Proton inelastic diffraction by a black nucleus and the size of excited nuclei

TL;DR

This paper introduces a method to estimate the size of low-lying excited nuclei using proton inelastic diffraction data, revealing that excited states are generally larger than the ground state, especially for the Hoyle state.

Contribution

It develops a systematic approach to determine the size of excited nuclei from diffraction peak angles, extending the black sphere model to inelastic channels.

Findings

Excited nuclei have larger black sphere radii than ground states.

The radius increase correlates with excitation energy.

The Hoyle state shows a significant size increase.

Abstract

We systematically derive a length scale characterizing the size of a low-lying, beta stable nucleus from empirical data for the diffraction peak angle in the proton inelastic differential cross section of incident energy of \sim 1 GeV. In doing so, we assume that the target nucleus in the ground state is a completely absorptive "black" sphere of radius a. The cross section \pi a^2, where a is determined in such a way as to reproduce the empirical proton diffraction peak angle in the elastic channel, is known to agree with empirical total reaction cross sections for incident protons to within error bars. By comparing the inelastic diffraction patterns obtained in the Fraunhofer approximation with the experimental ones, one can likewise derive the black sphere radius a_l for the excited state with spin l. We find that for ^{12}C, ^{58,60,62,64}Ni, and ^{208}Pb, the value of a_l obtained from the inelastic channel is generally larger than the value of a from the elastic channel and tends to increase with the excitation energy. This increase is remarkable for the Hoyle state. Finally, we discuss the relation between a_l and the size of excited nuclei.