Determination of nuclear matter radii by means of microscopic optical potentials: the case of $^{78}$Kr

In this work we use microscopic Nucleon-Nucleus Optical Potentials (OP) to analyze elastic scattering data for the differential cross section of the $^{78}$Kr (p,p) $^{78}$Kr reaction, with the goal of extracting the matter radius and estimating the neutron skin, quantities that are both needed to determine the slope parameter $L$ of the nuclear symmetry energy. Our analysis is performed with the factorized version of the microscopic OP obtained in a previous series of papers within the Watson multiple scattering theory at the first order of the spectator expansion, which is based on the underlying nucleon-nucleon dynamics and is free from phenomenological inputs. Differently from our previous applications, the proton and neutron densities are described with a two-parameter Fermi (2pF) distribution, which makes the extraction of the matter radius easier and allows us to make a meaningful comparison with the original analysis, that was performed with the Glauber model. With standard minimization techniques we performed data analysis and extracted the matter radius and the neutron skin. Our analysis produces a matter radius of $R_m^{{\rm (rms)}} = 4.12$ fm, in good agreement with previous matter radii extracted from $^{76}$Kr and $^{80}$Kr, and a neutron skin of $\Delta R_{np} \simeq - 0.1$ fm, compatible with a previous analysis. Our factorized microscopic OP, supplied with 2pF densities, is a valuable tool to perform the analysis of the experimental differential cross section and extract information such as matter radius and neutron skin. Without any free parameters it provides a reasonably good description of the experimental differential cross section for scattering angles up to $\approx$ 40 degrees. Compared to the Glauber model our OP can be applied to a wider range of scattering angles and allows one to probe the nuclear systems in a more internal region.