= Fermionic Einstein-coefficient relations
{title2=$R_\downarrow=A(1-f)$}
For an ideal emitter able to exchange one <fermion> with a zero-<chemical potential> bath, <Pauli blocking> gives downward rate $A(1-f)$ rather than the bosonic $A(1+f)$. If $u_\nu=h\nu\mathcal D_\nu f$ and $C=A/(h\nu\mathcal D_\nu)>0$, the rate is $A-Cu_\nu$. <Detailed balance> with a <Fermi-Dirac distribution> implies $g_1B_{12}=g_2C$ and $A/C=h\nu\mathcal D_\nu$. For $d$ massless helicity states, $\mathcal D_\nu=d\,4\pi\nu^2/c^3$. Thus an additive induced-emission coefficient would be negative, expressing blocking rather than a negative total rate. The emitter must change its <fermion parity>; two ordinary electronic <energy levels> cannot exchange a single <neutrino> this way.
Back to article page
