# Fragments features and Isoscaling in Ni+Ca systems at the entrance of Fermi energy domain

E Geraci, E de Filippo, G Cardella, M Colonna, E Gambera, B Gnoffo, C

Maiolino, N.S Martorana, A Pagano, E.V Pagano, et al.

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E Geraci, E de Filippo, G Cardella, M Colonna, E Gambera, et al. Fragments features and Isoscaling in Ni+Ca systems at the entrance of Fermi energy domain. Nuclear Physics A, 2025, 1059, pp.123076. 10.1016/j.nuclphysa.2025.123076. hal-05026631

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# Fragments features and Isoscaling in Ni+Ca systems at the entrance of Fermi energy domain

E. Geraci<sup>a,b,g,*</sup> <sup>Δ</sup>, E. De Filippo<sup>b</sup>, G. Cardella<sup>b</sup>, M. Colonna<sup>c</sup>, E. Gambera<sup>a,c</sup>,

B. Gnoffo<sup>a,b</sup>, C. Maiolino<sup>c</sup>, N.S. Martorana<sup>b</sup>, A. Pagano<sup>b</sup>, E.V. Pagano<sup>c</sup>, S. Pirrone<sup>b</sup>,

G. Politi<sup>a,b</sup>, F. Rizzo<sup>a,c</sup>, P. Russotto<sup>c</sup>, M. Trimarchi<sup>b,d</sup>, S. Barlini<sup>e</sup>, R. Bougault<sup>f</sup>,

G. Casini<sup>e</sup>, N. Le Neindre<sup>f</sup>, S. Piantelli<sup>e</sup>

## ARTICLE INFO

**Keywords:**

Reaction mechanism

Fermi energies

Multifragmentation

Isoscaling

Thermodynamical features

## ABSTRACT

First results on central collisions for <sup>62</sup>Ni+<sup>48</sup>Ca system at 35 AMeV are presented, analyzing experimental data acquired with CHIMERA 4 π multidetector, installed at INFN-LNS in Italy.

The features of the reaction mechanisms involved, and the characteristics of the fragments produced in central collisions were analyzed for <sup>62</sup>Ni+<sup>48</sup>Ca system and compared with the results obtained for <sup>58</sup>Ni+<sup>40</sup>Ca at the same incident energy. The isoscaling properties of fragments produced were used to assess the hypothesis of thermal and chemical equilibrium of the sources formed in the two reactions.

## 1. Introduction

Heavy ion collisions at Fermi energies are a powerful tool to explore nuclear matter at sub-saturation densities [1]. In this energy regime, extremely complex scenarios are produced, where heavy ions reaction mechanisms are governed by mean field effects (associated to one-body dissipation mechanism, predominant at low energies) as well as two-body dissipation mechanisms (typical of high energy regimes, where nucleon-nucleon interactions prevail).

In central collisions, models predict that after an early stage in which projectile and target interact to form a compressed phase, the system undergoes an expansion phase that brings it into the so called spinodal region. In this region, fragments are formed simultaneously, and the sources generated in an incomplete fusion reaction can undergo multifragmentation process.

The occurrence of multifragmentation phenomena, highlighting the evolution of the reaction mechanisms at the entering of the Fermi energy domain, enables access to regions of nuclear matter with a density ranging from the saturation values to lower ones; this allows to investigate properties of the equation of state of nuclear matter far from saturation point [2–5].

<footnote><sup>a</sup> Dipartimento di Fisica e Astronomia "E. Majorana", Università degli Studi di Catania, Italy</footnote>

<footnote><sup>b</sup> INFN, Sezione di Catania, Catania, Italy</footnote>

<footnote><sup>c</sup> INFN, Laboratori Nazionali del Sud, Catania, Italy</footnote>

<footnote><sup>d</sup> MIFT, Università degli Studi di Messina, Messina, Italy</footnote>

<footnote><sup>e</sup> INFN, Sezione di Firenze and Università degli Studi di Firenze, Firenze, Italy</footnote>

<footnote><sup>f</sup> LPC Caen, ENSICAEN, University of Caen, CNRS/IN2P3, Caen France</footnote>

<footnote><sup>g</sup> Centro Siciliano di Fisica Nucleare e Struttura della Materia, Catania, Italy</footnote>

<footnote>* Corresponding author.
E-mail address: elena.geraci@ct.infn.it (E. Geraci).</footnote>
The present study originates from the experiments performed at INFN Laboratori Nazionali del Sud, with the CHIMERA 4π multidetector [6], an experimental apparatus characterized by low identification thresholds, wide employ of the time-of-flight method in addition to energy and charge measurement of the emitted fragments; in some cases also the fragment mass identification is achieved [7,8].

In particular, with the aim of exploring thermodynamical features of sources of about one hundred nucleons, with excitation energy of approximately 2–4 AMeV, formed in central collisions, beams of $^{58,62}$Ni were accelerated by the Super-Conductive Cyclotron at 25 AMeV and 35 AMeV on $^{40,48}$Ca targets.

The fragment features of $^{58}$Ni+$^{40,48}$Ca at 25 AMeV, emitted in central collisions, were analyzed [9], and the presence of two predominant reaction mechanisms was observed, corresponding on the one side to events where an Evaporation Residue survives from the collision and on the other side where multifragmentation process develops. A smooth transition between the two reaction mechanisms was observed, correlated with the IMF multiplicity.

The fragment production evolution as a function of incident energy was examined for central collisions produced in $^{58}$Ni+$^{40}$Ca at 25 and 35 AMeV, toward the low side of Fermi energies, where multifragmentation onsets [10]. There is a distinct change in the fragment sizes that are generated, with the size of the emitted fragments decreasing as the incident energy rises. At 25 AMeV incident energy, a unique behavior is seen, which could be linked to the start of multifragmentation: the largest fragment of the event is still a very massive fragment, even in the most dissipative collisions characterized by higher IMF multiplicities.

## 2. The $^{62}$Ni+$^{48}$Ca reactions at 35 AMeV

The central collisions for the $^{62}$Ni+$^{48}$Ca reaction at 35 AMeV were analyzed for the first time with the aim to investigate the influence of isospin degree of freedom on the fragments production. A first selection of the events was made imposing that the events analyzed satisfied the completeness requirement, i.e. selecting only events with a total detected charge (Ztot) in the range 80% < Ztot < 105% of sum of projectile and target charges and the total reconstructed longitudinal momentum (Pz) in the range 80% < Pz < 105% of the linear momentum of the projectile.

The raw data were treated employing the $\Delta E - E$ identification technique, using the Silicon and Fast CsI(Tl) signals, to obtain the charge of the fragments punching through the silicon detector and the mass of fragments with $3 \le Z \le 8$ for laboratory polar angles greater than 13°. The TOF technique [7] allowed the direct measurement of fragment velocities that combined with energy measurements grants the mass assignment for reaction products stopped in silicon detectors. Currently excluded from this analysis are the most energetic light charged particles ($Z<2$), which are usually identified by means of the fast-slow CsI(Tl) technique.

A correlation of the total kinetic energies (TKE), defined as the sum of the kinetic energies of all reaction products with a charge $Z \ge 3$, with the emission angle of the biggest fragment in the center of mass reference frame was used as impact parameter selector of the collisions. As shown in Fig. 1, imposing a cut on $\Theta_{\text{BIG}}<30$, very peripheral collisions are selected, where a quasi-projectile and a quasi-target emerge from the collisions. The constraint $30^\circ < \Theta_{\text{BIG}}<150^\circ$ and $\text{TKE}>1250$ MeV isolates more dissipative inelastic collisions, still with the presence of a well-recognized pair of PLF and TLF. Finally, events where $30^\circ < \Theta_{\text{BIG}}<150^\circ$ and $\text{TKE}<1250$ MeV are associated to the more central collisions. These latter events amount to 10% of the well reconstructed events.

### 2.1. Central collisions results

As it can be seen in the right panel of Fig. 1, the most central events are characterized by fragments with a charge Z lower than 30 and longitudinal velocities symmetrically distributed around the velocity of the center of mass. Such characteristics support the scenario of a multifragmenting source. The charge distribution of fragments shows a monotonically decreasing trend, as shown in left panel of Fig. 2, and the charge distribution centroids of the three biggest fragments (middle panel) are partially overlapped, as expected in multifragmentation where fragments are expected to be produced with similar sizes. The IMF multiplicity (right panel of Fig. 2) reaches values up to 5–6 and from the comparison with the $^{58}$Ni+$^{40}$Ca NIMF, it can be observed that the neutron rich system

<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Correlation of the charge of the emitted fragments as a function of the longitudinal velocity in the laboratory reference frame, for three different selections of the TKE and the emission angle of the biggest fragment in the CM.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 2. Charge distribution (left panel) and charge distributions of the three biggest fragments (middle panel) for $^{62}$Ni+$^{48}$Ca reactions at 35 AMeV. The IMF multiplicity for $^{58}$Ni+$^{40}$Ca (blue line) and $^{62}$Ni+$^{48}$Ca (red line) at 35 AMeV (right panel).</figcaption></figure>

favors larger IMF multiplicities with respect to the neutron poor one, as already observed [11].

Predictions of a dynamical approach based on the Boltzmann-Langevin-One-Body (BLOB) model are in progress in order to study the dynamics of fragment formation and extract excitation energy values [12].

Two decades ago, isoscaling received great attention, being related to the phase transition of a Fermi liquid and a nucleonic gas at sub-saturation densities and extreme temperature [13,11]. Multifragmentation has been associated with a region of mixed phase and a fractionation, where the neutron content of the gas phase significantly exceeds the liquid phase one, has been predicted.

In the grand canonical ensemble limit, with thermal and chemical equilibrium, the ratio of the detected light isotopes can be analyzed to obtain information on the isospin fractionation and a description of the thermodynamical coordinates of the emitting excited systems.

In particular, the ratio R$_{21}$(N,Z), which represents the relative ratio of isotopes emitted in two similar reactions differing only for isospin, can be related to the relative neutron and proton densities of the free nucleon :

$$R_{21}(N, Z) = \frac{Y_2(N, Z)}{Y_1(N, Z)} = C e^{N \Delta \mu_n / T} e^{Z \Delta \mu_p / T} = C \left( \frac{\rho_{n,2}}{\rho_{n,1}} \right)^N \left( \frac{\rho_{p,2}}{\rho_{p,1}} \right)^Z = C \hat{\rho}_n^N \hat{\rho}_p^Z$$

In Fig. 3 the R$_{21}$ ratio as a function of the neutron numbers is shown for the isotopes emitted in central collisions at 35 AMeV. Fits were performed for each Z; fit parameters α=0.31 and β=1.00, obtained as averaged value, are shown in Fig. 3 as grey lines. The fit parameters can then be related with the relative neutron and proton densities, being $e^{aZ} = \hat{\rho}_n$ and $e^{bZ} = \hat{\rho}_p$. At this stage of the analysis, the isoscaling, i.e. the occurrence of two parameters that can reproduce the scaling of the ratio R21 for different Z, is just a hint due to the large experimental error bars. As soon as further analysis will enable to better establish this preliminary conclusion, it will be possible to interpret this feature as an indication that the two sources under investigation, those produced in central collisions of $^{62}$Ni+$^{48}$Ca and $^{58}$Ni+$^{40}$Ca at 35 AMeV, have both reached the same thermal and chemical equilibrium. Further analysis, including a constrained fit of the isotopic ratios measured for two reactions and of the isobar ratios for mirror nuclei, is in progress, in order to extract more robust information on relative nucleonic densities and fractionation [14–17].

<figure><img src="image_7.png" /><figcaption>Fig. 3. Isotopic Ratio R$_{21}$, normalized with respect to R$_{21}$( $^{6}$Li), versus the number of neutrons of the detected fragments. Fragment mass and charge were experimentally extracted with the ΔE-E method.</figcaption></figure>
### 3. Conclusions

Central collisions for $^{62}$Ni+$^{48}$Ca system at 35 AMeV were studied benefiting of the peculiarities of the CHIMERA 4 $\pi$ multidetector installed at INFN-LNS in Italy. The features of the fragments produced in these collisions were analyzed, and at this stage they are consistent with the onset of multifragmentation processes. A comparison with fragments produced in $^{58}$Ni+$^{40}$Ca central collisions at 35 AMeV allowed to study the isoscaling. Its occurrence, if confirmed with further analysis, supports the idea of a thermal and chemical equilibrium reached by the two formed sources. Comparisons with predictions of the BLOB transport dynamical model are in progress in order to study the dynamics of fragment formations and the influence of the isospin degree of freedom. Future investigations, in reactions with isospin degree of freedom strongly enhanced using radioactive beams [18,19], are planned for the coming years to obtain more information on the behavior of the nuclear matter at sub saturation density.

### 4. Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work the authors used Quillbot in order to improve the language. After using this tool/service, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

### CRediT authorship contribution statement

E. Geraci: Conceptualization, Data curation, Formal analysis, Writing – original draft, Writing – review & editing. E. De Filippo: Conceptualization, Data curation, Formal analysis, Writing – review & editing. G. Cardella: Data curation, Methodology, Software, Validation. M. Colonna: Conceptualization, Methodology, Software. E. Gambera: Formal analysis, Methodology. B. Gnoffo: Investigation, Methodology. C. Maiolino: Investigation, Methodology. N.S. Martorana: Investigation, Methodology, Writing – review & editing. A. Pagano: Conceptualization, Formal analysis, Investigation, Methodology. E.V. Pagano: Investigation, Methodology. S. Pirrone: Investigation, Methodology. G. Politi: Investigation, Methodology. F. Rizzo: Investigation, Methodology. P. Russotto: Data curation, Investigation, Methodology, Software. M. Trimarchi: Investigation, Methodology. S. Barlini: Investigation, Methodology. R. Bougault: Investigation, Methodology. G. Casini: Investigation, Methodology, Writing – review & editing. N. Le Neindre: Investigation, Methodology, Writing – review & editing. S. Piantelli: Investigation, Methodology.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

Data will be made available on request.

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