Scaling phenomena of isobaric yields in projectile fragmentation, spallation, and fission reactions

Abstract

Background: The isobaric ratio difference scaling phenomenon, which has been found for the fragments produced in projectile fragmentation reactions, is related to the nuclear density change in reaction systems.Purpose: To verify whether the isobaric ratio difference scaling exists in the fragments produced in the spallation and fission reactions.Methods: The isobaric ratio difference scaling, denoted by ${S}_{\mathrm{\ensuremath{\Delta}}ln{R}_{21}}$, is in theory deduced within the framework of the canonical ensemble theory at the grand-canonical limitation. The fragments measured in a series of projectile fragmentation, spallation, and fission reactions have been analyzed.Results: A good ${S}_{\mathrm{\ensuremath{\Delta}}ln{R}_{21}}$ scaling phenomenon is shown for the fragments produced both in the projectile fragmentation reactions and in the spallation reactions, whereas the ${S}_{\mathrm{\ensuremath{\Delta}}ln{R}_{21}}$ scaling phenomenon for the fragments in the fission reaction is less obvious.Conclusions: The ${S}_{\mathrm{\ensuremath{\Delta}}ln{R}_{21}}$ scaling is used to probe the properties of the equilibrium system at the time of fragment formation. The good scaling of ${S}_{\mathrm{\ensuremath{\Delta}}ln{R}_{21}}$ suggests that the equilibrium state can be achieved in the projectile fragmentation and spallation reactions. Whereas in the fission reaction, the result of ${S}_{\mathrm{\ensuremath{\Delta}}ln{R}_{21}}$ indicates that the equilibrium of the system is hard to achieve.