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

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.

16 pages, 3 figures

References in corpus (3)

• Fullerenes and endohedrals as "big atoms"
• Slow long-range decay of bound Hartree-Fock orbitals and enhancement of the exchange interaction and tunneling
• Exchange interaction and correlations radically change behaviour of a quantum particle in a classically forbidden region