Rev. 91, 100 (1953).

    Article  ADS  Google Scholar 

  21. L. M. Delves, Phys. Rev. 118, 1318 (1960).

    Article  ADS  Google Scholar 

  22. A. S. Reiner, Phys. Lett. B 28B, 387 (1969).

    ADS  Google Scholar 

  23. J. S. Whiting and M. G. Fuda, Phys. Rev. C 14, 18 (1976).

    Article  ADS  Google Scholar 

  24. V. E. Kuz’michev, Ukr. Fiz. Zh. (Russ. Ed.) 23, 188 (1978).

    Google Scholar 

  25. B. A. Girard and M. G. Fuda, Phys. Rev. C 19, 579 (1979).

    ADS  Google Scholar 

  26. S. A. Adhikari and J. R. A. Torreao, Phys. Lett. B 132B, 257 (1983).

    ADS  Google Scholar 

  27. I. V. Simenog, A. I. Sitnichenko, and D. V. Shapoval, Yad. Fiz. 45, 60 (1987) [Sov. J. Nucl. Phys. 45, 37 (1987)].

    Google Scholar 

  28. C. R. Chen, G. L. Payne, J. L. Friar, and B. F. Gibson, Phys. Rev. C 39, 1261 (1989).

    ADS  Google Scholar 

  29. Yu. V. Orlov and L. I. Nikitina, Yad. Fiz. 61, 833 (1998) [Phys. At. Nucl. 61, 750 (1998)].

    Google Scholar 

  30. Yu. V. Orlov, Yu. P. Orevkov, and L. I. Nikitina, Yad. Fiz. 65, 396 (2002) [Phys. At. Nucl. 65, 371 (2002)].

    Google Scholar 

  31. D. Y. Wong and H. P. Noyes, Phys. Rev. 126, 1866 (1962).

    ADS  Google Scholar 

  32. H. P. Noyes, Phys. Rev. 130, 2025 (1963).

    Article  ADS  Google Scholar 

  33. H. P. Noyes, Annu. Rev. Nucl. Sci. 22, 465 (1972).

    Article  ADS  Google Scholar 

  34. L. Mathelitsch and B. J. VerWest, Phys. Rev. C 29, 739 (1984).

    Article  ADS  Google Scholar 

  35. J. R. Bergervoet, P. C. van Campen, W. A. van der Sanden, and J. J. de Swart, Phys. Rev. C 38, 15 (1988).

    ADS  Google Scholar 

  36. V. M. Galitsky, B. M. Karnakov, and V. I. Kogan, Problems in Quantum Mechanics (Nauka, Moscow, 1992) [in Russian].

    Google Scholar 

  37. J. M. Blatt and J. D. Jackson, Phys. Rev. 76, 18 (1949).

    Article  ADS  Google Scholar 

  38. L. Hulthén and M. Sugawara, in Handbuch der Physik, Ed. by S. Flügge (Springer-Verlag, New York, Berlin, 1957), p. 1.

    Google Scholar 

  39. R. A. Arndt, W. J. Briscoe, R. L. Workman, and I. I. Strakovsky, Partial-Wave Analysis Facility SAID [http://gwdac.phys.gwu.edu].

  40. T. D. Cohen and J. M. Hansen, Phys. Rev. C 59, 13 (1999).

    ADS  Google Scholar 

  41. T. D. Cohen and J. M. Hansen, Phys. Rev. C 59, 3047 (1999).

    ADS  Google Scholar 

  42. R. Wilson, The Nucleon-Nucleon Interaction (Interscience, New York, 1963).

    Google Scholar 

  43. T. L. Houk and R. Wilson, Rev. Mod. Phys. 39, 546 (1967).

    Article  ADS  Google Scholar 

  44. T. L. Houk, Phys. Rev. C 3, 1886 (1971).

    Article  ADS  Google Scholar 

  45. E. L. Lomon and R. Wilson, Phys. Rev. C 9, 1329 (1974).

    Article  ADS  Google Scholar 

  46. W. Dilg, Phys. Rev. C 11, 103 (1975).

    Article  ADS  Google Scholar 

  47. M. W. Kermode, A. McKerrell, J. P. McTavish, and L. J. Allen, Z. Phys. A 303, 167 (1981).

    Google Scholar 

  48. C. W. Wong, Nucl. Phys. A 536, 269 (1992).

    ADS  Google Scholar 

  49. W. van Dijk, M. W. Kermode, and D.-C. Zheng, Phys. Rev. C 47, 1898 (1993).

    ADS  Google Scholar 

  50. J. J. de Swart, C. P. F. Terheggen, and V. G. J. Stoks, Invited Talk at the 3rd International Symposium “Dubna Deuteron 95,” Dubna, Russia, July 4–7, 1995; nucl-th/9509032.

  51. M. W. Kermode, S. A. Moszkowski, M. M. Mustafa, and W. van Dijk, Phys. Rev. C 43, 416 (1991).

    Article  ADS  Google Scholar 

  52. D. W. L. Sprung, in Proceedings of IX European Conference on Few-Body Problems in Physics, Tbilisi, Georgia, USSR, Aug. 1984 (World Sci., Singapore, Philadelphia, 1984), p. 234.

    Google Scholar 

  53. S. Klarsfeld, J. Martorell, J. A. Oteo, et al., Nucl. Phys. A 456, 373 (1986).

    ADS  Google Scholar 

  54. D. W. L. Sprung, H. Wu, and J. Martorell, Phys. Rev. C 42, 863 (1990).

    Article  ADS  Google Scholar 

  55. R. K. Bhaduri, W. Leidemann, G. Orlandini, and E. L. Tomusiak, Phys. Rev. C 42, 1867 (1990).

    Article  ADS  Google Scholar 

  56. V. A. Babenko and N. M. Petrov, Yad. Fiz. 66, 1359 (2003) [Phys. At. Nucl. 66, 1319 (2003)].

    Google Scholar 

  57. http://nn-online.sci.kun.nl

  58. R. V. Reid, Jr., Ann. Phys. (N.Y.) 50, 411 (1968).

    Article  Google Scholar 

  59. O. Dumbrajs, R. Koch, H. Pilkuhn, et al., Nucl. Phys. B 216, 277 (1983).

    Article  ADS  Google Scholar 

  60. G. L. Squires and A. T. Stewart, Proc. R. Soc. London, Ser. A 230, 19 (1955).

    ADS  Google Scholar 

  61. G. E. Brown and A. D. Jackson, The Nucleon-Nucleon Interaction (North-Holland, Amsterdam, 1976).

    Google Scholar 

  62. H. P. Noyes and D. Y. Wong, Phys. Rev. Lett. 3, 191 (1959).

    Article  ADS  Google Scholar 

  63. T. E. O. Ericson, Nucl. Phys. A 416, 281 (1984).

    ADS  Google Scholar 

  64. G. L. Greene, E. G. Kessler, Jr., R. D. Deslattes, and H. Boerner, Phys. Rev. Lett. 56, 819 (1986).

    Article  ADS  Google Scholar 

  65. I. Borbély, W. Grüebler, V. König, et al., Phys. Lett. B 160B, 17 (1985).

    ADS  Google Scholar 

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  1. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Metrologicheskaya ul. 14b, Kiev, 03143, Ukraine

    V. A. Babenko & N. Petrov

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  1. V. A. Babenko
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__________

Translated from Yadernaya Fizika, Vol. 68, No. 2, 2005, pp. 244–258.

Original Russian Text Copyright © 2005 by Babenko, Petrov.

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Babenko, V.A., Petrov, N. Description of scattering and of a bound state in the two-nucleon system on the basis of the Bargmann representation of the S matrix. Phys. Atom. Nuclei 68, 219–233 (2005). https://doi.org/10.1134/1.1866377

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