= Relaxation time conventions in stellar dynamics
{title2=$D_v=8\pi nG^2m^2\ln\Lambda/u$}
Weak equal-mass <small-angle gravitational encounters> give a single-star transverse kick $2Gm/(bu)$ and a relative-velocity kick twice as large. With encounter rate $2\pi b\,db\,nu$, the single-star squared-velocity diffusion rate is the displayed $D_v$, while the relative rate is $4D_v$. A chosen reference squared velocity divided by either rate defines a relaxation estimate; specifying which rate and reference are used is essential to a numerical prefactor. If $u=\sqrt2\sigma$, the convention $3\sigma^2/(4D_v)$ gives $3\sigma^3/(16\pi\sqrt2\,nG^2m^2\ln\Lambda)$. The single-star convention $3\sigma^2/D_v$ is four times larger. Velocity-distribution averaging further changes numerical coefficients, while the scaling and <Coulomb logarithm in stellar dynamics> persist. The factor $n$ must be <number density>, not a dimensionless population count.
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