Energy levels of doubly excited states of He

The doubly excited states of He, having both electrons in the same $n$ shell, are investigated by constructing a diagonal approximation for $R_{12}^2$ in terms of SO(4) operators. By inverting this operator and taking the square root, an approximate operator expression for $\frac{1}{R_{12}}$ is obtained. Energies of states in the ${\mathrm{}(n=3\mathrm{})\mathrm{}}^2$ shell of He are calculated using this expression and compared with results of more elaborate calculations. Good agreement is found in most cases.