Quadratic momentum dependence in the nucleon-nucleon interaction

Abstract

We investigate different choices for the quadratic momentum dependence required in nucleon-nucleon potentials to fit phase shifts in high partial waves. In the Argonne ${v}_{18}$ potential ${\mathbf{L}}^{2}$ and ${(\mathbf{L}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S})}^{2}$ operators are used to represent this dependence. The ${v}_{18}$ potential is simple to use in many-body calculations since it has no quadratic momentum-dependent terms in $S$ waves. However, ${\mathbf{p}}^{2}$ rather than ${\mathbf{L}}^{2}$ dependence occurs naturally in meson-exchange models of nuclear forces. We construct an alternate version of the Argonne potential, designated Argonne ${v}_{18pq}$, in which the ${\mathbf{L}}^{2}$ and ${(\mathbf{L}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S})}^{2}$ operators are replaced by ${\mathbf{p}}^{2}$ and ${Q}_{ij}$ operators, respectively. The quadratic momentum-dependent terms are smaller in the ${v}_{18pq}$ than in the ${v}_{18}$ interaction. Results for the ground-state binding energies of $^{3}\text{H}$, $^{3}\text{He}$, and $^{4}\text{He}$, obtained with the variational Monte Carlo method, are presented for both the models with and without three-nucleon interactions. We find that the nuclear wave functions obtained with ${v}_{18pq}$ are slightly larger than those with ${v}_{18}$ at interparticle distances $<1\phantom{\rule{0.3em}{0ex}}\text{fm}$. The two models provide essentially the same binding in the light nuclei, although ${v}_{18pq}$ gains less attraction when a fixed three-nucleon potential is added.