Analytical Solutions for Velocity-Dependent Nuclear Potentials

Abstract

The two-nucleon potential, with the necessary invariance requirements, is assumed to be a quadratic function of momentum: v= -VoJi(r) -(\/M) p-^Wp, where Ji(r) and J%(r) are two short-range functions. For simplicity -Ji{r) is assumed to be a square well of unit depth. The Schrodinger equation is solved (neglecting Coulomb forces) for three different choices of Ji (r). Numerical results for the phase shifts are given for these three potentials (vi, v 2 , and v$) for the singlet S, D, and G states. Reasonably good fits are obtained.

Exact solvability of potentials with spatially dependent effective masses

“…There are many examples of physically important systems, for which such ambiguity is quite relevant. For instance we can cite the problem of impurities in crystals [17][18] [19], the dependence of nuclear forces on the relative velocity of the two nucleons [20] [21], and more recently the study of semiconductor heterostructures [22] [23]. A very important example of ordering ambiguity is that of the minimal coupling in systems of charged particles interacting with magnetic fields [24].…”

Supersymmetric Approach to Exactly Solvable Systems With Position-Dependent Effective Masses

“…There are many examples of physically important systems, for which such ambiguity is quite relevant. For instance we can cite the problem of impurities in crystals [4,5,6], the dependence of nuclear forces on the relative velocity of the two nucleons [7,8], the minimal coupling problem in systems of charged particles interacting with magnetic fields [9], and more recently the study of semiconductor heterostructures [1,10,11].…”

Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

“…This kind of potential was first proposed in order to describe the large backward scattering of mesons from the complex nuclei, and to explain the p-wave nature of elementary pion-nucleon coherent scattering in nuclear physics [1]. The velocity-dependent potentials were also used for modeling nucleon-nucleon interaction, and the 1 S, 1 D, 1 G singlet-even phase shifts were re-produced well [2]. Furthermore, in order to describe the single-particle energy levels of the neutron in the nuclei, the velocity-dependent potentials, which have the Wood-Saxon type form factor, were used, and the velocitydependent effective potential was fitted by using the Morse function, in order to obtain the analytical energy eigenvalue equation of the neutron in the nuclei [3].…”