Influence of in-medium $NN$ cross sections, symmetry potential, and impact parameter on isospin observables

We explore the influence of the in-medium nucleon-nucleon cross section, symmetry potential, and impact parameter on isospin sensitive observables in intermediate-energy heavy-ion collisions with the ImQMD05 code, a modified version of the quantum molecular dynamics model. At incident velocities above the Fermi velocity, we find that the density dependence of the symmetry potential plays a more important role on the double neutron-to-proton ratio DR$(n/p)$ and the isospin transport ratio $R_i$ than the in-medium nucleon-nucleon cross sections, provided that the latter are constrained to a fixed total $NN$ collision rate. We also explore both DR$(n/p)$ and $R_i$ as a function of the impact parameter. Since the copious production of intermediate mass fragments is a distinguishing feature of intermediate-energy heavy-ion collisions, we examine the isospin transport ratios constructed from different groups of fragments. We find that the values of the isospin transport ratios for projectile rapidity fragments with $Z⩾20$ are greater than those constructed from the entire projectile rapidity source. We believe experimental investigations of this phenomenon can be performed. These may provide significant tests of fragmentation time scales predicted by ImQMD calculations.

Figure 1

The symmetry energy for cold nuclear matter plotted as a function of density for ${\gamma }_i=0.5$ and $2.0$ (solid line) for symmetry potentials used in ImQMD05 simulations Eq. (6). For comparison, we show the symmetry energies used in IBUU04 for $x=0$ and $-1$ (dashed lines) from Ref. [29].

Figure 2

Time evolution of the nucleon density in the reaction plane for ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ collisions at $E/A=50$ MeV at $b=0$ (top panels) and 6 (bottom panels) fm.

Figure 3

The charge (left panels) and mass (right panels) distributions for ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ at $b=2$ (top panels), 6 (middle panels), and 8 (bottom panels) fm. The solid symbols are for ${\gamma }_i=2.0$ and open symbols are for ${\gamma }_i=0.5$.

Figure 4

Multiplicity of fragments with charge $Z$ as a function of their scaled rapidity $y/y_{\mathrm{beam}}^{\mathrm{c}.\mathrm{m}.}$ for ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ at $E/A=50$ MeV for $b=2$ fm (left panel), 6 fm (middle panel), and 8 fm (right panel).

Figure 5

(Left panel) Double $n/p$ yield ratios, DR($n/p$), from transverse emitted nucleons as a function of kinetic energy. The solid stars are data from Ref. [21]. (Right panel) DR($n/p$) from transverse emitted high kinetic energy nucleons ($E_{\mathrm{c}.\mathrm{m}.}>40$ MeV) as a function of impact parameter. The upper shaded region is for ${\gamma }_i=0.5$ and the lower shaded region is for ${\gamma }_i=2.0$.

Figure 6

Effects of different in-medium $NN$ cross sections on the DR($n/p$) from transverse emitted high-energy nucleons ($E_{\mathrm{c}.\mathrm{m}.}>40$ MeV). The inverted triangles are for the free space $NN$ cross section (case 1 in text). The open squares are for the isospin-dependent in-medium $NN$ cross section with a phenomenological formula (case 2). The solid circles are for the isospin-independent in-medium $NN$ cross section (case 3).

Figure 7

Isospin transport ratios as a function of impact parameter with two tracers for a soft-symmetry case (${\gamma }_i=0.5$, open symbols) and a stiff-symmetry case (${\gamma }_i=2.0$, closed symbols). Upright triangle symbols are for the tracer defined by the isospin asymmetry of all fragments and unbound nucleons with velocity cut ($v_z^{N,\mathrm{frag}}>0.5v_{\mathrm{beam}}^{\mathrm{c}.\mathrm{m}.}$), $X={\delta }_{N,\mathrm{frag}}$. Circles denote the tracer defined by the heaviest fragment with $Z_{\max }>20$ in the projectile region, $X={\delta }_{Z_{\max }>20}$.

Figure 8

(Left panel) Experimental $R_i$ as a function of rapidity for three centrality gates [16]. (Middle panel) The calculated results of $R_i(X={\delta }_{N,\mathrm{frag}})$ as a function of rapidity for $b=2,4,6,8$ fm for ${\gamma }_i=0.5$ and (right panel) ${\gamma }_i=2.0$.

Figure 9

The effects of different in-medium $NN$ cross sections on $R_i(X={\delta }_{N,\mathrm{frag}})$. The inverted triangles are for the free space $NN$ cross section ${\sigma }_{nn/np}^{*}={\sigma }_{nn/np}^{\mathrm{free}}$ (case 1 in text). The open squares are for the isospin-dependent in-medium $NN$ cross section with phenomenological formula ${\sigma }_{nn/np}^{*}=(1-0.2\rho /{\rho }_0){\sigma }_{nn/np}^{\mathrm{free}}$ (case 2). The solid circles are for the isospin-independent in-medium $NN$ cross section ${\sigma }_{nn}^{*}={\sigma }_{pp}^{*}={\sigma }_{np}^{*}$ (case 3).