An efficient method for the calculation of generalized overlap amplitudes for core photoelectron shake-up spectra

Using a Gelfand-Tsetlin N-electron basis and a graphical unitary group approach, an efficient method is derived for the calculation of generalized overlap amplitudes of the formX⁽ⁿ⁾ _p = < Ψ⁽ⁿ⁾)(N-1) |ψa_p|ψ⁽⁰⁾ (N) >, whereψ⁽ⁿ⁾(N-1) and ψ⁽⁰⁾(N) denote complete active space wavefunctions and p is a core orbital index. Using this method the computational effort to obtain X ⁿ _p is negligible compared to the wavefunction optimization.