Microscopic determination of the interacting boson-fermion model Hamiltonian from the nuclear energy density functional

A microscopic formulation of the interacting boson-fermion model for odd-$A$ nuclei is made using the nuclear energy density functional framework. Strength parameters for the bosonic Hamiltonian and boson-fermion interactions are shown to be determined completely so that energy surfaces and deformed single-particle energies of the Bose-Fermi systems should match the corresponding self-consistent mean-field solutions for fermionic systems. In an illustrative application to axially symmetric odd-$A$ Eu, this procedure is shown to be valid in describing spherical-to-deformed shape phase transitions in odd-$A$ and even-even systems.