Nuclear multifragmentation, percolation, and the fisher droplet model: common features of reducibility and thermal scaling

Nuclear multifragmentation time scale and fluctuations of the largest fragment size

Distributions of the largest fragment charge, Zmax, in multifragmentation reactions around the Fermi energy can be decomposed into a sum of a Gaussian and a Gumbel distribution, whereas at much higher or lower energies one or the other distribution is asymptotically dominant. We demonstrate the same generic behavior for the largest cluster size in critical aggregation models for small systems, in or out of equilibrium, around the critical point. By analogy with the time-dependent irreversible aggregation model, we infer that Zmax distributions are characteristic of the multifragmentation time scale, which is largely determined by the onset of radial expansion in this energy range.

Experimental determination of in-medium cluster binding energies and Mott points in nuclear matter

In-medium binding energies and Mott points for d, t, 3He and α clusters in low-density nuclear matter have been determined at specific combinations of temperature and density in low-density nuclear matter produced in collisions of 47A MeV 40Ar and 64Zn projectiles with 112Sn and 124Sn target nuclei. The experimentally derived values of the in-medium modified binding energies are in good agreement with recent theoretical predictions based upon the implementation of Pauli blocking effects in a quantum statistical approach.

Phase transition in liquid drop fragmentation

A liquid droplet is fragmented by a sudden pressurized-gas blow, and the resulting droplets, adhered to the window of a flatbed scanner, are counted and sized by computerized means. The use of a scanner plus image recognition software enables us to automatically count and size up to tens of thousands of tiny droplets with a smallest detectable volume of approximately 0.02 nl . Upon varying the gas pressure, a critical value is found where the size distribution becomes a pure power law, a fact that is indicative of a phase transition. Away from this transition, the resulting size distributions are well described by Fisher's model at coexistence. It is found that the sign of the surface correction term changes sign, and the apparent power-law exponent tau has a steep minimum, at criticality, as previously reported in nuclear multifragmentation studies. We argue that the observed transition is not percolative, and introduce the concept of dominance in order to characterize it. The dominance probability is found to go to zero sharply at the transition. Simple arguments suggest that the correlation length exponent is nu=1/2 . The sizes of the largest and average fragments, on the other hand, do not go to zero abruptly but behave in a way that appears to be consistent with recent predictions of Ashurst and Holian.

Liquid to vapor phase transition in excited nuclei

The thermal component of the 8 GeV/c pi+ Au data of the ISiS Collaboration is shown to follow the scaling predicted by Fisher's model when Coulomb energy is taken into account. Critical exponents tau and sigma, the critical point (p(c),rho(c),T(c)), surface energy coefficient c(0), enthalpy of evaporation DeltaH, and critical compressibility factor C(F)(c) are determined. For the first time, the experimental phase diagrams, (p,T) and (T,rho), describing the liquid vapor coexistence of finite neutral nuclear matter have been constructed.

Event-by-event analysis of proton-induced nuclear multifragmentation: determination of the phase transition universality class in a system with extreme finite-size constraints

A percolation model of nuclear fragmentation is used to interpret 10.2 GeV/c p+197Au multifragmentation data. Emphasis is put on finding signatures of a continuous nuclear matter phase transition in finite nuclear systems. Based on model calculations, corrections accounting for physical constraints of the fragment detection and sequential decay processes are derived. Strong circumstantial evidence for a continuous phase transition is found, and the values of two critical exponents, sigma = 0.5+/-0.1 and tau = 2.35+/-0.05, are extracted from the data. A critical temperature of T(c) = 8.3+/-0.2 MeV is found.

Precise simulation of criticality in asymmetric fluids

Extensive grand canonical Monte Carlo simulations have been performed for the hard-core square-well fluid with interaction range b=1.5 sigma. The critical exponent for the correlation length has been estimated in an unbiased fashion as nu=0.63+/-0.03 via finite-size extrapolations of the extrema of properties measured along specially constructed, asymptotically critical loci that represent pseudosymmetry axes. The subsequent location of the critical point achieves a precision of five parts in 10(4) for Tc and about 0.3% for the critical density rhoc. The effective exponents gamma+(eff) and beta(eff) indicate Ising-type critical-point values to within 2% and 5.6%, respectively, convincingly distinguishing the universality class from the "nearby" XY and n=0 (self-avoiding walk) classes. Simulations of the heat capacity CV(T,rho) and d2psigma/dT2, where psigma is the vapor pressure below Tc, suggest a negative but small Yang-Yang anomaly, i.e., a specific-heat-like divergence in the corresponding chemical potential derivative (d2 musigma/dT2) that requires a revision of the standard asymptotic scaling description of asymmetric fluids.

Model for studying branching processes, multiplicity distributions, and non-Poissonian fluctuations in heavy-ion collisions

A change is made in a statistical framework by introducing a set of variables called ancestral or stochastic. This leads to an underlying dynamics based on branching laws, lines of descent in an hierarchical topology, period doublings, cascades, and clans. Above a certain branching probability, a percolative feature suddenly appears. Power laws emerge and cascade points arise and end at golden mean (square root (5-1)/2.