Optimal Nuclear Single-Particle Potential

Subject to the validity of the $K$-matrix approximation for atomic nuclei, it is shown that the best single-particle wave functions are obtained from a self-consistent potential with rearrangement terms. These terms are derived from variational calculus and it is demonstrated that the solution of the Euler-Lagrange equations provides the single determinant wave function with maximal overlap with the true wave function. We solve the equation for the rearrangement term due to the removal of one particle and show that all $K$ matrix elements are on the energy shell.