Dynamical breakup of projectile-like fragments (PLF) following dissipative reactions of Ca-48 projectiles with Sn-112 and Sn-124 is shown to exhibit "isoscaling" regularities that can be understood in terms of phase space governed by ground state masses. Ambiguities in isoscaling parameters obscure information on nuclear symmetry energy at subnormal densities

Amorini, F.

Anzalone, A.

Auditore, L.

Cardella, G.

Cavallaro, S.

Chatterjee, M. B.

De Filippo, E.

Geraci, E.

Grzeszczuk, Andrzej

Guazzoni, P.

Henry, E.

La Guidara, E.

Lanzalone, G.

Lo Nigro, S.

Loria, D.

Maiolino, C.

Pagano, A.

Papa, M.

Pawelczak, I.

Pirrone, S.

Politi, G.

Porto, F.

Quinlan, M.J.

Rizzo, F.

Russotto, P.

Schroder, W.U.

Singh, H.

Toke, J.

Trifiro, A.

Trimarchi, M.

Verde, G.

Vigilante, M.

Zetta, L.

EPJ Web of Conferences

English

Dynamical breakup of projectile-like fragments (PLF) following dissipative reactions of 48 Ca projectiles with 112 Sn and 124 Sn is shown to exhibit “isoscaling” regularities that can be understood in terms of phase space governed by ground state masses. Ambiguities in isoscaling parameters obscure information on nuclear symmetry energy at subnormal densities

H. Singh

M.J. Quinlan

J. Tõoke

I. Pawelczak

E. Henry

J.D. Schröder

F. Amorini

A. Anzalone

C. Maiolino

L. Auditore

D. Loria

A. Trifirò

M. Trimarchi

G. Cardella

E. De Filippo

A. Pagano

M. Papa

S. Pirrone

G. Verde

M.B. Chatterjee

S. Cavallaro

E. Geraci

S. Lo Nigro

G. Politi

F. Porto

F. Rizzo

P. Russotto

A. Grzeszczuk

P. Guazzoni

L. Zetta

E. La Guidara

G. Lanzalone

M. Vigilante

EDP Sciences OAI-PMH repository (1.2.0)

Isoscaling in dissipative projectile breakup

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

             Title: Isoscaling in dissipative projectile breakup  Author: H. Singh, M.J. Quinlan, J. Toke, I. Pawelczak, E. Henry, W.U. Schroder, Andrzej Grzeszczuk i in.   Citation style: Singh H, Quinlan M.J., Toke J., Pawelczak I., Henry E., Schroder W.U., Grzeszczuk Andrzej i in. (2012). Isoscaling in dissipative projectile breakup. “EPJ Web of Conferences” (vol. 31 (2012), art. no. 00014), doi 10.1051/20123100014        Isoscaling in dissipative projectile breakupH. Singh1, M.J. Quinlan1, J. To˜ke1, I. Pawelczak1, E. Henry1,W.U. Schro¨der1, F. Amorini2, A. Anzalone2, C. Maiolino2,L. Auditore3, D. Loria3, A. Trifiro`3, M. Trimarchi3,G. Cardella4, E. De Filippo4, A. Pagano4, M. Papa4,S. Pirrone4, G. Verde4, M.B. Chatterjee5, S. Cavallaro2,6,E. Geraci4,6, S. Lo Nigro6, G. Politi4,6, F. Porto2,6, F. Rizzo2,6,P. Russotto2,6, A. Grzeszczuk7, P. Guazzoni8, L. Zetta8,E. La Guidara4,9, G. Lanzalone10, M. Vigilante111 Departments of Chemistry and Physics, University of Rochester,Rochester NY, USA2 INFN Laboratori Nazionali del Sud, Catania, Italy3 INFN-Gr. Coll. Messina and Dip. di Fisica Universita`, Messina, Italy4 INFN Sez. di Catania, Italy5 Saha Institute for Nuclear Physics, Kolkata, India6 Dip. di Fisica e Astronomia, Universita` di Catania, Italy7 Institute of Physics, University of Silesia, Katowice, Poland8 INFN Sez. di Milano and Dip. di Fisica Universita` di Milano, Italy9 CSFNSM, Catania, Italy10 INFN LNS, Catania and Universita` Kore Enna, Italy11 INFN Sez. di Napoli and Dip. di Fisica Universita`, Napoli, ItalyAbstractDynamical breakup of projectile-like fragments (PLF) following dis-sipative reactions of 48Ca projectiles with 112Sn and 124Sn is shown toexhibit “isoscaling” regularities that can be understood in terms ofphase space governed by ground state masses. Ambiguities in isoscal-ing parameters obscure information on nuclear symmetry energy atsubnormal densities.EPJ Web of ConferencesDOI: 10.1051/,epjconf 2012/00014 (2012)313100014This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. C© Owned by the authors, published by EDP Sciences , 2012 - SIFArticle available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201231000141 IntroductionThe CECIL collaboration has studied multi-particle correlations in48Ca+112Sn and 48Ca+124Sn reactions at E/A = 45 MeV using theCHIMERA array [1]. Experimental objective was to explore regularitiesin the isotopic distributions of products emitted following dissipative inter-actions [2] of (48Ca) with targets of different A/Z, in relation to the nuclearsymmetry energy [3,4] at subnormal matter densities that could be accessi-ble [5,6]. Attention was paid to the possible contribution of non-equilibriumeffects [7] and the degree of equilibration reached by the systems. Earlierwork [8] had demonstrated the role of pre-equilibrium emission altering nu-clear identities and limiting excitation.2 Experimental proceduresIsotopically enriched, self-supporting targets of 124Sn and 112Sn with thick-nesses of 689 μg/cm2 and 627 μg/cm2, respectively, placed in the center ofCHIMERA, were bombarded with pulsed, E/A=45-MeV, 48Ca beams fromthe LNS K800 cyclotron. 12C and 16O beams from the LNS MP Tandemwere used for detector calibration, along with elastically scattered 48Ca pro-jectiles. Reaction products were characterized by atomic number Z, massnumber A, energy and emission angles, utilizing time-of-flight (TOF), energyand light output information provided by the Si− CsI telescopes.The present study focusses on data collected in the forward angular re-gion (6o ≤ θ ≤20o), comprising projectile-like fragments (PLF) and theirdecay products, much of it in form of correlated pairs of an IMF (3≤Z≤5)and a corresponding heavier PLF remnant. Experimental details are pro-vided elsewhere [9].3 Reaction mechanismAn overview over the reaction scenario is provided in Fig. 1 displaying yieldsfor the reaction 48Ca+112Sn in form of Wilczyn´ski-type contour diagrams ofreconstructed PLF kinetic energy (TPLF , top), or velocity (|v|PLF , bottom),vs. lab angle.Obviously, average yields evolve with PLF laboratory angle and kineticenergy as expected [2] for a dissipative reaction. Calculations with dissipa-tive reaction code CLAT [10] (Fig. 1a), symbols and curves) agree quan-titatively with the data. Open symbols indicate primary yields, solid onesEPJ Web of Conferences00014-p.2Figure 1: Experimental Wilczyn´ski contour diagrams for the reaction 48Ca+124Snat E/A=45 MeV. Top: PLF energy vs. angle, bottom: PLF velocity vs. angle.Symbols and curves represent mean predictions by the nucleon exchange model(CLAT). See text.account for evaporation calculated with GEMINI [11]. However, plottingyields (Fig. 1b) vs. PLF velocity instead of energy, significant discrepanciesbetween theory and data appear. Less velocity damping occurs than pre-dicted, indicating a fortuitous agreement between theory and kinetic-energydata in Fig. 1a.The above inconsistencies are attributed to dynamical breakup of thePLF following dissipative interactions, instead of statistical decay assumedin the CLAT/GEMINI simulations. The PLF breakup mechanism is notpredicted by microscopic QMD simulations [12], either, but is supportedby several pieces of experimental evidence: Neither heavy nor light PLFremnants exhibit random Galilei invariant cross section patterns expectedfor statistical decay but show strong forward/backward asymmetries of bothbreakup cross section and mass asymmetry, as well as large relative veloci-ties of the PLF breakup fragments [9]. Dynamical PLF breakup resemblingternary fission [13, 14] is well known at Fermi energies [15], especially forcluster nuclei. Potential energy surfaces evaluated for the present systemssupport the observed evolution of the reaction mechanism with relative an-gular momentum.IWM2011 00014-p.34 Isoscaling in PLF breakup4.1 General considerationsSince the symmetry energy at subnormal mass densities is currently of highinterest, the investigation focussed on nuclear clusters which, unlike nucle-ons, can be emitted statistically only from hot, diluted nuclei [5, 6]. There-fore, early work [16] on cluster emission in low-energy reactions did notprovide new insights into the density dependence of the symmetry energy.To substantially dilute matter requires high excitation which, unfortunately,associates with non-equilibrium emission [7].To reduce susceptibility to systematic uncertainties, previous work[17–21] considers ratios R12 of cluster (Nc, Zc) yields from different par-ent nuclei (i = 1, 2) at similar excitations. Since the nuclear binding energydepends quadratically on neutron and proton numbers, statistical yields areapproximately Gaussians. Consequently, yield ratios depend approximatelyexponentially on Nc and Zc:R12(Nc, Zc) = Y2(Nc, Zc)/Y1(Nc, Zc) ∝ exp{αNc + βZc} (1)Here, isoscaling parameters α and β reflect principal curvatures of the βstable valley for the two emitters (i = 1, 2) at the effective temperature.For systems at constant temperature T, the following relations have beensuggested [17,18] between isoscaling parameters and symmetry energy coef-ficient Csym:β = CsymΔ(N,A)/T ; α = CsymΔ(Z,A)/T ; (2)with the neutron or proton excess difference functions Δ defined asΔ(X,A) = 4[(X/A)21 − (X/A)22](3)4.2 Experiment results and discussionIn the following, measured cluster isotope yields from PLF ∗ breakup areplotted as ratios vs. cluster neutron or proton numbers (N,Z) in the formRatio(N,Z) = YN,Z(48Ca +124 Sn)/YN,Z(48Ca +112 Sn) (4)Measured Li, Be, B, C and N isotope ratios shown in Fig. 2 vs. cluster neu-tron number N, demonstrating isoscaling, where isotopic ratios trace parallellogarithmic straight lines. Isotone ratios show corresponding behavior whenEPJ Web of Conferences00014-p.4Figure 2: Isoscaling plot for Li, Be, B, C, and N clusters from PLF breakup.plotted vs. cluster-Z value. These observations contrast with other studiesof projectile fragmentation [22,23] showing isoscaling effects only after PLFreconstruction.In further data reduction, average (“global”) isoscaling parameters ofα¯ = (0.23±0.02) and β¯ = (−0.12±0.01) were obtained from simultaneous fitsto all isotope or isotone ratios. The errors contain systematic uncertaintiesevaluated from variations of constraints imposed on data selection. It isinteresting that the present parameters are by factors of 3 to 4 smaller thanreported for other projectile fragmentation studies [17–24].The further analysis varied PLF ∗i atomic and mass numbers, with dif-ferences ΔB = B2 − B1 in energy cost for emission from PLF ∗1 and PLF ∗2evaluated for all clusters from ground state masses, until the entire data setwas on average well reproduced by the exponentialR21(N,Z) =YN,Z(48Ca +124 Sn)/YN,Z(48Ca +112 Sn)≈ exp{[B2(N,Z)−B1(N,Z)]Teff}= exp(ΔBTeff)(5)Identical effective temperatures Teff were taken for both emitters. Experi-mental energy spectra suggest 3MeV ≤ Teff ≤ 4MeV as acceptable range.Results are depicted in Fig. 3 for experimental yield ratios vs. clusterground state plotted vs. binding energy differences ΔB for breakup pairPLF ∗1 = (Z1 = 20, A1 = 49) and PLF ∗2 = (Z2 = 18, A2 = 43). Theline drawn through the data corresponds to an effective temperature T =(2.6 ± 0.3) MeV. An equally good fit is obtained using the pair PLF ∗1 =IWM2011 00014-p.5Figure 3: Scaling of experimental cluster yield ratios for 48Ca + 124,112Sn reactionsat E/A=45 MeV based on ground-state binding energy differences (cf. Eq. 5).(Z1 = 25, A1 = 48) and PLF ∗2 = (Z2 = 26, A2 = 49). However, this lattercase corresponding to significant proton pickup and a high value Teff =(5.5± 0.3) MeV is deemed highly unlikely, based on driving potentials andsimilar 40,48Ca+112Sn experiments [25].Discrepancies between present and literature isoscaling parameters posethe question whether or not scaling with ground state binding energies (cf.Figure 4: Scaling of experimental yield ratios with binding energy differences for86,78Kr + 64,58Ni reactions at E/A=35 MeV. Data imported from [22].EPJ Web of Conferences00014-p.6Fig. 3) is specific to the present reactions. The question is answered byresults (cf. Fig. 4) of a similar analysis of data [22] for the reactions 86Kr+ 64Ni and 78Kr + 58Ni at E/A=35 MeV.For the latter reactions, search for a PLF ∗ pair whose ground statebinding energy patterns represent experimental yield ratios yielded PLF ∗1 =(Z1 = 40, A1 = 89) and PLF ∗2 = (Z2 = 39, A2 = 84) for a reasonabletemperature of T = (2.2 ± 0.2) MeV. As shown in Fig. 4, experimentaldata [22] are well fit with this parameterization. Data from the presentexperiment included in this figure merge well with the 78,86Kr + 58,64Ni datademonstrating a remarkable agreement of diverse data sets with a ground-state binding-energy systematics.5 ConclusionsIn summary, experimental data are presented for a dynamical breakup pro-cess of a fairly light projectile (Ca) following a dissipative primary reaction.The breakup produces intermediate-mass clusters exhibiting isoscaling con-sistent with populations according to ground-state Q values and symmetryenergies at normal density. Therefore, such reaction data do not provide un-ambiguous symmetry energies at subnormal matter densities. Ambiguitiescan be reduced by precise knowledge about underlying reaction mechanismsinvolving simpler composite systems produced close to equilibrium.AcknowledgmentsWork supported by the US Department of Energy Grant No. DE-FG02-88ER40414. Authors express their gratitude to the LNS for hospitality andexcellent beams.References[1] A. Pagano et al., Nucl. Phys. A 734, 504 (2004).[2] W.U. Schro¨der and R.J. Huizenga, Treatise on Heavy Ion Science,edited by D.A. Bromley (Plenum Press, New York, 1984).[3] J.P. Blaizot, Phys. Reports 64, 171 (1980).[4] B.A. Li, L.W. Chen, C.M. Ko, Phys. Reports 464, 113 (2008) andreferences.IWM2011 00014-p.7[5] J. To˜ke and W.U. Schro¨der, Phys. Rev. Letters 82, 5008 (1999).[6] J. To˜ke, J. Lu and W.U. Schro¨der, Phys. Rev. C 67, 034609 (2003).[7] E. Gadioli and P.E. Hodgson, Pre-Equilibrium Nuclear Reactions,Clarendon Press, Oxford (1992).[8] W.U. Schro¨der and J. To˜ke, Nucl. Phys. A 681, 418c (2001).[9] M.J. Quinlan, PhD Thesis, University of Rochester, 2011, and to bepublished.[10] W.U. Schro¨der et al., Proc. Int. Symp. Nucl. Fission and Heavy-Ion-Induced Reactions, Harwood Academic Press, New York, Nucl. Sci. Res.Conf. Ser. Vol. 11, 255 (1987).[11] R.J. Charity et al., Nucl. Phys. A. 483, 371 (1988).[12] J. Lukasik and Z. Majka, Acta Phys. Pol. 24, 1959 (1993).[13] I. Halpern, Annu. Rev. Nucl. Sci. 21, 245 (1971).[14] J.P. Lestone, Phys. Rev. C 70, 021601(R) (2004).[15] H. Fuchs and K. Mo¨hring, Rep. Prog. Phys. 57, 231 (1994).[16] V.V. Volkov, Phys. Rep. 44, 93 (1978) and references.[17] M. B. Tsang et al., Phys. Rev. Lett. 86, 5023 (2001).[18] A.S. Botvina et al., Phys. Rev. C. 65, 044610 (2002).[19] J. Brzychczyk et al., Phys. Rev. C. 47, 1553 (1993).[20] Z. Chen et al., Phys. Rev. C. 81, 064613 (2010).[21] A.B. McIntosh et al., Phys. Rev. C 81, 034603 (2010).[22] S. Wuenschel et al., Phys. Rev. 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Isoscaling in dissipative projectile breakup

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