Relativistic description of 0 + ⇌ 0 − weak-axial transitions in A = 16 nuclei

Abstract

We consider 0 + ⇌ 0 − weak-axial transitions in A = 16 nuclei using the Dirac equation with real Lorentz scalar and time-like vector potentials as the relevant nucleon wave equation. We first examine the 16 N(0 −) → 16 O(0 +) first-forbidden β-decay using the theory of Schopper and show that the relativistic dynamics strongly enhances the anomalously reduced non-relativistic β- decay rate bringing it closer to the experimental rate. The sensitivity of the β-decay rate to the nuclear model parameters is discussed. We then study the inverse process, the 16 O(0 +) → 16 N(0 −) muon-capture, using a new formalism and show that the μ- capture rate may be reproduced simultaneously with the β-decay rate. An analysis of the sensitivity of the μ-capture rate to the induced pionic term and to nuclear model parameters is also made. Overall, although the relativistic effects are appreciable and produce new qualitative features which improve on the standard non-relativistic approach, no conclusive empirical evidence supporting the necessity of adopting the relativistic framework can be inferred.