What can we learn from recent 2νββexperiments?

Recent measurements of the two neutrino double beta decay high precision electron spectra,combined with charge exchange orβ-decay experimental data,have revealed severe constraints across current nuclear many body calculations.Our calculations show that the quasi-particle random phase approximation(QRPA)approach can adequately reproduce the measured spectra for the two open shell nuclei,^(82)Se and ^(100)Mo.For the closed shell nucleus ^(136)Xe,QRPA can also reproduce the spectra with proper treatments.Considering the high-lying state reduction,we also find that the nuclear shell model can also adequately reproduce the spectra and Gamow-Teller transition strength under a unique quenched axial-vector coupling constant gA.For ^(136)Xe,we find that flipping the sign for the decay strength causes the spectra to go beyond the so-called high-lying state dominance hypothesis.These results call for future high precision measurements of charge-exchange reactions.