  In heavy atoms and ions, nuclear structure effects are significantly enhanced
due to the overlap of the electron wave functions with the nucleus. This
overlap rapidly increases with the nuclear charge $Z$. We study the energy
level shifts induced by the electric dipole and electric quadrupole nuclear
polarization effects in atoms and ions with $Z \geq 20$. The electric dipole
polarization effect is enhanced by the nuclear giant dipole resonance. The
electric quadrupole polarization effect is enhanced because the electrons in a
heavy atom or ion move faster than the rotation of the deformed nucleus, thus
experiencing significant corrections to the conventional approximation in which
they `see' an averaged nuclear charge density. The electric nuclear
polarization effects are computed numerically for $1s$, $2s$, $2p_{1/2}$ and
high $ns$ electrons. The results are fitted with elementary functions of
nuclear parameters (nuclear charge, mass number, nuclear radius and
deformation). We construct an effective potential which models the energy level
shifts due to nuclear polarization. This effective potential, when added to the
nuclear Coulomb interaction, may be used to find energy level shifts in
multi-electron ions, atoms and molecules. The fitting functions and effective
potentials of the nuclear polarization effects are important for the studies of
isotope shifts and nonlinearity in the King plot which are now used to search
for new interactions and particles.
