Nuclear Multifragmentation Time Scale and Fluctuations of the Largest Fragment Size

Abstract

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 timedependent 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. Introduction In central heavy-ion collisions at beam energies of ∼20-150 MeV/A multiple production of nuclear fragments can be observed, compatible with the quasi-simultaneous break-up of finite pieces of excited nuclear matter [1][2][3][4][5][6][7]. This so-called "nuclear multifragmentation" is a fascinating process [8] which has long been associated with a predicted liquid-gas coexistence region in the nuclear matter phase diagram at sub-critical temperatures and sub-saturation densities [9][10][11]. Statistical [12][13][14][15][16][17][18][19] and dynamical [20][21][22][23][24] aspects have been widely studied, and evidences supporting equally well either a continuous phase transition of the liquid-gas universality class [13,14,[25][26][27][28][29][30], a discontinuous ("first-order") transition occurring within the coexistence region [29][30][31][32][33][34][35], or indeed the survival of initial-state correlations in a purely dynamical picture [36,37] have been presented. This state of affairs well demonstrates the difficulty of quantitatively identifying a phase transition in small systems such as atomic nuclei, where finite-size effects blur the nature of the transition [38][39][40] whose order may indeed change with the size of the system [29,30], along with the importance of long-range Coulomb forces [4,19,41,42], and presence of dynamical effects such as radial flow [43][44][45][46][47][48][49].In this context we have tried to establish generic features of multifragmentation in order to deduce its nature in a less model-dependent way. In our previous works [50], we used the model-independent universal fluctua-

Comparison of radial flow effects on partitions of multifragmenting sources formed in symmetric and asymmetric central collisions

“…As in [21], it can be seen that Eq. 2 nicely reproduces the non-trivial shapes of these distributions.…”

“…Another, indirect, method to gauge the importance of radial flow in multifragmentation reactions was suggested in [21], where it was shown that the Z max distributions in central Xe+Sn collisions evolve with bombarding energy in a manner similar to the largest cluster size distribution in numerical simulations of the Smoluchowski equations for irreversible aggregation in finite systems: for short clusterisation times, s max is an extremal order parameter characterised by the Gumbel distribution; over long timescales s max becomes an additive order parameter characterised by the Gaussian distribution; for intermediate timescales (around the critical gelation time), the s max distribution can be approximated by an admixture of the two asymptotic forms,…”

Liquid–Gas phase transition in nuclei

“…Moreover the composition of the fit evolves in a regular way from gaussian to gumbellian (R goes from positive to negative values in Fig. 42 By analogy with the irreversible aggregation model the authors of [253] therefore proposed that the exact form of the charge distribution of the largest fragment in nuclear multifragmentation, and hence its fluctuations, are also determined by the timescale of fragment formation in such reactions. The onset and increase of radial expansion at beam energies above 25 MeV per nucleon [87], essential to drive the system towards the onset of spinodal instability and initiation of the break-up into fragments [5], will also effectively shorten the time available for primary fragments to coalesce.…”

Nuclear thermodynamics and isospin degree of freedom

“…In that case multifragmentation should be an aggregation phenomenon; this was proved by the observation of a universal (Δ)-scaling law of the fluctuations of Z max , which is thus related to an order parameter [7,8].…”