Predicted features of the beta decay of neutron-rich $\mathrm{sd}$-shell nuclei

The Gamow-Teller beta-decay transitions of $\mathrm{sd}$-shell nuclei with five or more excess neutrons are calculated from complete ($0d_{\frac{5}{2}}, 1s_{\frac{1}{2}}, 0d_{\frac{3}{2}}$) space shell-model wave functions. These wave functions are obtained from diagonalizations of a model Hamiltonian formulation which reproduces observed energy-level structures throughout the $\mathrm{sd}$ shell. The calculations are carried out with both the "free-nucleon" normalization for the Gamow-Teller single-nucleon matrix elements and one based on the empirical values obtained for these quantities from a comparison of corresponding theoretical and experimental Gamow-Teller magnitudes near the line of stability. The phase-space factors $f$ which connect the reduced Gamow-Teller strengths to the total half-lives and the individual decay probabilities are calculated both from the energies obtained in the shell-model calculations and, alternatively, from hybrid energy spectra in which available experimental energies are substituted for the corresponding calculated values wherever possible. Comparisons of the beta-decay predictions to existing experimental results are presented and discussed.

RADIOACTIVITY Predictions of total half-lives and decay probabilities to individual daughter states of the isotopes of O, F, Ne, Na, Mg, Al, Si, and P which have neutron excesses of five and greater; shell-model calculations, complete $0d_{\frac{5}{2}}-1\mathrm{}{s}_{\frac{1}{2}}-0\mathrm{}{d}_{\frac{3}{2}}$ basis space, empirical $\mathrm{sd}$-shell Hamiltonian.