updated information from recent developments in hypernuclear physics. As for the ΛΛ pairing interaction used in the gap equation, we adopt several ΛΛ potentials that have been used in double-Λ hypernuclei studies. Some simulate the experimental value of B$_{ΛΛ}$ ( 6 $_{ΛΛ}$He) from the Nagara event. With the effective mass and the Fermi momentum of Λ hyperons obtained in the RMF approach, the gap equation [Eq. (15)] is solved numerically. In Fig. 2, we show the resulting $^{1}$S$_{0}$ pairing gap of Λ hyperons at the Fermi surface, Δ$_{F}$ , as a function of the baryon density, ρ$_{B}$ , in neutron star matter. The results of TM1 and NL3 are plotted in Fig. 2 (top) and Fig. 2 (bottom), respectively. In the case of TM1 (NL3), the threshold density of Λ is around 0 . 31 fm − 3 (0 . 28 fm − $^{3}$), and Λ hyperons form a $^{1}$S$_{0}$ superfluid as soon as they appear in neutron star matter. With increasing baryon density, Δ$_{F}$ increases first, reaching a maximum value at ρ$_{B}$ ∼ 0 . 34 fm − 3 ( ρ$_{B}$ ∼ 0 . 30 fm − $^{3}$), then decreases and finally vanishes at ρ$_{B}$ < 0 . 46 fm − 3 ( ρ$_{B}$ < 0 . 38 fm − $^{3}$) for the case of TM1 (NL3) with the ESC00 potential. It is found that the maximal pairing gap is about 0.8 MeV with the ESC00 potential in the TM1 case. This is because the ESC00 potential has the strongest attraction among the ΛΛ interactions used here. The pairing gaps with the ND1 and ND2 potentials are of the order of 0 . 1–0 . 2 MeV, as shown in Fig. 2. In addition, we find that the pairing gaps are of the order of 10 − 4 MeV (TM1) or absent (NL3) with the NSC97e, NFs, NSC97s, and Urbana potentials. The Λ pairing does not appear for the NSC97b and NSC97f potentials. We present in Table II the maximal pairing gap at the Fermi surface (Δ max F ) and the corresponding baryon density ( ρ$_{B}$ ), effective Λ mass ( m ∗ $_{Λ}$), and Fermi momentum ( k Λ $_{F}$) using these potentials with the TM1 and NL3 parameter sets. The Λ pairing gap Δ$_{F}$ depends not only on the ΛΛ interaction but also on the properties of Λ hyperons in neutron star matter. In Fig. 3, we show the particle fraction, Y$_{i}$ = ρ$_{i}$/ρ$_{B}$ , as a function of the baryon density, ρ$_{B}$ , using the RMF model with the TM1 (Fig. 3, top) and NL3 (Fig. 3, bottom) parameter sets. It is seen that Λ hyperons appear around 0 . 31 fm − 3 (TM1) or 0 . 28 fm − 3 (NL3) and then increase rapidly with increasing density. We note that hyperon threshold densities, fractions, and effective masses are dependent on the RMF parameters used. This dependence has an effect on the resulting pairing gap, as shown in Fig. 2. Our results with the ND1 potential can be compared with those in Table III of Ref. [24], where the same ΛΛ interaction (called the ND-Soft potential) was used. The difference is in the treatment of neutron star matter, for which they use a nonrelativistic G matrix-based effective interaction approach, whereas we use the RMF approach. In our case 10