Simulation study of nuclear shell model using sine basis

Sharma

Gora

et al. 2021

Self Cite

In this paper, we model the nuclear potential using Woods-Saxon and Yukawa interaction as the mean field in which each nucleon experiences a central force due to rest of the nucleons. The single particle energy states are obtained by solving the time independent Schrodinger wave equation using matrix diagonalization method with infinite spherical well wave-functions as the basis. The best fit model parameters are obtained by using variational Monte-Carlo algorithm wherein the relative mean-squared error, christened as chi-squared value, is minimized. The universal parameters obtained using Woods-Saxon potential are found to be matched with literature reported data resulting a chi-square value of 0.066 for neutron states and 0.069 for proton states whereas the chi-square value comes out to be 1.98 and 1.57 for neutron and proton states respectively by considering Yukawa potential. To further assess the performance of both the interaction potentials, the model parameters have been optimized for three different groups, light nuclei up to 16O - 56Ni, heavy nuclei 100Sn - 208Pb and all nuclei 16O - 208Pb. It is observed that Yukawa model performed reasonably well for light nuclei but did not give satisfactory results for the other two groups while Woods-Saxon potential gives satisfactory results for all magic nuclei across the periodic table.

Section: E Formentioning

confidence: 99%

Section: Rephrasing Of Potentials In Appropriate Unitsmentioning

confidence: 99%

Section: Optimization Of Woods -Saxon Parameters Using Monte-carlo Approachmentioning

confidence: 99%

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Comparative Analysis of Woods-Saxon and Yukawa Model Nuclear Potentials

Sharma

Gora

et al. 2021

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“…The matrix method technique as proposed by Marsglio et al [24] where in the potential under consideration is embedded within an infinite potential well, whose sine wave-functions are employed as basis, has been successful for obtaining the energies and corresponding wave-functions for simple central potentials such as spherical well, Coulomb and Yukawa. Our group has applied this technique to solving Harmonic Oscillator (HO) [25], Anharmonic oscillator (AHO) [26], Woods-Saxon [27] and Morse potential [28]. Here, we utilize this numerical technique to obtain the ground state energy of Deuteron for MT, MR and Morse potentials.…”

Section: Introductionmentioning

confidence: 99%

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

Khachi

Kumar

2021

The scattering phase shifts for n-p scattering have been modeled using various two term exponential type potentials such as Malfliet-Tjon, Manning-Rosen and Morse to study the phase shifts in the S-channels. As a first step, the model arameters for each of the potentials are determined by obtaining binding energy of the deuteron using matrix methods vis-a-vis Variational Monte-Carlo (VMC) technique to minimize the percentage error w.r.t. the experimental value. Then, the first order ODE as given by phase function method (PFM), is numerically solved using 5th order Runge-Kutta (RK-5) technique, by substituting the obtained potentials for calculating phase shifts for the bound 3S1 channel. Finally, the potential parameters are varied in least squares sense using VMC technique to obtain the scattering phase-shifts for each of the potentials in the 1S0 channel. The numerically obtained values are seen to be matching with those obtained using other analytical techniques and a comparative analysis with the experimental values up to 300 MeV is presented.

“…To achieve this, we employ a methodology which is a combination of various numerical techniques. On one hand, 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.…”

Section: Introductionmentioning

confidence: 99%

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

Khachi

Kumar

et al. 2021

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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.