Neutron $3s_{1/2}$ occupation change across the stable tin isotopes investigated using isotopic analysis of proton scattering at 295 MeV

TL;DR

This study investigates the neutron 3s_{1/2} orbital occupation change across stable tin isotopes using proton scattering at 295 MeV, combining reaction and nuclear structure calculations to analyze isotopic variations.

Contribution

It demonstrates the sensitivity of proton scattering cross section ratios to neutron orbital occupations and compares relativistic and nonrelativistic nuclear density models for isotopic analysis.

Findings

The SKM* density model reproduces experimental cross section ratios better than DD-ME2.

The neutron 3s_{1/2} occupation does not increase rapidly from $^{116}$Sn to $^{122}$Sn.

Results align with direct measurements of neutron occupations in tin isotopes.

Abstract

The isotopic systematics of Sn isotopes in the range A=116--124 were investigated by combining the nuclear structure and reaction calculations for the analysis of Sn(p,p) reactions at 295 MeV. The Sn(p,p) reactions were calculated employing relativistic impulse approximation (RIA) with theoretical densities obtained for the Sn isotopes from relativistic Hartree-Bogoliubov (RHB) calculations with the DD-ME2 interaction and nonrelativistic Skyrme Hartree-Fock-Bogoliubov (SHFB) calculations with the SKM* interaction. Calculation using the DD-ME2 density reproduced the experimental data for $^{122}$Sn(p,p) but overestimated the $^{116}$Sn(p,p) and $^{118}$Sn(p,p) cross sections at backward angles. In the isotopic analysis of the cross section ratio $R(\sigma)$ of $^{122}$Sn to $^{116}$Sn, a calculation using the SKM* density reproduced the peak amplitudes of $R(\sigma)$ obtained from the experimental cross sections, whereas a calculation using the DD-ME2 density did not. The ratio $R(\sigma)$ was found to be sensitive to the isotopic change of the neutron $3s_{1/2}$ occupation through the isotopic difference of the surface neutron density around r=4--5 fm. Isotopic analysis indicated that a rapid increase of the $3s_{1/2}$ occupation from $^{116}$Sn to $^{122}$Sn obtained by the DD-ME2 calculation is unlikely. This result derived from the 295 MeV Sn(p,p) cross section data is consistent with the direct measurement of the neutron occupations in Sn isotopes by neutron transfer and pick-up reactions.