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

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