Power densities for two-stepγ-ray transitions from isomeric states

We have calculated the incident photon power density $P_2$ for which the two-step induced emission rate from an isomeric nucleus becomes equal to the natural isomeric decay rate. We have analyzed two-step transitions for isomeric nuclei with a half-life greater than 10 min, for which there is an intermediate state of known energy, spin and half-life, for which the intermediate state is connected by a known $\gamma$-ray transition to the isomeric state and to at least another intermediate state, and for which the relative intensities of the transitions to lower states are known. For the isomeric nucleus ${}^{166m}\mathrm{Ho},$ which has a $1200\hspace{0.5em}y$ isomeric state at 5.98 keV, we have found a value of $P_2=6.3\mathrm{}\times {10}^7\hspace{0.5em}{\mathrm{W}\mathrm{\hspace{0.5em}}\mathrm{cm}}^{-2},$ the intermediate state being the 263.8 keV level. We have found power densities $P_2$ of the order of ${10}^{10}\hspace{0.5em}{\mathrm{W}\mathrm{\hspace{0.5em}}\mathrm{cm}}^{-2}$ for several other isomeric nuclei.