J̃ -pseudospin states and the crystal field of cubic systems

The theory of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$ pseudospin for the $f$ element in a cubic environment is developed. By fulfilling the symmetry requirements and the adiabatic connection to the atomic limit, the crystal-field states are uniquely transformed into $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$-pseudospin states. In terms of the pseudospin operators, both the total angular momentum and the crystal-field Hamiltonian contain higher-rank tensor terms than the traditional ones do, which means the present framework naturally includes effects such as covalency and $J$ mixing beyond the $f$-shell model. Combining the developed theory with ab initio calculations, the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$-pseudospin states for ${\mathrm{Nd}}³⁺$ and ${\mathrm{Np}}⁴⁺$ ions in octahedral sites of insulators are derived.