Nathanael A. Fortune edited Cu nuclear moment.tex  over 8 years ago

Commit id: 957c065fa094214c142a828f193c1f5ccaada379

deletions | additions      

       

\section{Cu nuclear moment}  ${}^{\ 63}_{\ 29}\textrm{Cu}$ and ${}^{\ 65}_{\ 29}\textrm{Cu}$ are the two most common stable Cu isotopes. ${}^{\ 63}_{\ 29}\textrm{Cu}$ has a nuclear spin $I = 3/2$ and a nuclear magnetic moment $\mu = 2.2228$ 2.2228 \mu_N$  while ${}^{\ 65}_{\ 29}\textrm{Cu}$ has a nuclear spin $I = 3/2$ and a nuclear magnetic moment $\mu = 2.3812$ 2.3812 \mu_N$  \cite{Fuller_1976}. Here, $\mu_N$ is the nuclear magneton (given by $\mu_N = \frac{h e}{4 \pi M_p c} = 5.051 10^_-27 \textrm{ J/T}$), $g = \mu / I$ and the resulting energy splitting in applied field is $\Delta = g \mu_n H / k$.  Substituting $g_N = \mathrm{1.5}$ --- the weighted average nuclear g-factor for these two most common Cu isotopes \cite{Leyarovski_1988}--- into Eq.~\ref{eq:CurieConstant} gives a theoretical value $\lambda_{\mathrm{Cu}} = 3.93 \cdot 10^{-12} \textrm{ K}{\textrm{ m}}^3 {\textrm{ mol}}^{-1}$. Experimentally, \cite{Leyarovski_1988} find a value of $\lambda_{\mathrm{Cu}} = 4.03 \cdot 10^{-12} \textrm{ K}{\textrm{ m}}^3 {\textrm{ mol}}^{-1}$ upon fitting Eq.~\ref{eq:SchottkyTail} to their measurements of the specific heat of Cu taken between 0.3 K and 1 K in an applied field of 14 T.