Nucleardynamicsand thermodynamics INDRA FAZIA group

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1 Nucleardynamicsand thermodynamics INDRA FAZIA group Permamentstaff : R. Bougault, N. Le Neindre, O. Lopez, E. Vient PhD Student: M. Kabtoul, E. Legouée Collaborations: LPC: F.Gulminelli (Théorie), D.Durand(Théorie), M. Parlôg Institut de Physique Nucléaire d Orsay, GANIL Caen, Conservatoire National des Arts et Métiers de Paris, Université et INFN de Florence (Italie), Université et INFN, Bologne (Italie), Université et INFN, Naples (Italie), Laboratoire National de Legnaro, LNL-INFN, Legnaro(Italie), Laboratoire National du Sud, LNS-INFN, Catane (Italie), Université et INFN, Catane (Italie), Université Jagiellonian, Institut de Physique, Cracovie (Pologne), InstytutFizykiJądrowejPAN, Cracovie (Pologne), Heavy Ion Laboratory, Université de Varsovie, Varsovie (Pologne), National Institute for Physics and Nuclear Engineering, Bucarest(Roumanie), Université de Huelva, Département de Physique Appliquée, Huelva (Espagne) Background The research goal is to study and characterize the nuclear matter equation of state (EOS). The EOS determines the way nuclei respond to external excitations such as those found in nucleus-nucleus collisions or during type-ii supernovæ collapse. Knowledge of this EOS is an important theme of nuclear physics, both for its fundamental character as well as for predicting the evolution of stellar objects such asneutron stars. The meansto achievethisgoalis the study of nucleus-nucleus (heavy ions) collisions around the Fermi energy (E Fermi = 38 MeV/u), which brings experimental constraints concerning the dynamics of the collisions (transport properties) and the thermodynamics of the nuclear systems produced in them (nuclear matter phase diagram). Low energy reactions are also studied to characterize the liquid phase of nuclear matter. The experimental device is the INDRA multi-detector (collaboration between 4 IN2P3 laboratories), using data collected at GANIL (stable and SPIRAL beams) or GSI in Germany. Studies are also carried out in partnership with the CHIMERA collaboration (LNS Catania, Italy). Over the last few years a major effort was committed to research and development for a new detection system using digital techniques: this is the European project FAZIA which is now in the phase of building a demonstrator for SPIRAL2 (Memorandum of Understanding signed by IN2P3, GANIL, Italy, Poland, and Romania). This demonstrator will be coupled with the INDRA array in

2 INDRA and the FAZIA demonstrator Nuclear matter equation of state (EOS) The nuclear matter equation of state characterizes nuclear matter properties under extreme conditions of temperature, T, compression, ρ, and isospin, I=(N-Z)/A. Figure 1 : Nuclear symmetry potential energy E sym as a function of density p. On the left, results obtained with different nuclear models. On the right, the situation for densities close to saturation density p 0 = 0.17 fm -3. The values given in the lefthand figure are the values of E sym calculated with the different models at ρ=ρ 0. The equation of state determines the collective response of nuclei such as their compressibility (via the modulus of incompressibility, K ) and the collective modes of monopole (GMR) or dipole (GDR) oscillations, whether isoscalar (depending only on the density, ρ) or isovector (depending on proton, ρ P, and neutron, ρ N, densities) in nature, the latter bringing in to play the symmetry energy term of the EOS. In addition, the collapse of proto-neutron stars (type-ii supernovæ) as well as the associated cooling phase are intimately linked to the characterization of volume, surface, Coulomb, and symmetry parameters, and their dependence on density, temperature and isospin. Figure 1 presents theoretical predictions [1] for the density-dependence of the isovector part of the equation of state: more precisely, these predictions concern its potential part, as the kinetic part is known. The large spread of the theoretical predictions can be noted, including at low and sub-saturation densities (Fig.1, right). Heavy-ion collisions are one of the experimental tools allowing to constrain this dependence and to study nuclear matter under thermodynamical conditions favoring the determination of the different terms of the equation of state. 22

3 Stopping power of the nuclear matter The stopping power is closely related to transport properties of nuclear matter. Those properties govern the energy dissipation in nuclear collisions, the onset and the dynamics of the large amplitude motions such as expansion, deformation, as well as the competition between reaction mechanisms (deep inelastic, fusion and neck emission). The comparison of experimental data with transport models should allow to better constraint their ingredients at the fundamental level and bring important information about the nuclear equation of state and the in-matter nucleon-nucleon cross section. In the following, we have analysed the quite unique data set obtained with the INDRA 4pi array during the last decades, coming from GANIL and GSI campaigns. These data entangle the largest dataset accumulated so far in the Fermi energy domain with the same array, covering nuclear (mainly symmetric) systems as Ar+KCl, Ni+Ni, Xe+Sn and Au+Au from 10A up to 100A MeV. This systematics in terms of total mass and incident energy allows indeed a complete survey of nuclear reactions properties in the Fermi energy range. Stopping power in central (violent) collisions We have selected central collisions by requiring the highest total multiplicities M tot [2]. Doing so, we have obtained a typical experimental cross-section of about 100mb, which corresponds to an impact parameter of b=2fm. The multiplicity selection has been chosen here in order to avoid strong (self-) correlations between the analysed observable (here the isotropy ratio, see below) and the selection variable. This is thus different from other analyses (thermodynamical studies for example). Figure 2 : Isotropy ratio for central collisions with average values (top) and standard deviations (bottom). Extracted from[2] 23

4 We have then determined the isotropy ratio R E defined as the ratio between the total (among all detected particles, here charged) transverse energy (transverse to the beam axis) over the total longitudinal energy(parallel to the beam axis) for the central collisions selected as indicated above. A large value close to 0 is associated to a complete or quasi-complete stopping while a value close to 1 is associated at variance to a full transparency. The results are presented in Fig. 2 for the whole INDRA dataset for symmetric systems [2]. The different curves correspond to the excitation function of various systems (Ar+KCl, Ni+Ni, Xe+Sn and Au+Au), which encompass as explained before a total mass range between 70 and 400. The dashed curve displays the value of the isotropy ratio if no stopping is present, i.e. full transparency. The top panel corresponds to the mean isotropy ratio R E and the bottom one to the standard deviation. We observe two separate regimes, one associated to a low incident energy range from 10A to 40A MeV (Fermi energy), the second associated to a high incident energy range from 40A to 100A MeV. The first regime (10A- 40A MeV) can be understood as the progressive weakening of the mean-field effects, which are responsible of the fusion process at very low incident energy and to incomplete fusion at higher energies (around and above the Fermi energy). These mechanisms are then associated to a complete toward incomplete stopping power when the incident energy is increasing and correspond to the one-body dissipation by the mean-field. The second regime corresponds on the contrary to the onset of 2-body dissipation effects, because the elastic (hard) nucleon-nucleon (NN) collisions become larger since the Pauli blocking is ineffective at high incident energy (while NN collisions are conversely inhibited at low incident energy). The minimum value is obtained around the Fermi energy (38A MeV), and one could note a slight increase of RE at higher energies due to the increasing number ofnncollisions.itisworthwhiletomentionthattheminimumvalueis always close to the value corresponding to the full transparency, suggesting that the full stopping is far from being achieved in the whole incident energy domain whatever the total system mass is. This result is in itself an important constraint to any transport model aiming to describe nuclear collisions in this energy range. We observe also a mass hierarchy in the isotropy ratio and hence the stopping for the high incident energy part; this is attributed to the increasing number of NN collisions (participants) when looking at heavier systems. At variance, we should observe a relatively small mass dependence of the isotropy ratio for the low incident energy part since this part is mainly governed by mean-field effects which is largely independent on the system size. This behaviour cannot be seen here since only Xe+Sn data are available below 32A MeV. Isospin dependence of the stopping power We have also studied the isospin dependence of the isotropy ratio by looking at selected isospin-defined systems as presented in the table 1. The isotropy ratios are displayed for the seven Xe+Sn systems available with INDRA (some combinations are however missing). The event selection (here central events) is the same as the one discussed above. We can conclude from the values that no strong isospin effect is evidenced, all values being dispatched within 10 %. Once again, this result provides a strong constraint to any kind of transport models. 24

5 Table 1 : Values of R E central for different Xe+Sn systems at 32, 45 and 100 MeV. System N/Z 32 MeV/A 45 MeV/A 100 MeV/A 124 Xe+ 112 Sn 1,27 0,54 0,53 0, Xe+ 112 Sn 1,32 0,6 124 Xe+ 124 Sn 1,38 0,54 0, Xe+ nat Sn 1,38 0,55 0, Xe+ 112 Sn 1,38 0,5 0, Xe+ 124 Sn 1,43 0, Xe+ 124 Sn 1,5 0,49 0,52 Characterization of the anisotropy component The measured isotropy ratio below unity in central collision discussed previously is related to a production of particles in non-equilibrated processes. This pre-equilibrium production is also measured for peripheral reactions and in that case it is superimposed to the evaporation production from the excited Projectile-Like and Target- Like Fragments (PLF and TLF). A previous study allowed us to finalize an experimental method giving the probability for a particle to be emittedbyahotplf.wedecidedtousethisinformationtodetermine the probability not to be evaporated for a particle, produced during a nuclear reaction. We can thus characterize eventually the preequilibrium component or the neck emission, when this contribution exists. We have begun by the study of the system Ni + Ni at different incidental energies 32, 40, 52, 63, 74, 82 A.MeV [3]. For each type of particle, the knowledge of the probability to be evaporated by the PLF or by thetlfallowed usto build different energy spectra, asshown in figure 3. This figure concerns the tritons for Ni + Ni at 52 A.MeV. For the left side of the figure, the kinetic energies are defined in the PLF framewhereastheyaredefinedinthetlfframefortherightside. Figure 3 : Energy spectra of tritons defined in two different frames, according to different origins. The red curves (full) correspond to the total contribution, the green (dash) to the PLF contribution, the blue (dash and dotted) to the TLF contribution. The black curves (dotted) are obtainedby a simple subtraction to the red distribution of the blue and green contributions. The probability distribution of not to be evaporated by the PLF or the TLFcan thusbeobtainedbyasimpledivisionoftheblackcurveby the red curve. 25

6 by a simple subtraction to the red distribution of the blue and green contributions. The probability distribution of not to be evaporated by the PLF or the TLF can thus be obtained by a simple division of the blackcurvebytheredcurve. If the method was perfect, the two histograms should be perfectly identical. It is not exactly true. We observe some small differences, but the results are reasonably compatible. The adequacy between the two histograms is less good for the other light charged particles. For this reason, we have initiated a complementary study. We are using an event generator, like HIPSE, to verify the validity of our method and understand to what extent the experimental set-up breaks the symmetry of the entrance channel and perturbs our measurements. Projectile-Like Fragments produced in symmetric collisions, comparison with models The characterization of hot quasi-projectiles produced in symmetric or quasi-symmetric reactions (Au+Au, Xe+Sn, Ni+Ni, Ar+KCl) at different incident energies are estimated by means of two different procedures. The advantages and disadvantages of each method are analyzed on the basis of simulations using events produced by two slightly different models: HIPSE(Heavy Ion Phase Space Exploration) and ELIE. The essential difference between the two models lies in the excitation energy distribution in the fragments since in the ELIE case, the limiting temperature (5.5 MeV) limits E* to around 3 MeV/u while for HIPSE, the amount of excitation energy can extend to much larger values (see blue histograms in figure 5. Figure 4 : Particle multiplicities cross-sections (from protons to IMF as indicated in each panel) for Xe+Sn central collisions at 50 A.MeV. Black points are INDRA data while the histograms are for ELIE data. For such central collisions, particle multiplicities are correctly reproduced by the model. Other observables have been considered and a general good agreement has been reached between INDRA data and ELIE data. Same conclusions can be reached as far as HIPSE is concerned. These models are therefore sufficiently realistic to allow a check of the calorimetric methods. PLF's characteristics (mass, charge and excitation energy) are measured by two different calorimetric methods: a standard and the so-called3d calorimetry. 26

7 Figure 5 : Mean PLF excitation energy per nucleon (MeV/u) as a function of impact parameter evaluator (large value for central events) for Ni+Ni at 52 A.MeV. Left, ELIE data. Right: HIPSE data, both compared with INDRA data (red crosses and open points). Preliminary results of the studies figure 5 are rather contrasted. None of the methods can reproduce the excitation energy values given by the ELIE model. However, for excitation energies lower than 2 MeV/u, the 3D method gives good results. As for HIPSE, the 3D calorimetry reproduces the excitation energy distribution while the standard method leads to a systematic over-estimation. It is worth to note that, whatever the method applied to INDRA data, very high excitation energies are achieved: a point which remains to be understood. Work is still in progress to improve the 3D calorimetry[3}. INDRA VAMOS Experiment The data reduction concerning INDRA-Vamos experiment is now almost achieved and analyses should start in The aim of this experiment was to study the whole complete de-excitation chain process of fused light system (Ar+Ni Pd at 13.0 A MeV). By mixing different isotopes of projectile Ar and target Ni we were able to register decay events corresponding to Pd allowing to probe isospin effects. Measuring the whole de excitation sequence of all evaporated particles and fragment should allow to constraint de-excitation models and determine how evolves the level density parameter with isospin. This complete measurement has been made possible by the coupling, for the very first time, of a 4π multidetector (INDRA) and a spectrometer (Vamos). The goal is to detect the fusion residue nuclei in Vamos and the corresponding evaporated particles and light fragments with INDRA. Already, analyses about fusion nuclear cross section of those systems have shown that they decrease when isospin decreases, from 914+/-30 mbarn for 34 Ar+ 58 Nito 1691+/-139 mbarnfor 40 Ar+ 64 Ni[4]. Collaboration with CHIMERA(LNS-Catania) The data analysis of the test experiment performed in 2004 in LNS Catania with the CHIMERA multidetector has been achieved. The goal of this experiment was to benefit from the high granularity (1192 telescopes Si-CsI(Tl))of the CHIMERA array to probe for the first time, by fragmentation of quasi projectiles from the nuclear reaction 40 Ca + 12 C at 25 MeV/nucleon, the production of excited states candidates to alpha-particle condensation. The case of the Hoyle state is particularly suggestive, it pleads in favor of a structure, that is a mixture of various pre-formed alphaconfigurations. They are conjectured to be a generic feature of medium-size self-conjugated 4N nuclei whose excitation lies in the vicinity of the N-apha decay threshold. Supposing that equal values of kinetic energy of the emitted alpha-particles represent a sufficient criterion for establishing the existence of alpha-particle condensation, we have found that the complete kinematic characterization of individual decay events reveals that 7.5+/-4.0% of the particle decays 27

8 of the Hoyle state of 12C correspond to direct decays in three equalenergy alpha-particles[5]. The very same study was performed for 16O, but the lack of statistics prevent to any conclusion. Anyway the method is promising and has demonstrated its capabilities. A similar experiment with the same apparatus will be proposed. FAZIA PSA capabilities Two experiments have been achieved in the last two years, Ganil in 2010 and LNS Catania in Those experiments have validated the R&D program and the choices concerning detectors characteristics, electronics and Pulse Shape Analysis (PSA) capabilities. We remember that the goal of the FAZIA collaboration is to construct a new generation multi-detector able to work at low thresholds with very high detection efficiency both in charge Z and Mass A. The low thresholds determination, see figure 6, is achieved via PSA thanks to a severe constraint on silicon detector characteristics, homemade preamplifier of both charge and current signals (PACI) and dedicated low noise digital electronics and sampling [6]. Moreover it allows also a large improvement of the usual DE-E technique see in the following, now allowing isotopic resolution up to Z 22 (instead of Z 4 for INDRA). The recipes are the following, good resistivity homogeneity ( 5%) for ntd-silicon detectors, purposely random cut to appear like an amorphous material for impinging particles (channeling effect), rear side mounting of the silicon detectors (particles enter by the low electric field), dedicated pre-amplifiers for both charge and current with adapted gains (two gains for the first silicon layer to reduce the thresholds and improve isotopic separation) and finally optimization of the digital treatment of the sampled pulse shapes. Figure 6 : Energy thresholds (in energy per nucleon) for Z identification with DE(300µm)-E technique (black triangles) and with PSA technique (energy vs charge rise time: red points rear injection and blue squares front injection ) as a function of atomic number Z. Extended isotopic identification for the FAZIA project The main achievement of the FAZIA project is to realize a unsurpassed isotopic (mass) discrimination by using a full digital electronics (allowing then a powerful -online- pulse shape analysis), and high quality detectors(silicon NTD and highly-doped CsI(Tl)). To fulfil these goals, we need to push to the limit all detection capabilities, not only the detection threshold or the mass(and charge) identification with the pulse shape analysis (see after or above), but also the more traditional and robust identification methods such as the well-known E-DE method. This requires at least a 2-layers telescope, such as those tested for the FAZIA phase 2 program (2 thin Silicon layers followed by a thick CsI crystal). 28

9 Using the formalism developed by M. Parlog [7] which takes into account the carrier recombination (plasma) and the δ-rays (electrons) produced by an impinging nucleus in the detector material (Silicon or CsI), it has been proposed the following formula for the signal L (either light for CsI or electric signal for Si) as a function of the atomic number(z),atomicmass(a)andincidentenergy Eofagivennucleus: where the 4 parameters a G,a R, a n and E d are adjusted to the specific detector (layer) response by a fit to known isotopes. The mass number A and atomic number Z dependence are embedded into the electronic S e and nuclear S n stopping powers. By performing the fit, it is possible to build identification grids which can fit the experimental matrices E-DE, such as the one displayed below for a Silicon-Silicon matrix obtained within the FAZIA project(figure 7). Figure 7 : E-DE (Si-Si) correlation for a FAZIA telescope. The data have been obtained by impinging a 84 Kr beam at 35A MeV on a thin 120 Sn target at the LNS facility (Catania, Italy). The curves represent the identification grid (only one curve per element) and are superimposed to the experimental data (see legend for details). It is then straightforward to get the linearization of the data as displayed in the following figure. As we can see, we are able to achieve the full isotopic identification forelementsrangingfromz=1uptoz= [8] Figure 8 : Particle Identification 8Z+A for the data displayed in the previous figure 29

10 For heavier elements(z>22), it is still possible to have a partial isotopic resolution by estimating the different isotopic contributions as seen in the following figure for iron(z=26) isotopes. Figure 9 : particle Identification 8Z+A for iron isotopes (Z=26). The interest of this identification technique is two-fold. First, it can be implemented in a semi-automatic way, which is indeed mandatory for detection arrays with a large number of telescopes in one wants in order to save time. Second, this allows to assign quite unambiguously the mass number since it relies on a formula which is explicitly depending through the stopping powers on the mass number A. Once the fit is done with some known isotopes, the extrapolation to rare isotopes can safely applied and thus permits to recover those species, even if it is hard to identify them directly on the E-DE matrix because of the smaller statistics(figure for the red-labelled isotopes). Description of current pulses induced by heavy ions in silicon detectors The high frequency sampling of the current or charge signals induced by charged reaction products in silicon detectors gives access to their shape versus time. The signals generated by heavy ions have a longer duration as compared to those corresponding to light particles like protons, due to a slower charge carrier collection - the plasma delay phenomenon. The dependence of this shape on the nature (Z, A, E) of the impinging particlevia thespecificrateofenergy lossbecameoneoftherunways used for the heavy ion identification in the framework of the FAZIA collaboration. The description of the signal shape by realistic simulations will hopefully provide automatic procedures of calibration and nuclear fragment identification in large scale arrays in nuclear physics, provided that the preamplifier transfer function be known. In collaboration with IPN Orsay, we have recently developed a charge carrier collection treatment which considers the progressive extraction of the electrons and holes from the high carrier density zone along the ionizing particle track [9]. This region is assumed to present a supplementary dielectric polarization and consequently a disturbed electric field. The figures 10 & 11 presents the exact coordinate dependence of the modified electric field, inside and outside the 80 MeV 12 C ion range, found as the solution of the one dimensional Maxwell's equation for the electric field in this inhomogeneous medium. The quality of the simulation is illustrated in the following figure, for the signals induced by the same ion impinging ontherear 30

11 or the front side of the same neutron transmutation doped silicon detector. Figure 10 : The distorted electric field strength inside the silicon detector, at different moments, due to the ionized column induced by 80 MeV 12 C ions penetrating on the rear side (left, x = 0 at the rear side contact) and the front side (right, x = 0 at the front side contact) of the detector. The straight dashed line gives in each case the undisturbed electric field. The current signals of 10 different heavy ion species at known energies around 10 AMeV were quite well reproduced by the fit procedure based on this formalism. The two main fit parameters dependofthenatureoftheparticleinapredictableway. Figure 11 : mean experimental current signals induced by 80 MeV 12 C ions impinging on the rear side (left) and on the front side (right) of a silicon detector - full line; the simulation using a distorted electric field - dashed line. Study of the experimental potentiality of the FAZIA detector Within the framework of the collaboration FAZIA, it was developed a program package, called PANFORTE, allowing to simulate the detection of heavy ions by an experimental set-up like INDRA or FAZIA. With the help of the event generator HIPSE, we have made a study to verify to what extent the FAZIA detector is a real improvement to detect and perform the calorimetry of hot nuclei. We present on figure 12, a two-dimension graph of the total detected charge normalized to the total charge of the system as a function of the total parallel detected pseudo-impulse (velocity multiplied by the charge) normalized to the initial value of this quantity. This graph permits to judgethequalityoftheevent detectionforcollisionsxeonsnfrom25 to50a.mev. 31

12 Figure 12 : Graph of the total detected charge normalized to the total charge of the system as a function of the total parallel detected pseudo-impulse (velocity multiplied by the charge) normalized to the initial value of this quantity. Graphs show the proportion of events detected with a quality of 80 % or 90 % as a function of the incidental energy per nucleon for the INDRA detector and FAZIA detector We look at the proportion of events, which are correctly detected by the INDRA detector or by the FAZIA detector in its first geometry. We consider as well detected the events the events falling on the dotted rectangle of the two-dimension graph of the figure(top). This criterion corresponds to a quality of detection of 80 %. We have made the samekindofstudywithaqualityof90%. With this first geometry, the FAZIA detector allows clearly to keep an important cross section, much more than the INDRA detector in spite of strict criteria of quality of detection.[10] [1] M.B. Tsang, Prog. Part. Nucl. Phys. 66 (2011) 400 [2] G. Lehautet al, Phys. Rev. Lett. 104 (2010) [3] E. Legouée, PhD thesis, Université de Caen, in progress [4] P. Marini et al, CNR*09, Second Int. Workshop on Compound Nuclear Reactions, Bordeaux (2009) [5] Ad. Radutaet al, Phys. Lett. B 705 (2011) 65 [6] N. Le Neindreet al, NIM A 701 (2013) 145 [7] M. Parlôget al, NIM A 482 (2002) 674 [8] O. Lopez et al, IWM 09 (2009) [9] H. Hamritaet al, NIM A 642 (2011) 59 [10] P. Napolitaniet al, Phys. Rev. C 89 (2010)