Dependence of two-nucleon momentum densities on total pair momentum

Abstract

Two-nucleon momentum distributions are calculated for the ground states of $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ as a function of the nucleons' relative and total momenta. We use variational Monte Carlo wave functions derived from a realistic Hamiltonian with two- and three-nucleon potentials. The momentum distribution of $\mathit{pp}$ pairs is found to be much smaller than that of $\mathit{pn}$ pairs for values of the relative momentum in the range 300--500 MeV/$c$ and vanishing total momentum. However, as the total momentum increases to 400 MeV/$c$, the ratio of $\mathit{pp}$ to $\mathit{pn}$ pairs in this relative momentum range grows and approaches the limit 1/2 for $^{3}\mathrm{He}$ and 1/4 for $^{4}\mathrm{He}$, corresponding to the ratio of $\mathit{pp}$ to $\mathit{pn}$ pairs in these nuclei. This behavior should be easily observable in two-nucleon knock-out processes, such as $A(e,{e}^{'}\mathit{pN})$.