Nucleon-Nucleon Potentials and Computation of Scattering Phase Shifts

Jhasaketan Bhoi, Ujjwal Laha

Abstract

By judicious exploitation of supersymmetry formalism of quantum mechanics higher partial wave nucleon-nucleon potentials are generated from its ground state interactions. The nuclear Hulthen potential and the corresponding ground state wave function with the parameters of Arnold and MacKellar are used as the starting point of our calculation. We compute the scattering phase shifts for our constructed potentials through Phase Function Method to examine the merit of our approach to the problem.

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References

Witten, E. 1981. Dynamical breaking of supersymmetry. Nucl. Phy B, Vol. 188, Page 513-554.

Cooper, F., and Freedman, B. 1983. Aspects of supersymmetric quantum mechanics. Ann. Phys., Vol. 146, Page 262-288.

Sukumar, C. V. 1985. Supersymmetry, factorisation of the Schrödinger equation and a Hamiltonian hierarchy. J. Phys. A: Math. Gen., Vol. 18, L57-64; Supersymmetric quantum mechanics of one-dimensional systems. Vol.18, Page 2917-2939.

Laha, U., Bhattacharyya, C., Roy, K., and Talukdar, B. 1988. Hamiltonian hierarchy and the hulthen Potential. Phys. Rev C, Vol. 38, Page 558-560.

Bhoi, J., and Laha, U. 2013. Hamiltonian hierarchy and n-p scattering. J. Phys. G: Nucl. Part. Phy., Vol. 40, Page 045107(1-7).

Laha, U., and Bhoi, J. 2013. On the nucleon-nucleon scattering phase shifts through supersymmetry and factorization. Pramana-J. Physics, Vol. 81, Page 959-973.

Laha, U., and Bhoi, J. 2015. Two-nucleon Hulthen type interactions for few higher partial waves., Pramana-J Physics, Vol. 84, Page 555-567.

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

Gross, F., and Stadler, A. 2008. Covariant spectator theory of np scattering: Phase shifts obtained from precision fits to data below 350 MeV. Phys. Rev. C, Vol. 78, Page 014005.

Calogero, F. 1967. Variable Phase Approach to Potential Scattering. New York: Academic.

Yamaguchi, Y. 1954. Two nucleon problem when the potential is nonlocal but separable. 1. Phys. Rev., Vol. 95, Page 1628-1634.

Arnold, L. G., and MacKellar, A.D. 1971. Study of Equivalent Local Potentials Obtained from Separable Two-Nucleon Interactions. Phys. Rev. C, Vol. 3, Page 1095-1104.

Talukdar, B., Chatterjee, D., and Banarjee, P. 1977. Phase-amplitude method for a separable non-local Optical potential. J. Phys. G: Nucl. Phys., Vol. 3, Page 813-820.

Sett, G. C., Laha, U., and Talukdar, B. 1988. Phase function method for Coulomb–distorted nuclear Scattering. J. Phys. A: Math. Gen., Vol. 21, Page 3643-3657.

Michel, F., and Reidemeister, G. 1985. Connection between deep- and shallow-type potential descriptions of elastic α particle scattering. J. Phys. G: Nucl. Phys., Vol. 11, Page 835-842.

Baye, D. 1987. Supersymmetry between deep and shallow nucleus-nucleus potentials. Phys. Rev. Lett., Vol. 58, Page 2738-2741.

Ali, S., and Bodmer, A. R. 1966. Phenomenological α-α potentials. Nucl. Phys., Vol. 80, Page 99-112.

Buck, B., Friedrich, H., and Wheatley, C. 1977. Local potential models for the scattering of complex nuclei. Nucl. Phys. A, Vol. 275, Page 246-268.

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