Search for classification of helium atom twice excited states for an intermediate range of quantum numbers

The possibility of classification of twice excited states in an intermediate range of n1, n2 electron main quantum numbers and the total orbital momentum (L) is analyzed. The approximate integrals of motion that determine the classification of two-electron states are known for the cases of n1 approximately n2, L approximately 1 and n1>>n2, L>>1. The possibility of constructing the classifying operators in the intermediate range of quantum numbers of n1, n2, L is discussed. The results are compared with those of numerical calculations