A. Pagano1*
G. Cardella1E. De Filippo1E. Geraci1,2B. Gnoffo1,2G. Lanzalone3,4C. Maiolino3N. S. Martorana2,3
E. V. Pagano3S. Pirrone1G. Politi1,2F. Risitano1,5F. Rizzo2,3P. Russotto3
A. Trifirò1,5M. Trimarchi1,5- 1INFN, Sezione di Catania, Catania, Italy
- 2Dipartimento di Fisica ed Astronomia, Università di Catania, Catania, Italy
- 3INFN, Laboratori Nazionali del Sud, Catania, Italy
- 4Università Kore di Enna, Enna, Italy
- 5Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy
The study of heavy-ion collisions in the Fermi energy domain (20 MeV/nucleon < E/A < 100 MeV/nucleon) is a fundamental research topic in modern nuclear physics. In the case of semi-peripheral collisions, the Fermi energy regime is characterized by the formation of a transient, neck-like structure that connects a projectile-like fragment (PLF) with a target-like fragment (TLF). The neck structure represents a precursor of the fireball which is a typical overlap of participating nucleons at relativistic energies (E/A> 200 MeV/nucleon). It undergoes an expansion phase in a short time scale of the order of 100 fm/c with the formation of a low-density region of nuclear matter, therefore favoring the clusterization of intermediate mass fragments (IMFs) of atomic number Z (typically) less than 20. Particular emphasis is given to some relevant results obtained by the CHIMERA collaboration in the last decade, regarding the time scale of the production mechanisms of the intermediate mass fragments in neck fragmentation and their neutron enrichment.
1 Introduction
Heavy-ion collisions (HICs) at the Fermi energy constitute a very interesting case in contemporary nuclear physics studies (1). The Fermi energy regime locates between the low-energy Coulomb regime, where the one-body (mean-field) dissipation mechanism plays the major role in deep inelastic collisions, fusion–fission or fusion–evaporation, and the relativistic regime, where the two-body (nucleon–nucleon collisions) dissipation becomes the dominant mechanisms (2). Thus, the Fermi energy is a transition regime where it is possible to carefully test the in-medium properties of the nuclear interaction in a, somehow complicated, multi-body case. Many innovative studies have been performed in the last decades in several laboratories worldwide. Research studies conducted at MSU and GSI discovered a characteristic rise and fall of the intermediate mass fragment (IMF) mean multiplicity by increasing the energy beam (3). A possible liquid–gas phase transition has been also evidenced (4–6) in projectile fragmentation. Important efforts have also been accomplished in order to face the complexity of new detection systems able to measure the charges (masses) of mostly the reaction products in a 4π geometry (7, 8). At the same time, studies on the isotope composition of IMFs were carried out at GANIL laboratories by using the INDRA multi-detector, carefully investigating central collisions and their thermo-dynamic properties (9). Research studies carried out at Texas A&M laboratories characterized reaction mechanisms, thermo-dynamic description, time scale of the IMF emission, and limiting temperature (10, 11).
The isotopic composition of the quasi projectile residues has been exploited by the FAZIA detector, suggesting neutron enrichment when the target is a neutron-rich isotope (12). In this mini-review, we will focus on a limited part of results obtained at the INFN-Laboratori Nazionali del Sud (LNS) by using the CHIMERA multi-detector (13–17), concerning the time scale and neutron enrichment in fragment production.
2 Time scale of neck fragmentation
At the Fermi energy (20–100 MeV/nucleon), signals of deep inelastic binary collisions (low-energy regime) and the participant–spectator scenario (high-energy regime) coexist in the same scheme (18, 19). The participating region (i.e., the overlapping matter between the projectile and the target nuclei) in semi-peripheral collisions assumes the characteristic of a transiently expanding neck structure that connects (on a short time scale ∼100 fm/c) the projectile-like (PLF) and target-like (TLF) nuclei (20). The dynamic evolution of this neck fragmentation process has been clearly elucidated in the context of data taken with CHIMERA that is able to detect fragments from a very slow TLF to a very fast PLF, allowing in studying the correlations among various observables (14). The three fragments PLF, TLF, and IMF in the final state are observed together with a few light particles. It should be noted that neutrons are not observed. However, especially for future experiments with exotic beams, some experimental efforts are underway to upgrade the device for neutron detection (21). An example of correlation is given in Figure 1, where the atomic number (Z) against the laboratory velocity parallel to the beam direction (Vpar) of the three main fragments PLF, TLF, and IMF is displayed, for the reaction 64Ni + 124Sn at the beam energy of 35 MeV/nucleon, corresponding to Vpar ∼ 8 cm/ns. TLF fragments (Sn-like elements) are detected with a broad velocity distribution in the range of 0.4 cm/ns–1.3 cm/ns, approximately. Figure 1 has been obtained by a constraint on the charged particle multiplicity (M ≤ 7) in order to select semi-peripheral collisions.
FIGURE 1. Typical correlation between the atomic number and velocity for the PLF, TLF, and IMF fragments.
Important findings on the mechanism of the production of these three fragments were obtained from the analysis of the relative fragment–fragment velocities, as follows. The relative velocity of the IMF with respect to the PLF and the relative velocity of the IMF relative to the TLF, that is, VREL (IMF and PLF) and VREL (IMF and TLF), respectively, have been measured in an event-by-event analysis. The two relative velocities have been normalized to the corresponding relative velocity as evaluated by the Viola systematics (22–24) that gives the relative kinetic energy of the pure Coulomb repulsion between the two sub-systems PLF–IMF and TLF–IMF, respectively. In Figure 2, the experimental correlation plots VREL/VVIOLA (IMF and PLF) and VREL/VVIOLA (IMF and TLF) are shown for light IMFs of atomic number in the range 4 ≤ ZIMF ≤ 10, for the same reaction of Figure 1.
FIGURE 2. WILC2-Plot relative velocity correlations for semi-peripheral collisions in the reaction 64Ni +124Sn at the beam energy of 35 MeV/nucleon. The labels 1, 2, and 3 indicate chronological steps of different emission times of fragments from the prompt emission (40 fm/c) to a more delayed emission (>120 fm/c). The time chronology has been evaluated by Wilczynski et al. (20, 24) under the assumption of a sequential two-step model.
Simple kinematical analysis (20, 24) showed that the correlation between the two ratios gives information on the IMF emission scenario, in particular on the time scale in which the neck region re-separates from the PLF or TLF (or both in the case of instantaneous ternary emission). In Figure 2, as a solid line, an evaluation of the time scale of the process is shown. It is obtained by assuming that the IMF splits into a collinear configuration with respect to the relative velocity vector PLF–TLF, and it is evaluated by assuming a two-step process: in the first step, the projectile and the target undergo a fast inelastic scattering producing a PLF–TLF (excited) binary system. After a short delay (second step), the PLF (or the TLF) emits the IMF. Along with the two lines perpendicular to the X and Y axes (at a value equal to one), the IMF experiences the pure sequential Coulomb repulsion either from TLF or, alternatively, PLF residues. As an example of calculations, the second step separation times (ternary emission) of 40, 80, and 120 fm/c, respectively, have been considered after the first (binary) separation step of TLF–PLF [more details and kinematic calculations are reported in the appendix of (24)].
The time scale calibration reported earlier was an important step in understanding the dynamic component of the reaction mechanism: the fragmentation of the neck processes. The new type of the Wilczynski plot (WILC2-Plot, Figure 2) is the most convincing correlation for calibrating the time scale of IMF emission in semi-peripheral collisions, providing that, in addition to the IMF, both the slow TLF and fast PLF are measured in the same event (triple coincidence folding). The assumption of collinear emission PLF–IMF–TLF is crucial in reproducing the pattern emission of Figure 2. Both reverse and direct kinematics were investigated for the 58,64Ni and 112,124Sn isotopes at the energy of 35 MeV/nucleon. The analysis of the emission chronology was supported by different transport model simulations such as the stochastic mean-field (SMF) (19) and the constrained molecular dynamic model (CoMD-II) (25). The experimental WILC2-Plot (as described earlier) gives the time of separation of the IMF from the neck starting from the beginning of the separation between the PLF and the TLF. It gives us no information about the initial phase of overlap and compression which, at present, is estimated by the simulation of the transport code to be about 120 fm/c (26). Complementary experimental methods to define the time scale of the first phase of IMF production could be obtained by particle–particle (intensity interferometry methods) correlation (including uncharged particles) function (27). The stochastic mean-field (SMF) transport model (19, 28, 29) followed by sequential evaporation allows to accurately constrain the asymmetry term of the nuclear equation of state (NEOS) for the dynamical production of the light IMFs (30, 31). For the light IMF production in neck fragmentation, also a clear tendency of migration of neutrons against protons from high-density regions (PLF and TLF) toward the low-density neck region and consequent neutron enrichment of IMFs emitted by the neck has been evidenced, in favor of an asy-stiff symmetry energy behavior (30). The production of heavy fragments (Z > 10) has been interpreted within a larger time scale ranging from a non-equilibrated fission process (>300 fm/c) to a full equilibrated fission process of much longer times (32, 33). However, for the production of heavy fragments, the comparison between data and transport simulations either with the (CoMD-II) (25) or (AMD) (26) model requires some further improvements.
In conclusion, the experimental information obtained in these studies allowed for a more complete understanding of the light cluster production mechanism in heavy-ion collisions at the Fermi energy.
By using the CHIMERA detector, much effort has been recently devoted to fission studies and heavy residue production in central collisions by comparing different entrance isospin degrees of freedom enhancing the role of the neutron-rich isotopes (15) in view of new investigations with exotic beams by exploiting the incoming upgrade of the high-intensity beams at LNS in Catania (34) and the possibility offered by the “In Flight method” (35) that has been proven to be also implemented at the LNS (7, 36).
These envisaged studies will, therefore, open a fascinating perspective for future analyses with heavy ions at the Fermi energy. It should be noted that, in exotic nuclei, the detection of neutrons along with charged particles will be a necessary requirement for new investigations. Furthermore, with the implementation of the high intensity of the primary beam of a factor ≥20 that is expected to be operational in the next future at LNS, the exotic fragmentation will be a strong opportunity for developing more sophisticated experimental equipment incorporating neutron detection (21, 37, 38).
3 Conclusion
The time scale of a nuclear reaction and the isospin degree of freedom are important concepts in heavy-ion physics in order to describe the dynamical character of the reaction from the first phase of the collision (10 fm/c) up to the last stage of the sequential decay and equilibrium emission (≥1,000 fm/c). In the study, the time scale of neck fragmentation and the neutron enrichment of the neck have been emphasized. However, the measurements of the reaction time involved in different reaction channels are unique tools to probe the in-medium effective interaction and to constrain modern advanced transport simulations in order to predict the collision dynamics of heavy ions. We also emphasize the importance for reaction studies induced by exotic beams for future investigations. These reactions represent fundamental and necessary steps toward the study of the dependence of the equation of state of nuclear matter with respect to the baryon density and the isospin degrees of freedom.
Author contributions
All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.
Acknowledgments
The authors thank the INFN-LNS staff for providing both beams and targets of excellent quality. They are also grateful to the electronics, advanced technology, and mechanical design staff of the INFN division of Catania. This work was supported in part by the Italian Ministero dell’Istruzione, dell’Universita’ e della Ricerca (MIUR) under the PRIN contract 2020H8YFRE.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
References
1. Alamanos N, Bertulani C, Bonaccorso A, Bracco A, Brink DM, Casini G, et al. Editorial: Re-writing nuclear physics textbooks. Eur Phys J Plus (2022) 137:350. doi:10.1140/epjp/s13360-022-02552-7
2. Peilert G, Stocker H, Greiner W. Physics of high-energy heavy-ion collisions. Rep Prog Phys (1994) 57:533–602. doi:10.1088/0034-4885/57/6/001
3. Lynch WG. Fragmentation in exclusive measurements. Nucl Phys A (1995) 40:471–9. doi:10.1016/0375-9474(94)00707-t
4. Pochodzalla J. Probing the nuclear liquid-gas phase transition, Phys Rev Lett (1995) 75:1040. doi:10.1103/PhysRevLett.75.1040
5. Borderie B, Rivet MF. Nuclear multifragmentation and phase transition for hot nuclei. Prog Part Nucl Phys (2008) 61(2):551–601. doi:10.1016/j.ppnp.2008.01.003
6. Borderie B, Frankland JD. Liquid–Gas phase transition in nuclei. Prog Part Nucl Phys (2019) 105:82–138. doi:10.1016/j.ppnp.2018.12.002
7. de Souza RT, Le Neindre N, Pagano A, Schmidt KH. Detection. Eur Phys J A (2006) 30:275–91. doi:10.1140/epja/i2006-10123-8
8. Badalà A, La Cognata M, Nania R. Trends in particle and nuclei identification techniques in nuclear physics experiments, La Rivista Del Nuovo Cimento (2022) 45(3):189–276.
9. Frankland JD. INDRA collaboration, Nucl Phys A (2001) 689 (3–4):940–964. doi:10.1016/S0375-9474(00)00607-2
10. Natowitz JB, Hagel K, Ma Y, Murray M, Qin L, Wada R, et al. Limiting temperatures and the equation of state of nuclear matter. Phys Rev Lett (2002) 89:212701. doi:10.1103/physrevlett.89.212701
11. McIntosh AB, Yennello SJ. Interplay of neutron–proton equilibration and nuclear dynamics. Prog Part Nucl Phys (2019) 108:103707. doi:10.1016/j.ppnp.2019.06.001
12. Piantelli S. Isospin transport phenomena for the systems 80 Kr+ 40, 48Ca at 35 MeV/nucleon, Phys Rev C (2021) 103(1):014603. doi:10.1103/PhysRevC.103.014603
13. Geraci E. Isoscaling in central 124Sn + 64Ni, 112Sn + 58Ni collisions at 35 AMeV, Nucl Phys A (2004) 732:173–201. doi:10.1016/j.nuclphysa.2003.11.055
14. Pagano A. Fragmentation studies with the CHIMERA detector at LNS in Catania: recent progress, Nucl Phys A (2004) 734:504c. doi:10.1016/j.nuclphysa.2004.01.093
15. Pirrone S. Isospin influence on fragments production in 78Kr + 40Ca and 86Kr + 48Ca collisions at 10 MeV/nucleon, Eur Phys J A (2019) 55:22. doi:10.1140/epja/i2019-12695-4
16. Russotto P. Dynamical versus statistical production of Intermediate Mass Fragments at Fermi Energies, Eur Phys J A (2020) 56:12. doi:10.1140/epja/s10050-019-00011-z
17. Skwira-Chalot I, Siwek-Wilczyńiska K, Wilczyńska J, Amorini F, Anzalone A, Auditore L, et al. Fast Ternary and Quaternary Breakup of the 197 Au+ 197 Au System in Collisions at 15MeV/nucleon, PRL (2008) 101:262701. doi:10.1103/PhysRevLett.101.262701
18. Guerreau D. Transitional mechanisms for fragment production in peripheral collisions at intermediate energies. Nucl Phys A (1985) 447:37c–65. doi:10.1016/0375-9474(86)90597-x
19. Baran V, Colonna M, Di Toro M. Neck fragmentation reaction mechanism. Nucl Phys A (2004) 730:329–54. doi:10.1016/j.nuclphysa.2003.10.022
20. Wilczyn´ski J, De Filippo E, Pagano A, Amorini F, Anzalone A, Auditore L, et al. How to calibrate the time scale of emission of intermediate mass fragments, Int.J Mod Phy E (2004) 14:353
21. Pagano EV, Auditore L, Cardella G, D’Andrea M, De Filippo E, Geraci E, NArCoS: The new hodoscope for neutrons and charged particles (2022).
22. Viola VE, Kwiatkowski K, Walker M. Systematics of fission fragment total kinetic energy release. Phys Rev C (1985) 31:1550–2. doi:10.1103/physrevc.31.1550
23. Hinde DJ, Leigh JR, Bokhorst JM, Newton JO, Walsh RL, Boldeman JE. Mass-split dependence of the pre- and post-scission neutron multiplicities for fission of 251Es. Nucl Phys A (1987) 472:318–32. doi:10.1016/0375-9474(87)90213-2
24. De Filippo E, Pagano A, Wilczyn´ski J, Amorini F, Anzalone A, Auditore L, et al. How to calibrate the time scale of emission of intermediate mass fragments, Phys Rev C (2005) 71:044602. doi:10.1103/PhysRevC.71.044602
25. Papa M, Amorini F, Anzalone A, Auditore L, Baran V, Brzychczyk J, et al. Dynamical multi-breakup processes in the 124 Sn+ 64 Ni system at 35 MeV/nucleon. Phys. Rev. C (2007) 75:054616. doi:10.1103/PhysRevC.75.054616
26. Colonna M, Baran V, Toro MD, Rizzo C. Exploring the nuclear matter phase diagram with heavy ion reactions. J Phys : Conf Ser (2013) 413:012018. doi:10.1088/1742-6596/413/1/012018
27. Ghetti R, Helgesson J, Lanzano G, De Filippo E, Geraci M, Aiello S, et al. Correlation functions of light charged particles from projectile-like fragment source in and 77 MeV 40Ar + 27Al collisions. Nucl Phys A (2006) 765:307–18. doi:10.1016/j.nuclphysa.2005.11.019
28. Di Toro M, Baran V, Colonna M, Greco V. Probing the nuclear symmetry energy with heavy-ion collisions. J Phys G: Nucl Part Phys (2010) 37:083101. doi:10.1088/0954-3899/37/8/083101
29. Colonna M, di Toro M, Guarnera A, Maccarone S, Zielinska-Pfabe M, Wolter H. Fluctuations and dynamical instabilities in heavy-ion reactions. Nucl Phys A (1998) 642:449–60. doi:10.1016/s0375-9474(98)00542-9
30. De Filippo E, Pagano A, Russotto P, Amorini F, Anzalone A, Auditore L, et al. Correlations between emission timescale of fragments and isospin dynamics in 124 Sn+ 64 Ni and 112 Sn+ 58 Ni reactions at 35 A.MeV, Phys Rev C (2012) 86:014610. doi:10.1103/PhysRevC.86.014610
31. Pagano A, De Filippo E, Geraci E, Pagano EV, Russotto P, Siwek-Wilczynska K. Nuclear neck-density determination at Fermi energy with CHIMERA detector Eur. Phys. J. A (2020) 56:102
32. Russotto P. Strong enhancement of dynamical emission of heavy fragments in the neutron-rich 124 Sn + 64 Ni reaction at 35 A.MeV, Phys Rev C (2010) 81:064605. doi:10.1103/PhysRevC.81.064605
33. Piantelli S. Dynamical fission of the quasiprojectile and isospin equilibration for the system 80 Kr+ 48 Ca at 35 MeV/nucleon, Phys Rev C (2020) 101:034613. doi:10.1103/PhysRevC.101.034613
34.Agenda INFN. HIB2015-workshop. Available at: http://agenda.infn.it/conferenceDisplay.py?confId=10053. Accessed December 14–15, 2015
35. Morrissey DJ, Sherrill BM. In-flight separation of projectile fragments. Lect Notes Phys (2004) 651:113–35.
36. Raciti G, Rapisarda E, De Napoli M, Amorini F, Calabretta L, Cardella G, Intermediate energies tagged RIBs. Nucl Instr Methods Phys Res Section B: Beam Interactions Mater Atoms (2008) 266:4632–6. doi:10.1016/j.nimb.2008.05.153
37. Russotto P, Calabretta L, Cardella G, Cosentino G, De Filippo E, Gnoffo B, Status and perspectives of the INFN-LNS in-flight fragment separator. J Phys : Conf Ser (2018) 1014:012016. doi:10.1088/1742-6596/1014/1/012016
Keywords: multifragmentation, nuclear density, clusters, neutron enrichment, Fermi energy
Citation: Pagano A, Cardella G, De Filippo E, Geraci E, Gnoffo B, Lanzalone G, Maiolino C, Martorana NS, Pagano EV, Pirrone S, Politi G, Risitano F, Rizzo F, Russotto P, Trifirò A and Trimarchi M (2022) Characteristic time scale of cluster production at the Fermi energy. Front. Phys. 10:1050450. doi: 10.3389/fphy.2022.1050450
Received: 21 September 2022; Accepted: 03 October 2022;
Published: 26 October 2022.
Edited by:
Leandro Gasques, University of São Paulo, BrazilReviewed by:
Tobias Frederico, Instituto Tecnológico de Aeronáutica, BrazilCopyright © 2022 Pagano, Cardella, De Filippo, Geraci, Gnoffo, Lanzalone, Maiolino, Martorana, Pagano, Pirrone, Politi, Risitano, Rizzo, Russotto, Trifirò and Trimarchi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: A. Pagano, angelo.pagano@ct.infn.it