Isospin diffusion in binary collisions of ${}^{32}\mathrm{S}+{}^{40,48}\mathrm{Ca}$ and ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ti}$ at 17.7 MeV/nucleon

The systems ${}^{32}\mathrm{S}+{}^{40,48}\mathrm{Ca}$ and ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ti}$ at 17.7 MeV/nucleon were investigated with the setup general array for fragment identification and for emitted light particles in dissipative collisions (GARFIELD) plus ring counter (RCo) at Laboratori Nazionali di Legnaro (LNL) of Istituto Nazionale di Fisica Nucleare (INFN). Fusion evaporation (FE), fusion fission (FF), and deep inelastic (DIC) events were identified, also through the comparison with the prediction of a transport model (stochastic mean field, SMF), coupled to GEMINI++ as an afterburner. This work mainly deals with the study of isospin transport phenomena in DIC events. In particular, the isospin diffusion is highlighted by comparing the average isotopic content of the quasiprojectile (QP) remnants observed when the target is the $N=Z$ nucleus ${}^{40}\mathrm{Ca}$ and when it is the neutron-rich ${}^{48}\mathrm{Ca}$. Also, the $d/p$ and $t/p$ ratios for particles forward emitted with respect to the QP were found to increase with increasing $N/Z$ of the target.

Figure 1

Particle identification (PI) spectrum obtained from the Si-Csi(Tl) correlation of a typical telescope of RCo. Continuous line: ${}^{32}\mathrm{S}+{}^{40}\mathrm{Ca}$ system; red dotted line: ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$ system. Spectra are normalized to the same integral. In the upper part of the plot, the mass numbers corresponding to some identified isotopes are shown.

Figure 2

Event produced by twingo with $b=5.8$ fm for the reaction ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$. Each picture represents a screenshot of the system at a given time. Each point represents the position of a test particle.

Figure 3

Continuous black line: impact parameter distribution given as input to twingo; the binning of the abscissa is 0.1 fm. Dotted blue line (coincident with the black one below 5 fm): impact parameter distribution associated with fusion events. Dashed red line: impact parameter distribution associated with DIC events. The coalescence algorithm was applied at 300 fm/c.

Figure 4

Experimental data: distribution of events as a function of total detected charge and total momentum along the beam axis, normalized to the beam value, for the system ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$. The hatched area represents the region of events excluded in the analysis. The area inside the continuous ellipse corresponds mainly to fusion events, while the area inside the dotted ellipse includes incomplete DIC (where only the QP is detected) or incomplete FF events (where only one fission fragment is detected).

Figure 5

Yields as a function of the charge $Z$ and the c.m. velocity for all the fragments with $Z\ge 3$ for the reaction ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$. Distributions are normalized to unitary integral. (a) Experimental data; events belonging to the hatched area of Fig. 4 are not included. (b) Simulated events produced by twingo followed by gemini++, filtered by means of a software replica of the detection system.

Figure 6

Simulated contour plots of differential cross sections for the reaction ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$ as a function of the ${\vartheta }_{\mathrm{flow}}$ angle (binning: $1^{\circ }$) and of the total charge $Z_{\mathrm{tot}}$ (binning: 1 unit of charge). Calculations have been performed with the twingo code followed by gemini++ and the simulated events have been filtered by means of a software replica of the setup. (a) Events corresponding to fusion (both FE and FF); (b) events corresponding to DIC. The color scale indicated on the left is in units of mbarn/deg for each $Z_{\text{tot}}$ value.

Figure 7

Experimental contour plots as a function of the ${\vartheta }_{\mathrm{flow}}$ angle and of the total charge $Z_{\text{tot}}.\text{(a)}{}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$. (b) ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ti}$. (c) ${}^{32}\mathrm{S}+{}^{40}\mathrm{Ca}$. The continuous black rectangle in the lower left corner corresponds to the adopted selection for DIC events (“DIC cut”), while the dotted black rectangle in the upper right corner corresponds to the adopted selection for FF and FE events (“fusion cut”).

Figure 8

Charge distribution of the ER in FE events. Symbols: experimental data (full circles: ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$, open circles: ${}^{32}\mathrm{S}+{}^{40}\mathrm{Ca}$). Lines: Simulated data produced by twingo followed by gemini++ as afterburner. Continuous line: ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$, dotted line:${}^{32}\mathrm{S}+{}^{40}\mathrm{Ca}$. Data are normalized to the maximum, which corresponds, in the model calculation for ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$, to 22.7 mbarn.

Figure 9

Event distribution as a function of ${\vartheta }_{\mathrm{rel}}^{\mathrm{c}.\mathrm{m}.}$ and ${\mathrm{v}}_{\mathrm{rel}}$ for experimental data corresponding to the reaction ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$, belonging to the fusion selection (inside the dotted rectangle of figure 7) and with two detected fragments with $Z>3$. The black rectangle corresponds to the selection adopted for FF.

Figure 10

Experimental distribution of charge $Z$ of the ER (full circles) in FE events and of the total charge of the fragments $Z_1+Z_2$ in FF events (open circles). (a) ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$; (b) ${}^{32}\mathrm{S}+{}^{40}\mathrm{Ca}$. Spectra are normalized to unitary area to better compare the distribution shapes.

Figure 11

(a) Distribution of experimental events, as a function of ${\vartheta }_{\mathrm{rel}}^{\mathrm{c}.\mathrm{m}.}$ and of $Z_1+Z_2$, associated to the detection of two fragments for the reaction ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$. The inner black dotted gate is the region used to extract the ${}^{12}\mathrm{C}$ background; the outer black continuous gate is another possible normalization region for the evaluation of the ${}^{12}\mathrm{C}$ background. (b) The same for the reaction ${}^{32}\mathrm{S}+{}^{12}\mathrm{C}$ analyzed as ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$. (c) Projection on the ${\mathrm{Z}}_1+{\mathrm{Z}}_2$ axis of part (a) (red lines) and part (b) (black lines) for the region inside the outer black continuous gate (continuous lines) and for the region inside the inner black dotted gate (dotted lines).

Figure 12

(a) c.m. velocity distribution for the QP (normalized to 1) after subtracting the ${}^{12}\mathrm{C}$ contribution for the three investigated reactions. The arrow corresponds to the beam velocity. (b) Charge distribution of the QP, normalized to 1, after subtracting the ${}^{12}\mathrm{C}$ contribution. Full circles correspond to the reaction ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$, open circles to ${}^{32}\mathrm{S}+{}^{40}\mathrm{Ca}$, crosses to ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ti}$. The vertical dotted line shows the lower limit for the QP charge used in our analysis, while the dotted histogram corresponds to the charge distribution of the QP before ${}^{12}\mathrm{C}$ subtraction for the reaction ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$.

Figure 13

Yields (arb. units) as a function of $v_{\text{perp}}$ and $v_{\text{par}}$ for protons emitted in DIC events for the reaction ${}^{32}\mathrm{S}+{}^{40}\mathrm{Ca}$. (a) Experimental data after subtracting the ${}^{12}\mathrm{C}$ contribution. (b) Simulated data (twingo followed by gemini++).

Figure 14

Measured average $\langle N\rangle /Z$ of the QP as a function of its charge. Full (open) symbols (circles for ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$, squares for ${}^{32}\mathrm{S}+{}^{40}\mathrm{Ca}$, and triangles for ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ti}$) refer to the experimental data before (after) the subtraction of the ${}^{12}\mathrm{C}$ background. Only statistical errors (smaller than the symbol size) are included for full symbols, while the gray band is the systematic error due to the ${}^{12}\mathrm{C}$ subtraction procedure. Data refer only to QP detected in the ring counter through the Si-CsI(Tl) correlation, where information on the ion mass is available.

Figure 15

Isotopic distribution (relative yields) of the QP after subtracting the ${}^{12}\mathrm{C}$ background. Each panel refers to a different element. For $Z=14$ (not shown in the figure), the $N$ value ranges between 14 and 16 for ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$ and ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ti}$ and between 13 and 16 for ${}^{32}\mathrm{S}+{}^{40}\mathrm{Ca}$. Only statistical errors are shown.

Figure 16

Simulated data, $\langle N\rangle /Z$ of the QP as a function of the impact parameter. (a) primary data (twingo only). (b) secondary data (twingo plus gemini++), not filtered with the software replica of the experimental setup. Full crosses: ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$ with asystiff parametrization for the symmetry energy term; open diamonds [only in part (a)]: ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$ with asysoft parametrization. Open crosses: ${}^{32}\mathrm{S}+{}^{40}\mathrm{Ca}$ with asystiff parametrization.

Figure 17

twingo simulation, primary data. Event distribution as a function of the impact parameter $b$ and the charge $Z$ of the QP for the reaction ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$ with asystiff parametrization. The color scale gives the differential cross section $d\sigma /db$ in units of mbarn/fm for each $Z$ value; the binning of the abscissa is 1 unit of charge, while the binning of the ordinate is 0.4 fm.

Figure 18

Simulated data. Parts (a) and (b): $\langle N\rangle /Z$ for the QP as a function of its charge for primary (twingo only) and secondary data (twingo followed by gemini++ as afterburner, not filtered with the software replica of the experimental setup), respectively. Full crosses [open diamonds in part (a) only]: ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$ with asystiff (asysoft) parametrization for the symmetry energy term. Open crosses: ${}^{32}\mathrm{S}+{}^{40}\mathrm{Ca}$ with asystiff parametrization. Parts (c) and (d): cross section as a function of the charge $Z$ of the QP for primary and secondary data (not filtered with the software replica of the experimental setup), respectively. Full [dotted in part (c) only] black line: ${}^{32}\mathrm{S}+{}^{48}\mathrm{Ca}$ with asystiff (asysoft) parametrization for the symmetry energy term. Dashed red line: ${}^{32}\mathrm{S}+{}^{40}\mathrm{Ca}$ with asystiff parametrization. The binning of the abscissa is 1 unit of charge.

Figure 19

$\langle N\rangle /Z$ for the QP as a function of its charge. Open circles and open squares: experimental data after subtracting the ${}^{12}\mathrm{C}$ background (the gray area corresponds to the systematic error associated to the subtraction procedure). Crosses: simulation, secondary data (twingo followed by gemini++), filtered by means of the software replica of the setup.