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allowed values analytic asymptotic axis behavior Brueckner Brueckner-Goldstone calculated closed shell cluster expansion coefficient compute contribution core correct defined degenerate subspace dependence derive determined diagonal differential equation eigenstates eigenvalues energy denominators equal estimate evaluate exponentially expression fermi sea formula G-matrix given gmn(Z graphs half sphere Hamiltonian infinite nuclear matter interaction intermediate k-space integral kinetic energy leading term matrix elements MeV f mn|G|mn momentum mx nx nuclear matter nuclear surface nucleons numerical obtain one-particle wave functions operator partial wave particle density perturbation theory phase space Phys power series proportional quantity reference equation reference spectrum approximation reference spectrum method regular singular points relative error result S-wave self-consistency Simpson's rule sine wave sine wave fit singular point Slater determinant smallest pole solution surface energy surface region two-body potential vanishes variable vector write zero