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We describe a procedure for mapping a self-consistent mean-field theory (alsoknown as density functional theory) into a shell model Hamiltonian thatincludes quadrupole-quadrupole and monopole pairing interactions in a truncatedspace. We test our method in the deformed N=Z sd-shell nuclei Ne-20, Mg-24 andAr-36, starting from the Hartree-Fock plus BCS approximation of the USD shellmodel interaction. A similar procedure is then followed using the SLy4 Skyrmeenergy density functional in the particle-hole channel plus a zero-rangedensity-dependent force in the pairing channel. Using the ground-state solutionof this density functional theory at the Hartree-Fock plus BCS level, aneffective shell model Hamiltonian is constructed. We use this mappedHamiltonian to extract quadrupolar and pairing correlation energies beyond themean field approximation. The rescaling of the mass quadrupole operator in thetruncated shell model space is found to be almost independent of the couplingstrength used in the pairing channel of the underlying mean-field theory.

Effective shell model Hamiltonians from density functional theory: quadrupolar and pairing correlations