Shell Model Calculations of the D-State Admixture in the Ground-State Wave Functions of Tritium, HELIUM-3, and HELIUM-4 Using Various Realistic Potentials

Several different theoretical methods have been developed to investigate the ground-state properties of ^3H, ^3He, and ^4He nuclei. Previously, the properties of these nuclei have been investigated using variational and hyperspherical methods. However, the Faddeev method, which yields essentially exact results has been used for A = 3 and the coupled-cluster method for mass 4. The error inherent in the hyperspherical method is not known, so the development of alternative method may be useful. In this work we have developed a set of effective operators to be used in the shell-model calculations. The m-scheme shell-model method is used in a systematic study of the binding energy and D-state probability obtained for the ground state of ^3H, ^3He, and ^4He nuclei using a variety of realistic nucleon-nucleon potentials. Since the main contribution to the binding energy comes from the ^1S_0 and ^3S_1 -^3D_1 nucleon -nucleon channels, and the main contribution to the D-state probability comes from the ^3S _1-^3D_1 tensor interaction, we will include only these channels in our calculations. Furthermore, this restriction will allow us to compare our results with the Faddeev five -channel calculations in coordinate space for ^3 H and ^3He. For the trinucleon calculations, we find that our results are in substantial agreement with those of Faddeev calculations. The difference between our results and those of Faddeev calculations is found to be between -0.38 MeV and 0.19 MeV for the triton binding energy and between -0.6% and 0.0% for the triton ground-state D-state probability. For the mass 4 calculations, we compare our results with the published results of hyperspherical, variational, and coupled-cluster calculations. The agreement between this work and that of the URBANA group (48) and Goldhammer (51) is excellent for the binding energy calculations. Our systematic study shows the binding energy (without the static Coulomb contribution) of the alpha particle to be between 24.5 and 26.8 MeV for modern realistic two-body potentials (PARIS, URBANA, ARGONNE V_{14 }, and BONN-OBEPR). Further, we find the D -state probability to lie between 10 and 15% while previously published reports suggest 5% and 13%.