Origin of discrepancy between proton radii from hydrogen vs carbon targets for neutron-rich nitrogen isotopes

Determine the physical mechanism that causes the systematic discrepancy in proton radii deduced from charge-changing cross sections measured on hydrogen targets compared to those measured on carbon targets for neutron-rich nitrogen isotopes at approximately 900 A MeV, under Glauber-model analyses with the S1-based scaling. Specifically, ascertain why the hydrogen-target–derived proton radii are systematically smaller than the carbon-target–derived values as neutron excess increases in nitrogen isotopes.

Background

Using charge-changing cross sections at about 900 A MeV on hydrogen and carbon targets, the authors introduced a new empirical scaling based on S1 to calibrate Glauber-model calculations and deduce proton radii for p-shell isotopes. For carbon isotopes, the proton radii deduced from hydrogen and carbon targets agree well; matter radii also agree across targets.

For nitrogen isotopes, matter radii from both targets agree, but the proton radii deduced from the hydrogen target are systematically smaller than those from the carbon target toward the neutron-rich side. The authors discuss potential sensitivities of the targets to the projectile’s proton density (e.g., surface sensitivity of carbon and broader sensitivity of hydrogen) and potential odd-Z effects, but conclude that a definitive explanation is not yet established.