Term Formulae for the Configurationd5

Term formulae for a configuration of five equivalent $d$ electrons have hitherto not been published. They are given below for the case of Russell-Saunders coupling. A surprising result is that although several terms appear more than once (two ${}_{}{}^2{}_{}{}^{}G$, two ${}_{}{}^2{}_{}{}^{}F$, three ${}_{}{}^2{}_{}{}^{}D$) and are therefore expected to depend irrationally upon the radial integrals, this is only so for two out of the three ${}_{}{}^2{}_{}{}^{}D$ terms. For the other of the above terms the secular equation possesses roots linear in the radial integrals. The formulae obtained are able to represent satisfactorily the $d^5$ terms of Cr II.