ON THE SYMMETRIC S-STATE COMPONENT OF THE TRITON WAVE FUNCTION

Abstract

Approximate forms of the symmetric S-state component of the triton wave function are found which are improvements on the well-known exponential and Irving functions. The method does not involve variational parameters; the functions are obtained from reduced Schrödinger equations found using the methods of Feshbach and Rubinow and of Morpurgo. Some properties of these equations and their solutions are given. The reduced equations are solved numerically for various phenomenological nucleon-nucleon potentials without hard cores, and the functions are presented graphically. The eigenvalves of the reduced equations differ from the experimental triton energy, as is to be expected if only the symmetric S-state component is considered, and in an effort to simulate the effect of the other components, the depth of the nucleon–nucleon potential is increased until the computed eigenvalues equal the experimental triton energy. The corresponding eigenfunctions are given graphically. The Coulomb radius of ³He has been calculated with each of the functions, and the values found are generally reasonable.