Big consequences of small changes (Non-locality and non-linearity of Hartree-Fock equations)

TL;DR

This paper explores how the non-local and non-linear nature of Hartree-Fock equations significantly alters their solutions compared to traditional Schrödinger solutions, impacting physical predictions in atomic physics.

Contribution

It demonstrates the profound effects of non-locality and non-linearity in Hartree-Fock equations on solution properties and physical process probabilities.

Findings

Hartree-Fock solutions have extra zeroes and different asymptotics.

Solutions can violate gauge invariance and have multiple solutions with same quantum numbers.

Physical process probabilities, like ionization, are significantly affected.

Abstract

It is demonstrated that non-locality and non-linearity of Hartree-Fock equations dramatically affect the properties of their solutions that essentially differ from solutions of Schr?dinger equation with a local potential. Namely, it acquires extra zeroes, has different coordinate asymptotic, violates so-called gauge-invariance, has different scattering phases at zero energy, has in some cases several solutions with the same set of quantum numbers, usually equivalent expressions of current and Green's functions became non-equivalent. These features result in a number of consequences for probabilities of some physical processes, leading e. g. to extra width of atomic Giant resonances and enhance considerably the ionization probability of inner atomic electrons by a strong field.