Construction of trial functions for nuclear groundstate problems

Abstract

Variational calculations yield upper bounds on the groundstate energy which often become approximately stationary when the flexibility of the trial function is increased. It is shown that this apparent convergence is no safe criterion for a good approximation of the groundstate energyE ₀. To avoid this uncertainty it is proposed to expand the trial function with respect to the function basis {H ^v · ϕ₀} where ϕ₀ is a suitable zeroth order approximation of the wave function. The application of this method to a threeparticle system with the central potential of Bakeret al. yields an upper bound¯E ₀=−12.3 MeV which is lower than the upper bounds published so far except that obtained by Appel. The computational effort is very small.