PROTON INELASTIC DIFFRACTION BY A BLACK NUCLEUS AND THE SIZE OF EXCITED NUCLEI

Abstract

We systematically derive a length scale characterizing the size of a low-lying, β stable nucleus from empirical data for the diffraction peak angle in the proton inelastic differential cross-section of incident energy of ~ 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 πa2, 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 al for the excited state with spin l. We find that for 12 C , 58, 60, 62, 64 Ni , and 208 Pb , the value of al 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 al and the size of excited nuclei.