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The $2\nu\beta\beta$-decay nuclear matrix elements (NMEs) for 11 nuclei arestudied with the self-consistent quasiparticle random phase approximation(QRPA) based on Skyrme Hartree-Fock-Bogoliubov (Skyrme HFB) model. As a commonfeature pointed out inhttps://journals.aps.org/prc/abstract/10.1103/PhysRevC.98.064325 Phys. Rev. C98, 064325 (2018), negative contributions in the running sums of NMEs arefound, and play important roles in the fulfillment of the single-statedominance or low-lying-states dominance hypothesis. By comparing the results ofQRPA model and quasiparticle Tamm-Dancoff approximation (QTDA) model, we findthat the negative contributions are due to the enhanced ground-statecorrelations, which are brought by the backward amplitude in QRPA model andtuned by strong isoscalar pairing interaction. The enhancement of ground-statecorrelations will change the signs of GT$^{+}$ transition amplitudes ofhigher-lying states and leads to the negative contributions in the running sum.

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