= Radiative balance in a nondegenerate two-level atom
{title2=$R_{\rm sp}/R_{\rm st}=(N_1-N_2)/N_2$}
Let $A_{21}$ be the <spontaneous emission> coefficient and let $B\rho$ be the induced transition rate per atom under a resonant radiation spectral energy density $\rho$. For nondegenerate levels the <Einstein coefficients> obey $B_{12}=B_{21}=B$. In a closed <two-level system> with no collisional or other population transfer, steady state requires
$$
N_1B\rho=N_2B\rho+N_2A_{21}.
$$
For nonzero upper population and drive, division gives the ratio of total spontaneous and stimulated emission rates in the title. In particular $N_1>N_2$ when $A_{21}>0$; continuous driving of this closed model approaches equal populations but cannot create a <population inversion>. No thermal population law is assumed.
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