= Langevin diamagnetic susceptibility
{c}
{title2=$\chi=-\mu_0 nZe^2\langle r^2\rangle/(6m_e)$}
For identical isotropic closed-shell atoms of <number density> $n$, with $Z$ electrons and mean squared radius $\langle r^2\rangle$ per electron, the quadratic <magnetic field> energy is $Ze^2B^2\langle r^2\rangle/(12m_e)$. It follows from the $e^2\mathbf A^2/(2m_e)$ term with $\mathbf A=\mathbf B\times\mathbf r/2$. Differentiating the energy with respect to field and using $B\simeq\mu_0H$ yields the negative SI volume <magnetic susceptibility>. For <helium>, $Z=2$; combining it with the independent spin-one-half nuclear response $\mu_0n\mu_a^2/(k_BT)$ gives a density-independent sign-change scale $T_0=3m_e\mu_a^2/(e^2k_B\langle r^2\rangle)$.
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