Microscopic origins of effective charges in the shell model

We use a large-scale $6ħ\Omega$ calculation for ${}^6$Li with microscopically derived two-body interaction to construct the $0ħ\Omega$ $0p$ shell effective Hamiltonian, electric quadrupole, and magnetic dipole operators. While the E2 and M1 $6ħ\Omega$ operators are one-body operators with free nucleon charges, the effective operators are two-body operators with substantially different renormalization for the isoscalar and isovector matrix elements, especially for the E2 operator. We show that these operators can be very well approximated by one-body operators provided that effective proton and neutron charges are used. The obtained effective charges are compatible with those used in phenomenological shell-model studies. The two-body part of the effective operators is estimated.