Configuration space Faddeev calculations. II. Trinucleon Coulomb energy

Abstract

Coordinate space Faddeev techniques and a variety of potentials are used to calculate energies and wave functions for the trinucleon system, both with and without a static Coulomb interaction between the two protons. The wave functions are used to calculate first- and second-order perturbation theory contributions to the Coulomb energy of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. Because too few partial-wave components of the potential are kept, the energy eigenvalues themselves are an inaccurate gauge of the Coulomb effect. The approximate hyperspherical formula was tested after calculating charge densities and found to be accurate to better than 2 percent. It is demonstrated that when using a phenomenological approach to the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ Coulomb energy, the second-order contribution increases the Coulomb energy by roughly 4 ± 1 keV. Finally, sum rules relating to the $T=\frac{3}{2}$ state probability and the size of the second-order contribution are discussed.