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We systematically derive a length scale characterizing the size of alow-lying, beta stable nucleus from empirical data for the diffraction peakangle 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 stateis a completely absorptive "black" sphere of radius a. The cross section \pia^2, where a is determined in such a way as to reproduce the empirical protondiffraction peak angle in the elastic channel, is known to agree with empiricaltotal reaction cross sections for incident protons to within error bars. Bycomparing the inelastic diffraction patterns obtained in the Fraunhoferapproximation with the experimental ones, one can likewise derive the blacksphere 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 inelasticchannel is generally larger than the value of a from the elastic channel andtends to increase with the excitation energy. This increase is remarkable forthe Hoyle state. Finally, we discuss the relation between a_l and the size ofexcited nuclei.

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