Experiments on neutrinoless double beta (O nu beta beta) decay to excited 0(+) states are a promising tool to study neutrino and weak-interaction properties by reducing the background of the measured spectra by the associated gamma-coincidence signals. Drawbacks are the lower Q value of the decays and possibly the smallness of the involved nuclear matrix elements as compared to the decays to the final ground state. In this Rapid Communication it is suggested that the first excited 0(+) state in Mo-96 can be described as a monopole-vibrational state and 0 nu beta beta decay of Zr-96 to this particular state could yield to 8 X 10(-2) eV limit for the Majorana-neutrino mass in modern underground experiments using huge active-mass detectors.
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