Auxiliary potential in no-core shell-model calculations

The Lee-Suzuki iteration method is used to include the folded diagrams in the calculation of the two-body effective interaction ${\mathit{v}}_{\mathrm{eff}}^{\mathrm{}\left(2\right)\mathrm{}}$ between two nucleons in a no-core model space. This effective interaction still depends upon the choice of single-particle basis utilized in the shell-model calculation. Using a harmonic-oscillator single-particle basis and the Reid-soft-core NN potential, we find that ${\mathit{v}}_{\mathrm{eff}}^{\mathrm{}\left(2\right)\mathrm{}}$ overbinds ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in 0, 2, and 4ħΩ model spaces. As the size of the model space increases, the amount of overbinding decreases significantly. This problem of overbinding in small model spaces is due to neglecting effective three- and four-body forces. Contributions of effective many-body forces are suppressed by using the Brueckner-Hartree-Fock single-particle Hamiltonian.