Microscopic anharmonic vibrator approach for beta decays

We formulate a microscopic description of charge-changing excitations, including dynamical mixture of one- and two-phonon states. The present formalism generalizes our previous microscopic anharmonic vibrator approach (MAVA), designed to treat charge-conserving two- and four-quasiparticle degrees of freedom and their mixing. In the present formalism, the proton–neutron MAVA, pnMAVA, the main building blocks are the quasiparticle random-phase approximation (QRPA) phonons in the charge-conserving channels, and the proton–neutron QRPA (pnQRPA) phonons in the charge-changing channels. The QRPA and pnQRPA equations are directly used in deriving the equations of motion for two-phonon states. The beta-decay Gamow–Teller matrix elements, connecting the 1+ states of a double-odd nucleus with two-phonon 0+ and 2+ states of the neighboring double-even nucleus, contain contributions from the metric matrix and scattering terms of the beta-decay operator. The pnMAVA has been applied to predict β−-decay and β+-decay amplitudes for transitions feeding the one- and two-phonon states in the palladium isotopes 106,108Pd. A fair agreement with the data has been achieved.