Nuclear spin polarization (source code)

= Nuclear spin polarization
{title2=$P=(N_+-N_-)/(N_++N_-)$}

For two levels separated by $\Delta E$ and with the plus label assigned to the upper level, thermal equilibrium gives $P=-\tanh(\Delta E/(2k_BT))$. The weak-splitting limit is $P\simeq-\Delta E/(2k_BT)$. Labels based on the lower-energy aligned moment reverse the reported sign without changing the population imbalance.