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

Anil Khachi,Shikha Awasthi,Osks Sastri,Lalit Kumar

doi:10.15415/jnp.2021.91014

Abstract

In this paper, the phase-shifts for neutron-dueteron (n-d) scattering have been determined using the molecular Morse potential as theoretical model of interaction. The Triton (n-d) 2S1/2 ground state initially has been chosen as -7.61 MeV to determine the model parameters using variational Monte-Carlo technique in combination with matrix methods numerical approach to solving the time independent Schrodinger equation (TISE). The obtained potential is incorporated into the phase function equation, which is solved using Runge-Kutta (RK) 4,5 order technique, to calculate the phaseshifts at various lab energies below 15 MeV, for which experimental data is available. The results have been compared with those obtained using another molecular potential named Manning-Rosen (MR) and have been observed to fare better. Finally, the Triton ground state has been chosen as its binding energy (BE), given by -8.481795 MeV, as determined from experimental atomic mass evaluation data and the calculations are repeated. It has been found that these phase-shifts from BE data are slightly better matched with experimental ones as compared to those obtained using -7.61 MeV ground state for Triton (n-d two-body system) modeled using Morse potential.

Highlights

Understanding the nucleon-nucleon and nucleon-nucleus interactions for very light nuclei are of importance to gaining insights into various aspects of two-particle and three-particle interactions that might be the underlying reasons for stability of nuclei
It is generally found to be fading away as the distance between the neutron and deuteron increases and increases with decreasing inter nucleon-nucleus distance suggesting an attractive potential with an exponentially decaying tail and has a repulsive core. This is very much what one observes in molecular interactions between neutral atoms where in the secondary interactions of Vander-walls (VW) type come into picture
Hestenes [6], utilising the numerical method of matrix diagonalisation [7] in tandem with variational Monte-Carlo [8] to obtain the ground state of Triton, abstracting the Morse potential with best fit parameters that model the interaction. This is utilised in the non-linear differential equation [nonlinear 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]

Summary

Introduction

Understanding the nucleon-nucleon and nucleon-nucleus interactions for very light nuclei are of importance to gaining insights into various aspects of two-particle and three-particle interactions that might be the underlying reasons for stability of nuclei. It is generally found to be fading away as the distance between the neutron and deuteron increases and increases with decreasing inter nucleon-nucleus distance suggesting an attractive potential with an exponentially decaying tail and has a repulsive core This is very much what one observes in molecular interactions between neutral atoms where in the secondary interactions of Vander-walls (VW) type come into picture. Hestenes [6], utilising the numerical method of matrix diagonalisation [7] in tandem with variational Monte-Carlo [8] to obtain the ground state of Triton, 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].

Modeling Triton using Two-term Potentials

Simulation of Results and Discussion

Conclusion