Effect of tensor force on 2<i>νββ</i> and 0<i>νββ</i> decays in ⁷⁶Ge, ⁸²Se, ¹³⁰Te, and ¹³⁶Xe*

Abstract The effects of the tensor force on the and decay nuclear matrix elements (NMEs) of , , , and are studied using the Hartree-Fock-Bogoliubov (HFB) plus proton-neutron quasi-particle random phase approximation (pnQRPA) model based on the Skyrme energy density functional. We include the full spectra of intermediate states with up to the energy cutoff E = 60 MeV, which is sufficient for convergence of NME calculations. The isovector (IV) pairing and tensor interactions are considered in both HFB and QRPA calculations, while the isoscalar (IS) pairing interaction is included only in QRPA calculations. We found that the tensor force shifts Gamow-Teller (GT) transition strengths substantially to low-energy regions and enhances the decay NME. The inclusion of tensor force enhances the NME by approximately 13% for and and 30% for and , for a fixed IS pairing strength. We found that the intermediate 2 - state makes an important contribution to the NME, which is slightly enhanced by the inclusion of the tensor force. We also found that the contribution of the state makes important differences through the inclusion of the tensor force, which enhances the contribution largely. However when the IS pairing strength is increased, the contributions from 1 + states are rapidly reduced to be very small, resulting in even negative contributions. Thus, tensor and IS pairing effects cancel each other, making the net effect on the NME relatively small. Due to this cancellation, if the IS pairing strength is optimized separately for cases with and without the tensor interaction to reproduce the experimental NME, the consequent NME with the tensor interaction is close to that without the tensor interaction within a 10% difference.