Allowed β-transitions, weak magnetism and nuclear structure in light nuclei

The general formalism for allowed β-transitions is derived in the framework of the elementary particle as well as in the impulse approximation treatment. Explicit expressions for the shape factor, the asymmetry and anisotropy of electrons emitted from oriented nuclei, the β-γ (CP) correlation and the β-γ angular correlation are given. Emphasis is imputed to the question how model independently these quantities can be evaluated. This problem has been studied in detail for the β-transitions in the nuclei ¹²B ¹²N, ²⁰F ²⁰Na, ²²Na and ²⁴Na ²⁴Al. The computations of the nuclear matrix elements are carried out for the A = 12 system in intermediate coupling and for the sd-shell nuclei in the SU(6)- SU(3) coupling scheme using different residual interactions. Comparison to experiments is made. All results can be explained with ordinary CVC predictions without invoking second class currents.