exotic nuclei structure and reaction noyaux exotiques ... - IPN - IN2P3

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for peripheral ones. In experiments radial collective energy was recognized, in most of the cases, from comparisons of kinetic properties of fragments with models/ simulations.The mean relative velocity between fragments, β rel , independent of the reference frame, allows to compare radial collective energy for both types of sources (QF or QP). The effect of the source size (Coulomb contribution on fragment velocities) can be removed by using a simple normalization which takes into account, event by event, the Coulomb influence, in velocity space, of the mean fragment charge. All the quantitative information concerning the evolution of radial energy, E R , with excitation energy for both types of sources is presented in figure 1. At an excitation energy of about 5 AMeV, the β rel Figure 2: Left and right sides refer respectively to the mean charge of the heaviest fragment of partitions , and to the generalized asymmetry in charge of the fragment partitions without the heaviest one, Az\{Z1}, (see text) as a function of the reduced fragment multiplicity, Mfrag/, for different total excitation per nucleon of the sources. Full squares, open and full circles stand respectively for QF sources and QP sources produced at 80 and 100 AMeV incident energies. values corrected from Coulomb effects and corresponding to QF and QP sources are similar. We have also added the E R values published by the ISIS collaboration [3] corresponding to the π - +Au reactions which provide sources equivalent to the QP ones in terms of excitation energy range and size. The observed evolution of E R for such sources is almost the same as for QP sources. For hadron-induced reactions the thermal pressure is the only origin of radial expansion, which indicates that it is the same for QP sources. To be fully convincing, an estimate of the part of the radial collective energy due to thermal pressure calculated with the EES model [4] for an excited nucleus identical to QF sources produced at 50 AMeV incident energy is also reported (open square) in figure 1. We have shown that radial collective energy is essentially produced by thermal pressure in semi- peripheral heavy-ion collisions as it is in hadroninduced reactions. For QF sources produced in central heavy-ion collisions the contribution from the compression-expansion cycle becomes more and more important as the incident energy increases. Those observations show that the radial collective energy does influence the fragment partitions. Moreover it is observed that, at fixed total excitation energy per nucleon, the evolution of the average fragment multiplicity normalized to the source charge/size = is fixed by the value of the radial collective energy: when E R increases more fragments are produced. Scalings of partitions Does the intensity of the radial collective energy also govern the details of fragment partitions, namely the relative charge/size of fragments in partitions. One can first consider the evolution of the size of the heaviest fragment, for given total excitation energies, with the reduced fragment multiplicities M frag /. On the left panel of figure 2 average values of the heaviest fragment charge for QP and QF sources are reported: they follow exactly the same evolution. Finally the division of the charge among other fragments is investigated using the generalized asymmetry in charge of the fragment partitions. One can re-calculate the generalized asymmetry by removing Z 1 from partitions, noted A Z \{Z 1 }. The results, displayed in figure 2 (right panel) do not depend on the source type at a given total excitation energy and a given reduced fragment multiplicity. Note that the general asymmetry follows a linear trend except for the lower reduced fragment mutiplicity which corresponds to M frag =2; indeed in that case, after removing Z 1 , only one fragment is available for the asymmetry calculation and in each event the heavier Z of the partition below Z equal 5 was taken. Such a result shows the subtle role played by the radial collective energy. It influences the overall degree of fragmentation but it does not affect the relative size of fragments in partitions for fixed reduced fragment multiplicities. Those scalings represent a benchmark against which models describing fragmentation of finite systems should be tested. In particular the peculiar role of the freeze-out volume in reproducing or not those scalings must be investigated. References [1] B. Borderie and M. F. Rivet, Prog. Part. Nucl. Phys. 61, 551, 2008. [2] E. Bonnet et al. (INDRA and ALADIN Collaborations), Nucl. Phys. A, 1., 2009. [3] L. Beaulieu et al., Phys. Rev. C 64, 064604, 2001. [4] W. A. Friedman, Phys. Rev. C 42, 667, 1990. [5] E. Bonnet et al. (INDRA and ALADIN Collaborations), submitted to Phys. Rev. Lett. 107
Latent heat of the phase transition for hot heavy nuclei IPNO Participation: B. Borderie, E. Galichet, M. F. Rivet Collaborations : INDRA and ALADIN LPC Caen, ENSICAEN, Université de Caen, CNRS/IN2P3, Caen, France GANIL, CEA et CNRS/IN2P3, Caen, France IPN Lyon, Université Claude Bernard Lyon1, CNRS/IN2P3, Villeurbanne, France IRFU/SPhN, CEA/Saclay Gif-sur-Yvette, France Laboratoire de Physique Nucléaire, Université Laval, Québec, Canada Dpt de Scienze Fisiche e Sez. INFN, Università di Napoli « Federico II », Napoli, Italy NIPNE, Bucharest Magurele, Romania Institute of Nuclear Physics IFJ-PAN, Krakov, Poland The Andrzej Soltan Institute for Nuclear Studies, Warsaw, Poland La distribution en charge du plus gros fragment détecté lors de la désexcitation de noyaux chauds par multifragmentation est bimodale. Les noyaux chauds étudiés sont des quasi-projectiles produits dans des réactions semi-périphériques entre noyaux d’or aux énergies incidentes de 60-100 MeV par nucléon. Ce signal de bimodalité est générique d’une transition de phases du premier ordre dans un système fini. En utilisant deux méthodes de sélection des noyaux quasi-projectiles chauds et les différentes énergies incidentes la chaleur latente de la transition a pu, pour la première fois, être estimée. Bimodality and first order phase transition for finite systems At a first-order phase transition, the distribution of the order parameter in a finite system presents a characteristic bimodal behavior in the canonical or grandcanonical ensemble [1,2]. The bimodality comes from an anomalous convexity of the underlying microcanonical entropy [2,3]. It physically corresponds to the simultaneous presence of two different classes of physical states for the same value of the control parameter, and can survive at the thermodynamic limit in a large class of physical systems subject to long-range interactions. Indeed if one considers a finite system in contact with a reservoir (canonical sampling), the value of the extensive variable (order parameter) X may fluctuate as the system explores the phase space. The entropy function F(X) is no more addititive due to the fact that surfaces are not negligible for finite systems and the resulting equilibrium entropy function has a local convexity. The Maxwell construction is no longer valid. The associated distribution at equilibrium, P(X)~exp(S(X)-λX) where λ is the corresponding Lagrange multiplier, acquires a bimodal character (see figure 1). In the case of nuclear multifragmentation, we have shown that the size of the heaviest cluster produced in each collision event is an order parameter. A difficulty comes however from the absence of a true canonical sorting in the data. The statistical ensembles produced by selecting hot nuclei are neither canonical nor microcanonical. Recently a simple weighting of the probabilities associated to each excitation energy bin for quasi-projectile events was proposed to allow the comparison with the canonical ensemble [4].That weighting procedure is used to test the independence of the decay Figure 1: Canonical ensemble for finite systems; the bimodal equilibrium distribution is given by P(X)~exp(S(X)-λX). The figure shows the case when the Lagrange multiplier λ is equal to the slope of the common tangent. from the dynamics of the entrance channel and to compare data with canonical expectations for quasi-projectile sources produced in Au + Au collisions at incident energies from 60 to 100 AMeV. Then, a double saddle-point approximation is applied to extract from the measured data equivalentcanonical distributions [4]. Estimation of the latent heat In this incident energy regime, a part of the cross section corresponds to collisions with dynamical neck formation [5]. We thus need to make sure that the observed change in the fragmentation 108
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EXOTIC NUCLEI STRUCTURE AND REACTIO
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in the spectra by analyzing their t
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were taken from ref. [5]. Concernin
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keV -ray with the particles and the
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the 605.9 keV line of the 74 Zn 2+
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Figure 2 a n d analysis. Figure 2 s
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ing particles was thus obtained by
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First p-p p collisions in the ALICE
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Quarkonia physics with ALICE IPNO P
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NA50 updated puzzle IPNO Participat
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Status of the HADES experiment (I):
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Status of the HADES experiments (II
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Status of the HADES experiment (III
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Hadron physics in pbar-p p annihila
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Hadron Electrodynamics IPNO Partici
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G0 experiment at Jefferson Lab. IPN
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GEp-III and GEp-2 at Jefferson Lab
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Exotic low mass narrow baryons from
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The PVA4 parity violation experimen
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Etude des Distributions de Partons
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Latest Results from GRAAL IPNO Part
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Persistence of the Polarization in
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The northern site of the Pierre Aug
Page 47 and 48: The Pierre Auger southern Observato
Page 49 and 50: In figure 4 we plot the differentia
Page 51 and 52: THEORETICAL PHYSICS Research in the
Page 53 and 54: transfer reaction, the 34 Si(d, 3 H
Page 55 and 56: Collective excitations with SKYRME
Page 57 and 58: Pairing and nuclear incompressibili
Page 59 and 60: Pairing properties in nuclei and in
Page 61 and 62: Evaporation-residue residue cross s
Page 63 and 64: Extending the VMI model: normal and
Page 65 and 66: Alpha particle condensation in nucl
Page 67 and 68: Collective Modes in Ultracold Trapp
Page 69 and 70: Exploring key unknown neutrino prop
Page 71 and 72: Relic astrophysical and cosmologica
Page 73 and 74: After a term by term Borel resummat
Page 75 and 76: Chiral expansions of the π 0 lifet
Page 77 and 78: IPNO Participation: H. Sazdjian Eff
Page 79 and 80: fer is used to extract f + (0). We
Page 81 and 82: cleon. The spectrum becomes strongl
Page 83 and 84: A pseudo Coulombian potential in D=
Page 85 and 86: The many-body problem with an energ
Page 87 and 88: The rotational spectrum and the att
Page 89 and 90: Z-identification of very heavy nucl
Page 91 and 92: The Pegase project, a new solid sur
Page 93 and 94: But at 80 keV total energy ( 200 eV
Page 95 and 96: Isospin effects on fragment and par
Page 97: Radial collective energy and fragme
Page 101 and 102: Alpha-particle particle condensatio
Page 103 and 104: Fluo X: Deexcitation time measureme
Page 105 and 106: ENERGY AND ENVIRONMENT The increasi
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Page 111 and 112: 3D coupling of Monte-Carlo neutroni
Page 113 and 114: Fission cross sections of actinides
Page 115 and 116: Studies and synthesis of specific m
Page 117 and 118: Chemistry and Electrochemistry of T
Page 119 and 120: function of temperature. The recent
Page 121 and 122: global electron number of the redox
Page 123: (D 0 /D)-1 ln complexes of Pa(V). I
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