Sum rules for the total- and scissors-mode $M1\mathrm{}$ strength in odd- $A$ nuclei are derived within the single- $j$ interacting boson-fermion model. We discuss the physical content and geometric interpretation of these sum rules and apply them to ${}^{167}\mathrm{Er}$ and ${}^{161}\mathrm{Dy}$. We find consistency with the former measurements but not with the latter.

• Received 10 March 1997

DOI:https://doi.org/10.1103/PhysRevLett.79.813