2νββ-decay to first 2⁺ states with partial isospin symmetry restoration from spherical QRPA calculations *

Abstract

Using partially restored isospin symmetry, we calculate the nuclear matrix elements for a special decay mode of a two-neutrino double beta decay – the decay to the first 2+ excited states. Employing the realistic CD–Bonn nuclear force, we analyze the dependence of the nuclear matrix elements on the isovector and isoscalar parts of proton–neutron particle–particle interactions. The dependence on the different nuclear matrix elements is observed, and the results are explained. We also provide the phase space factors using numerical electron wavefunctions and properly chosen excitation energies. Finally, we present our results for the half-lives of this decay mode for different nuclei.

NMEs for $0νββ(0^+\rightarrow2^+)$ of two-nucleon mechanism for $^{76}$Ge

“…So we also test such dependence in current calculations. As we have shown in [22] for the case of 2νββ to 2 + states, the GT type decays are also sensitive to g T =1 pp since the isovector particle-particle residue force affects the structure of 2 + states in QRPA calculations. In fig.…”

“…g T =0 pp is fixed by reproducing the experimental 2νββ and g T =1 pp are fixed to put to zero the 2νββ Fermi matrix elements due to isospin symmetry restoration [23]. For more details, one can refer to the our previous work [22]. For a baseline calculation, we consider the CD-Bonn src bare axial vector coupling constant g A0 = 1.27.…”

“…For the reduced one-body density for transitions from intermediate states to final 2 + , the expression is complicated [22]:…”

“…Here X's and Y 's are the amplitudes for pn-QRPA (proton-neutron Quasi-particle Random Phase Approximation) describing the intermediate states and X 's and Y's are the amplitudes for CC-QRPA (Charge Conserving QRPA) describing the final 2 + state [22]. And u's and v's are the BCS coefficients.…”

“…The details of derivations of the BCS coefficients and respective QRPA amplitudes for the current work are presented in [22].…”