Abstract
The phase shifts for α- α scattering have been modeled using a two parameter Gaussian local potential. The time independent Schrodinger equation (TISE) has been solved iteratively using Monte-Carlo approach till the S and D bound states of the numerical solution match with the experimental binding energy data in a variational sense. The obtained potential with best fit parameters is taken as input for determining the phase-shifts for the S channel using the non-linear first order differential equation of the phase function method (PFM). It is numerically solved using 5th order Runge-Kutta (RK-5) technique. To determine the phase shifts for the ℓ=2 and 4 scattering state i.e. D and G-channel, the inversion potential parameters have been determined using variational Monte-Carlo (VMC) approach to minimize the realtive mean square error w.r.t. the experimental data.
Highlights
Modeling the α-α interaction using local potentials in a phenomenological approach [1] has been found to be able to reproduce the scattering data [2] quite well
Buck [1] and his collaborators have argued at length as to how the microscopic resonating group methods (RGM) could be reduced to orthogonal condition model (OCM) by using simple factorization assumption, which in turn makes local potentials to be used as a plausible model
We conclude that α-α scattering phase shifts for S, D and G channels are in good fit with experimental data up to 23 MeV of laboratory energy using three parameter Gaussian local potential along with Coulomb potential defined through an erf function
Summary
Modeling the α-α interaction using local potentials in a phenomenological approach [1] has been found to be able to reproduce the scattering data [2] quite well. Myagmarjav et al [6] calculated the scattering cross section for various potential systems for α-α using complex scaling method (CSM) These scattering phase-shifts are obtained analytically using either S-matrix [7] or Jost function [8] methods. There has been renewed interest in application of PFM [9, 10], 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]. We solve TISE for obtaining bound state energies using matrix methods (MM) with sine basis [16,17,18,19], while on the other hand, the model parameters are optimized using variational Monte-Carlo (VMC) as proposed in [16,17,18,19], in tandem
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