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

摘要

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_(ΔlnR21), 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_(ΔlnR21) scaling phenomenon is shown for the fragments produced both in the projectile fragmentation reactions and in the spallation reactions, whereas the S_(ΔlnR21) scaling phenomenon for the fragments in the fission reaction is less obvious. Conclusions: The S_(ΔlnR21) scaling is used to probe the properties of the equilibrium system at the time of fragment formation. The good scaling of S_(ΔlnR21) suggests that the equilibrium state can be achieved in the projectile fragmentation and spallation reactions. Whereas in the fission reaction, the result of S_(ΔlnR21) indicates that the equilibrium of the system is hard to achieve.