= Photon absorption recoil correction
{title2=$h\nu=\Delta E+\Delta E^2/(2Mc^2)$}
An initially stationary isolated <chemical atom> of <rest mass> $M$ absorbing a single <photon> must recoil. If the internal excitation changes its <rest mass> by $\Delta M=\Delta E/c^2$, <conservation of energy> and <conservation of momentum> give $Mc^2+h\nu=\sqrt{(Mc^2+\Delta E)^2+(h\nu)^2}$ and hence the exact formula in the title. The additional positive <energy> supplies recoil. An external body sharing the <momentum>, or an initially moving <chemical atom>, changes this laboratory resonance condition.
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