Test of the $\xi$-Approximation in Some First-Forbidden $2^{-}$ → $2^{+}$ $\beta$ Transitions

The $\beta -\gamma$ directional correlations of the first-forbidden nonunique $2^{-}$ → $2^{+}$ $\beta$ transitions of ${\mathrm{K}}^{42}$, ${\mathrm{Sb}}^{122}$, and ${\mathrm{Au}}^{198}$ were investigated and compared with the predictions of the $\xi$ approximation, whose range of applicability is discussed. Upper limits for the contribution of the tensor-type matrix element $\int B_{\mathrm{ij}}$ to the $\beta$ transitions were estimated on the basis of the modified $B_{\mathrm{ij}}$ approximation.