Slow long-range decay of bound Hartree-Fock orbitals and enhancement of   the exchange interaction and tunneling
  Exchange interaction strongly influences the long-range behaviour of localised electron orbitals. It violates the oscillation theorem (creates extra nodes) and produces a power-law decay instead of the usual exponential decrease at large distances. For inner orbitals inside molecules decay is 1/r^2, for macroscopic systems cos(k_f r)/r^n, where k_f is the Fermi momentum and n=3 for 1D, n=3.5 for 2D and n=4 for 3D crystal. Slow decay increases the exchange interaction between localised spins and the under-barrier tunneling amplitude.The under-barrier transmission coefficients in solids (e.g. for point contacts) become temperature-dependent. 
V.V. Flambaum