Group theoretic prediction of configuration mixing effects due to Coulomb repulsions in atoms with applications to doubly-excited spectra

A group theoretical method which predicts Coulomb repulsion mixing coefficients of doubly−excited atomic states is presented. Good agreement with calculated mixings in helium is found. Two new quantum numbers and three rules classify and predict the energy level orderings. The exact mathematical construction of 1/r12 in the group theoretical configuration−mixed basis is given. It leads naturally to a formulation of the corresponding many−electron problem of configurational mixings.