gValues of thed1T22Ground Term in the Presence of a Dynamic Jahn-Teller Effect

Analytical expressions are given for the $g$ values of the excited levels of the $d^1{}_{}{}^2{}_{}{}^{}T_2^{}{}_{}{}^{}\mathrm{}(0,0)\mathrm{}$ ground term in the presence of a dynamic Jahn-Teller effect. These apply to $d^1$ impurities in trigonally distorted cubic sites and are good to second order in the vibronic coupling to $E_g$ modes.