Reaction and fusion cross sections for the near-symmetric system ${}^{129}\mathrm{Xe}+{}^{\mathrm{nat}}\mathrm{Sn}$ from $8A$ to $35A$ MeV

Background: We study heavy-ion reactions from barrier up to Fermi energy. The data were acquired with the INDRA detector at the GANIL (Caen, France) facility.

Purpose: We aim to determine the reaction and fusion cross sections for the reactions induced by ${}^{129}\mathrm{Xe}$ projectiles on ${}^{\mathrm{nat}}\mathrm{Sn}$ targets for incident energies ranging from $8A$ to $35A$ MeV. In particular, the evaluation of the fusion and incomplete fusion cross sections is the main purpose, altogether with the comparison with the systematics of Eudes et al. [Europhys. Lett. 104, 22001 (2013)].

Method: The reaction cross sections are evaluated at each beam energy with data acquired thanks to the INDRA $4\pi$ array. The events are sorted with the help of the observable $E_{\text{iso,max}}$. We focus therefore our study on a selected sample of events, in such a way that the fusion and incomplete fusion cross sections can be estimated.

Results: We present the excitation function of reaction and fusion cross sections for the heavy and nearly symmetric system ${}^{129}\mathrm{Xe}+{}^{\mathrm{nat}}\mathrm{Sn}$ from $8A$ to $35A$ MeV. For the fusion excitation function the comparison with the systematics of Eudes et al. seems to be in a fair agreement starting from the beam energy $20A$ MeV. For the lower beam energies ($8A$ and $12A$ MeV) discrepancies are observed.

Conclusions: The evaluated fusionlike cross sections show a good agrement with a recent systematics for beam energies greater than $20A$ MeV. For low beam energies the cross-sectional values are lower than the expected ones. A probable reason for these low values is in the fusion hindrance at energies above or close to the barrier.

Figure 1

(a) Experimental reaction cross sections for all beam energies. (b) Experimental reaction cross sections normalized to the theoretical values of the following parametrizations: Bass [70], Kox [71], Tripathi [72], and Shen [73].

Figure 2

$E_{\text{iso,max}}$ vs $\sqrt{E_{\perp \mathrm{LCP}}}$ for the system at $15A$ MeV. $E_{\text{iso,max}}$ appears subdivided in three zones: A, B, and C. See text for details.

Figure 3

(a) Simulation of $E_{\text{iso,max}}$ for pure central collisions with unique source formation. In this case the observable is perfectly symmetric around zero [74, 75]. (b) Experimental $E_{\text{iso,max}}$ at $15A$ MeV. In order to appreciate this symmetry, more hidden for experimental data, the negative part has been reversed and superimposed to the positive values. The labels A, B, and C refer to the zones discussed in the text.

Figure 4

Heaviest fragment CM parallel velocity for three different bins of $E_{\text{iso,max}}$ for the system at $15A$ MeV. $A$ represents event selected with $E_{\text{iso,max}}\le 0$ MeV/nucleon, $B$ with $2\le E_{\text{iso,max}}\le 4$ MeV/nucleon, and $C$ with $E_{\text{iso,max}}>4$ MeV/nucleon.

Figure 5

Heaviest fragment charge for bins of $E_{\text{iso,max}}$ as Fig. 4 for $15A$ MeV. The yields are expressed in mb.

Figure 6

Correlation of the second heaviest fragment charge with the heaviest fragment charge for the system at $15A$ MeV for events with two fragments in the exit channel. (a) No selection on $E_{\text{iso,max}}$. $\text{(b)}{E}_{\text{iso,max}}\le 0$

Figure 7

Total kinetic energy versus flow angle for the system at $15A$ MeV for events with two fragments in the exit channel. (a) No selection on $E_{\text{iso,max}}$. (b) $E_{\text{iso,max}}\le 0$ MeV/nucleon.

Figure 8

Particle charge distributions at all beam energies. See text for details.

Figure 9

Correlation for the heaviest fragment charge vs $E_{\text{iso,max}}$ for $E_{\mathrm{Beam}}=18A$ MeV.

Figure 10

Heaviest fragment charge at incident energies $18A$ to $35A$ MeV with the $E_{\text{iso,max}}\le 0$ MeV/nucleon selection. The vertical black line gives the cut at $Z_{\max }=15$.

Figure 11

(a) Experimental fusion cross section. (b) Fusion cross section normalized for the Shen total reaction cross section.