= FRET efficiency
{c}
{title2=$E$}
<FRET efficiency> is the <probability> that an excitation of the <FRET donor> ends in transfer to the <FRET acceptor>. Write $k_D=k_{\rm r}+k_{\rm nr}$ for the total decay rate without a <FRET acceptor>, including radiative <fluorescence> and other decay, and $k_T$ for the transfer rate. For constant competing rates,
$$
k_T=k_D\left(\frac{R_0}{r}\right)^6,\qquad E=\frac{k_T}{k_D+k_T}=\int_0^\infty k_T e^{-(k_D+k_T)t}\,dt.
$$
The <integral> counts transfer events among all excitations in a population with <exponential decay>. Substitution gives the separation law above. This short rate argument assumes one <FRET donor>, one <FRET acceptor>, weak coupling, an available <FRET acceptor>, and fixed geometry during the decay; it is not a model for arbitrary interacting labels.<Advanced Fluorescence Microscopy Techniques—FRAP, FLIP, FLAP, FRET and FLIM by Hellen C. Ishikawa-Ankerhold and others>[§3.1, equations 14–16 and discussion before §3.3: single-pair assumptions and transfer efficiency]{ref}
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