Are Multifragment Emission Probabilities Reducible to an Elementary Binary Emission Probability

Abstract

Experimental intermediate-mass-fragment multiplicity distributions for the E/A = 80 and 110 MeV Ar + ' Au reactions are shown to be binomial at all excitation energies. From these distributions, a single binary event probability p can be extracted that has a thermal dependence.Thus, it is inferred that multifragmentation is reducible to a combination of nearly independent emission processes. If sequential decay is assumed, the increase of p with excitation energy implies a contraction of the time scale that is qualitatively consistent with recent fragment-fragment correlation data. pACS numbers: 25.70.pq At low excitation energies, complex fragments are emitted with low probability by a compound nucleus mechanism [1,2]. At increasingly larger energies, the probability of complex fragment emission increases dramatically, until several fragments are observed within a single event [3 -5]. The nature of this multifragmentation process is at the center of much current attention. For example, the time scale of fragment emission and the associated issue of sequentiality vs simultaneity are the objects of intense theoretical [3 -8] and experimental [9 -17] study. Recent experimental work [18,19] has shown that the excitation functions for the production of two, three, four, etc. fragments give a characteristically linear Arrhenius plot [20], suggesting a statistical energy dependence.A fundamental issue, connected in part to those mentioned above, is that of reducibility: Can multifragmentation be reduced to a combination of (nearly) independent emissions of fragments? More to the point, can the probability for the emission of n fragments be reduced to the emission probability of just one fragment?In what follows, we show evidence that the n-fragment emission probabilities are indeed reducible to an elementary binary emission probability. Furthermore, we shallshow that the energy dependence of the extracted elementary probabilities gives a linear Arrhenius plot. Thus, these probabilities are likely to be thermal. While reducibility does not strictly imply time sequentiality, we point out in the following the time implications associated with a temporal reading of a reducible thermal theory.The partial decay width I associated with a given binary channel can be approximated by I = Acope where cop is a frequency characteristic of the channel under consideration, B is the barrier associated with the channel, and T is the temperature. For instance, in fission, cup is the collective frequency of assault on the barrier and B is the fission barrier.

Z-Dependent Barriers in Multifragmentation from Poissonian Reducibility and Thermal Scaling

“…An historic overview of low energy reactions shows that the emission probabilities and excitation functions are by far the best observables in distinguishing between statistical processes (dominated by phase space, as in the case of light particle evaporation and fission), and prompt, dynamical processes (like direct reactions) [3]. Indeed, several aspects of nuclear multifragmentation may be understood in terms of nearly independent fragment emission from multifragmenting sources with thermal-like probabilities [4][5][6][7][8][9].…”

“…It was found [4][5][6] that the experimental Z integrated fragment multiplicity distributions P m n are binomially distributed in each transverse energy (E t ) window, where n is the number of emitted fragments and m is the number of throws. The transverse energy E t is calculated from the kinetic energies E i of all the charged particles in an event and their polar angles θ i , as E t = i E i sin 2 θ i .…”

“…excitation functions) when log 1/p is plotted vs 1/ √ E t . If the excitation energy E * is proportional to E t and consequently, the temperature T to √ E t , these linear Arrhenius plots suggest that p has the Boltzmann form p ∝ exp(−B/T ) [4][5][6].…”

“…Thus, the Arrhenius plot generated with the resulting one fragment probability p is an average over a range of Z values. Fortunately, it has been shown that the Arrhenius plots should survive such a Z averaging, and yield an effective "barrier" (slope) dominated by the lowest Z value [4][5][6]. However, this procedure clearly implies a substantial loss of information, and renders the binomial parameters p and m difficult to interpret.…”

Fragment multiplicity distributions, a signal of true nuclear multifragmentation

“…Recently, Moretto and collaborators [12] have put forth the measurement of fragment multiplicity distributions as an insightful tool for understanding the mechanisms and the driving principles of nuclear fragmentation. Experimental fragment yields have shown themselves to be well described by binomial distributions, while the interpretation of the binomial parameters has been deeply debated [13][14][15].…”