Correlation between time and angular alignment in molecular dynamics simulations of heavy ion collisions

Neutron-proton equilibration is a process which has been used to study the density dependence of the symmetry energy term in the nuclear equation-of-state. This study utilizes constrained molecular dynamics (CoMD) simulations of ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ with collision energies of 35 and 45 MeV/nucleon. An algorithm is used which searches through CoMD events and identifies the PLF* after it separates from the target and determines its lifetime, $\mathrm{\Delta }t$. It also determines the fragments that the PLF* breaks apart into and determines their angular alignment. This technique gives an opportunity to explore how the average alignment of dynamically produced fragments, ${〈\alpha 〉}_{\mathrm{dyn}}$, evolves with PLF* lifetime. An approximately linear relationship was determined with $d{〈\alpha 〉}_{\mathrm{dyn}}/d\mathrm{\Delta }t=0.98\pm 0.08\mathrm{rad}/\mathrm{zs}$ and $1.06\pm 0.09\mathrm{rad}/\mathrm{zs}$ for the 35 and $45\mathrm{MeV}/\mathrm{nucleon}$, respectively, indicating a correlation with magnitude consistent with classically determined values which were used for prior experimental studies.

Figure 1

Depiction of the breakup mechanism of interest in this work. Blue regions indicate regions of higher neutron density, and red regions indicate lower neutron density. PLF* rotation and neutron-proton equilibration take place between $t_{s1}$ and $t_{\mathrm{s}2}$. The alignment angle, $\alpha$, is defined as the angle between the relative and center-of-mass velocity vectors.

Figure 2

Cartoon depicting merging heaviest-daughter chains. Equilibration and rotation persist until the HF and LF's last breakup. Here, blue and red coloring indicate relative neutron and proton richness, respectively.

Figure 3

(a) Yield of events accepted by the event tree analysis and the experimental assumptions (E.A.) and each energy as a function of impact parameter (out of $800000$ total events). (b) Same as panel (a), but normalized by the yield of total events for each impact parameter (following a triangular distribution).

Figure 4

Angular alignment distributions found by the event tree analysis and experimental assumptions for 35 and $45\mathrm{MeV}/\mathrm{nucleon}$ collisions. Each distribution is fit to a model accounting for isotropic decay, dynamic breakup, and flipped dynamic events.

Figure 5

Angular alignments calculated by each of the two methods for the (a) 35 and (b) $45\mathrm{MeV}/\mathrm{nucleon}$ data. A primary peak is shown along the main diagonal, ${\alpha }_{\mathrm{tree}}={\alpha }_{\mathrm{E}.\mathrm{A}.}$. A secondary peak is populated on the off diagonal ${\alpha }_{\mathrm{tree}}={180}^{\circ }-{\alpha }_{\mathrm{E}.\mathrm{A}.}$. There are also large amount of the data on neither diagonal.

Figure 6

Depictions of how a PLF* decaying multiple times may cause different types of disagreement between the event tree analysis and experimental assumptions.

Figure 7

Ratio of yields from the flipped peak to the dynamic peak as a function of the charge asymmetry of the PLF* breakup.

Figure 8

The angular alignment is plotted against the time between the PLF*/TLF* breakup and HF/LF breakup for the 35 and $45\mathrm{MeV}/\mathrm{nucleon}$ collision energies. The determinations of $〈{\alpha }_{\mathrm{dyn}}〉$ for each $\mathrm{\Delta }t$ are plotted as solid black points. The data are fitted linearly and the average values of the total yield, $〈\alpha 〉$, are also plotted as open circles.