Single-state or low-lying-states dominance mechanism of $2\nu\beta\beta$-decay nuclear matrix elements

The $2\nu\beta\beta$-decay nuclear matrix elements (NMEs) for 11 nuclei are studied with the self-consistent quasiparticle random phase approximation (QRPA) based on Skyrme Hartree-Fock-Bogoliubov (Skyrme HFB) model. As a common feature pointed out in https://journals.aps.org/prc/abstract/10.1103/PhysRevC.98.064325 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 QRPA model and 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 QRPA model and tuned by strong isoscalar pairing interaction. The enhancement of ground-state correlations will change the signs of GT$^{+}$ transition amplitudes of higher-lying states and leads to the negative contributions in the running sum.