Free-space electric-dipole spontaneous emission rate
= Free-space electric-dipole spontaneous emission rate
{title2=$A_{21}=\omega_{21}^3|\mathbf d_{12}|^2/(3\pi\epsilon_0\hbar c^3)$}
For a specified electric-dipole transition, summing free radiation modes gives $A_{21}=\omega_{21}^3|\mathbf d_{12}|^2/(3\pi\epsilon_0\hbar c^3)$. Unresolved degenerate levels require sums over final substates and appropriate initial-state averages. Modified radiation environments alter the available modes.