Second-Order Nonradiative Processes in CaF2:Sm2+

It was first shown by Axe and Sorokin that nonradiative decay of the terminal optical maser level (${}_{}{}^7{}_{}{}^{}F_1^{}{}_{}{}^{}$) Ca${\mathrm{F}}_2$: ${\mathrm{Sm}}^{2+}$ is forbidden to first order even though many phonon states are available with the proper energy for the transition. At first sight this would indicate the ${}_{}{}^7{}_{}{}^{}F_1^{}{}_{}{}^{}$ level to be metastable. It is shown that a second-order two-phonon emission transition can alleviate this bottleneck, and the decay process rate is computed. This process, involving virtual transitions to a higher level (${}_{}{}^7{}_{}{}^{}F_2^{}{}_{}{}^{}$), is shown to be very effective and to lead to a nonradiative lifetime of ∼${10}^{-6\mathrm{}}$ sec, in accord with the necessary conditions for the existence of optical maser action in Ca${\mathrm{F}}_2$: ${\mathrm{Sm}}^{2+}$.