Independent-pair wave functions for the three- and four-body nuclei

Abstract

A method which was described previously for generating independent-pair wave functions for three-nucleon systems is generalized so that the S′ state with mixed symmetry can be included in three-body calculations and so that the method can be used to generate independent pair wave functions for the alpha particle. This procedure is used to find approximate ground-state functions for several three- and four-body Hamiltonians. The functions so obtained are used to calculate an upper and, in some cases, a lower bound to the ground-state energy and to calculate the charge form factors for these three- and four-body systems. When the interactions are chosen so that both low- and high-energy two-nucleon data are correctly predicted, then the calculated binding energies are slightly too large, the ratio of the form factors for 3H to that of 3He is consistent with the experimental ratio, and the form factors for all three nuclei are too large at large momentum transfers. By increasing the radius of the hard core, the calculated form factor functions are decreased closer to the experimental ones.