Dynamical and statistical bimodality in nuclear fragmentation

Abstract

The origin of bimodal behavior in the residue distribution experimentally measured in heavy ion reactions is reexamined using Boltzmann-Uehling-Uhlenbeck simulations. We suggest that, depending on the incident energy and impact parameter of the reaction, both entrance channel and exit channel effects can be at the origin of the observed behavior. Specifically, fluctuations in the reaction mechanism induced by fluctuations in the collision rate, as well as thermal bimodality directly linked to the nuclear liquid-gas phase transition are observed in our simulations. Both phenomenologies were previously proposed in the literature, but presented as incompatible and contradictory interpretations of the experimental measurements. These results indicate that heavy ion collisions at intermediate energies can be viewed as a powerful tool to study both bifurcations induced by out-of-equilibrium critical phenomena, as well as finite size precursors of thermal phase transitions.

Experimental liquid-gas phase transition signals and reaction dynamics

“…It is expected to occur when the nucleus is heated to a moderate temperature and breaks up on a short time scale into light particles and IMFs with Z ≥ 3. Based on a statistical equilibrium assumption of the generated hot nuclear matter, different measures have been proposed to probe the liquid-gas phase transition, such as the nuclear specific heat capacity (the caloric curve) [12][13][14][15][16][17][18][19][20], the negative heat capacity [21,22], the bimodality in charge asymmetry [8,[23][24][25], the Fisher droplet model analysis [26][27][28][29][30][31][32], the Landau free energy approach [31][32][33][34][35][36][37], the moment of the charge distributions [28,[38][39][40][41], the fluctuation properties of the heaviest fragment size (charge) [28,29,[41][42][43], the Zipf's law [44,45], the multiplicity derivatives recently proposed by S. Mallik et al [46] and the derivative of cluster size [47]. With these features, considerable progress has been accomplished o...…”

“…However Moretto et al cast doubt on the observation [61]. Bimodality has also been reported from the INDRA-ALADIN collaboration [24] and the INDRA collaboration [8,62,63] as well as a recent theoretical work of Mallik et al [25]. On the other hand bimodality has also been successfully reproduced by quantum molecular dynamics(QMD) [64][65][66] and Boltzmann-Uehling-Uhlenbeck (BUU) [67] calculations where memory of the entrance channel is clearly present and thermal equilibrium is not achieved.…”

Sensitivity of the evaporation residue observables to the symmetry energy

“…To do that, we have followed the recently developed computationally efficient prescription described in Ref. [29][30][31], which leads to a correct propagation if the collision partners contain a sufficiently large number of nucleons. According to this prescription, the nucleon-nucleon collisions are computed at each time step with the physical isospin dependent cross-section only among the A P + A T test-particles belonging to the same event.…”

Liquid–Gas phase transition in nuclei

“…Jacobi transition of highly deformed systems [212] or self-organized criticality induced by nucleon-nucleon collisions [213,214]. Recently BUU simulations suggest that, depending on the bombarding energy and impact parameter of the reaction, both entrance channel and exit channel effects can be at the origin of the bimodality [215]: fluctuations in the reaction mechanism induced by fluctuations in the collision rate for central collisions, which agrees with [214], as well as thermal bimodality directly linked to the LG phase transition for more peripheral collisions, which strongly supports the results just presented.…”