Comparison of the pn quasiparticle RPA and shell model for Gamow-Teller beta and double-beta decays

We examine the validity of the pn quasiparticle RPA (pnQRPA) as a model for calculating ${\mathrm{\beta }}^{+}$ and 2νββ Gamow-Teller decays by making a comparison of the pnQRPA with a large-basis shell-model calculation within the 0f1p shell. We employ A=46 nuclei (those with six valence nucleons) for this comparison. Our comparison includes the decay matrix elements summed over final states, the strength distributions, and, for the first time, the coherent transition matrix elements (CTME). The pnQRPA overestimates the total ${\mathrm{\beta }}^{+}$ and 2νββ matrix elements. There are large differences in the shape of the spectra as well as in the CTME between the pnQRPA and shell-model results. Empirical improvements for the pnQRPA are discussed.