dorsal/arxiv
View SchemaReaction cross section described by a black sphere approximation of nuclei
| Authors | Akihisa Kohama, Kei Iida, Kazuhiro Oyamatsu |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0410032 |
| URL | https://arxiv.org/abs/nucl-th/0410032 |
| DOI | 10.1103/PhysRevC.72.024602 |
| Journal | Phys.Rev. C72 (2005) 024602 |
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 $\sim800$ 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 $A\gtrsim50$. This tendency suggests a significant change of the nuclear matter distribution from a rectangular one for $A\lesssim50$, which is consistent with the behavior of the empirical charge distribution.
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"abstract": "We identify a length scale that simultaneously accounts for the observed\nproton-nucleus reaction cross section and diffraction peak in the proton\nelastic differential cross section. This scale is the nuclear radius, $a$,\ndeduced from proton elastic scattering data of incident energies higher than\n$\\sim800$ MeV, by assuming that the target nucleus is a ``black\u0027\u0027 sphere. The\nvalues of $a$ are determined so as to reproduce the angle of the first\ndiffraction maximum in the scattering data for stable nuclei. We find that the\nabsorption cross section, $\\pi a^2$, agrees with the empirical total reaction\ncross section for C, Sn, and Pb to within error bars. This agreement persists\nin the case of the interaction cross section measured for a carbon target. We\nalso find that $\\sqrt{3/5}a$ systematically deviates from the empirically\ndeduced values of the root-mean-square matter radius for nuclei having mass\nless than about 50, while it almost completely agrees with the deduced values\nfor $A\\gtrsim50$. This tendency suggests a significant change of the nuclear\nmatter distribution from a rectangular one for $A\\lesssim50$, which is\nconsistent with the behavior of the empirical charge distribution.",
"arxiv_id": "nucl-th/0410032",
"authors": [
"Akihisa Kohama",
"Kei Iida",
"Kazuhiro Oyamatsu"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevC.72.024602",
"journal_ref": "Phys.Rev. C72 (2005) 024602",
"title": "Reaction cross section described by a black sphere approximation of nuclei",
"url": "https://arxiv.org/abs/nucl-th/0410032"
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