An Alternative Calculation Technique in the Generator-Coordinate Method (GCM) to Determine the Ground State Energies of ²H and ⁴He and the Electric Quadrupole Moment of ²H

Abstract

An alternative calculation technique in the generator-coordinate method (GCM) has been proposed in which square-well potential between nucleon-pairs is employed, instead of the harmonic oscillator potential of the HOSM (harmonic oscillator shell model.) The eigen-function of the Schroedinger equation with nucleon-pair Hamiltonian replaces the HOSM wave function and its kernels. The GCM kernels are projected out on an arbitrary non-orthonormal function, whereas the total wave function is expanded in terms of this function to obtain standard eigenvalue equation. Ground state energies of ²H and ⁴He and the electric quadruple moment of ²H were calculated and the results were compared to the Variational Monte Carlo (VMC) calculation and experimental data.

Keywords:

• generator-coordinate method
• nucleon-pair
• square-well based potential