Using a direct calculation, the line intensity of the two-photon $\left({}_{}{}^7{}_{}{}^{}F_6^{}{}_{}{}^{}\right){\Gamma }_{1g}-{\Gamma }_{1g}\left({}_{}{}^5{}_{}{}^{}D_4^{}{}_{}{}^{}\right)$ transition of ${\mathrm{Tb}}^{3+}$ in the elpasolite lattice has been accounted for under third-order perturbation theory. Employing the appropriate $4f^{7}5d$ intermediate levels, $\chi$ and $\mu$, the transition moment has been written in terms of electric-dipole allowed transitions between the $4f^8$ and $4f^{7}5d$ configurations, and of the spin-orbit coupling between the intermediate states. The calculated line strength is sensitive to the locations of the intermediate-state energy levels.

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