A unified formalism for the basic nuclear matrix elements in semi-leptonic processes

A general compact formalism, appropriate for the description of transition amplitudes in semi-leptonic processes involving lepton–nucleus interactions, is presented. Closed analytic expressions for the reduced matrix elements of all the basic tensor operators originating from a multipole expansion of the relevant hadronic current density and the use of harmonic oscillator basis are derived. The method improves over the well-known Horie–Sasaki formalism used the last decades as well as over other similar methods employed in nuclear many-body calculations. As a concrete application, we present results of differential cross sections for the neutral-current neutrino–nucleus reaction obtained with state-by-state calculations in the context of the quasi-particle random phase approximation (QRPA).