The experimental liquid–vapor phase diagram of bulk nuclear matter

Abstract

The modern investigation of clusters, for which 1 ≪ N ≪ ∞, requires a generalization of the thermodynamics developed for infinite systems. For instance, in finite systems, phase transitions and phase coexistence become ill-defined with ambiguous signals. The existence of phase transitions in nuclear systems, in particular of the liquid–vapor kind, has been widely discussed and even experimentally claimed. A consistent and unambiguous approach to this problem requires a connection between finite systems and the corresponding infinite systems. Historically, this has been achieved at temperature T = 0 by the introduction of the liquid drop model and the extraction of the volume term, which is a fundamental quantity of nuclear matter. This work extends this approach to T > 0, by determining the liquid–vapor coexistence line and its termination at the critical point. Since there is no known experimental situation where a nuclear liquid and vapor are in coexistence, we establish a relationship between evaporation rates and saturated vapor concentration and characterize the saturated vapor with Fisher's droplet model. We validate this approach by analyzing cluster concentrations in the Ising and Lennard-Jones models and extracting the corresponding first-order coexistence line and critical temperature. Since the vapor of clusters coexists with a finite liquid drop, we devise a finite size correction leading to a modified Fisher equation. The application of the above techniques to nuclear systems requires dealing also with the Coulomb force. Nuclear cluster evaporation rates can be corrected for Coulomb effects and can be used to evaluate the cluster concentrations in the ‘virtual’ equilibrium vapor. These cluster concentrations, determined over a wide temperature range, can be analyzed by means of a modified Fisher formula. This leads to the extraction of the entire liquid–vapor coexistence line terminating at the critical point. A large body of experimental data has been analyzed in this manner and the liquid–vapor phase diagram of nuclear matter has been extracted.