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Analysis of Hartree-Fock equations and Koopman's theorem

We can thus make our first interpretation of the separation energies in terms of the simplest possible many-body theory. If we also recall that the so-called energy gap for neutrons (or protons) is defined as ΔSn=2BE(N,Z)BE(N1,Z)BE(N+1,Z), for neutrons and the corresponding gap for protons ΔSp=2BE(N,Z)BE(N,Z1)BE(N,Z+1), we can define the neutron and proton energy gaps for 16O as ΔSν=ϵHF0dν5/2ϵHF0pν1/2, and ΔSπ=ϵHF0dπ5/2ϵHF0pπ1/2.