Triplet-odd pairing in finite nuclear systems: Even-even singly closed nuclei

TL;DR

This study investigates the coexistence of spin-singlet and spin-triplet pairing condensates in finite nuclei, revealing the crucial role of spin-orbit splitting in their emergence through Hartree-Fock-Bogoliubov calculations.

Contribution

It demonstrates how spin-orbit splitting influences the coexistence of different pairing types in nuclei using Skyrme energy-density functionals.

Findings

Spin-triplet pairing can coexist with spin-singlet pairing due to spin-orbit effects.

Discarding spin-orbit EDF results in only spin-singlet pairing.

Spin-orbit splitting is essential for the coexistence of pairing condensates.

Abstract

Background: The appearance of the pairing condensate is an essential feature of many-fermion systems. There are two possible types of pairing: spin-singlet and spin-triplet. However, an open question remains as to whether the spin-triplet pairing condensate emerges in finite nuclei. Purpose: The aim of this work is to examine the coexistence of the spin-singlet and spin-triplet like-particle pairing condensates in nuclei. We also discuss the dependence on the type of pairing functional. Method: The Hartree-Fock-Bogoliubov calculations with a Skyrme $+$ local-pair energy-density functional (EDF) are performed to investigate the pairing condensate in the spherical ground states of Ca and Sn isotopes. Results: The spin-singlet pair EDF induces not only the spin-singlet but also the spin-triplet pairing condensates due to a strong spin-orbit splitting. By discarding the spin-orbit EDF, only the spin-singlet pairing condensate appears. The spin-triplet pair EDF, however, induces the spin-orbit splitting and accordingly the spin-singlet pairing condensate. Conclusions: The spin-orbit splitting plays an essential role in the coexistence of the spin-singlet and spin-triplet pairing condensates in nuclei.