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 ${}^{76}\mathrm{Ge}$, ${}^{100}\mathrm{Mo}$, and ${}^{130}\mathrm{Te}$. 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.

• Received 19 July 2007

DOI:https://doi.org/10.1103/PhysRevC.77.025502