Soft-core potential in the triton

Abstract

The triton binding energy has been calculated for several soft-core nucleon-nucleon potentials using the Rayleigh-Ritz variational method. When Gaussian-type trial functions are employed, it is found that such functions can easily be decomposed into a sum of terms, each of which has pure two-body LSJ dependence. This is a necessary feature in order to do the calculation with the Reid soft-core potential. The calculations were done for the Bressel and Reid potentials. In order to test the accuracy of the trial function, the attractive Pease-Feshbach potential and the central soft-core Coester-Yen potential were also used. It was found that regardless of the number of terms, the superposition of Gaussians is inferior to exponential-type trial functions. Realizing the deficiency of Gaussian-type trial functions, one can consider that the modern realistic soft-core potentials give results consistent with binding albeit with large uncertainty limits. The Coester-Yen potential, although it is “unrealistic” in the sense that it has no tensor part, yields a binding energy and radius of the triton which are in close agreement with experiment.