gFactors of Excited Nuclear States by Resonant Scattering

If a resonant nuclear state is excited during a scattering process in the presence of a known magnetic field, the state, and so the angular distribution of its decay products, will precess through an angle $\delta$ which can be used to measure the $g$ value of the state if its lifetime $\tau =\frac{\hslash }{\Gamma }$ is known. We investigate the influence of the bandwidth $\Delta$ of the incident wave packet on this angle, and find that it varies smoothly from $\delta =\Omega \tau$ ($\Omega =\mathrm{Larmor}\mathrm{precession}\mathrm{frequency}$) for $\Delta \gg \Gamma$ to $\delta =2\mathrm{}\Omega \tau$ for $\Delta \ll \Gamma$.