Spectral Multiplets Belonging to Configurations of the Typedkmsanddkmsns

Abstract

The Dirac vector model, as considered by Van Vleck, has been applied to calculate the energy values of configurations of the type $d^{\mathrm{k}}\mathrm{m}s$ and $d^{\mathrm{k}}\mathrm{m}s\mathrm{n}s$, in cases where the $d^{\mathrm{k}}$ core conforms to Russell-Saunder's coupling. The spin-orbit energy is not assumed small compared to the electrostatic energy coupling $d^{\mathrm{k}}$ to $\mathrm{m}s$ or $d^{\mathrm{k}}$ to $\mathrm{n}s$. Johnson's formulas for the four vector problem have been used to set up a general secular determinant for configurations of the type $d^{\mathrm{k}}\mathrm{m}s\mathrm{n}s$. The special cases where $d^{\mathrm{k}}\mathrm{m}s\mathrm{n}s$ may be treated as a three vector problem or as a case of Russell-Saunder's coupling are also considered. The following multiplets have been examined: Y I, $4d\left({}_{}{}^2{}_{}{}^{}D\right)5s6s$; Cu I, $3d^9\left({}_{}{}^2{}_{}{}^{}D\right)4s5s$; Zr I, $4d^2\left({}_{}{}^3{}_{}{}^{}F\right)5s6s$; Ni I, $3d^8\left({}_{}{}^3{}_{}{}^{}F\right)4s5s$; Co I, $3d^7\left({}_{}{}^4{}_{}{}^{}F\right)4s5s$; Fe I, $3d^6\left({}_{}{}^5{}_{}{}^{}D\right)4s5s$; and Ti I, $3d^2\left({}_{}{}^3{}_{}{}^{}F\right)4s6s$. The exchange integrals are considered as parameters and chosen to give the best fit with experimental data. The agreement with experiment for $d^{\mathrm{k}}\mathrm{m}s\mathrm{n}s$ is better, as it ought to be, with the four vector problem (${\mathrm{L}}_d$, ${\mathrm{S}}_d$, ${\mathrm{s}}_{\mathrm{m}}$, ${\mathrm{s}}_{\mathrm{n}}$) than with the three vector problem (${\mathrm{L}}_d$, ${\mathrm{S}}_{d+\mathrm{m}}$, ${\mathrm{s}}_{\mathrm{n}}$) which in turn agrees better with experiment than does the two vector problem (${\mathrm{L}}_d$, ${\mathrm{S}}_{d+\mathrm{m}+\mathrm{n}}$), the case resulting from the assumption of Russell-Saunder's coupling. Configurations $d^{\mathrm{k}}\mathrm{m}s$ (other than Houston's singlet-triplet case) have been examined as a three vector problem (${\mathrm{L}}_d$, ${\mathrm{S}}_d$, ${\mathrm{s}}_{\mathrm{m}}$). Some examples treated are: Ti II, $3d^2\left({}_{}{}^3{}_{}{}^{}F\right)5s$; Ni II, $3d^8\left({}_{}{}^3{}_{}{}^{}F\right)5s$; Co I, $3d^8\left({}_{}{}^3{}_{}{}^{}F\right)5s$; Co I, $3d^8\left({}_{}{}^3{}_{}{}^{}F\right)4s$; Pd II, $4d^8\left({}_{}{}^3{}_{}{}^{}F\right)6s$; Fe I, $3d^7\left({}_{}{}^4{}_{}{}^{}F\right)5s$; Co II, $3d^7\left({}_{}{}^4{}_{}{}^{}F\right)5s$.