Neutrinoless double-β decay (0νββ) is a unique process that could reveal physics beyond the Standard Model. Essential ingredients in the analysis of 0νββ rates are the associated nuclear matrix elements. Most of the approaches used to calculate these matrix elements rely on the closure approximation. Here we analyze the light neutrino-exchange matrix elements of 48 Ca 0νββ decay and test the closure approximation in a shell-model approach. We calculate the 0νββ nuclear matrix elements for 48 Ca using both the closure approximation and a nonclosure approach, and we estimate the uncertainties associated with the closure approximation. We demonstrate that the nonclosure approach has excellent convergence properties which allow us to avoid unmanageable computational cost. Combining the nonclosure and closure approaches we propose a new method of calculation for 0νββ decay rates which can be applied to the 0νββ decay rates of heavy nuclei, such as 76 Ge or 82 Se.

We calculated the contribution of internal nucleon electric dipole moments to the Schiff moment of 199 Hg. The contribution of the proton electric dipole moment was obtained via core polarization effects that were treated in the framework of random phase approximation with effective residual forces. We derived a new upper bound |dp| < 5.4 × 10 −24 e·cm of the proton electric dipole moment.

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Schiff moments were calculated for a set of nuclei with full account of core polarization effects. A finite range P and T violating weak nucleon-nucleon interaction has been used in the calculations. While in the absence of core polarization the Schiff moment depends on one combination of the weak interaction constants, in the presence of core polarization the Schiff moment depends on all three constants separately. The dominant contribution comes from isovector, ∆T = 1, part of the weak interaction. The effects of core polarization were found to have in general a large effect on the Schiff moments.