“…The are the rates of population transfers from states | J M 〉 to states | J ′ M ′ 〉, and are the rates of pure dephasing of the | J M 〉〈 J ′ M | coherences. The ECS expression of the former, derived from Hartmann and Boulet by introducing adiabaticity corrections into the infinite order sudden equations, is which is used for downward transitions, the upward ones being deduced from detailed balance. Similarly, starting from Strekalov and Dickinson the dephasing contribution is …”