= Transverse nuclear magnetization decay
{title2=$T_2$}
<Transverse relaxation> describes loss of ensemble transverse <magnetization>. It must not automatically be identified with pure <dephasing>. In a simple completely positive two-level relaxation model,
$$
\frac1{T_2}=\frac1{2T_1}+\frac1{T_\phi},
$$
where $T_\phi$ describes additional pure <dephasing>. Thus population recovery itself contributes to transverse decay. A spread of static <magnetic fields> can further cancel ensemble phases without the same microscopic relaxation; an observed free signal may have an effective $T_2^*$ rather than homogeneous $T_2$. The simple exponential examples below assume a uniform field and a single homogeneous $T_2$.
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