Effective interactions: Qualitative discussion of Hartree-Fock effects

We calculate the effective interaction for O18 in a simulated Hartree-Fock basis by taking a fixed oscillator parameter of 1.7 fm for the s and p shells and a variable parameter bu for the sd and pf shells. A central interaction is used and diagrams of first, second, and third order in V are calculated. The dominant effect is one of scaling with diagrams of second and third order all decreasing in the same exponential fashion as a function of bu. Comparing pure oscillator (bu=1.7 fm) and simulated Hartree-Fock (bu=2.0 fm) results, we find a reduction factor of roughly 0.7, 0.72, and 0.73 for first, second, and third order, respectively. Diagrams containing a particle-particle ladder usually fall off somewhat less rapidly than the others. The implications of these model results are discussed. NUCLEAR STRUCTURE Effective interaction theory; model simulation of a Hartree-Fock basis.