Dispersive optical model analysis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Pb</mml:mi><mml:mprescripts/><mml:none/><mml:mn>208</mml:mn></mml:mmultiscripts></mml:math> generating a neutron-skin prediction beyond the mean field
M. C. Atkinson, Mojtaba Mahzoon, Michael A. Keim, Blake Bordelon, C. D. Pruitt, R. J. Charity, W. H. Dickhoff
Abstract
A nonlocal dispersive optical model analysis is carried out for neutrons and protons in $^{208}\mathrm{Pb}$. Elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, neutron and proton numbers, the charge distribution, and the binding energy are fitted to extract the neutron and proton self-energies both above and below the Fermi energy. From the single-particle propagator derived from these self-energies, we determine the charge and matter distributions in $^{208}\mathrm{Pb}$. The predicted spectroscopic factors are consistent with results from the $(e,{e}^{\ensuremath{'}}p)$ reaction and inelastic-electron-scattering data to very high-spin states. Sensible results for the high-momentum content of neutrons and protons are obtained, with protons appearing more correlated, in agreement with experiment and ab initio calculations of asymmetric matter. A neutron skin of $0.25\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.28em}{0ex}}\mathrm{fm}$ is deduced. An analysis of several nuclei leads to the conclusion that finite-size effects play a nonnegligible role in the formation of the neutron skin in finite nuclei.