Neutrinoless Double $\beta$ Decay within QRPA with Proton-Neutron Pairing

We have investigated the role of proton-neutron pairing in the context of the Quasiparticle Random Phase approximation formalism. This way the neutrinoless double beta decay matrix elements of the experimentally interesting A= 48, 76, 82, 96, 100, 116, 128, 130 and 136 systems have been calculated. We have found that the inclusion of proton-neutron pairing influences the neutrinoless double beta decay rates significantly, in all cases allowing for larger values of the expectation value of light neutrino masses. Using the best presently available experimental limits on the half life-time of neutrinoless double beta decay we have extracted the limits on lepton number violating parameters