Momentum distribution and correlation of two-nucleon relative motion in ⁶He and ⁶Li

The momentum distribution of relative motion between two nucleons gives information on the correlation in nuclei. The momentum distribution is calculated for both $^{6}$He and $^6$Li which are described in a three-body model of $\alpha$+$N$+$N$. The ground state solution for the three-body Hamiltonian is obtained accurately using correlated basis functions. The momentum distribution depends on the potential model for the $N$-$N$ interaction. With use of a realistic potential, the $^6$He momentum distribution exhibits a dip around 2 fm$^{-1}$ characteristic of $S$-wave motion. In contrast to this, the $^6$Li momentum distribution is very similar to that of the deuteron; no dip appears because it is filled with the $D$-wave component arising from the tensor force.