S-wave Pairing of $\Lambda$ Hyperons in Dense Matter

In this work we calculate the $^1S_0$ gap energies of $\Lambda$ hyperons in neutron star matter. The calculation is based on a solution of the BCS gap equation for an effective G-matrix parameterization of the $\Lambda-\Lambda$ interaction with a nuclear matter background, presented recently by Lanskoy and Yamamoto. We find that a gap energy of a few tenths of MeV is expected for $\Lambda$ Fermi momenta up to about 1.3 fm$^{-1}$. Implications for neutron star matter are examined, and suggest the existence of a $\Lambda$ $^1S_0$ superfluid between the threshold baryon density for $\Lambda$ formation and the baryon density where the $\Lambda$ fraction reaches $15-20$.