$\tilde{J}$-pseudospin states and the crystal field of cubic systems

Theory of $\tilde{J}$-pseudospin for $f$ element in cubic environment is developed. By fulfilling the symmetry requirements and the adiabatic connection to atomic limit, the crystal-field states are uniquely transformed into $\tilde{J}$-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 include the effects such as the covalency and $J$-mixing beyond the $f$-shell model. Combining the developed theory with {\it ab initio} calculations, the $\tilde{J}$-pseudospin states for Nd${}^{3+}$ and Np${}^{4+}$ ions in octahedral sites of insulators are derived.