What is the relationship between the energy absorbed and emitted by an atom with the model of Lorentz?
In the Lorentz model of an atom, we have that, using the effective cross-sections we might get somewhere since it is the relationship between the power emitted and the Poynting vector: $$\sigma_e=\frac{\langle P_e\rangle}{\langle |S|\rangle}=\frac{c\epsilon_0 q^2}{m_e}\frac{\gamma \omega^2}{(\omega^2-\omega_0^2)^2+\omega^2\gamma^2}$$ but how would one find the relationship between the energies and not the power and the poynting vector? I'm thinking something to do with time?
Or maybe since the Poynting vector is the power absorbed? Maybe use something with that?
