content_image/331722.jpg content_image/331723.jpg content_image/331721.jpg content_image/331724.jpg content_image/331725.jpg content_image/331726.jpg
of baryons and leptons are given by 

respectively. The electric charge neutrality condition is expressed by 

<img src='content_image/331722.jpg'>

<img src='content_image/331723.jpg'>

<img src='content_image/331721.jpg'>

where ρ$_{i}$ = ( k i $_{F}$) $^{3}$/ (3 π $^{2}$) is the number density of species i . We solve the coupled Eqs. (2)– (6), (8)–(11), and (14) self-consistently at a given baryon density ρ$_{B}$ . Then we can calculate the EOS and the composition of neutron star matter as well as the effective mass and the Fermi momentum of Λ hyperons, which are crucial in the study of ΛΛ pairing. 

## III. GAP EQUATION AND ΛΛ INTERACTION 

We study the $^{1}$S$_{0}$ superfluidity of Λ hyperons in neutron star matter. The crucial quantity in determining the onset of superfluidity is the energy gap function Δ ( k ), which can be obtained by solving the gap equation 

<img src='content_image/331724.jpg'>

where E ( k ) is the single-particle energy of Λ with momentum k . For Λ hyperons in neutron star matter, the single-particle energy in the RMF approach is given by 

<img src='content_image/331725.jpg'>

The effective mass m ∗ Λ and the Fermi momentum k Λ F are computed self-consistently at a given baryon density ρ$_{B}$ within the RMF approach. 

For the ΛΛ pairing interaction in the $^{1}$S$_{0}$ channel, the potential matrix element can be written as 

<img src='content_image/331726.jpg'>

where j$_{0}$ ( kr ) = sin( kr ) / ( kr ) is the spherical Bessel function of order zero and V$_{ΛΛ}$ ( r ) is the $^{1}$S$_{0}$ ΛΛ interaction potential in coordinate space. Because of large uncertainties in the 

