Closed expressions for the nuclear moments in semi-leptonic processes

We discuss a general formalism needed for a unified description of the weak and electromagnetic processes in nuclei which is based on the multipole decomposition of the hadronic currents. The use of harmonic oscillator single-particle basis, which is commonly employed in many-body nuclear calculations, simplifies the relevant expressions. We present analytic formulas for the corresponding radial integrals which enter the transition matrix elements of one-body operators in various semi-leptonic nuclear processes. As an example, we apply our formalism in order to simplify previous formalism giving the nuclear moments for the $0\nu\beta\beta$ - decay. Our results for the radial integrals refer to the 1s-0d-1p-0f model space.