Partial cancellation of correlations in the nonrelativistic high-energy asymptotics of the photoeffect

We investigate the total effect of correlations on photoionization of atomic states with nonzero orbital momentum in the nonrelativistic high-energy asymptotic limit, considering the exclusive case of the dominant final state of an initial neutral atom. We find that the substantial cancellation of the dominant intrashell correlations, which had been reported earlier, can be understood utilizing the closure properties satisfied by the eigenfunctions of the nonrelativistic Hamiltonian. Considering the sum of correlations with all states, occupied or not, we show that complete sum is equal to the contribution of the high-energy part of the continuum. Consequently there is a total cancellation between the contributions of the bound states (occupied and unoccupied) and the low-energy part of the continuum states. This means that the real correlations in the physical atom due to the sum rule over the occupied states can be also obtained as the negative of the sum of contributions of low-energy bound and continuum unoccupied states. We calculate this in the framework of the quantum-defect model. As we would expect, the results are close to those obtained earlier in particular cases by direct summation over the occupied states. However this approach also allows us to see that the sum of correlations over the occupied states is smaller than the dominant intrashell correlation. Hence, there is a partial cancellation between correlations with the occupied states. We can also obtain some limits on the correlation effects by considering calculations with the screened Coulomb functions. The role of correlations in the exclusive photoionization processes, also the modification of correlations in the case of atomic ions, is discussed.