Abstract It is shown that, as a consequence of the energy independence of the boundary condition f on the radial Schroedinger wave function u at r 0, u = 0 for r < r 0, and that the boundary condition is equivalent to replacing Vu, in the equation for u in r < r 0, by an expression linear in u( r 0 + ϵ) and u′( r 0 + ϵ). The Bethe-Goldstone wave function u N is determined by the same replacement in its integral equation. But u N ≠ 0 in r < r 0, so that u N depends on an extra parameter b , the boundary condition at r 0 − ϵ. Pseudopotentials at r 0 which give the boundary condition exactly are presented. The self-consistent single particle potential energy in nuclear matter is investigated with a simple S state boundary condition, without a potential tail. The effective mass approximation is found inadequate. For the same interaction, the effect of summing the hole-hole contributions is found to be important for the two-body correlations, and small but significant for the saturation and binding energy. A calculation is made with a more realistic model with a potential tail. A modified Moszkowski-Scott type expansion, separated at r 0, is used. Convergence is poor and binding is not obtained. More recent nucleon-nucleon boundary condition models may give convergence and binding.