Dineutron correlations in quasi two-dimensional systems in a simplified model and possible relation to neutron-rich nuclei

Two-neutron correlation in the $^1S$ channel in quasi two-dimensional (2D) neutron systems at zero temperature is studied by means of the BCS theory with finite-range effective nuclear forces. The dineutron correlation in low density neutron systems confined in an infinite slab is investigated in a simplified model that neutron motion of one direction is frozen. When the slab is thin enough, two neutrons form a tightly bound dineutron with a small size in the quasi-2D system, and a Bose dineutron gas is found in low density limit. With increase of Fermi momentum, the neutron system changes from the Bose-gas phase to the superfluid Cooper pair phase. The density dependence of the neutron pairing shows the BCS-BEC crossover phenomena at finite low-density region. In the transition region, the size shrinking of neutron pair and enhancement of pairing gap are found. The relation to dineutron correlation at surface of neutron-rich nuclei is also discussed.