Superallowed Beta Transitions in theN−Z=3Series

A number of fast beta transitions have been found in the $N-Z=3\mathrm{}$ series of radioactive nuclides. King has suggested that some of these transitions (for $A<\mathrm{}27\mathrm{}$) occur within the lowest [4...421] or [4...432] supermultiplet; hence are superallowed (or favored). Matrix elements of ${\left|\int \sigma \right|}^2$ within the [21] and [32] supermultiplets are computed with the aid of two-way displacement operators on the eigenvalues of $T_3$, $S_z$, and $Y_{3z}$. In the application to ${}_8{}^{}{}_{}{}^{}\mathrm{O}_{11}^{}{}_{}{}^{}$ the only spin assignments consistent with an $\mathrm{LS}$ coupling interpretation of the fast transition are $I_i=\frac{5}{2}$, $I^{*}=\frac{3}{2}(S^{*}=\frac{1}{2})$. These are the value favored by the available experimental information. The $\mathrm{jj}$ coupling value of ${\left|\int \sigma \right|}^2$ for the ${}_8{}^{}{}_{}{}^{}\mathrm{O}_{11}^{}{}_{}{}^{}$ transition is too large by a factor of five.