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Nathanael A. Fortune edited section_Nuclear_Schottky_effect_In__.tex
over 8 years ago
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In closed form,
\begin{equation}
\label{eq:ClosedFormSolution}
c_N = R \left(\frac{x}{2I}\right)^2
\{{\textrm{Csch}}^2\left(\frac{x}{2I}\right) \left[{\textrm{Csch}}^2\left(\frac{x}{2I}\right) - 2(2I+1)^2
{\textrm{Csch}}^2[(2I+1)\frac{x}{2I}]\} {\textrm{Csch}}^2[(2I+1)\left(\frac{x}{2I}\right)]\right]
\end{equation}
The Zeeman splitting of the nuclear energy levels leads to a broad peak in the specific heat when $k_b T$ is on the order of the energy splitting $\mu H$, but because the energy splittings are small\footnote{the nuclear magneton is a factor of 1836.1 smaller than the Bohr magneton $\mu_B$}, only the high temperature $(\mu H/k_B T)^2$ tail of specific heat peak is seen. Assuming that the zero field field splitting (ZFS) is negligible in comparison to that from the applied field $H$, then \cite{Lounasmaa1974, Leyarovski_1988},