E1 moments from a coherent set of measured photoneutron cross sections

Abstract

Recently, the $E1$ photoneutron cross sections were measured consistently using quasimonochromatic laser Compton-scattering $\ensuremath{\gamma}$-ray beams at NewSUBARU (Japan) for a set of ten odd-even nuclei, spherical as well as deformed, covering relatively widely light to heavy species and at energies ranging between the neutron threshold and 40 MeV. This consistent set of experimental photoneutron cross sections allow us to estimate the total $E1$ photoabsorption cross sections, through validated theoretical models, by excluding the quasideuteron component and by including the missing low-energy and charged-particle emission contributions. In turn, the total $E1$ photoabsorption cross sections are used to derive the three main moments of the $E1$ distributions, namely the integrated cross section, the centroid energy, and the polarizability. These so-called model-dependent experimental moments follow a rather smooth trend with atomic mass, as theoretically expected, except for the specific case of $^{209}\mathrm{Bi}$ which presents a surprising 10% increase of both the integrated strength and the polarizability with respect to its even-even spherical neighbor $^{208}\mathrm{Pb}$. A rather consistent value for the enhancement factor of the $E1$ energy-weighted sum rule could be extracted from the present experimental data. The experimentally derived moments are compared for the ten odd-even systems with calculations based on the mean-field plus quasiparticle random phase approximation (QRPA). Spherical as well as axially deformed predictions based on the Skyrme and Gogny interactions are considered to discuss the results. Special attention is also paid to the approximate treatment of odd systems of nucleons in this context. It is found that in general theoretical predictions can rather well describe the data for the full set of nuclei, except for $^{209}\mathrm{Bi}$ presenting a kink in all the three main $E1$ moments with respect to the well-studied $^{208}\mathrm{Pb}$ case. Such an experimental determination cannot be explained by mean-field plus QRPA calculations. New measurements of photoabsorption cross section on $^{208}\mathrm{Pb}$ and $^{209}\mathrm{Bi}$ in the 14--19 MeV range as well as future theoretical calculations, in particular of odd-even systems, may help to solve such a mystery. The present data are also used to reinvestigate the correlation between the nuclear matter symmetry energy and its slope at saturation density. The analysis based on both Skyrme and Gogny Hartree-Fock-Bogolyubov (HFB) plus QRPA calculations confirm previous results, though quantitatively larger variations of the correlation parameters are found.