Approximate solutions of the particle-rotor model for decoupled bands

The particle-rotor model with a single nucleon in a configuration with large fixed $j$ is treated by means of the Holstein-Primakoff expansion. The small-oscillation approximation yields relatively simple analytic expressions for energies, alignments, electromagnetic moments, and transition rates of decoupled bands, which are surprisingly accurate over a broad range of $\frac{C}{A}$.