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Theory of $\tilde{J}$-pseudospin for $f$ element in cubic environment isdeveloped. By fulfilling the symmetry requirements and the adiabatic connectionto atomic limit, the crystal-field states are uniquely transformed into$\tilde{J}$-pseudospin states. In terms of the pseudospin operators, both thetotal angular momentum and the crystal-field Hamiltonian contain higher-ranktensor terms than the traditional ones do, which means the present frameworknaturally 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.

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