A shell-model study is made of second-forbidden unique β decay of ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$, and ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$. Calculations were made with a p-shell interaction for ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ and the sd-shell interaction of Wildenthal for ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ and ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$. The resulting second-forbidden unique matrix elements are consistently larger than experiment. The ratio is discussed in terms of two effects: the ‘‘collective suppression’’ discussed in 1970 by Warburton, Garvey, and Towner and in-medium quenching of the spin operator. Comparison is made to similar effects for M3 transitions.

• Received 9 May 1991

DOI:https://doi.org/10.1103/PhysRevC.45.463