Description of double β decay within the continuum quasiparticle random-phase approximation

A method to calculate the nuclear double beta decay (2 nu beta beta and 0 nu beta beta) amplitudes within the continuum quasiparticle random phase approximation (cQRPA) is formulated. Calculations of the beta beta transition amplitudes within the cQRPA are performed for Ge-76, Mo-100, and Te-130. A rather simple nuclear Hamiltonian consisting of a phenomenological mean field and a zero-range residual particle-hole and particle-particle interaction is used. The calculated 2 nu beta beta amplitudes are almost unaffected when the single-particle continuum is taken into account, whereas we find a regular suppression of the 0 nu beta beta amplitudes that can be associated with additional ground-state correlations owing to collective states in the continuum. It is expected that inclusion of nucleon pairing in the single-particle continuum will somewhat compensate this suppression.