Correlations between emission timescale of fragments and isospin dynamics in ${}^{124}$Sn+${}^{64}$Ni and ${}^{112}$Sn+${}^{58}$Ni reactions at 35$A$ MeV

We present a new experimental method to correlate the isotopic composition of intermediate mass fragments (IMF) emitted at midrapidity in semiperipheral collisions with the emission timescale: IMFs emitted in the early stage of the reaction show larger values of $\langle N/Z\rangle$ isospin asymmetry, stronger angular anisotropies, and reduced odd-even staggering effects in neutron to proton ratio $\langle N/Z\rangle$ distributions than those produced in sequential statistical emission. All these effects support the concept of isospin “migration”, that is sensitive to the density gradient between participant and quasispectator nuclear matter, in the so called neck fragmentation mechanism. By comparing the data to a stochastic mean field (SMF) simulation we show that this method gives valuable constraints on the symmetry energy term of nuclear equation of state at subsaturation densities. An indication emerges for a linear density dependence of the symmetry energy.

Figure 1

For the ${}^{124}$Sn+${}^{64}$Ni reaction and $M\le 6$ a) correlations between relative velocities V${}_{\mathrm{REL}}$/V${}_{\mathrm{Viola}}$ of the three biggest fragments of the event for IMFs ($3\le 18$); b) distribution of $\cos \left({\theta }_{\mathrm{PROX}}\right)$ for $Z=3$ (dotted line), $Z=6$ (thick line), and $Z=18$ (thin line); c) as a) with the condition $\cos \left({\theta }_{\mathrm{PROX}}\right)>0.8$; d) as a) with the condition $\cos \left({\theta }_{\mathrm{PROX}}\right)<0$; e) Invariant cross section for $Z=6$ IMFs. f) as e) with the condition $\cos \left({\theta }_{\mathrm{PROX}}\right)<0$; the circumference shows a Coulomb ridge centered at PLF source velocity and 2.1 cm/ns radius.

Figure 2

For the ${}^{124}$Sn+${}^{64}$Ni reaction and $M\le 6$: $\langle N/Z\rangle$ for charge $Z=6$ for different bins in the $r_1$-$r_2$ plane. The dashed contour, projected in the $r_1$-$r_2$ plane gives a schematical selection of the zone with values of $r_1$ and $r_2$ simultaneously larger than unity.

Figure 3

Experimental $\langle N/Z\rangle$ distribution of IMFs as a function of charge $Z$ for statistical emitted particles (solid squares) and dynamical emitted particles (solid circles), for the reactions a) ${}^{124}$Sn+${}^{64}$Ni and b) ${}^{112}$Sn+${}^{54}$Ni.

Figure 4

Experimental $\langle N/Z\rangle$ distribution of IMFs as a function of charge $Z$ for statistically emitted particles (solid squares) and dynamical emitted particles (solid circles), for the reaction ${}^{124}$Sn+${}^{64}$Ni. Blue hatched area: SMF-GEMINI calculation for dynamical emitted particles and asy-stiff parametrization; magenta hatched area: asy-soft parametrization. The $\langle N/Z\rangle$ of primary dynamical emitted IMFs as a function of their atomic number $Z$, obtained from SMF calculations, are plotted in the inset. The hatched zone indicates the error bars in the calculations.

Figure 5

For the ${}^{124}$Sn+${}^{64}$Ni reaction, (empty, black) experimental velocity spectra $V_{\parallel }$ (in the c.m. system) of dynamically emitted intermediate mass fragments from charge $Z=3$ to charge $Z=6$ and (hashed, red) calculated velocity spectra (SMF+GEMINI) for the same reaction. Calculations have been normalized to data as explained in the text. The arrows indicate the c.m. beam velocity as reference. Calculated data are filtered for detector acceptance.

Figure 6

For the ${}^{124}$Sn+${}^{64}$Ni reaction, experimental charge distribution of dynamically emitted IMFs. The squares correspond to the SMF+GEMINI calculation. Red circles: filtered calculated data. The large effect of detector filter on charge $Z=4$ is due to the unbound ${}^8$Be isotope that is present in the calculation but filtered because it is not identified in the data analysis.

Figure 7

a) $\langle N/Z\rangle$ as a function of $\cos \left({\theta }_{\mathrm{PROX}}\right)$ for charges $5\le 8$: solid circles: experimental points; SMF calculations are shown for primary fragments as empty circles (asy-stiff) and empty squares (asy-soft); SMF-GEMINI calculation for asy-stiff (blue hatched area) and asy-soft (red hatched area) parametrization. b) experimental correlation for statistically emitted particles (see text). The dashed line gives the average $N/Z$ over the whole $\cos \left({\theta }_{\mathrm{PROX}}\right)$ interval.