Comparison of Impulse-Approximation and Elementary-Particle Treatments in NuclearβDecay

Abstract

We have compared the usual impulse-approximation and the elementary-particle treatments of nuclear processes using nuclear $\beta$ decays as examples. Both treatments are shown to lead to essentially equivalent results for allowed transitions and for natural-parity forbidden transition of the types $\Delta J^{P_i{P}_f}=1^{-} \mathrm{and}\mathrm{possibly} 2^{+},3^{-},\dots$. There exist, however, some differences in detailed structures in small correction terms. In the case of unnatural-parity forbidden transitions, in particular, $J_i^{P_i}\left(0^{-}\right)\to J_f^{P_f}\left(0^{+}\right)+e^{-}+{\overline{\nu }}_e$, there exist some discrepancies between the two approaches, suggesting an important role of meson-exchange corrections in the impulse approximation.