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Exchange interaction strongly influences the long-range behaviour oflocalised electron orbitals. It violates the oscillation theorem (creates extranodes) and produces a power-law decay instead of the usual exponential decreaseat large distances. For inner orbitals inside molecules decay is 1/r^2, formacroscopic systems cos(k_f r)/r^n, where k_f is the Fermi momentum and n=3 for1D, n=3.5 for 2D and n=4 for 3D crystal. Slow decay increases the exchangeinteraction between localised spins and the under-barrier tunnelingamplitude.The under-barrier transmission coefficients in solids (e.g. for pointcontacts) become temperature-dependent.

Slow long-range decay of bound Hartree-Fock orbitals and enhancement of the exchange interaction and tunneling