Double-beta decay to excited0+states: Decay ofMo100

We develop a formalism for describing the 2ν mode of double-beta decay to an excited final state in the quasiparticle random phase approximation (QRPA). With this, we deduce the half-lives for the ${}_{}{}^{100}{}_{}{}^{}\mathrm{Mo}$ double-beta decays to both the ground and 1130 keV excited $0^{+}$ states in ${}_{}{}^{100}{}_{}{}^{}\mathrm{Ru}$. We predict the matrix elements of these two transitions to be of a similar magnitude. We also calculate the strengths of the associated single-beta decays from the ground state of the intermediate nucleus, ${}_{}{}^{100}{}_{}{}^{}\mathrm{Tc}$, and compare them with experiment. We find that the QRPA cannot simultaneously reproduce all of the experimental quantities, and, in particular, the single-beta transition between the initial and intermediate nuclei is overestimated by the theory. In addition, we demonstrate that the influence of the particle-particle force is an important factor in the calculation of both ${\mathrm{\beta }}^{\mathrm{-}}$ and ${\mathrm{\beta }}^{+}$ transition strengths.