Molecular symmetry in two-electron excited and ionized states

It is well established that lower-lying doubly excited two-electron resonant states can be described by approximate collective quantum numbers. These quantum numbers appear naturally if the problem is treated in 'molecular' coordinates using the interelectronic vector as an adiabatic variable. The appropriateness of these coordinates is demonstrated further using some recent numerical calculations on negative ion excitation. As the threshold of the two-electron continuum is approached from below and different manifolds of resonances overlap, it is believed that these quantum numbers cease to be applicable. However, one quantum number, the saddle-inversion quantum number, usually denoted by A = +/-1, is preserved through the threshold. A detailed analysis of the T-matrix for photo-double-ionization is given with the aim of emphasizing the role played by the saddle-inversion symmetry.