Dynamical evolution of spectator systems produced in ultrarelativistic heavy-ion collisions

In peripheral heavy-ion collisions at ultrarelativistic energies, usually only parts of the colliding nuclei effectively interact with each other. In the overlapping zone, a fireball or quark-gluon plasma is produced. The excitation energy of the heavy remnant can range from a few tens to several hundreds of MeV, depending on the impact parameter. The decay of these excited spectators is investigated in this work for the first time within a dynamical approach based on the multidimensional stochastic Langevin equation. The potential of this exploratory work to understand the connection between electromagnetic fields generated by the heavy spectators and measured pion distributions is discussed.

Figure 1

Mass of the spectator produced in three geometrical scenarios described in the text as a function of the impact parameter for ${}^{208}\mathrm{Pb}+{}^{208}\mathrm{Pb}$ collisions.

Figure 2

Dependence of the prefragment excitation energy for the three geometrical scenarios described in the text, on (a) impact parameter, and on (b) mass. The arrow indicates the impact parameter considered in Ref. [2]. Crosses in (b) mark the nuclei selected as typical examples for further dynamical calculations.

Figure 3

Dependence of the spectator prefragment excitation energy on its mass for various LDM realizations: Myers-Swiatecki [18], FRLDM [19], FRLDM [20], Moretto [21], and LSD [13].

Figure 4

Correlation between the prefragment excitation energy on (a) its mass, and on (b) impact parameter for events ending with the formation of a single heavy ER, or with fission, as predicted by the abrabla code. For comparison, the correlation computed in the geometrical macroscopic model for the sphere-cylinder is shown again.

Figure 5

Impact parameter distribution obtained from the Glauber formula [Eq. (11)] and from the geometrical prescription. The arrow marks the $b$ value studied in Ref. [2].

Figure 6

Correlation between the spectator mass and impact parameter of the collision as obtained from the Glauber formula [Eq. (11)].

Figure 7

Fission barrier in the ($T$, $q_3$) plane for a sample of nuclei. Here the barrier is defined as the difference between the free energy at the conditional ($q_3$-constrained) saddle point and the ground-state equilibrium point. The landscapes are presented for ${}^{100}\mathrm{Y}$, ${}^{142}\mathrm{Ba}$, ${}^{168}\mathrm{Dy}$, and ${}^{194}\mathrm{Os}$.

Figure 8

Charge distribution of the evaporation residues produced along the decay of the set of prefragments selected for the LSD-Lang calculation. The spectator is specified next to each curve. The integral of each distribution was scaled according to the probability that the decay ends in the ER channel.

Figure 9

Charge distribution of the fission fragments produced along the decay of the set of prefragments selected for the LSD-Lang calculation. The spectator is specified next to each curve. The integral of the curves do not reflect the fission probabilities (which are given in Table 1); curves were displaced arbitrarily in the vertical direction for better legibility.

Figure 10

Fission probability and mean multiplicities of neutrons, protons, $\alpha$ particles, deuterons, and tritons emitted along the deexcitation of the excited spectator on its way to either formation of an evaporation residue (green triangles), or fission (green squares). The average multiplicities, irrespective of the decay channel, are shown also (orange dots).

Figure 11

Charge distribution of (a) the evaporation residues and (b) fission fragments obtained with the abra-Lang (dashed line) and abrabla (full line) codes. Weighting by the impact parameter distribution predicted by abra is performed in both cases. The integral distributions including ER and fission channels are shown in (c); normalization to absolute cross sections is performed using the nuclear-induced reaction cross section extracted in experiment [39]. The total distribution predicted by the abrabla code, with no event selection (that is, including electromagnetic-induced interactions, and breakup processes) is displayed as well with the dash-dotted curve; absolute normalization is directly taken from the total reaction cross section predicted by abrabla. Experimental data are from Refs. [39, 40].

Figure 12

Mean fission time as a function of spectator mass in the LSD-Lang code. The left-side $y$ axis gives the time as output from the Langevin calculation, in the fission frame, and which is transformed to the overall center-of-mass time on the right-side $y$ axis. Horizontal lines indicate the mean fission time averaged over all spectators for the LSD-Lang (green dashed) and abra-Lang (orange full) codes.

Figure 13

Charge distribution of the products (ER and fission fragments) predicted with three abrasion models combined with the same Langevin decay code, for the restricted range of impact parameter $b\in$ (10–11) fm.

Figure 14

The cuts of the sphere in various planes. The red circle presents the spectator-target; blue, projectile; green, one layer in $z$ direction.