Valence-core self-consistency in theA=17system

We develop a systematic approach to the calculation of self-consistency effects in core plus valence nucleon systems. A detailed calculation of the effective one-body Hamiltonian for $A=17\mathrm{}$ in an $11\hslash \Omega$ model space is readily extrapolated to a $20\hslash \Omega$ model space which is sufficient to develop accurate tails for the single-particle wave functions. The effective one-body interaction is found using a Brillouin-Wigner type perturbation theory which eliminates folded diagrams and leads to a manifestly Hermitian interaction. A renormalized Brueckner calculation is performed for $A=16\mathrm{}$ and the results are employed in a shell-model study of $A=17\mathrm{}$. The self-consistent results still have a weak dependence on the initial unperturbed Hamiltonian. However, we find a single unperturbed Hamiltonian which yields a reasonable binding energy for $A=16\mathrm{}$ and, except for a weak spin-orbit splitting, reasonable results for the lowest states in the $A=17\mathrm{}$ system. This agreement is important for continued valence $s-d$ shell studies.