Particle cancellation of correlations in nonrelativistic high energy asymptotics of photoeffect

TL;DR

This paper analyzes how correlations affect photoionization in nonrelativistic high energy regimes, revealing a total cancellation of dominant intra-shell correlations due to sum rules and eigenfunction properties.

Contribution

It demonstrates that total correlations in photoionization cancel out when summing over all states, providing a new understanding of correlation effects in atomic photoeffect.

Findings

Complete sum of correlations equals high energy continuum contribution.

Total cancellation occurs between bound and low energy continuum states.

Dominant intra-shell correlation is effectively canceled in the high energy limit.

Abstract

We investigate the total effect of correlations on photoionization of atomic shells 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 intra-shell carrelations, which had been reported earlier, can be understood utilizing the closure properties satisfied by the eigen functions 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 and the low energy part of the continuum states. This means that the real correlations in the physical atom can be obtained as the negative of the total contribution of low energy states and continuum unoccupied states. We calculate this in framework of the quantum defect number. The approach allows us to see that the dominant intrashell correlation is going to be cancelled. 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 is discussed.