Speaker
Description
A qualitative difference in the running sum to the nuclear matrix element of the two-neutrino double-$\beta$ decay of $^{136}$Xe has been found four years ago between QRPA and shell model calculations. The former result has large increase and decrease with respect to the excitation energy of the intermediate state, and the latter one is an almost monotonically and mildly increasing function. My QRPA calculations independent of the above one do not have a remarkable decrease. This discrepancy is a serious problem affecting the reliability of calculations of the neutrinoless double-$\beta$ decay, and the cause was unknown. I perform several relevant test calculations and consider analytically to find the cause, which is found to be in the strength of the attractive interactions. The possible major local decrease in the running sum is also explained analytically. The interactions of my QRPA calculation are appropriate in terms of the strength, thus, the almost monotonic behavior is reasonable.
