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Nuclear Hulthén Potential and the Scattering Phase Shifts For 𝓁 = 3


Affiliations
1 Department of Physics, National Institute of Technology, Jamshedpur 831 014, India
 

Simple potential models of nuclear Hulthén type are proposed and parameterized to reproduce the nucleon– nucleon scattering phase shifts for the partial wave 𝓁 = 3. The phase shifts are computed utilizing the phase function method for neutron–proton (n–p) and proton–proton (p–p) systems and compared with standard data to judge the merits of our models. Reasonable agreement in phase shifts is achieved with the results of more sophisticated calculations. Particularly, our models reproduce better results for n–p system over the p–p system.

Keywords

Nuclear Potential, Phase Function Method, Scattering Phase Shifts, Partial Wave.
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  • Yukawa, H., On the interaction of elementary particles. Proc. Phys. Math. Soc. Jpn, 1935, 17, 48–57.

  • Taketani, M., Machida, S. and O-Numa, S., The meson theory of nuclear forces, I*: the deuteron ground state and low energy neutron–proton scattering. Prog. Theor. Phys., 1952, 7, 45–56.

  • Brueckner, K. A. and Watson, K. M., Nuclear forces in pseudoscalar meson theory. Phys. Rev., 1953, 92, 1023–1035.

  • Signell, P. S. and Marshak, R. E., Phenomenological two-nucleon potential up to 150 Mev. Phys. Rev., 1957, 106, 832–833.

  • Partovi, M. H. and Lomen, E. L., Field-theoretical nucleon– nucleon potential. Phys. Rev. D, 1970, 2, 1999–2032.

  • Jackson, A. D., Riska, D. O. and Verwest, B., Meson exchange model for the nucleon–nucleon interaction. Nucl. Phys. A, 1975, 249, 397–444.

  • Cottingham, W. N., Lacombe, M., Loiseau, B., Richard, J. M. and Vinh Mau, R., Nucleon–nucleon interaction from pion–nucleon phase-shift analysis. Phys. Rev. D, 1973, 8, 800–819.

  • Nagels, M. M., Rijken, T. A. and de Swart, J. J., Low-energy nucleon–nucleon potential from Reggepole theory. Phys. Rev. D, 1978, 17, 768–776.

  • Machleidt, R., Holinde, K. and Elster, Ch., The Bonn mesonexchange model for the nucleon–nucleon interaction. Phys. Rep., 1987, 149, 1–89.

  • Lacombe, M., Seau, E. L., Richard, J. M., Vinh Mau, Cote, R. J., Pires, P. and de Tourreil, R., Parametrization of the Paris N–N potential. Phys. Rev. C, 1980, 21, 861–873.

  • Stoks, V. G. J., Klomp, R. A. M., Terheggen, C. P. E. and de Swart, J. J., Construction of high-quality NN potential models. Phys. Rev. C, 1994, 49, 2950–2962.

  • Machleidt, R., High-precision, charge-dependent Bonn nucleon– nucleon potential. Phys. Rev. C, 2001, 63, 024001.

  • Gross, F., van Orden, J. W. and Holinde, K., Relativistic oneboson-exchange model for the nucleon–nucleon interaction. Phys. Rev. C, 1992, 45, 2094–2132.

  • Zaitsev, S. A. and Kramar, E. I., NN potentials from inverse scattering in the J-matrix approach. J. Phys. G, 2001, 27, 2037–2050.

  • Bugg, D. et al., Proton–proton elastic scattering from 150 to 515 MeV. J. Phys. G, 1978, 4, 1025–1046.

  • Feshbach, H., Theoretical Nuclear Physics: Nuclear Reactions, Wiley, New York, USA, 1992.

  • Machleidt, R., The meson theory of nuclear forces and nuclear structure. Adv. Nucl. Phys., 1989, 19, 189–376; Machleidt, R. and Slaus, I., The nucleon-nucleon interaction. J. Phys. G, 2001, 27, R69–R108.

  • MacGregor, M. H., Arndt, R. A. and Wright, R. M., Determination of the nucleon–nucleon scattering matrix X(p, p) and (n, p) analysis from 1 to 450 MeV. Phys. Rev., 1969, 182, 1714–1728.

  • Seamon, R. E., Friedman, K. A., Breit, G., Haracz, R. D., Holt, J. M. and Prakash, A., Phenomenological phase–parameter fits to N–N data up to 350 MeV. Phys. Rev., 1969, 165, 1579–1586.

  • Arndt, R. A., Roper, L. D., Bryan, R. A., Clark, R. B., VerWest, B. J. and Signell, P., Nucleon–nucleon partial-wave analysis to 1 GeV. Phys. Rev. D, 1983, 28, 97–122.

  • Allgower, C. E. et al., Angular dependence of the p–p elastic scattering spin correlation parameter A00nn between 0.8 and 2.8 GeV: results for 1.80–2.24 GeV. Phys. Rev. C, 2000, 62, 064001.

  • Bugg, D. V., Nucleon–nucleon physics up to 1 GeV. Annu. Rev. Nucl. Sci., 1985, 35, 295–350.

  • Schwinger, W., Plessas, W., Kok, L. P. and van Haeringen, H., Separable representation of the nuclear proton–proton interaction. Phys. Rev. C, 1983, 27, 515–522.

  • Lechanoine-Leluc, C. and Lehar, F., Nucleon–nucleon elastic scattering and total cross sections. Rev. Mod. Phys., 1993, 65, 47–86.

  • Haidenbauer, J. and Plessas, W., Separable approximations of two-body interactions. Phys. Rev. C, 1983, 27, 63–70.

  • Wiringa, R. B., Stoks, V. G. J. and Schiavilla, R., An Accurate nucleon–nucleon potential with charge independence breaking. Phys. Rev. C, 1995, 51, 38–51.

  • Gross, F. and Stadler, A., Covariant spectator theory of n–p scattering: phase shifts obtained from precision fits to data below 350 MeV. Phys. Rev. C, 2008, 78, 014005.

  • Bhoi, J. and Laha, U., Hamiltonian hierarchy and n–p scattering. J. Phys. G, 2013, 40, 045107.

  • Laha, U. and Bhoi, J., On the nucleon–nucleon scattering phase shifts through supersymmetry and factorization. Pramana – J. Phys., 2013, 81, 959–973.

  • Bhoi, J., Laha, U. and Panda, K. C., Nucleon–nucleon scattering in the light of supersymmetric quantum mechanics. Pramana – J. Phys., 2014, 82, 859–865.

  • Laha, U. and Bhoi, J., Hulthén potential models for α–α and α-He3 elastic scattering. Pramana – J. Phys., 2017, 88, 42.

  • Laha, U. and Bhoi, J., Parameterization of the nuclear Hulthén potentials. Phys. At. Nucl., 2016, 79, 62–66.

  • Calogero, F., Variable Phase Approach to Potential Scattering, Academic Press, New York, USA, 1967.

  • Arnold, L. G. and Mackellar, A. D., Study of equivalent local potentials obtained from separable two-nucleon interactions. Phys. Rev. C, 1971, 3, 1095–1103.

  • Laha, U. and Talukdar, B., Half-shell T matrix for Coulombmodified Graz separable potential. Pramana – J. Phys., 1991, 36, 289–304.

  • Flügge, S., Practical Quantum Mechanics, Springer, Berlin, Germany, 1971.

  • Talukdar, B., Chatterjee, D. and Banarjee, P., A generalized approach to the phase–amplitude method. J. Phys. G, 1977, 3, 813– 820.

  • Laha, U., Haque, N., Nandi, T. and Sett, G. C., Phase-function method for elastic α–α scattering. Z. Phys. A, 1989, 332, 305–309.

  • Sett, G. C., Laha, U. and Talukdar, B., Phase-function method for Coulomb-distorted nuclear scattering. J. Phys. A: Math. Gen., 1988, 21, 3643–3658.


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  • Nuclear Hulthén Potential and the Scattering Phase Shifts For 𝓁 = 3

Abstract Views: 351  |  PDF Views: 81

Authors

U. Laha
Department of Physics, National Institute of Technology, Jamshedpur 831 014, India

Abstract


Simple potential models of nuclear Hulthén type are proposed and parameterized to reproduce the nucleon– nucleon scattering phase shifts for the partial wave 𝓁 = 3. The phase shifts are computed utilizing the phase function method for neutron–proton (n–p) and proton–proton (p–p) systems and compared with standard data to judge the merits of our models. Reasonable agreement in phase shifts is achieved with the results of more sophisticated calculations. Particularly, our models reproduce better results for n–p system over the p–p system.

Keywords


Nuclear Potential, Phase Function Method, Scattering Phase Shifts, Partial Wave.

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DOI: https://doi.org/10.18520/cs%2Fv118%2Fi4%2F582-586