Fragmentation paths in dynamical models

We undertake a quantitative comparison of multifragmentation reactions, as modeled by two different approaches: the antisymmetrized molecular dynamics (AMD) and the momentum-dependent stochastic mean-field (SMF) model. Fragment observables and pre-equilibrium (nucleon and light cluster) emission are analyzed, in connection with the underlying compression-expansion dynamics in each model. Considering reactions between neutron-rich systems, observables related to the isotopic properties of emitted particles and fragments are also discussed, as a function of the parametrization employed for the isovector part of the nuclear interaction. We find that the reaction path, particularly the mechanism of fragmentation, is different in the two models and reflects on some properties of the reaction products, including their isospin content. This should be taken into account in the study of the density dependence of the symmetry energy from such collisions.

Figure 1

Equation of state (EOS) of symmetric nuclear matter, corresponding to the Gogny (solid) and BGBD (dashed) interactions.

Figure 2

Parametrizations of the density behavior of the symmetry energy adopted in the calculations: asy-soft (black lines), asy-stiff (gray lines). Solid lines correspond to the Gogny forces, whereas dashed lines are for the BGBD forces.

Figure 3

Mean-field potential, for neutrons (gray lines) and protons (black lines) in asymmetric matter ($\beta =0.2$) at density $\rho =0.085\hspace{0.5em}{\text{fm}}^{-3}$ [(a) and (b)], $\rho =0.17\hspace{0.5em}{\text{fm}}^{-3}$ [(c) and (d)], $\rho =0.34\hspace{0.5em}{\text{fm}}^{-3}$ [(e) and (f)], as a function of the momentum $k$. Solid lines correspond to the Gogny forces, whereas dashed lines are for the BGBD forces. Left panels, asy-soft interaction; right panels, asy-stiff interaction.

Figure 4

Contour plots of the density projected on the reaction plane calculated with SMF (top) and AMD (bottom) for the central reaction ${}^{112}\mathrm{Sn}$$+$${}^{112}\mathrm{Sn}$ at 50 MeV/nucleon, at several times (fm/$c$). The lines are drawn at projected densities beginning at 0.07 fm${}^{-2}$ and increasing by 0.1 fm${}^{-2}$. The size of each box is 40 fm.

Figure 5

Density profiles, at several times, as obtained in the SMF (a) and AMD (b) case, for the reaction ${}^{112}\mathrm{Sn}$$+$${}^{112}\mathrm{Sn}$.

Figure 6

Time evolution of the total number of neutrons (black lines) and protons (gray lines) contained in emitted particles with $1⩽A⩽4$, in the case of the reaction ${}^{124}\mathrm{Sn}$$+$${}^{124}\mathrm{Sn}$. Dashed line, asy-soft parametrization; solid line, asy-stiff parametrization. The dot-dashed lines represent the time evolution of the total number of neutrons and protons contained in emitted particles with $1⩽A⩽15$, for the asy-soft parametrization. Left panel, SMF results; right panel, AMD results.

Figure 7

The same as in Fig. 6, for the system ${}^{112}\mathrm{Sn}$$+$${}^{112}\mathrm{Sn}$.

Figure 8

Charge distribution as obtained in AMD (solid histogram) and in SMF (dashed histogram), for the reaction ${}^{124}\mathrm{Sn}$$+$${}^{124}\mathrm{Sn}$, at $t=200$ fm/$c$ (left) and $t=300$ fm/$c$ (right).

Figure 9

Ratio $R_Z$ between the fragment yield observed in the angular domain $60<\theta <120$ (rescaled by a factor 2) and the total yield, as a function of the fragment charge, evaluated at $t=300$ fm/$c$ for the same system of Fig. 8. Notations are the same as in Fig. 8.

Figure 10

IMF multiplicity distribution as obtained in the two models for the same reaction of Fig. 8, at $t=300$ fm/$c$. Solid lines, IMFs with charge $Z>2$ are considered; dashed lines, IMFs with charge $Z>6$ are considered.

Figure 11

IMF average kinetic energy as a function of the charge Z, as obtained in the two models at $t=200$ fm/$c$ (dashed lines) and at $t=600$ fm/$c$ (solid lines), for the same reaction of Fig. 8. The solid and hatched gray areas mark the change during this time interval for AMD and SMF, respectively.

Figure 12

Time evolution of the $N/Z$ content of the pre-equilibrium emission, as obtained in the two models (left and right panels), for the ${}^{112}\mathrm{Sn}$$+$${}^{112}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}$$+$${}^{124}\mathrm{Sn}$ reactions. Solid lines, asy-stiff interaction; dashed lines, asy-soft.

Figure 13

Time evolution of the isotopic content of the “liquid” phase, as obtained in the two models (left and right panels), for the ${}^{112}\mathrm{Sn}$$+$${}^{112}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}$$+$${}^{124}\mathrm{Sn}$ reactions. Solid lines, asy-stiff interaction; dashed lines, asy-soft.