Core polarization revisited

Abstract

The core-polarization process which has been so important in determining the twoparticle effective shell-model interaction is re-examined so as to include effects not present in previous calculations as well as to consolidate effects included in separate calculations. The effects considered here are (i) using reaction matrix elements G with the proper starting energy for their position in the diagram, (ii) summing to intermediate excitations of 10 hQ so as to saturate the effect due to the tensor force and (iii) treating the intermediate-state spectrum consistently in calculating both G and the core polarization. Our calculations are performed in a shifted harmonic oscillator basis, and we discuss the importance of the choice of the unperturbed Hamiltonian used in the calculations. Our results indicate that the core polarization is significantly changed from the lowest-order results when the correct starting energies and higher intermediate-state summations are included. We present our results as a function of the shift and find that agreement with experiment is better for a small shift. We conclude that at the very least one should always include the correct starting energy effect in computing the higherorder terms.