= Impurity band
{title2=$W\sim E_b\exp[-n^{-1/3}/a_b]$}
An <energy band> formed when localized <impurity levels> hybridize. For <hydrogenic donor states>, a typical donor separation $n^{-1/3}$ gives an exponentially small <hopping integral> and hence an exponentially narrow <bandwidth> when $n^{-1/3}\gg a_b$. An idealized half-filled band with two <spin> states per donor has spin-summed <density of states> of order $2n/W$ per volume; its <Pauli paramagnetism> is $\chi\sim\mu_0(g\mu_B/2)^2(2n/W)$. That expression requires $k_BT\ll W$ and does not by itself describe localization or strong <Coulomb interactions>.
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