Isospin diffusion measurement from the direct detection of a Quasi-Projectile remnant
A. Camaiani, G. Casini, S. Piantelli, A. Ono, E. Bonnet, R. Alba, S. Barlini, B. Borderie, R. Bougault, C. Ciampi, A. Chbihi, M. Cicerchia, M. Cinausero, J.A. Dueñas, D. DellAquila, Q. Fable, D. Fabris, C. Frosin, J. D. Frankland, F. Gramegna, D. Gruyer, K. I. Hahn, M. Henri, B. Hong, S. Kim, A. Kordyasz, M. J. Kweon, H. J. Lee, J. Lemarié, N. LeNeindre, I. Lombardo, O. Lopez, T. Marchi, S. H. Nam, P. Ottanelli, M. Parlog, G. Pasquali, G. Poggi, J. Quicray, A. A. Stefanini, S. Upadhyaya, S. Valdré, E. Vient
IIsospin diffusion measurementfrom the direct detection of a Quasi-Projectile remnant
A. Camaiani,
1, 2, ∗ G. Casini, S. Piantelli, A. Ono, E. Bonnet, R. Alba, S. Barlini,
1, 2
B.Borderie, R. Bougault, C. Ciampi, A. Chbihi, M. Cicerchia, M. Cinausero, J.A. Due˜nas, D.Dell’Aquila,
11, 12
Q. Fable, D. Fabris, C. Frosin,
1, 2
J. D. Frankland, F. Gramegna, D. Gruyer, K. I.Hahn, M. Henri, B. Hong,
15, 16
S. Kim, A. Kordyasz, M. J. Kweon,
15, 19
H. J. Lee, J. Lemari´e, N. LeNeindre, I. Lombardo, O. Lopez, T. Marchi, S. H. Nam,
15, 16
P. Ottanelli,
1, 2
M. Parlog,
7, 21
G.Pasquali,
1, 2
G. Poggi,
1, 2
J. Quicray, A. A. Stefanini,
1, 2
S. Upadhyaya, S. Valdr´e, and E. Vient Dipartimento di Fisica, Universit`a di Firenze, Italy INFN, Sezione di Firenze, Italy Department of Physics, Tohoku University, Sendai 980-8578, Japan SUBATECH, Universit´e de Nantes, IMT Atlantique,IN2P3/CNRS, 4 Rue Alfred Kastler, 44307 Nantes Cedex 3, France INFN Laboratori Nazionali del Sud, Via S. Sofia 62, 95125 Catania, Italy Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France Normandie Universit´e, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, 14000 Caen, France Grand Acc´el´erateur National d’Ions Lourds (GANIL),CEA/DRF - CNRS/IN2P3, Boulevard Henri Becquerel, F-14076 Caen, France INFN Laboratori Nazionali di Legnaro, 35020 Legnaro, Italy Depto. de Ingenier´ıa El´ectrica y Centro de Estudios Avanzados en F´ısica,Matem´aticas y Computaci´on, Universidad de Huelva, 21007 Huelva, Spain Dipartimento di Chimica e Farmacia, Universit`a degli Studi di Sassari, Sassari, Italy INFN - Laboratori Nazionali del Sud, Catania, Italy INFN Sezione di Padova, 35131 Padova, Italy Department of Science Education, Ewha Womans University, Seoul 03760, Republic of Korea Center for Extreme Nuclear Matters (CENuM),Korea University, Seoul 02841, Republic of Korea Department of Physics, Korea University, Seoul 02841, Republic of Korea Department of Science Education, Ewha Womans University, Seoul 03760, Republic of Korea Heavy Ion Laboratory, University of Warsaw, 02-093 Warszawa, Poland Department of Physics, Inha University, Incheon 22212, Republic of Korea INFN Sezione di Catania, 95123 Catania, Italy ”Horia Hulubei” National Institute of Physics and Nuclear Engineering (IFIN-HH), RO-077125 Bucharest Magurele, Romania Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Kracow, Poland
The neutron-proton equilibration process in Ca+ Ca at 35 MeV/nucleon bombarding energyhas been experimentally estimated by means of the isospin transport ratio. Experimental datahave been collected with a subset of the FAZIA telescope array, which permitted to determine Z and N of detected fragments. For the first time, the QP evaporative channel has been comparedwith the QP break-up one in a homogeneous and consistent way, pointing out to a comparable n-pequilibration which suggests close interaction time between projectile and target independently ofthe exit channel. Moreover, in the QP evaporative channel n-p equilibration has been compared withthe prediction of the Antisymmetrized Molecular Dynamics (AMD) model coupled to the GEMINIstatistical model as an afterburner, showing a larger probability of proton and neutron transfers inthe simulation with respect to the experimental data. I. INTRODUCTION
Since the end of the ’80s some experiments, mostlyfocused on dissipative collisions below 20 MeV/nucleon,investigated how a colliding system with projectile andtarget with different “chemical” composition, evolves to-wards the charge equilibration [1–4]. Later on, the so-called isospin dynamics, namely the neutron-proton (n-p) exchange between two interacting nuclei, gained much ∗ alberto.camaiani@fi.infn.it attention at Fermi energies (20-100 MeV/nucleon), wherenuclear subsystems relatively far from the saturationvalue of the baryon density can be explored; this, in turn,allows to investigate how the nuclear Equation of State(nEoS) rules the dynamics [5, 6]. In the Fermi energydomain, interesting signals have been found mainly inbinary semi-peripheral collisions, mosrly the clear evi-dence of a neutron enrichment of the fragments emit-ted from the phase-space region between the two mainreaction products (also labeled mid-velocity or neck re-gion) [7–10]. A theoretical interpretation was proposedand timely developed in the framework of nuclear reac-tion models, in order to describe the isotopic composi- a r X i v : . [ nu c l - e x ] J a n tion of the emerging excited Quasi-Projectile (QP) andQuasi-Target (QT) after the collision: the n-p equilibra-tion is largely due to the initial different concentrationof neutrons and protons between projectile and target(isospin diffusion) while the neutron enrichment of themid-velocity zone is ascribed to the density gradient,which arises between the different regions of the collidingsystems (isospin drift) [11–13]. In this paper, we discussabout isospin diffusion and how it guides the system to-wards the n-p equilibration.The degree of charge equilibration is strictly relatedboth to the driving force which rules the n-p exchangeand to the interaction time. In particular, the isospin dif-fusion is sensitive to the symmetry energy term E sym ofthe nEoS [11, 13], and it has been used, in the past, to putsome constraints on that and on the whole parametriza-tion [5, 6, 14]. However, to date, a clear knowledge ofthe symmetry energy is still lacking, namely the Taylorexpansion coefficients are known with large uncertainties(first order term, L sym ) or not at all (second order, K sym ,and higher order coefficients) [15]. Concerning the inter-action time, for a given restoring potential, the longerthe interaction time the more equilibrated in isospin thesystem [5]. In this sense, different effects contribute tothe equilibration, such as in-medium effects which sig-nificantly reduce the nucleon-nucleon cross section withrespect to the nucleon-nucleon value [16], or cluster cor-relations that arise during the collision [17]. Therefore, acharacterization of the collision as a function of the reac-tion centrality is mandatory in order to explore differentinteraction times.During the years the experimental investigations fol-lowed two main paths. The first one exploited detectionarrays covering a large part of the solid angle in order toglobally characterize the acquired events, although withlimitations in terms of isotopic separation (typically be-low Z ≈
8) [18–20]. As a consequence, in such stud-ies [5, 6, 14, 21–23] only the lightest QP decay productscould be used to extract information on the isospin equi-libration. The second one adopted mass spectrometers,in order to directly access to the neutron-proton ratio(
N/Z ) of the QP remnants, at the expense of coveringa small part of the solid angle and detecting only themain fragment of the event. Consequently, no informa-tion on break-up events or Intermediate Mass Fragments(IMFs) and/or Light Charged Particles (LCPs) accom-panying the QP could be obtained in typical configura-tions [24, 25]. On the other hand, according to the litera-ture [13, 26], the experimental determination of the
N/Z content of the QP remnant could be a good probe to putconstraints on the symmetry energy. In such a scenario,it could be useful to directly detect the isospin content ofthe QP remnant, together with the accompanying par-ticles or fragments. An example in this direction is therecent paper of the NIMROD collaboration where the au-thors reconstructed the isospin of the QP remnant [27].The present work fits with this panorama, aiming atthe investigation of the isospin diffusion in peripheral and semi-peripheral reactions and trying to overcome thelimitation of previous detectors. In fact we investigatedthe asymmetric reaction Ca+ Ca at 35 MeV/nucleonby means of the
FAZIA multi-telescope array, mainlyfor two reasons. Firstly, Ca isotopes allow to stress theisospin unbalance of the entrance channel, moving from( NZ ) Ca = 1 . NZ ) Ca = 1. Secondly, for such reac-tions the FAZIA array allows a mass resolution compa-rable with that of a spectrometer [28], allowing to fullyaccess the isotopic content of the QP remnant. Moreover,thanks to the good granularity of the detector, we caninvestigate also the break-up channel in order to isotopi-cally reconstruct the QP from the detected pair [29]. Inlight of this, we measured the n-p equilibration in the QPevaporative channel, directly accessing the QP remnant;this will be compared for the first time, in a homoge-neous and coherent way, with the QP break-up channel,where the QP can be reconstructed from the daughterfragments.In order to extract the equilibration degree in Ca+ Ca system, referred in the following as the mixedone, we adopted the isospin transport ratio (also knownas imbalance ratio) [30], which normalizes an isospinrelated observable measured in the asymmetric systemto that measured for two symmetric reactions, wherethe isospin diffusion is absent by definition. For thisreason, Ca+ Ca and Ca+ Ca reactions, both at35 MeV/nucleon, have been also measured and used asreference. The isospin transport ratio is defined as fol-lows [30]: R ( X ) = 2 X − X − X X − X (1)where X is an isospin sensitive observable evaluatedfor the three systems. For the two symmetric systems Ca+ Ca and Ca+ Ca, R ( X ) assumes the value of+1 and -1, respectively. Such a method allows to en-hance the equilibration signal due to the isospin diffu-sion [5, 21, 27], reducing the effects of any unwantedoverlapping process, and effectively cancelling those in-troducing a linear transformation of X [31]. Moreover,we note that if the chosen variable linearly depends onthe isospin of the system, R ( X ) = ± R ( X ) = 0 the “Full Equili-bration” value [30]. As done in the past [1–4], in thispaper, the n-p equilibration is followed as a function ofthe reaction dissipation. Since the impact parameter isnot directly accessible as an experimental observable, asusual, we used a reaction centrality estimator whose ef-fectiveness to follow the impact parameter order has beentested by means of the Antisymmetrized Molecular Dy-namics (AMD) [32] model coupled with GEMINI++ [33]as an afterburner.This paper is organized as follows. In Section II the ex-perimental apparatus and the adopted theoretical mod-els are presented. Section III describes the event se-lection criteria; also the gross properties of the stud-ied systems are presented. The adopted method to esti- θ=2° θ=8°ϕ Figure 1. Schematic polar representation of the apparatus ge-ometry. The beam axis passes through the symmetry center.View from the target. mate the reaction centrality is presented in Section IV.The n-p equilibration in both the QP evaporative andQP break-up channels is presented in Section V, whilethe comparison of the QP evaporative channel with theAMD+GEMINI++ prediction is reported in Section VI.Summary and conclusions are given in Section VII.
II. INVESTIGATION APPROACH
We performed the experiment using beams of , Caat 35 MeV/nucleon, delivered by the SuperconductingCyclotron of INFN-LNS with an average current of0.1 pnA, impinging on , Ca targets with a thicknessof 500 µ g/cm . Approximately 110, 70 and 15 mil-lions of events have been collected for the Ca+ Ca, Ca+ Ca and Ca+ Ca, respectively. The vacuuminside the scattering chamber was 2 × − mbar duringthe whole experiment.In order to avoid Ca oxidation during the mounting ofthe targets, the Ca layers were sandwiched between twoCarbon foils of about 10 µ g/cm on both sides of eachtarget was used. Data of both , Ca beams impingingon C (300 µ g/cm thick) have been collected in order toestimate the carbon reaction background in the main re-action data. As observed in a previous analysis where thesame Ca targets have been used [34], no significant con-tribution of reactions on Carbon target has been found,thus concluding that the background due to reaction onCarbon negligibly affects the present results [35].Data have been collected with four FAZIA blocks [28,36] arranged in a wall configuration around the beam axiscovering polar angles from 2 ◦ up to 8 ◦ approximately,80 cm far from the target. A schematic representation ofthe apparatus geometry is shown in Fig. 1. The main features and performances of the FAZIA multi-telescopearray are fully described elsewhere [28, 36–38]. Here,we remind that each block consists of 16 2 × Si-Si-CsI(Tl) telescopes, where the thickness of differentlayers is 300 µ m, 500 µ m, and 10 cm, respectively. Thetelescopes are directly coupled to “custom” FEE cards,featuring the preamplifiers and the fast digital samplingstages, also allowing the on-line extraction of the en-ergy parameters from the signals [36]. Each FAZIA tele-scope allows to identify iostopes in charge and mass up to Z ≈
25 with the ∆E-E technique [39] and up to Z ≈ K sat = 230 MeV for the incompressibil-ity modulus of the nuclear-matter and ρ = 0 .
16 fm − forthe saturation density. Two parametrizations of the sym-metry energy can be tested within AMD: an asym-softone with E sym = 32 MeV and L sym = 46 MeV, and anasym-stiff one with L sym = 108 MeV and the same valuefor E sym , obtained by changing the density dependentterm in the SLy4 force [43]. Such recipes are compat-ible with the reported values for realistic parametriza-tions [15]. Nucleon-nucleon collisions are taken into ac-count by implementing test particles which are randomlygenerated at every time step [42, 45]. The transitionprobability depends on the in-medium nucleon-nucleoncross section, which can be considered, within some lim-its, as a free parameter of the model. In this used codeversion, the parametrization proposed in Ref. [17] hasbeen used, i.e. σ = σ tanh ( σ free /σ ), with σ = yρ − / ,where y is a screening parameter, set at y = 0 .
85 (accord-ing to [17]). In order to take into account cluster corre-lations arising during the dynamics, cluster states are in-cluded among the possible achievable final states [42, 45–47].We produced about 40000 events for each system andsymmetry energy parametrization, stopping the dynam-ical calculation at 500 fm/c, a time when the dynamicalphase is safely concluded and the Coulomb interactionamong QP and QT can be considered negligible [45].Impact parameters up to the grazing values b gr (10.4,10.1 and 9.7 fm for the n-rich, mixed and n-deficient sys- - - -
10 [mm/ns] par v50 100 Z =1 BF M a) c.m. v beam v - - -
10 [mm/ns] par v50 100 Z =2 BF M b) c.m. v beam v FastSlow HeavyLight - - -
10 [mm/ns] rel v0 20 40 60 [ d e g ] re l q =2 BF M c) Figure 2. (Color online) Experimental data for the Ca+ Ca reaction. Panel a-b) Charge vs. parallel velocity correlation inlaboratory frame of BF ejectiles. a): events with M BF = 1, the rectangle shows the QP R selection; b) events with M BF = 2.Beam ( v beam ) and c.m. system ( v cm ) velocity are pointed out by the arrows. Panel c) θ rel vs. v rel correlation between the two BF s of the same events as in panel b); the rectangle points out the QP B selection. Each correlation is normalized to unitaryintegral. tem, respectively) have been randomly sorted, with atriangular distribution. For each primary event, 2000secondary events have been generated by means of theGEMINI++ [33] statistical Monte Carlo code. The sim-ulated data have then been filtered through a softwarereplica of the apparatus, that takes into account the ge-ometrical efficiency and the identification thresholds, inorder to consistently compare the simulation output withthe experimental results. III. EVENT SELECTION AND REACTIONCHARACTERIZATION
In order to show the criteria adopted for selectingevents we focus on the Ca+ Ca reaction for the sakeof brevity. The same selection criteria have been appliedto the other systems. First of all, due to pile-up events,events with the total detected charge Z T OT greater thanthe total system charge are rejected, as well as eventswith a total parallel momentum greater than the beammomentum (less than 2%). Only events with isotopicallyidentified ejectiles have been considered in the presentwork, which represents more than 80% of the total events.The event selection is based on a detected multiplicity( M ) condition. We define as Big Fragments ( BF s), anyejectile with Z ≥
5, and as IMFs only Lithium and Beryl-lium ions. This choice is motivated by the fact that mostparticles with
Z < i.e. the evaporative channel, and the break-up one. In theevaporative channel the primary QP de-excites emittingIMFs and LCPs, thus only a BF is expected. Differently,in the break-up channel, the primary QP splits in twoBFs, possibly excited above the energy threshold for par-ticle decay and thus undergoing subsequent evaporation.Consequently, the first class is identified by the presence of one BF ( M BF = 1), while the second one includestwo BF ( M BF = 2). It is worth mentioning that theseclasses correspond to 65% and 2% of the total numberof acquired events, respectively; the remaining part, dueto the limited solid angle coverage, contains events withonly LCP and/or IMF detected and it is discarded.Fig. 2(a,b) shows the BF charge vs. the parallel ve-locity (along the beam axis, v par ) correlation in the lab-oratory frame for events with M BF = 1 and M BF = 2,respectively. Beam ( v beam ) and center of mass ( v cm ) ve-locities are pointed out by the arrows. Panel a) shows aquite intense spot in the charge region 12 ≤ Z ≤
22, withparallel velocity between 60 and 80 mm/ns ( i.e. BF s thatpreserve down to the 75% of the projectile velocity). The BF s whose charge is greater than the projectile chargeare ascribable to a charge transfer from the target to theprojectile during the interaction phase. Both charge andvelocity are compatible with a BF that is the QP rem-nant after the de-excitation through the emission of LCPand/or IMF. The observed spot corresponds to a projec-tile that retains down to 60% of its initial charge: suchcharge range complies with analogous selections adoptedin literature [22, 48]. As a consequence, we select as QPevaporative channel (QP E ) those events containing a QPremnant (labeled as QP R ), i.e. a BF forward emittedwith Z = 12 ÷ E events represent 52% of the total col-lected data.Fig. 2(b) shows the Z − v par correlation for events thatwe mostly ascribe to QP break-up. Indeed four loci aremainly filled: according to the quadrants defined by thedashed lines, we verified that BF s with Z >
10 emit-ted at v par >
70 mm/ns “Heavy-Fast”) are mainly cor-related with lighter BF s with v par <
70 mm/ns “Light-Slow”); BF s with Z >
10 emitted at v par <
70 mm/ns(“Heavy-Slow”) are correlated with lighter BF s at v par >
70 mm/ns (“Light-Fast”). Such observation is compati-ble with the well known QP break-up scenario [49–52].
Z10 15 20 25 d N / d Z [ a r b . un i t s ] a) Ca Ca+ · [mm/ns] par v50 60 70 80 d N / d v [ a r b . un i t s ] b) · [deg] cm q [ a r b . un i t s ] q d N / d c) · : EXP B QPAMD+GEM++: EXP E QPAMD+GEM++: EXP B QPAMD+GEM++: EXP E QPAMD+GEM++
Z10 15 20 25 d N / d Z [ a r b . un i t s ] d) Ca Ca+ · [mm/ns] par v50 60 70 80 d N / d v [ a r b . un i t s ] e) · [deg] cm q [ a r b . un i t s ] q d N / d f) · : EXP B QPAMD+GEM++: EXP E QPAMD+GEM++: EXP B QPAMD+GEM++: EXP E QPAMD+GEM++
Figure 3. (Color online) Experimental (symbols) and simulated (lines) properties of the QP in the QP E (black) and QP B (red) channels, for the Ca+ Ca (a-c) and Ca+ Ca (d-f) reactions. Panel a,d): charge distributions. Panel b,e): parallelvelocity in the laboratory frame. Panel c,f): polar angle in the c.m. system. Each distribution is normalized to unitary integral.QP B distributions are scaled by a factor 0.5 for sake of clarity. Statistical errors are smaller than the marker size (line width). We can strenghten this selection by means of the cor-relation between the relative angle of the two detectedfragments θ rel (in the system center of mass) and theirrelative velocity v rel . Indeed, in such a correlation QPbreak-up events settle at low θ rel and at a v rel compatiblewith that of a Coulomb-driven split [34]. On the contrary,coincidence between QP and QT lies at θ rel values closeto 180 ◦ . Results are shown in Fig. 2(c). Consequently,the QP break-up (QP B ) channel events are selected re-quiring M BF = 2 and the two BF s in the phase-spaceregion within the red contour of Fig. 2(c). In addition, werequire that the total charge of the two BF s is within theaforementioned defined QP charge range ( i.e. − M BF = 2 sam-ple). A. Evaporative and break-up channelcharacterization
Since both selected channels could contain partiallydetected events of higher multiplicity, the study oftheir gross properties is mandatory in order to vali-date the selections. For such purpose, we exploited the AMD+GEMINI++ model, which has shown to be ableto reproduce the gross properties of heavy-ion collisionsin a large range of ions and bombarding energies [34, 45–47].Preliminary, the percentages predicted by the simula-tion for QP E and QP B events are 65% and 1.5%, i.e. inagreement with the values observed in the experimentaldataset. Moreover, the amount of QP B events within theQP E selection is below 2% (due to the limited geometri-cal acceptance), thus allowing to go further in the eventcharacterization.The measured distributions of the QP R charge, paral-lel velocity in the laboratory frame, and diffusion anglein the system center of mass are reported in Fig. 3(a, b,c), for the Ca+ Ca reaction, respectively; results forthe Ca+ Ca reaction are shown in fig Fig. 3(d, e, f).Both QP E and QP B channels are shown. Each distribu-tion is normalized to unity for a better shape comparisonwith the model prediction; QP B distributions are furtherscaled by a factor 0.5 for sake of clarity. We underlinethat in the QP B channel, the QP is reconstructed fromthe two detected BF s.For the experimental case, we observe that both theparallel velocity ( v par ) and the diffusion angle ( θ cm ) showtypical features of binary dissipative collisions. Indeed,for QP E events extends downwards starting from beamvelocity, while the θ cm is peaked at angles slightly largerthan the grazing angle [45]. Similar characteristics arealso found in the QP B distributions. However, somedifferences arise. The larger widths of the three distri-butions observed for QP B are consistent with the ex-pected broader phase-space region for QP B , and the lab-oratory velocity tends to be on average smaller than forQP E events. The AMD+GEMINI++ simulation is inglobal agreement with the observed distributions, as alsoshown in a recent investigation on Kr+Ca reactions at35 MeV/nucleon with four FAZIA blocks [34, 53]. We re-mind that the simulation was subjected to the same con-straints as the experimental data. For the QP E channel,the simulation follows the experimental trend, especiallyin the Ca+ Ca reaction, while some slight discrepan-cies appear for the Ca+ Ca reactions. Such differ-ences could be related to a different dissipation degreebetween the experimental and the simulated data. In-deed, the model seems to favor more dissipative events, i.e. lighter QP R (panel a), lower parallel velocity (panelb), and with larger diffusion angle. Similar findingshave been found also in the Kr+Ca comparison with theAMD+GEMINI++ predictions [34, 53].As a final note of this section we observe that the QPdistributions for the asymmetric Ca+ Ca system arevery similar to those of the symmetric Ca+ Ca case(fig. 3(a,b,c)). This is reasonable since we are observingvery similar QP R and none of the characteristics shown sofar take into account the detailed isotopic composition ofthe ejectiles. In conclusion, as also in the recently inves-tigated Kr+Ca reactions with four FAZIA blocks[34, 53],the AMD+GEMINI++ simulation offers a reasonable de-scription of both the QP E and QP B channels, thus con-firming the validity of the adopted selection criteria. IV. REACTION DISSIPATION ANDCENTRALITY
In this section, we aim at extracting an experimen-tal observable which can be used to order the events asa function of the reaction dissipation, to quantify theisospin diffusion from peripheral to more central events.The chosen observable is based on the momentum of thedetected (or reconstructed) QP R . We define the reducedmomentum ( p red ), defined as p red = (cid:18) p QPpar p beam (cid:19) cm , i.e.the QP remnant (or reconstructed) parallel momentum( p QPpar ) normalized to the beam momentum ( p beam ), bothof them in the c.m. frame.We first verify, for the experimental data, that the re-duced momentum scales as a function of the reactiondissipation. We report the results from the Ca+ Careaction as a representative case. We focus on the QP E channels since no significant amount of LCPs are de-tected in the QP B channel due to the limited angularsetup. For such purpose we exploited the LCPs for- ward emitted with respect to the QP R , that more re-liably can be attributed to the QP decay, being less af-fected by other contributions. However, in this phase-space other contributions could be present, as LCPs as-sociate to pre-equilibrium emissions. One expects thatthe LCP coming from the statistical decay of the QPpresent a Maxwellian-like kinetic energy spectra: the ap-parent temperature increases with the reaction dissipa-tion. Fig. 4(a) shows the experimental invariant pro-ton kinetic energy spectra, in the QP R frame, for the Ca+ Ca system: each distribution refers to a differ-ent bin of p red , according to the legend, and is normal-ized to unitary area for better shape comparison. Weobserve that each distribution presents two slopes, corre-sponding to two apparent temperatures T and T , andthis deserves some comments. The QP R is the matchingsource only for protons that contribute to the low energytail ( T ), i.e. the thermal-part of the distributions [54];the high energy tail ( T ) could be due to different mecha-nism, such as pre-equilibrium emission from the neck [54]or from the deformed QP [55–57], i.e. due to protonsemitted from different sources. For what is relevant tothe present discussion, a two-temperature fit can be usedin order to disentangle the thermal part from the non-thermal one, thus obtaining a crude indication on theexcitation scale of the QP source.The results of the fitting procedure using twoMaxwellian contributions are depicted in Fig. 4(a), su-perimposed to the experimental spectra. The values ofthe fitted parameter T are shown in Fig. 4(b) as a func-tion of p red for all the systems. The obtained T scalingas a function of the reduced momentum confirms that, onaverage, we are indeed selecting collisions with increasingdissipation when p red decreases from 1 to 0.3.Within the AMD+GEMINI++ model, on the otherhand, we can directly verify the relationship between p red and the reduced impact parameter b red ( b/b gr ). Fig. 4(c)shows the b red vs. p red correlation predicted by theAMD+GEMINI++ simulation, filtered with the detec-tor response: the correlation is narrow for peripheral col-lisions and tends to broaden for low b red . For this reason,we restrict the following analysis only to the upper-rightregion indicated by the dashed lines in the figure. Here,the correlation is relatively narrow and permits to reli-ably explore the range b red ≈ . −
1. These findingsare quite the same for the three studied Ca reactions asevidenced in Fig. 4(d) by the evolution of the averagereduced impact parameter ( (cid:104) b red (cid:105) ) as a function of p red .Finally, the QP R average charge (cid:104) Z (cid:105) and the rms width σ of the charge distribution are reported as a function of p red in Fig. 4(e). Panel f) is for the average QP R neutronnumber distribution (cid:104) N (cid:105) . In particular, the experimen-tal data are shown in black, with the bars indicating the ± σ values. The model results are in magenta and the ± σ values are drawn as a contour. As p red decreases, (cid:104) Z (cid:105) and (cid:104) N (cid:105) decrease starting from values very close tothe projectile ones. The average trends as a functionof p red are well reproduced by the simulation and, to a E [MeV]0 20 40 60 C o un t s - - - - = 0.4-0.5 red p = 0.5-0.6 red p = 0.6-0.7 red p = 0.7-0.8 red p a)Exp. red p0 0.5 1 [ M e V ] T Exp. - - - red p0 0.5 1 re d b red p0 0.5 1 > re d < b red p0 0.5 1 Z s – < Z > EXPAMD+GEM++ red p0 0.5 1 N s – < N > EXPAMD+GEM++ f) Figure 4. (Color online) Experimental data for the Ca+ Ca system: panel a) proton kinetic energy spectra in the QP R framefor different bins of p red , normalized to unitary area; panel b) average kinetic temperature T as a function of p red extractedfrom the Maxwellian fit (shown in panel a)) for the proton kinetic energy spectra; the results for the three systems are presentedwith symbols according to the legend; only statistical errors of the fit are shown. Simulated data (filtered AMD+GEMINI++simulation): panel c) reduced impact parameter b red vs. reduced momentum p red ; panel d) average reduced impact parameter (cid:104) b red (cid:105) vs. p red for each system. Comparison between experimental and simulated data for the Ca+ Ca system: panel e)average QP R charge and sigma of the charge distribution as a function of p red ; panel f) same as e) for the neutron numberdistribution. Symbols according to the legend. lower extent, also the σ of both distributions. The globalagreement between the experimental results and simula-tion strengthens the use of p red as an order variable, inorder to explore neutron-proton equilibration as a func-tion of the reaction centrality. V. NEUTRON-PROTON EQUILIBRATION:EVAPORATIVE AND BREAK-UP CHANNELS
The n-p equilibration can be now explored usingthe average neutron-proton ratio ( (cid:104)
N/Z (cid:105) ) of the vari-ous sources as a function of the reduced momentum.Fig. 5(a,b) shows the evolution of (cid:104)
N/Z (cid:105) vs. p red forthe three systems for both the QP E and the QP B chan- red p0.4 0.6 0.8 1 < N / Z > Z=20 a) Z=12 channel E QP red p0.4 0.6 0.8 1 < N / Z > b) channel B QP Figure 5. (Color online) Average neutron-proton ratio as afunction of p red . Panel a) QP E channel; panel b) QP B chan-nel. Magenta and cyan dashed arrow point out the EAL [58]value for Ca and Mg nuclei. Statistical errors are smaller thanthe marker size. Lines are drawn to guide the eyes. nel, respectively. In particular, in the QP E channel, thevalues refer to the QP R , while in the QP B channel tothe reconstructed (from the two BF s) QP. For sake ofclarity, we remind that the accompanying LCPs and/orIMFs are not taken into account.As suggested in Sec. III, we observe that the break-upchannel is detectable at lower p red . Apart from this, weobserve comparable trends in the two channels. Namely,the bound neutron abundances of the Ca and Ca de-tected (or recontructed) ejectiles are very different as ex-pected, with much larger values for the n-rich case. Sucheffects are in agreement with studies at lower bombard-ing energies, mainly dedicated to the investigation of theinitial neutron-proton unbalance effects in fusion reac-tions [59–61]. Moreover, the (cid:104)
N/Z (cid:105) ratios evolve withdissipation in a different way depending on the initialneutron abundance. Ca projectiles we observe a siz-able decrease of (cid:104)
N/Z (cid:105) with centrality, while for the Ca red p0.4 0.6 0.8 1 R ( < N / Z > ) No EquilibrationFull Equilibration channel E QP channel B QP Figure 6. Isospin transport ratio for the QP E and QP B chan-nels as a function of p red . Statistical errors are smaller thanthe marker size. Symbols according to the legend. Lines aredrawn to guide the eyes. case the n-p ratio is essentially constant after a slight in-crease in peripheral events. These different trends canbe interpreted in the light of a dominating statistical de-cay process for n-rich or n-deficient excited nuclei. In-deed, the steep decrease of the average (cid:104) N/Z (cid:105) with re-spect to the projectile values (1.4 and 1 for the n-richand n-deficient system, respectively) is mainly due to thestatistical decay [31]. As explained in [58], excited nucleifollow an average path in the N − Z plane during thedecay and, with increasing initial excitation, tend to ap-proach a specific region of that plane, called EvaporationActractor Line (EAL) [58], described by a N/Z ratio, de-pending on the nuclear size. In Fig. 5, just for reference,the EAL
N/Z ratios indicated with dashed arrows forion charges Z = 12 ,
20 representing relevant values forour QP remnant selection. We see that, with increasingdissipation, QP R from Ca and from Ca have (cid:104)
N/Z (cid:105) values that move towards the EAL predictions, althoughcoming from different sides.The comparison between the (cid:104)
N/Z (cid:105) of QP R from Caof the symmetric and asymmetric reactions reveals thetrend to isospin equilibration. Focusing on the QP E case (Fig. 5(a)), a clear hierarchy is observed: a re-duced neutron content is detected for the asymmetriccase (black solid circles in fig. 5(a)) with a gap with re-spect to the symmetric reference (green solid triangles infig. 5(a)) increasing towards central collisions, as the re-sult of the interaction with a n-deficient partner so thatthe two colliding nuclei tend to equilibrate their N/Z ra-tios [51, 62, 63]. Remarkably, very similar observationscan be repeated for the QP B channel, where the samehierarchy and evolution are evident.In order to more quantitatively establish the isospinequilibration process we show in Fig. 6 the isospin trans-port ratio R ( X ) built with X = (cid:104) N/Z (cid:105) (Eq.1) as a func-tion of the reaction dissipation represented by p red . Con-cerning the evaporative channel, we observe the expectedtrend. The equilibration degree smoothly and monoton-ically evolves from R ≈ p red ≈ R ≈ . p red ≈ .
3, which, according to the AMD average pre-diction (Fig. 4(d)), corresponds to a range of central-ity (cid:104) b red (cid:105) ∈ [1 , . N/Z values. Since the QP size selection is somewhat arbitrary(Sec. 3), we tested the result by changing the adopted QPcharge range. In particular, we increased and decreasedthe lower limit of two units with respect to our previous“standard” ( Z = 12) value (as done in [22, 48]), takinginto account other reasonable choices reported in the lit-erature. For instance Ref. [9] fixes as a lower limit of theQP charge the 36% of the projectile charge. By using theranges Z QP ∈ [14 ,
22] or Z QP ∈ [10 , R is negligibly affected in the studied rangeof p red [35].An important point of this work, as anticipated, is theaccess to the isospin diffusion process looking at the QP B channel, in a manner that - to our knowledge - has notbeen yet attempted before. In Fig. 6 the open dots showthe (cid:104) N/Z (cid:105) for QP reconstructed from the break-up frag-ments. As a first comment we can say that the generaltrend is the same, with slight differences: for the QP B wefind a weak process at least for the less dissipative acces-sible bins. It is very difficult to judge and conclude aboutthese small differences which, in any case, are out of sta-tistical errors. Such an observation suggests a heavierprimary source in the QP B channel, which can lead thesystem to a lower n-p equilibration for the most exploredperipheral events. For instance, the average charge andneutron number of the reconstructed QP in the QP B channel are on average 2 units larger than the values ofthe QP R in the evaporative channel. On the other hand,the differences can be also related to subtle effects asso-ciated to the different evaporation paths followed by theexcited break-up fragments (before and after the split)with respect to the case without break-up.Such a topic will be further investigate in the IN-DRA+FAZIA experimental campaign at GANIL, thuscombining with the isotopic capabilities of the FAZIAmulti-telescope array the large angular coverage of theINDRA detector, in order to more precisely select thereaction centrality. Here, we can only conclude that thisroughly common trend of the two geometrical loci in fig.6suggests that, irrespective of the final state channel, theisospin diffusion acts in a similar way. In other words, itappears that the isospin equilibration process acts beforeany de-excitation process. This observation is rather inline with some old results [1] for lower energy collisions.There, a general conclusion was suggested that the n-pdegree of freedom tends to relax rather quickly during the interaction. The complete equilibrium could be reachedonly for rather central impacts, not accessible here ac-cording to the AMD centrality estimation of Fig. 4(c,d),associated with relatively long interaction times. VI. NEUTRON-PROTON EQUILIBRATION:COMPARISON WITH THE SIMULATION
In this section, we aim at comparing the isospin evo-lution extracted from experimental data with that pre-dicted by the transport model AMD, coupled with GEM-INI++ as an afterburner. We will focus on the evapo-rative channel, as it corresponds to 65% of the collecteddata. The break-up channel is experimentally around 35times less abundant and since also the model predicts asimilar event partition, the simulation statistics resultsto be to low for a reliable comparison. For sake of clar-ity, we remind that the simulated data have been treatedas the experimental ones.Fig.7(a,b) shows the simulated (cid:104)
N/Z (cid:105) vs. p red trend(lines), compared with that obtained experimentally(same points of Fig. 5(a)) for the asym-stiff and asym-softparametrization of the symmetry energy, respectively. Asfor the experimental data, we observe the clear hierarchyamong the three systems, and the tendency to approach (cid:104) N/Z (cid:105) values around the EAL loci (magenta and cyanarrows for Z = 20 and Z = 12, respectively) with in-creasing dissipation. The agreement with the (cid:104) N/Z (cid:105) ofthe Ca data is excellent while, as noticed for the grossproperties of the QP R (see. Sec. 3), there are some dif-ferences for the Ca case. Weak differences between thetwo calculations can be seen, in particular, the asym-stiffchoice predicts a more neutron-rich QP R with respect tothe asym-soft one, as expected [11, 26].The corresponding isospin transport ratio are shown inFig. 8 as a function of p red , with dot-dashed and dottedline for the asym-stiff and asym-soft parametrizations, re-spectively. We first underline that the R variable dependson the gap between the asymmetric and the symmetricreferences. The way how the gap evolves vs. p red dic-tates the shape of the R as a function of the dissipation,thus a precise reproduction of the (cid:104) N/Z (cid:105) values is notmandatory. However, Fig 8 shows a sizable disagreementbetween experiment and model predictions concerningthe isospin diffusion process. In particular, the modelpredicts an initial fast relaxation followed by a slowertrend, whereas the experiment suggests a smoother evo-lution. As for the asym-stiffness, we can see that the verysmall differences in the two model results for (cid:104)
N/Z (cid:105) givea quite small gap in the equilibration degree; however, asexpected, the asym-soft assumption slightly favors theisospin relaxation.Some comments and arguments on the possible ori-gin of the observed disagreement are in order. A firstcomment deals with the role of the emissions from theprimary QP, i.e. the fragment emerging just at the endof the interaction which we would like to access in or-0 red p0.4 0.6 0.8 1 < N / Z > Z=20 a) Z=12
Exp.484840404840 Sim. asy-stiff484840404840 red p0.4 0.6 0.8 1 < N / Z > b) Exp.484840404840 Sim. asy-soft484840404840
Figure 7. Comparison of the measured average neutron-proton ratio for the QP E channel as a function of p red withthe AMD+GEMINI++ simulation. Panel a) AMD asym-stiffparametrization; panel b) AMD asym-soft parametrization.Magenta and cyan dashed arrow point out the EAL [58] forrelevant nuclei. Symbols according to the legend. Statisticalerrors are smaller than the marker size (line width). der to measure the isospin diffusion. Indeed, any par-ticle or fragment emission before the detection perturbsthe final isotopic distribution. One can thus wonder ifthe found disagreement is related to a partially wrongdescription of the dynamics (reaction times and/or nu-clear potential terms ruling the isospin transfer) or toa somehow wrong evaporation scheme. In this respect,we must stress that isospin transport ratio has been in-troduced [5, 30] just to bypass any perturbation whichintroduces a linear transformation of the isospin variablein use (Eq. 1). Such behavior has been recently investi-gated in a specific work [31], in a full model framework,for the systems here discussed. In this paper one demon-strates, by means of the AMD simulation coupled withstatistical models, that the charge equilibration processmeasured via isospin transport ratio is indeed affectedby perturbations introduced by the dynamical and sta- red p0.4 0.6 0.8 1 R ( < N / Z > ) No EquilibrationFull Equilibration
EXPAMD stiff + GEMINI++AMD soft + GEMINI++
Figure 8. Comparison of the isospin transport ratio for theQP E channel as a function of p red between the experimentalresults and the AMD+GEMINI++ simulation, using asym-stiff and asym-soft parametrizations. Statistical errors aresmaller than the marker size (line width). tistical emissions from the fragments after their separa-tion. In particular, the statistical emission (described by Gemini++ code) tends to introduce non-linear spuriousdistortions at low excitation energies (where structureeffects are well known to affect the particle emission [67–69]), i.e. for large impact parameters, while the distortionbecomes smoother and linear with increasing excitation.Instead, at least for the considered systems, the contribu-tion of emissions occurring during the interaction phasesand predicted by the AMD model, increases with central-ity but remains relatively scarce and negligibly affects the R variable. As a consequence, we checked that despitesome residual distortions related to emissions, the vari-able R is robust and keeps memory of the primary isospinhistory; this suggests that the observed discrepancy be-tween measured and predicted R can be safely ascribedto the dynamical modelization.By analyzing the evolving output of the model, wecan access to the end of the projectile-target interactionphase (labeled as t DIC ), by means of the procedure de-scribed in refs. [31, 34]. In order to pin down the mech-anism responsible for the observe discrepancies with ex-periment, we applied some special conditions on the an-alyzed events, as follows. The n-p equilibration obtainedat t DIC , for the asym-stiff simulation, is shown in Fig. 9as a black line; for sake of comparison also the experi-mental trend of Fig. 8 is here reported. For each sys-tem ( i.e. the asymmetric and the symmetric references),we start allowing only the net neutron transfers (greenline): this corresponds to retain only the reaction chan-nels where the QP emerges as a Ca isotope. Vice versa,we allow only the net proton exchanges (red line), i.e. events where the QP retains the neutron number of theprojectile. As expected, limiting the n-p exchange pro-duces a lower equilibration. More interesting, we observe1 red p0.4 0.6 0.8 1 R ( < N / Z > ) No EquilibrationFull Equilibration
EXP
DIC
AMD at t : only p transf.
DIC
AMD at t : only n transf.
DIC
AMD at t
DIC
Modified AMD at t
Figure 9. (Color online) Comparison of the experimentalisospin transport ratio with the equilibration obtained at theprojectile-target separation time ( t DIC ), for the asym-stiffparametrization; the isospin transport ratios only due to anet charge (red line) and neutron (green line) number changeare shown. The equilibration obtained after a re-scaling ofthe proton and neutron transfer probabilities is shown withmagenta line. See text for details. Errors are statistical. that the equilibration obtained via only charge changelies close to the total one, pointing out to an importantrole of the p transfers in the isospin equilibration mecha-nism. This can be quantitatively understood keeping intoaccount that, in order to restore the
N/Z unbalance, ap transfer is more effective than a n transfer, since theformer counts as 1/20 whereas the latter as 1/28.Starting from the indication that the nucleon trans-fer in AMD may be too frequent, we now aim at quan-tifying the degree of the overestimation of the transferprobability. We introduce a multiplying factor ( f ), de-pending on the net number of transferred neutrons andprotons, ∆ n and ∆ p respectively. Assuming that nu-cleon transfers in the same event are independent of eachother, we modelled a parametrization as: f = α | ∆ n | β | ∆ p | ,where α and β are parameters to suppress (or enhance)the net transfer probability of single neutrons and sin-gle protons, respectively. The probability of the non-transfer channel (at t dic ) is adjusted for the total proba-bility conservation. For each system, we then proceed toclassify the various channels as function on the net p/nchanges at t DIC : we modify these initial populations viaa change of the ( α, β ) pair and thus obtain different av-erage isospin values. The isospin transport ratio is thencomputed via eq.(1), adopting the (cid:104)
N/Z (cid:105) ( α, β ) as X vari-able ( R AMD ( α, β )). The parameters α and β have beenselected by means of fit procedure on the experimentaldata R exp . Specifically, we looked for the minimum of a M variable defines as follows: M = N (cid:88) i =0 (cid:2) R iexp − R iAMD ( α, β ) (cid:3) σ exp ( i ) + σ AMD ( i ) , (2) where R iexp and R iAMD are the values of the experimentaland simulated R at the i th point along the p red axis; σ exp ( i ) and σ AMD ( i ) the statistical errors of each point.The fitted values of the parameters are: α = 0 . ± . β = 0 . ± .
1. The equilibration degree obtained for suchvalues is shown in Fig. 9 with magenta line (ModifiedAMD), which follows the experimental trend proving thesatisfactory quality of the fit. This show that the nucleontransfer is overestimated in AMD by about a factor oftwo. Moreover, it is likely that proton transfer is moreoverestimated than neutron transfer.In conclusion, this first attempt to compare the n-pequilibration measured via the isospin transport ratiobuilt from the (cid:104)
N/Z (cid:105) of the QP R has shown a fasterequilibration of the model prediction with respect to thatobserved in the experimental sample. Such discrepancycan be recovered acting on the transfer probability, re-ducing it approximately of a factor two. It is not easy toidentify a reason behind this problem, as many factorscould contribute to it, e.g. the nucleon-nucleon cross sec-tion or the nucleon effective masses or their interplay. Forinstance, a simple variation of the screening paramenter y of the nucleon-nucleon cross section from y = 0 .
42 upto the free nucleon-nucleon cross section did not producesignificant variations of the isospin transport ratio. Suchtopics will be investigated in future works.
VII. SUMMARY AND CONCLUSION
In this paper, we have presented the experimental re-sults of an experiment dedicated to the investigation ofthe n-p equilibration in Ca+ Ca semi-peripheral re-actions at 35 MeV/nucleon, performed with four blocksof the
FAZIA multi-telescope array at the INFN-LNS.For the first time, thanks to the
FAZIA identificationperformances coupled to its good granularity, we couldstudy the isospin relaxation for the two main QP decaychannels, the evaporative and the break-up one.The equilibration trend has been investigated bymeans of the isospin transport ratio, which which im-proves the sensitivity to the effect sought after andnormalizes the mixed system evolution with the limit-ing values of the symmetric reactions Ca+ Ca and Ca+ Ca, investigated under the same experimentalconditions. Despite the relatively small coverage of thesetup (2 − ◦ in the laboratory frame), the main achieve-ments have been proved not to be strongly affected by theapparatus response: indeed we focus on the QP phase-space for which we have reasonable acceptance. We haveintroduced a reaction dissipation estimator ( p red ), whichhas been linked with the reaction centrality by means ofthe model.The results reported in this paper are the following.As expected, the relaxation of the isospin degree of free-dom has been observed in the Ca+ Ca, via the use ofthe isospin transport ratio of the average neutron-protonratio ( (cid:104)
N/Z (cid:105) ) of QP remnants.2The comparative analysis of the QP evaporative andbreak-up channels has shown the typical signature of theisospin diffusion: as the reaction centrality increases, thesystem evolves to restore the charge equilibrium. Thesimilarity of the behavior for the two channels suggests acomparable dynamical evolution before the decay, what-ever it is. Specifically, this is consistent with an isospinexchange mechanism that acts on a similar timescale(that of the interaction phase) shorter than the evapo-ration cascade or the QP split phase.Concerning the comparison with the AMD model cou-pled with the GEMINI++ statistical code, we observedthat the model globally reproduces the main features ofthe QP in both the evaporative and break-up channels;the agreement is better for the QP evaporation channelthan for the break-up one, where the model produceslighter and slower fragments than the measured ones.Also, the agreement is quite good for the Ca systemwhile for the Ca reactions it less nicely reproduces theQP data. The detailed isospin distributions of the final(post-evaporative) fragments are, again, less well repro-duced for the n-rich systems; for the Ca reaction thecomparison is excellent.The main difference between measured and model datais observed in the evolution towards the charge equilibra-tion for the evaporative exit channel. The model predictsa faster relaxation of the initial neutron-proton unbal-ance with respect to the experiment. This discrepancy seems to be associated with an overestimated probabilityof nucleon transfers, mainly and more specifically for theprotons: in particular a reduction of about a factor twoaccounts for the experimental path. However, a deeperinvestigation on this point is in program. In this respectwe plan to extend the analysis of this paper to the dataobtained by the first recent INDRA-FAZIA experimenton Ni+Ni reactions at comparable energies. Here, wehave the almost full isotopic identification of QP ejec-tiles coupled with a much larger acceptance, allowing toadopt and cross-check several variables, several variables,to extend the analysis to the full panel of exit channels,and to more precisely select the reaction centrality.
ACKNOWLEDGMENTS
This work required the use of a lot of computationtime for the production of the simulated data. We wouldlike to thank the GARR Consortium for the kind useof the cloud computing infrastructure on the platformcloud.garr.it. We would like to thank also the INFN-CNAF for the use of its cloud computing infrastructure.A. Ono was supported by JSPS KAK-ENHI Grant No.JP17K05432. This work was also supported by the Na-tional Research Foundation of Korea (NRF) (Grant No.2018R1A5A1025563). [1] R. Planeta, S. H. Zhou, K. Kwiatkowski, W. G. Wilson,V. E. Viola, H. Breuer, D. Benton, F. Khazaie, R. J.McDonald, A. C. Mignerey, A. Weston-Dawkes, R. T.de Souza, J. R. Huizenga, and W. U. Schr¨oder, Phys.Rev. C , 195 (1988).[2] P. Gippner et al. , Zeit. fur Phys. A (1988).[3] H. Madani, A. C. Mignerey, A. A. Marchetti, A. P.Weston-Dawkes, W. L. Kehoe, and F. Obenshain, Phys.Rev. C , 2562 (1995).[4] A. A. Marchetti, A. C. Mignerey, H. Madani, A. G¨okmen,W. L. Kehoe, B. Libby, K. Morley, H. Breuer, K. Wolf,and F. Obenshain, Phys. Rev. C , 266 (1993).[5] M. B. Tsang, T. X. Liu, L. Shi, P. Danielewicz, C. K.Gelbke, X. D. Liu, W. G. Lynch, W. P. Tan, G. Verde,A. Wagner, H. S. Xu, W. A. Friedman, L. Beaulieu,B. Davin, R. T. de Souza, Y. Larochelle, T. Lefort,R. Yanez, V. E. Viola, R. J. Charity, and L. G. Sobotka,Phys. Rev. Lett. , 062701 (2004).[6] M. B. Tsang, Y. Zhang, P. Danielewicz, M. Famiano,Z. Li, W. G. Lynch, and A. W. Steiner, Phys. Rev. Lett. , 122701 (2009).[7] J. (cid:32)Lukasik, J. Benlliure, V. M´etivier, E. Plagnol,B. Tamain, M. Assenard, G. Auger, C. O. Bacri, E. Bis-quer, B. Borderie, R. Bougault, R. Brou, P. Buchet,J. L. Charvet, A. Chbihi, J. Colin, D. Cussol, R. Dayras,A. Demeyer, D. Dor´e, D. Durand, E. Gerlic, S. Ger-main, D. Gourio, D. Guinet, P. Lautesse, J. L. Lav-ille, J. F. Lecolley, A. Le F`evre, T. Lefort, R. Legrain,O. Lopez, M. Louvel, N. Marie, L. Nalpas, M. Par- log, J. P´eter, O. Politi, A. Rahmani, T. Reposeur,M. F. Rivet, E. Rosato, F. Saint-Laurent, M. Squalli,J. C. Steckmeyer, M. Stern, L. Tassan-Got, E. Vient,C. Volant, J. P. Wieleczko, M. Colonna, F. Haddad,P. Eudes, T. Sami, and F. Sebille, Phys. Rev. C ,1906 (1997).[8] E. Plagnol, J. (cid:32)Lukasik, G. Auger, C. O. Bacri, N. Bel-laize, F. Bocage, B. Borderie, R. Bougault, R. Brou,P. Buchet, J. L. Charvet, A. Chbihi, J. Colin, D. Cus-sol, R. Dayras, A. Demeyer, D. Dor´e, D. Durand, J. D.Frankland, E. Galichet, E. Genouin-Duhamel, E. Ger-lic, D. Guinet, P. Lautesse, J. L. Laville, J. F. Lecol-ley, R. Legrain, N. Le Neindre, O. Lopez, M. Louvel,A. M. Maskay, L. Nalpas, A. D. Nguyen, M. Pˆarlog,J. P´eter, M. F. Rivet, E. Rosato, F. Saint-Laurent, S. Sa-lou, J. C. Steckmeyer, M. Stern, G. T˘ab˘acaru, B. Tamain,L. Tassan-Got, O. Tirel, E. Vient, C. Volant, and J. P.Wieleczko (The INDRA Collaboration), Phys. Rev. C ,014606 (1999).[9] D. Th´eriault, A. Vall´ee, L. Gingras, Y. Larochelle,R. Roy, A. April, L. Beaulieu, F. Grenier, F. Lemieux,J. Moisan, M. Samri, C. St-Pierre, S. Turbide, B. Bor-derie, R. Bougault, P. Buchet, J. L. Charvet, A. Chbihi,J. Colin, D. Cussol, R. Dayras, D. Durand, J. D. Frank-land, E. Galichet, D. Guinet, B. Guiot, P. Lautesse, J. F.Lecolley, N. L. Neindre, O. Lopez, A. M. Maskay, L. Nal-pas, M. Parlog, P. Pawlowski, M. F. Rivet, E. Rosato,J. C. Steckmeyer, B. Tamain, E. Vient, C. Volant, J. P.Wieleczko, I. Collaboration, S. J. Yennello, E. Martin, and E. Winchester, Phys. Rev. C , 014610 (2005).[10] D. Th´eriault, J. Gauthier, F. Grenier, F. Moisan, C. St-Pierre, R. Roy, B. Davin, S. Hudan, T. Paduszynski,R. T. d. Souza, E. Bell, J. Garey, J. Iglio, A. L. Kek-sis, S. Parketon, C. Richers, D. V. Shetty, S. N. Soisson,G. A. Souliotis, B. C. Stein, and S. J. Yennello, Phys.Rev. C , 051602 (2006).[11] V. Baran, M. Colonna, V. Greco, and M. D. Toro,Physics Reports , 335 (2005).[12] R. Lionti, V. Baran, M. Colonna, and M. D. Toro,Physics Letters B , 33 (2005).[13] P. Napolitani, M. Colonna, F. Gulminelli, E. Galichet,S. Piantelli, G. Verde, and E. Vient, Phys. Rev. C ,044619 (2010).[14] Z. Y. Sun, M. B. Tsang, W. G. Lynch, G. Verde,F. Amorini, L. Andronenko, M. Andronenko,G. Cardella, M. Chatterje, P. Danielewicz, E. De Filippo,P. Dinh, E. Galichet, E. Geraci, H. Hua, E. La Guidara,G. Lanzalone, H. Liu, F. Lu, S. Lukyanov, C. Maiolino,A. Pagano, S. Piantelli, M. Papa, S. Pirrone, G. Politi,F. Porto, F. Rizzo, P. Russotto, D. Santonocito, andY. X. Zhang, Phys. Rev. C , 051603 (2010).[15] J. Margueron, R. Hoffmann Casali, and F. Gulminelli,Phys. Rev. C , 025805 (2018).[16] O. Lopez, D. Durand, G. Lehaut, B. Borderie, J. D. Fran-kland, M. F. Rivet, R. Bougault, A. Chbihi, E. Galichet,D. Guinet, M. La Commara, N. Le Neindre, I. Lom-bardo, L. Manduci, P. Marini, P. Napolitani, M. Pˆarlog,E. Rosato, G. Spadaccini, E. Vient, and M. Vigilante(INDRA Collaboration), Phys. Rev. C , 064602 (2014).[17] D. D. S. Coupland, W. G. Lynch, M. B. Tsang,P. Danielewicz, and Y. Zhang, Phys. Rev. C , 054603(2011).[18] R. D. Souza, N. Carlin, Y. Kim, J. Ottarson, L. Phair,D. Bowman, C. Gelbke, W. Gong, W. Lynch, R. Pelak,T. Peterson, G. Poggi, M. Tsang, and H. Xu, NuclearInstruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and AssociatedEquipment , 109 (1990).[19] J. Pouthas, B. Borderie, R. Dayras, E. Plagnol, M. Rivet,F. Saint-Laurent, J. Steckmeyer, G. Auger, C. Bacri,S. Barbey, et al. , Nucl. Instr. and Methods A , 418(1995).[20] A. Pagano, Nuclear Physics News , 25 (2012).[21] T. X. Liu, W. G. Lynch, M. B. Tsang, X. D. Liu,R. Shomin, W. P. Tan, G. Verde, A. Wagner, H. F. Xi,H. S. Xu, B. Davin, Y. Larochelle, R. T. d. Souza, R. J.Charity, and L. G. Sobotka, Phys. Rev. C , 034603(2007).[22] E. Galichet, M. F. Rivet, B. Borderie, M. Colonna,R. Bougault, A. Chbihi, R. Dayras, D. Durand, J. D.Frankland, D. C. R. Guinet, P. Lautesse, N. L. Neindre,O. Lopez, L. Manduci, M. Pˆarlog, E. Rosato, B. Tamain,E. Vient, C. Volant, and J. P. Wieleczko (INDRA Col-laboration), Phys. Rev. C , 064614 (2009).[23] R. Bougault, E. Bonnet, B. Borderie, A. Chbihi,D. Dell’Aquila, Q. Fable, L. Francalanza, J. D. Fran-kland, E. Galichet, D. Gruyer, D. Guinet, M. Henri,M. La Commara, N. Le Neindre, I. Lombardo, O. Lopez,L. Manduci, P. Marini, M. Pˆarlog, R. Roy, P. Saint-Onge,G. Verde, E. Vient, and M. Vigilante (INDRA Collabo-ration), Phys. Rev. C , 024612 (2018).[24] G. A. Souliotis, D. V. Shetty, A. Keksis, E. Bell, M. Jan-del, M. Veselsky, and S. J. Yennello, Phys. Rev. C , 024606 (2006).[25] G. A. Souliotis, P. N. Fountas, M. Veselsky,S. Galanopoulos, Z. Kohley, A. McIntosh, S. J.Yennello, and A. Bonasera, Phys. Rev. C , 064612(2014).[26] V. Baran, M. Colonna, M. D. Toro, M. Zielinska-Pfab´e,and H. H. Wolter, Phys. Rev. C , 064620 (2005).[27] L. W. May, A. Wakhle, A. B. McIntosh, Z. Koh-ley, S. Behling, A. Bonasera, G. Bonasera, P. Cam-marata, K. Hagel, L. Heilborn, A. Jedele, A. Raphelt,A. R. Manso, G. Souliotis, R. Tripathi, M. D. Youngs,A. Zarrella, and S. J. Yennello, Phys. Rev. C , 044602(2018).[28] The FAZIA Collaboration, Bougault, R., Poggi, G., Bar-lini, S., Borderie, B., Casini, G., Chbihi, A., Le Nein-dre, N., Pˆarlog, M., Pasquali, G., Piantelli, S., Sosin,Z., Ademard, G., Alba, R., Anastasio, A., Barbey, S.,Bardelli, L., Bini, M., Boiano, A., Boisjoli, M., Bonnet,E., Borcea, R., Bougard, B., Brulin, G., Bruno, M., Car-boni, S., Cassese, C., Cassese, F., Cinausero, M., Ciolacu,L., Cruceru, I., Cruceru, M., D´Aquino, B., De Fazio,B., Degerlier, M., Desrues, P., Di Meo, P., Due˜nas, J. A.,Edelbruck, P., Energico, S., Falorsi, M., Frankland, J. D.,Galichet, E., Gasior, K., Gramegna, F., Giordano, R.,Gruyer, D., Grzeszczuk, A., Guerzoni, M., Hamrita, H.,Huss, C., Kajetanowicz, M., Korcyl, K., Kordyasz, A.,Kozik, T., Kulig, P., Lavergne, L., Legou´ee, E., Lopez,O., Lukasik, J., Maiolino, C., Marchi, T., Marini, P.,Martel, I., Masone, V., Meoli, A., Merrer, Y., Morelli,L., Negoita, F., Olmi, A., Ordine, A., Paduano, G., Pain,C., Palka, M., Passeggio, G., Pastore, G., Pawlowski,P., Petcu, M., Petrascu, H., Piasecki, E., Pontoriere, G.,Rauly, E., Rivet, M. F., Rocco, R., Rosato, E., Roscilli,L., Scarlini, E., Salomon, F., Santonocito, D., Seredov,V., Serra, S., Sierpowski, D., Spadaccini, G., Spitaels,C., Stefanini, A. A., Tobia, G., Tortone, G., Twar´og,T., Valdr´e, S., Vanzanella, A., Vanzanella, E., Vient, E.,Vigilante, M., Vitiello, G., Wanlin, E., Wieloch, A., andZipper, W., Eur. Phys. J. A , 47 (2014).[29] A. Camaiani et al. , Il Nuovo Cimento, in Proceedingsof the International Workshop on MultifragmentationIWM-EC 2018 (2018).[30] F. Rami, Y. Leifels, B. de Schauenburg, A. Gobbi,B. Hong, J. P. Alard, A. Andronic, R. Averbeck, V. Bar-ret, Z. Basrak, N. Bastid, I. Belyaev, A. Bendarag,G. Berek, R. ˇCaplar, N. Cindro, P. Crochet, A. De-vismes, P. Dupieux, M. Dˇzelalija, M. Eskef, C. Finck,Z. Fodor, H. Folger, L. Fraysse, A. Genoux-Lubain,Y. Grigorian, Y. Grishkin, N. Herrmann, K. D. Hilden-brand, J. Kecskemeti, Y. J. Kim, P. Koczon, M. Kire-jczyk, M. Korolija, R. Kotte, M. Kowalczyk, T. Kress,R. Kutsche, A. Lebedev, K. S. Lee, V. Manko, H. Merlitz,S. Mohren, D. Moisa, J. M¨osner, W. Neubert, A. Nian-ine, D. Pelte, M. Petrovici, C. Pinkenburg, C. Plettner,W. Reisdorf, J. Ritman, D. Sch¨ull, Z. Seres, B. Sikora,K. S. Sim, V. Simion, K. Siwek-Wilczy´nska, A. Somov,M. R. Stockmeier, G. Stoicea, M. Vasiliev, P. Wagner,K. Wi´sniewski, D. Wohlfarth, J. T. Yang, I. Yushmanov,and A. Zhilin (FOPI Collaboration), Phys. Rev. Lett. ,1120 (2000).[31] A. Camaiani, S. Piantelli, A. Ono, G. Casini, B. Bor-derie, R. Bougault, C. Ciampi, J. A. Due˜nas, C. Frosin,J. D. Frankland, D. Gruyer, N. LeNeindre, I. Lombardo,G. Mantovani, P. Ottanelli, M. Parlog, G. Pasquali, S. Upadhyaya, S. Valdr´e, G. Verde, and E. Vient, Phys.Rev. C , 044607 (2020).[32] A. Ono, H. Horiuchi, T. Maruyama, andA. Ohnishi, Progress of Theoretical Physics ,1185 (1992), http://oup.prod.sis.lan/ptp/article-pdf/87/5/1185/5272175/87-5-1185.pdf.[33] R. J. Charity, Phys. Rev. C , 014610 (2010).[34] S. Piantelli, G. Casini, A. Ono, G. Poggi, G. Pas-tore, S. Barlini, A. Boiano, E. Bonnet, B. Borderie,R. Bougault, M. Bruno, A. Buccola, A. Camaiani,A. Chbihi, M. Cicerchia, M. Cinausero, M. D’Agostino,M. Degerlier, J. A. Due˜nas, Q. Fable, D. Fabris, J. D.Frankland, C. Frosin, F. Gramegna, D. Gruyer, M. Henri,A. Kordyasz, T. Kozik, N. Le Neindre, I. Lombardo,O. Lopez, G. Mantovani, T. Marchi, L. Morelli, A. Olmi,P. Ottanelli, M. Pˆarlog, G. Pasquali, A. A. Stefanini,G. Tortone, S. Upadhyaya, S. Valdr´e, G. Verde, E. Vient,M. Vigilante, R. Alba, and C. Maiolino, Phys. Rev. C , 034613 (2020).[35] A. Camaiani, Complete isotopic characterization of pro-jectile fragments in Ca+Ca reactions at Fermi energieswith the FAZIA array , Ph.D. thesis, Universit`a degliStudi di Firenze (2019).[36] S. Valdre, G. Casini, N. L. Neindre, M. Bini, A. Boiano,B. Borderie, P. Edelbruck, G. Poggi, F. Salomon, G. Tor-tone, R. Alba, S. Barlini, E. Bonnet, B. Bougard,R. Bougault, G. Brulin, M. Bruno, A. Buccola, A. Ca-maiani, A. Chbihi, C. Ciampi, M. Cicerchia, M. Cinau-sero, D. Dell’Aquila, P. Desrues, J. Due˜nas, D. Fabris,M. Falorsi, J. Frankland, C. Frosin, E. Galichet, R. Gior-dano, F. Gramegna, L. Grassi, D. Gruyer, M. Guer-zoni, M. Henri, M. Kajetanowicz, K. Korcyl, A. Ko-rdyasz, T. Kozik, P. Lecomte, I. Lombardo, O. Lopez,C. Maiolino, G. Mantovani, T. Marchi, A. Margotti,Y. Merrer, L. Morelli, A. Olmi, A. Ordine, P. Ottanelli,C. Pain, M. Pa(cid:32)lka, M. Pˆarlog, G. Pasquali, G. Pastore,S. Piantelli, H. de Pr´eaumont, R. Revenko, A. Richard,M. Rivet, J. Ropert, E. Rosato, F. Saillant, D. Santonoc-ito, E. Scarlini, S. Serra, C. Soulet, G. Spadaccini,A. Stefanini, G. Tobia, S. Upadhyaya, A. Vanzanella,G. Verde, E. Vient, M. Vigilante, E. Wanlin, G. Wit-twer, and A. Zucchini, Nuclear Instruments and Meth-ods in Physics Research Section A: Accelerators, Spec-trometers, Detectors and Associated Equipment , 27(2019).[37] G. Pastore, D. Gruyer, P. Ottanelli, N. L. Neindre,G. Pasquali, R. Alba, S. Barlini, M. Bini, E. Bonnet,B. Borderie, et al. , Nucl. Instr. and Methods A , 42(2017).[38] C. Frosin, S. Barlini, G. Poggi, G. Casini, M. Bini,A. Stefanini, S. Valdr´e, D. Gruyer, M. Ciema(cid:32)la, A. Maj,M. Ziebli´nski, B. Sowicki, K. Mazurek, N. Cieplicka-Ory´nczak, M. Matejska-Minda, E. Bonnet, B. Bor-derie, R. Bougault, M. Bruno, A. Buccola, A. Cama-iani, A. Chibhi, M. Cinausero, M. Cicerchia, J. Due˜nas,D. Fabris, J. Frankland, F. Gramegna, M. Henri, A. Ko-rdyasz, T. Kozik, N. Le Neindre, I. Lombardo, O. Lopez,G. Mantovani, T. Marchi, A. Olmi, P. Ottanelli, M. Par-log, S. Piantelli, G. Pasquali, S. Upadhyahya, G. Verde,and E. Vient, Nuclear Instruments and Methods inPhysics Research Section A: Accelerators, Spectrome-ters, Detectors and Associated Equipment , 163018(2020).[39] S. Carboni, S. Barlini, L. Bardelli, N. L. Neindre, M. Bini, B. Borderie, R. Bougault, G. Casini, P. Edelbruck,A. Olmi, et al. , Nucl. Instr. and Methods A , 251(2012).[40] J. Aichelin and H. St¨ocker, Physics Letters B , 14(1986).[41] J. Aichelin, Physics Reports , 233 (1991).[42] A. Ono, Progress in Particle and Nuclear Physics ,139 (2019).[43] N. Ikeno, A. Ono, Y. Nara, and A. Ohnishi, Phys. Rev.C , 044612 (2016).[44] E. Chabanat, P. Bonche, P. Haensel, J. Meyer, andR. Schaeffer, Nuclear Physics A , 710 (1997).[45] S. Piantelli, A. Olmi, P. R. Maurenzig, A. Ono, M. Bini,G. Casini, G. Pasquali, A. Mangiarotti, G. Poggi, A. A.Stefanini, S. Barlini, A. Camaiani, C. Ciampi, C. Frosin,P. Ottanelli, and S. Valdr´e, Phys. Rev. C , 064616(2019).[46] G. Tian, R. Wada, Z. Chen, R. Han, W. Lin, X. Liu,P. Ren, F. Shi, F. Luo, Q. Sun, L. Song, and G. Q.Xiao, Phys. Rev. C , 044613 (2017).[47] G. Tian, Z. Chen, R. Han, F. Shi, F. Luo, Q. Sun,L. Song, X. Zhang, G. Q. Xiao, R. Wada, and A. Ono,Phys. Rev. C , 034610 (2018).[48] S. Galanopoulos, G. Souliotis, A. Keksis, M. Veselsky,Z. Kohley, L. May, D. Shetty, S. Soisson, B. Stein,S. Wuenschel, and S. Yennello, Nuclear Physics A ,145 (2010).[49] G. Casini, P. G. Bizzeti, P. R. Maurenzig, A. Olmi, A. A.Stefanini, J. P. Wessels, R. J. Charity, R. Freifelder,A. Gobbi, N. Herrmann, et al. , Phys. Rev. Lett. , 2567(1993).[50] A. A. Stefanini, G. Casini, P. R. Maurenzig, A. Olmi,R. J. Charity, R. Freifelder, A. Gobbi, N. Herrmann,K. D. Hildenbrand, M. Petrovici, et al. , Zeitschrift f¨urPhysik A Hadrons and Nuclei , 167 (1995).[51] De Filippo, E., A. Pagano, P. Russotto, F. Amorini,A. Anzalone, L. Auditore, V. Baran, I. Berceanu, B. Bor-derie, Bougault, et al. , Phys. Rev. C , 014610 (2012).[52] A. Jedele, A. B. McIntosh, K. Hagel, M. Huang, L. Heil-born, Z. Kohley, L. W. May, E. McCleskey, M. Youngs,A. Zarrella, and S. J. Yennello, Phys. Rev. Lett. ,062501 (2017).[53] S. Piantelli et al. , Phys. Rev. C accepted .[54] E. Vient, L. Augey, B. Borderie, A. Chbihi,D. Dell’Aquila, Q. Fable, L. Francalanza, J. D. Frank-land, E. Galichet, D. Gruyer, et al. , The European Phys-ical Journal A , 96 (2018).[55] S. Piantelli, L. Bidini, G. Poggi, M. Bini, G. Casini, P. R.Maurenzig, A. Olmi, G. Pasquali, A. A. Stefanini, andN. Taccetti, Phys. Rev. Lett. , 052701 (2002).[56] S. Piantelli, P. R. Maurenzig, A. Olmi, L. Bardelli,M. Bini, G. Casini, A. Mangiarotti, G. Pasquali,G. Poggi, and A. A. Stefanini, Phys. Rev. C , 061601(2007).[57] G. Rudolf, S. Tomasevic, M. Aboufirassi, J. Adloff,B. Bilwes, R. Bilwes, G. Bizard, R. Bougault, R. Brou,Y. Cassagnou, J. Colin, F. Cosmo, F. Delaunay, D. Du-rand, J. Ferrero, A. Genoux-Lubain, M. Glaser, F. Guil-bault, G. Jin, J. Laville, C. Le Brun, C. Lebrun, J. Lecol-ley, F. Lef`ebvres, R. Legrain, J. Lemi`ere, O. Lopez,M. Louvel, M. Mahi, A. P´eghaire, J. P´eter, B. Raste-gar, E. Rosato, F. Scheibling, J. Steckmeyer, L. Stuttg´e,and B. Tamain, Physics Letters B , 287 (1993).[58] R. J. Charity, Phys. Rev. C , 1073 (1998). [59] E. Bonnet, J. P. Wieleczko, J. G. Del Campo,M. La Commara, S. Barlini, C. Beck, B. Borderie,R. Bougault, A. Chbihi, R. Dayras, G. De Angelis,J. D. Frankland, A. Galindo-uribarri, T. Glodariou,V. Kravchuk, P. Lautesse, J. Moisan, N. Le Nein-dre, B. Martin, L. Nalpas, A. D. Onofrio, M. Parlog,D. Pierroutsakou, F. Rejmund, M. F. Rivet, M. Ro-moli, E. Rosato, R. Roy, D. Shapira, G. Spadaccini,B. Tamain, and M. Vigilante, International Journal ofModern Physics E , 2359 (2008).[60] G. Ademard, J. P. Wieleczko, J. Gomez del Campo,M. La Commara, E. Bonnet, M. Vigilante, A. Chbihi,J. D. Frankland, E. Rosato, G. Spadaccini, S. A. Ka-landarov, C. Beck, S. Barlini, B. Borderie, R. Bougault,R. Dayras, G. De Angelis, J. De Sanctis, V. L. Kravchuk,P. Lautesse, N. Le Neindre, J. Moisan, A. D’Onofrio,M. Parlog, D. Pierroutsakou, M. F. Rivet, M. Romoli,R. Roy, G. G. Adamian, and N. V. Antonenko, Phys.Rev. C , 054619 (2011).[61] S. Pirrone, G. Politi, B. Gnoffo, M. La Commara,E. De Filippo, P. Russotto, M. Trimarchi, M. Vigilante,M. Colonna, S. A. Kalandarov, F. Amorini, L. Audi-tore, C. Beck, G. Cardella, A. D’Onofrio, E. Geraci,D. Lacroix, E. La Guidara, G. Lanzalone, A. Pagano,E. V. Pagano, M. Papa, E. Piasecki, L. Quattrocchi,F. Rizzo, E. Rosato, G. Spadaccini, and A. Trifir`o, TheEuropean Physical Journal A , 22 (2019).[62] S. Barlini, S. Piantelli, G. Casini, P. R. Maurenzig,A. Olmi, M. Bini, S. Carboni, G. Pasquali, G. Poggi,Stefanini, et al. (FAZIA Collaboration), Phys. Rev. C , 054607 (2013).[63] S. Piantelli, S. Valdr´e, S. Barlini, G. Casini, M. Colonna, G. Baiocco, M. Bini, M. Bruno, A. Camaiani, et al. , Phys.Rev. C , 034622 (2017).[64] Q. Fable, Ph.D. thesis, Universit´e de Caen Normandie(2018).[65] Boisjoli, M., Chbihi, A., and Wigg, P. C., EPJ Web ofConferences , 00040 (2012).[66] Wigg, P.C., Boisjoli, M., Chartier, M., Chbihi, A., Lem-mon, R., Frankland, J.D., Le Neindre, N., and Marini,P., EPJ Web of Conferences , 00015 (2012).[67] A. Camaiani, G. Casini, L. Morelli, S. Barlini, S. Pi-antelli, G. Baiocco, M. Bini, M. Bruno, A. Buccola,M. Cinausero, M. Cicerchia, M. D’Agostino, M. Dege-lier, D. Fabris, C. Frosin, F. Gramegna, F. Gul-minelli, G. Mantovani, T. Marchi, A. Olmi, P. Ottanelli,G. Pasquali, G. Pastore, S. Valdr´e, and G. Verde, Phys.Rev. C , 044607 (2018).[68] L. Morelli, M. Bruno, M. D’Agostino, G. Baiocco,F. Gulminelli, S. Barlini, A. Buccola, A. Camaiani,G. Casini, C. Ciampi, C. Frosin, N. Gelli, A. Olmi, P. Ot-tanelli, G. Pasquali, S. Piantelli, S. Valdr´e, M. Cicerchia,M. Cinausero, F. Gramegna, G. Mantovani, T. Marchi,M. Degerlier, D. Fabris, and V. L. Kravchuk, Phys. Rev.C , 054610 (2019).[69] M. Bruno, M. D’Agostino, M. V. Managlia, L. Morelli,G. Baiocco, F. Gulminelli, C. Frosin, S. Barlini, A. Buc-cola, A. Camaiani, G. Casini, M. Cicerchia, M. Cinau-sero, M. Degerlier, D. Fabris, F. Gramegna, G. Manto-vani, T. Marchi, P. Ottanelli, G. Pasquali, S. Piantelli,and S. Valdr´e, Journal of Physics G: Nuclear and ParticlePhysics46