Upper and Lower Bound of the Eigenvalue of a Three-Body System

Abstract

A variational calculation is performed to determine the upper and lower bound of the eigenvalue of the ground state of a three-body system with two types of two-body, central potential without hard core. The trial wave function used is a function which is product of the solution of the two-nucleon Schrödinger equation up to a certain internucleon separation, which goes over into a variation function for larger distances. The calculation is done by a Monte Carlo method. The results show that with this type of trial wave function, the upper and lower bound are rather close to each other, with the difference between the values of the two bounds equal to only about 3% of the magnitude of the upper bound.