## Analysis of Hartree-Fock equations and Koopman's theorem

Similalry, we could interpret $$BE(^{17}\mathrm{O})-BE(^{16}\mathrm{O})\approx \epsilon_{0d^{\nu}_{5/2}}^{\mathrm{HF}},$$ and $$BE(^{17}\mathrm{F})-BE(^{16}\mathrm{O})\approx\epsilon_{0d^{\pi}_{5/2}}^{\mathrm{HF}}.$$ We can continue like this for all $$A\pm 1$$ nuclei where $$A$$ is a good closed-shell (or subshell closure) nucleus. Examples are $${}^{22}\mbox{O}$$, $${}^{24}\mbox{O}$$, $${}^{40}\mbox{Ca}$$, $${}^{48}\mbox{Ca}$$, $${}^{52}\mbox{Ca}$$, $${}^{54}\mbox{Ca}$$, $${}^{56}\mbox{Ni}$$, $${}^{68}\mbox{Ni}$$, $${}^{78}\mbox{Ni}$$, $${}^{90}\mbox{Zr}$$, $${}^{88}\mbox{Sr}$$, $${}^{100}\mbox{Sn}$$, $${}^{132}\mbox{Sn}$$ and $${}^{208}\mbox{Pb}$$, to mention some possile cases.