Medium-polarization effects in ${}^{3}SD_1$ spin-triplet pairing

Stimulated by the still puzzling competition between spin-singlet and spin-triplet pairing in nuclei, the ${}^{3}SD_1$ neutron-proton pairing is investigated in the framework of BCS theory of nuclear matter. The medium-polarization effects are included in the single-particle spectrum and also in the pairing interaction starting from the $G$ matrix, calculated in the Brueckner-Hartree-Fock approximation. The vertex corrections due to spin and isospin collective excitations of the medium are determined from the Bethe-Salpeter equation in the random-phase approximation (RPA) limit, taking into account the tensor correlations. It is found that the self-energy corrections confine the superfluid state to very low density, while remarkably quenching the magnitude of the energy gap, whereas the induced interaction has an attractive effect. The interplay between spin-singlet and spin-triplet pairing is discussed in nuclear matter as well as in finite nuclei.

Figure 1

Pairing interaction with screening: the first term on the right-hand side is the bare interaction; the second one is the induced interaction, where the dashed bubble insertion is the series of ring diagrams.

Figure 2

Energy gap with self-energy effects. Left: Comparison between ${}^{3}SD_1$ and ${}^{1}S_0$ gaps from bare interaction. Middle: ${}^{3}SD_1$ gaps with single-particle spectrum in the EMA (effective mass vs density in the inset). Right: Energy gap with depleted Fermi surface ($Z$ factor vs density in the inset).

Figure 3

Driving p-h interaction ${\mathcal{G}}_{l{l}^{\prime }}^{SJT}$ from the $G$ matrix in the $SD$ channel.

Figure 4

Comparison among ${}^{3}SD_1$ gaps from RPA induced interaction and previous effects and ${}^{1}S_0$ in full calculations.