Reaction cross section described by a black sphere approximation of nuclei

Abstract

We identify a length scale that simultaneously accounts for the observed proton-nucleus reaction cross section and diffraction peak in the proton elastic differential cross section. This scale is the nuclear radius, $a$, deduced from proton elastic scattering data of incident energies higher than $\sim 800$ MeV, by assuming that the target nucleus is a ``black'' sphere. The values of $a$ are determined so as to reproduce the angle of the first diffraction maximum in the scattering data for stable nuclei. We find that the absorption cross section, $\pi a^2$, agrees with the empirical total reaction cross section for C, Sn, and Pb to within error bars. This agreement persists in the case of the interaction cross section measured for a carbon target. We also find that $\sqrt{3/5}a$ systematically deviates from the empirically deduced values of the root-mean-square matter radius for nuclei having mass less than about 50, while it almost completely agrees with the deduced values for $A\gtrsim 50$. This tendency suggests a significant change of the nuclear matter distribution from a rectangular one for $A\lesssim 50$, which is consistent with the behavior of the empirical charge distribution.

5 pages, 4 figures. 1 table, 2 paragraphs, and some references were added

References in corpus (3)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• Renormalization of the isovector $\pi N$ amplitude in pionic atoms
• Nuclear radius deduced from proton diffraction by a black nucleus

Cited by in corpus (12)

• Reaction cross sections of carbon isotopes incident on a proton
• Systematic analysis of reaction cross sections of carbon isotopes
• Formula for proton-nucleus reaction cross section at intermediate energies and its application
• Nuclear Radii of Unstable Nuclei
• Nuclear surface diffuseness revealed in nucleon-nucleus diffraction
• Imprint of nuclear bubble in nucleon-nucleus diffraction
• Difference between interaction cross sections and reaction cross sections
• Effective radii of deuteron induced reactions
• Proton inelastic diffraction by a black nucleus and the size of excited nuclei
• Reaction cross sections for proton scattering from stable and unstable nuclei based on a microscopic approach
• Utility of antiproton-nucleus scattering for probing nuclear surface density distributions
• Incomplete absorption reactions at high energy