Electric dipole polarizability of low-lying excited states in atomic nuclei

New equations for the electric dipole polarizability α E1 of low-lying excited states in atomic nuclei—and the related (−2) moment of the total photo-absorption cross section, σ −2 —are inferred in terms of electric dipole and quadrupole matrix elements. These equations are valid for arbitrary angular momenta of the initial/ground and final/excited states and have been exploited in fully converged 1 ℏ ω shell-model (SM) calculations of selected p- and sd- shell nuclei that consider configuration mixing; advancing previous knowledge from 17 O to 36 Ar, where thousands of electric dipole matrix elements are computed from isovector excitations which include the giant dipole resonance (GDR) region. Our results are in reasonable agreement with previous SM calculations and follow—except for 6,7 Li and 17,18 O—Migdal’s global trend provided by the combination of the hydrodynamic model and second-order non-degenerate perturbation theory. Discrepancies in 6,7 Li and 17 O arise as a result of the presence of α -cluster configurations in odd-mass nuclei, whereas the disagreement in 18 O comes from the mixing of intruder states, which is lacking in the SM interactions. More advanced ab initio calculations of the dipole polarizability for low-lying excited states covering all the isovector states within the GDR region are missing and could be very valuable to benchmark the results presented here and shed further light on how atomic nuclei polarize away from the ground state