Free ions Pr IV ( $$4\text{ f }^{2}$$ 4 f 2 ) and Tm IV ( $$4\text{ f }^{12}$$ 4 f 12 ): intermediate versus LS coupling scheme

Abstract

The intermediate and LS-coupling schemes for the free lanthanide ions \(\text{ Pr }^{3+}\) and \(\text{ Tm }^{3+}\) have been compared by the matrix elements of the tensor operator \({{\varvec{U}}}^{({\varvec{k}})}, \text{ k } = 2, 4, 6\). The necessary eigenvectors and eigenvalues have been computed with the aid of four parameters, \(\text{ F }_{2}, \text{ F }_{4}, \text{ F }_{6}\), and \(\zeta _{4\mathrm{f}}\), known from free-ion spectra of the same ions. It has been found that both coupling types for each ion lead to close values of \({\vert }{{\varvec{U}}}^{({\varvec{k}})}{\vert }^{2}\) only for transitions from the ground level to certain lower-lying energy levels within the \(4\text{ f }^\mathrm{N}\) configuration.