where Q Ze i = Tr e -β Ĥ( mi ;B 0 ) is the partition function evaluated as the trace of the Hamiltonian matrix of Ĥ ( mi ; B 0 ) = Ĥ0 + ĤZe ( mi ; B 0 ). Ĥ0 and ĤZe ( mi ; B 0 ) are the unperturbed and the first-order Zeeman interaction Hamiltonian operators. E Ze ni and n Ze i are the eigenvalues and eigenvectors of Ĥ ( mi ; B 0 ), respectively.