Ground states of triton and alpha nuclei

Abstract

The few-body integrodifferential equations are approximations to the few-body Schr¨odinger equation in hyperspherical coordinates. The few-body integrodifferential equations for identical particles reduce to a single integrodifferential equation in two variables only. The structure of the integrodifferential equation does not dependent of the number of particles in the system. The integrodifferential equation has previously been solved using the adiabatic approximation method, the projection method and the perturba tion method. In this dissertation we solve the few-body integrodifferential equations directly using the Lagrange mesh method. We apply the equations to Triton and alpha nuclei which are three-body and four-body systems, respectively. We treat the nucleons as interacting through spin-dependent nucleon-nucleon potentials. The few-body inte-grodifferential equations develop into a system coupled integrodifferential equations in the case of spin-dependent potentials. All our results are compared to those found in literature.