  The density functional theory of nuclear structure provides a many-particle
wave function that is useful for static properties, but an extension of the
theory is necessary to describe correlation effects or other dynamic
properties. Here we propose a procedure to extend the theory by mapping the
properties of the self-consistent mean-field Hamiltonian onto an effective
shell-model Hamiltonian with two-body interactions. In this initial study, we
consider the sd-shell nuclei Ne-20, Mg-24, Si-28, and Ar-36. Our first
application is in the framework of the USD shell-model Hamiltonian, using its
mean-field approximation to construct an effective Hamiltonian and partially
recover correlation effects. We find that more than half of the correlation
energy is due to the quadrupole interaction. We then follow a similar procedure
but using the SLy4 Skyrme energy functional as our starting point and
truncating the space to the spherical $sd$ shell. The constructed shell-model
Hamiltonian is found to satisfy minimal consistency requirements to reproduce
the properties of the mean-field solution. The quadrupolar correlation energies
computed with the mapped Hamiltonian are reasonable compared with those
computed by other methods.
