We show that, within the quasiparticle random phase approximation (QRPA) and the renormalized QRPA (RQRPA) based on the Bonn-CD nucleon-nucleon interaction, the competition between the pairing and the neutron-proton particle-particle and particle-hole interactions causes contributions to the neutrinoless double-beta decay matrix element to nearly vanish at internucleon distances of more than 2 or 3 fermis. As a result, the matrix element is more sensitive to short-range/high-momentum physics than one naively expects. We analyze various ways of treating that physics and quantify the uncertainty it produces in the matrix elements, with three different treatments of short-range correlations.

We review the recent developments in the field of nuclear double beta decay, which is presently an important topic in both nuclear and particle physics. The mechanism of lepton number violation within the neutrinoless double beta decay (0νββ-decay) is discussed in the context of the problem of neutrino mixing and the R-parity violating supersymmetric extensions of the standard model. The problem of reliable determination of the nuclear matrix elements governing both two-neutrino and neutrinoless modes of the double beta decay is addressed. The validity of different approximation schemes in the considered nuclear structure studies is analysed and the role of the Pauli exclusion principle for a correct treatment of nuclear matrix elements is emphasized. The constraints on different lepton-number violating parameters such as effective electron neutrino mass, effective right-handed weak interaction parameters, effective Majoron coupling constant and R-parity violating SUSY parameters are derived from the best presently available experimental limits on the half-life of 0νββ-decay.

We have examined the importance of momentum dependent induced nucleon currents such as weak-magnetism and pseudoscalar couplings to the amplitude of neutrinoless double beta decay (0νββ-decay) in the mechanisms of light and heavy Majorana neutrino as well as in that of Majoron emission.Such effects are expected to occur in all nuclear models in the direction of reducing the light neutrino matrix elements by about 30%. To test this we have performed a calculation of the nuclear matrix elements of the experimentally interesting nuclei A = 76, 82, 96, 100, 116, 128, 130, 136 and 150 within the proton-neutron renormalized Quasiparticle Random Phase Approximation (pn-RQRPA). We have found that indeed such corrections vary * Permanent address:

Within the quasiparticle random-phase approximation (QRPA) we achieve partial restoration of the isospin symmetry and hence fulfillment of the requirement that the 2νββ Fermi matrix element M 2ν F vanishes, as it should, unlike in the previous version of the method. This is accomplished by separating the renormalization parameter g pp of the particle-particle proton-neutron interaction into isovector and isoscalar parts. The isovector parameter g T =1 pp needs to be chosen to be essentially equal to the pairing constant g pair , so no new parameter is needed. For the 0νββ decay the Fermi matrix element M 0ν F is substantially reduced, while the full matrix element M 0ν is reduced by ≈10%. We argue that this more consistent approach should be used from now on in the proton-neutron QRPA and in analogous methods.

A new scheme for testing nuclear matter equations of state (EoSs) at high densities using constraints from neutron star (NS) phenomenology and a flow data analysis of heavy-ion collisions is suggested. An acceptable EoS shall not allow the direct Urca process to occur in NSs with masses below 1.5M , and also shall not contradict flow and kaon production data of heavy-ion collisions. Compact star constraints include the mass measurements of 2.1 ± 0.2M (1σ level) for PSR J0751+1807 and of 2.0 ± 0.1M from the innermost stable circular orbit for 4U 1636-536, the baryon mass-gravitational mass relationships from Pulsar B in J0737-3039 and the mass-radius relationships from quasiperiodic brightness oscillations in 4U 0614+09 and from the thermal emission of RX J1856-3754. This scheme is applied to a set of relativistic EoSs which are constrained otherwise from nuclear matter saturation properties. We demonstrate on the given examples that the test scheme due to the quality of the newly emerging astrophysical data leads to useful selection criteria for the high-density behavior of nuclear EoSs.