The neutrinoless double-beta-decay $(0\mathrm{}\nu \beta \beta$ decay) transition to the first excited $0^{+}$ collective final state is examined for $A=76,$ 82, 100, and 136 nuclei by assuming light and heavy Majorana neutrino exchange mechanisms as well as the trilinear R-parity violating contributions. Realistic calculations of nuclear matrix elements have been performed within the renormalized quasiparticle random phase approximation. Transitions to the first excited two-quadrupole phonon $0^{+}$ state are described within a boson expansion formalism and alternatively by using the operator recoupling method. We present the sensitivity parameters to different lepton number violating signals, which can be used in planning the $0\nu \beta \beta$-decay experiments. The half-life of $0\nu \beta \beta$ decay to the first excited state $0_1^{+}$ is by a factor of 10–100 larger than that of the transition to the ground state, $0_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{+}.$

• Received 3 April 2001

DOI:https://doi.org/10.1103/PhysRevC.64.035501