The quantum statistical model of fragment formation: Entropy and temperature extraction in heavy ion collisions

Abstract

Quantum statistical model (QSM) calculations of nuclear fragment formation are presented. Various independent methods for extracting the temperature, T, and entropy, S A , from fragment- and pion yields in heavy-ion collisions are analysed. It is emphasized that stable and unstable medium mass fragments play an important role in determining T and S/ A: They alter the relation S/ A( R dp) dramatically and distort via feeding simple temperature measurements. However, these fragments allow by their very abundance for a variety of new, alternative methods to determine S/ A from data on multifragmentation (ratios of complex fragment yields, mass yield curves, and charged-particle multiplicities). Entropy values deduced from 4π plastic ball data exhibit a strong multiplicity dependence. For large multiplicities the entropy residing in nuclear fragments appears to be independent of the bombarding energy and low in absolute value, S/ A⋍3.5. The corresponding break-up temperatures of the fragment conglomerate are T = 12, 16, and 20 MeV at E lab = 400, 650, and 1050 MeV/ n, respectively. These values are much smaller (a factor 1 3 ) than the temperatures extracted from pion yields. This result can be understood only if the pions are created in the early, hot stage of the collision, while the fragments are formed after an isentropic expansion of the system at small densities where the temperature is low. This would imply that in the late stage of the reaction a large fraction (⋍80%) of the available center-of-mass energy resides in (possibly isotropic) flow.