Variational calculations on a simple triton model using a complete hyperspherical function basis

Abstract

Variational calculations which have been performed for the three-boson model of the triton are reported. The trial function is constructed using a denumerable, complete and orthonormal set of functions. Each of these functions is the product of a hyperspherical harmonic and a hyperradial function. This leads to a standard matrix eigenvalue problem. Various forms for the radial dependence of the two-particle interaction, with and without repulsion near the origin, and with and without a 1 r singularity in the origin, are investigated. Using a particular set of hyperspherical harmonics and introducing a new set of hyperradial functions, a considerable improvement is achieved compared with other calculations using hyperspherical function bases. Our results also compare favorably with those obtained using different methods or other types of trial functions. From this comparison and by investigating the convergence of the energy and of the trial function we find that the quality of the results ranges from excellent for the simplest interactions to acceptable for the more sophisticated ones. A few results of physical interest are given.