Shell model calculations using modified Sussex matrix elements forA≤4

Abstract

The $^{3}S_{1}$ and $^{3}S_{1}\ensuremath{-}^{3}D_{1}$ Sussex matrix elements are modified by the addition of the matrix elements of a potential whose radial form is that of a momentum-dependent delta function. The strength parameters of the potential are found by fitting to the binding energy and quadrupole moment of the deuteron. Shell model calculations in a $4\ensuremath{\hbar}\ensuremath{\omega}$ model space using the modified matrix elements and a size parameter of 1.5 fm give binding energies of 7.55, 6.79, and 27.77 MeV for $^{3}\mathrm{H}$, $^{3}\mathrm{He}$, and $^{4}\mathrm{He}$, respectively. The energies of the negative parity states in $^{4}\mathrm{He}$ are also calculated using the modified matrix elements in a $5\ensuremath{\hbar}\ensuremath{\omega}$ model space. It is found that their calculated absolute energies are much improved as compared to calculations using the unmodified matrix elements. The relative energies of these states are not significantly changed by the modifications, as expected.NUCLEAR STRUCTURE $^{3}\mathrm{H}$, $^{3,4}\mathrm{He}$. Calculated binding energies, negative parity states. Shell model, Sussex matrix elements.