= Superconducting coherence length
{title2=$\xi=\hbar/\sqrt{2m_*|\alpha|}$}
The gradient and quadratic terms of the stated model balance at the amplitude-variation scale $\xi$. It is a superconducting length scale, distinct from optical <coherence length>. The weak-field <London penetration depth> in the same normalization obeys
$$
\xi^2=\frac{\hbar^2}{2m_*|\alpha|},\qquad
\lambda^2=\frac{m_*}{\mu_0q^2|\psi_0|^2}.
$$
A core suppresses the pairing amplitude over a scale set by $\xi$; screening <electric currents> and the <magnetic field> involve $\lambda$. Neither scale is a universal particle size.
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