Single-state or low-lying-states dominance mechanism of 2νββ -decay nuclear matrix elements

Abstract

The $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay nuclear matrix elements (NMEs) for 11 nuclei are studied with the self-consistent quasiparticle random phase approximation (QRPA) based on the Skyrme Hartree-Fock-Bogoliubov (Skyrme HFB) model. As a common feature pointed out by \ifmmode \check{S}\else \v{S}\fi{}imkovic, Smetana, and Vogel [Phys. Rev. C 98, 064325 (2018)], negative contributions in the running sums of NMEs are found, and play important roles in the fulfillment of the single-state dominance or low-lying-states dominance hypothesis. By comparing the results of the QRPA model and the quasiparticle Tamm-Dancoff approximation (QTDA) model, we find that the negative contributions are due to the enhanced ground-state correlations, which are brought by the backward amplitude in the QRPA model and tuned by strong isoscalar pairing interaction. The enhancement of ground-state correlations will change the signs of ${\mathrm{GT}}^{+}$ (Gamow-Teller) transition amplitudes of higher-lying states and leads to the negative contributions in the running sum.