Dependence of two-nucleon momentum densities on total pair momentum

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 $A(e,e^{\text{'}}\mathit{pN})$.

Figure 1

The $\mathit{pn}$ (lines) and $\mathit{pp}$ (symbols) momentum distributions in ${}^3\mathrm{He}$ as functions of the relative momentum $q$ at total pair momentum $Q$ from 0 to 2 fm${}^{-1}$.

Figure 2

The $\mathit{pn}$ (lines) and $\mathit{pp}$ (symbols) momentum distributions in ${}^4\mathrm{He}$ as functions of the relative momentum $q$ at total pair momentum $Q$ from 0 to 2 fm${}^{-1}$.

Figure 3

The ratio of $\mathit{pp}$ to $\mathit{pn}$ pairs integrated over relative momentum $\mathbf{q}\Vert \mathbf{Q}$ of 1.5 to 2.5 fm${}^{-1}$ as a function of total momentum $Q$; red triangles are for ${}^3\mathrm{He}$ and blue squares are for ${}^4\mathrm{He}$.