Nucleon-Nucleon Scattering Phase Shifts via Supersymmetry and the Phase Function Method

Abstract

By adapting a suitable ground state interaction for the nucleon-nucleon system, the higher partial wave potentials are derived via a supersymmetry inspired factorization method. The merits of our generated interactions are examined by computing the scattering phase shifts through the judicious use of the phase function method and are compared with the standard results.

Neutron-Proton Scattering Phase Shifts in S-Channel using Phase Function Method for Various Two Term Potentials

“…The first successful theoretical description is given by Yukawa [4] which models the interaction as an exponentially decaying function with 1/r dependence, which typically only has attractive nature. Later many two term potentials, which also include a soft repulsive core, are suggested such as Modified Hulthen [5], Malfliet-Tjon (MT) [6], Manning-Rosen (MR) [7], Eckart [8], Morse [9] and Rosen-Morse [10], etc. The scattering at low energies also requires inclusion of spin and iso-spin dependent potentials for describing long-range interaction.…”

“…Also, vast literature related to scattering phase shift calculations can be found in [13][14][15][16][17][18][19][20][21][22][23][24][25]. Recently there has been renewed interest in the application of phase function method (PFM) [21], [22] also called as Variable Phase Approach (VPA) which has been extensively used by Laha, et al [5], [7]. The advantage of PFM [20], [21] over the former mentioned methods is that it requires only the potential function to obtain the scattering phase shifts without any need for determining the wave-functions.…”

Phase Shift Analysis for Alpha-alpha Elastic Scattering using Phase Function Method for Gaussian Local Potential

“…Typically, these scattering phase-shifts are obtained analytically using either S-matrix [7] or Jost function [8] methods. Recently there has been renewed interest in application of PFM [9,10], also called as Variable Phase Approach (VPA), which has been extensively used by Laha, et al [11][12][13][14][15]. They have applied this technique to study of nucleonnucleon [11], nucleon-nucleus [14] and nucleus-nucleus [15] scattering using a variety of two term potentials such as modified Hulthen [12] and Manning-Rosen [13].…”

“…Recently there has been renewed interest in application of PFM [9,10], also called as Variable Phase Approach (VPA), which has been extensively used by Laha, et al [11][12][13][14][15]. They have applied this technique to study of nucleonnucleon [11], nucleon-nucleus [14] and nucleus-nucleus [15] scattering using a variety of two term potentials such as modified Hulthen [12] and Manning-Rosen [13]. While traditional S-matrix approaches depend on wave-functions obtained by solving TISE, PFM requires only potential function to obtain the scattering phase shifts.…”

Triton Scattering Phase-Shifts for S-wave using Morse Potential

“…In the next section, we give a brief description of simulation methodology given by D. Hestenes [6], utilising the numerical method of matrix diagonalisation [7] in tandem with variational Monte-Carlo [8] to obtain the ground state of Triton, thus abstracting the Morse potential with best fit parameters that model the interaction. This is utilised in the non-linear differential equation [NDE] governing the scattering phase-shifts as obtained from variable phase approach (VPA) [9,10] or equivalent phase function method (PFM) [11,12]. The RK-4,5 numerical method is implemented in Scilab, a free open source software (FOSS) to solve the NDE and obtain the scattering phase-shifts at various lab energies.…”