We report on the results obtained by studying nuclear reactions between isotopes of Ca and Ti at 25MeV/nucleon. We used the multidetector CHIMERA to detect charged reaction products. In particular, we studied two main eﬀects: the isospin diﬀusion and the isospin drift. In order to study these processes we performed a moving-source analysis on kinetic energy spectra of the isobar nuclei 3H and3He. This method allows to isolate the emission from the typical sources produced in reactions at Fermi energy: projectile like fragment (PLF), target like fragment (TLF), and mid-velocity (MV) emission. The obtained results are compared to previous experimental investigations and to simulations obtained with CoMD-II model

Auditore, L.

Berceanu, I.

Cardella, G.

Chatterjee, M. B.

Martorana, N. S.

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DOI 10.1393/ncc/i2016-16412-9Colloquia: IWM-EC 2016IL NUOVO CIMENTO 39 C (2016) 412Study on the isospin equilibration phenomenon in nuclearreactions 40Ca + 40Ca, 40Ca + 46Ti, 40Ca + 48Ca, 48Ca + 48Caat 25 MeV/nucleon by using the CHIMERA multidetectorN. S. Martorana(1)(2), L. Auditore(3), I. Berceanu(4), G. Cardella(5),M. B. Chatterjee(6), S. De Luca(3), E. De Filippo(5), D. Dell’ Aquila(7),B. Gnoffo(8), G. Lanzalone(9), I. Lombardo(7), C. Maiolino(1), S. Norella(3),A. Pagano(5), E. V. Pagano(1)(2), M. Papa(5), S. Pirrone(5), G. Politi(2)(5),F. Porto(1)(2), L. Quattrocchi(5), F. Rizzo(1)(2), P. Russotto(5),A. Trifirò(3), M. Trimarchi(3), G. Verde(5) and M. Vigilante(7)(1) INFN, Laboratori Nazionali del Sud - Via S. Sofia, 62, Catania, Italy(2) Dipartimento di Fisica e Astronomia, Università di Catania - Catania, Italy(3) Dipartimento MIFT - Messina, Italy(4) Institute for Physics and Nuclear Engineering - Bucarest, Romania(5) INFN, Sezione di Catania - Via S.Sofia, 64, Catania, Italy(6) Saha Institute of Nuclear Physics - Kolkata, India(7) INFN, Sezione di Napoli and Dipartimento di Fisica, Università Federico II - Napoli, Italy(8) CSFNSM - Catania, Italy(9) Facoltà di Ingegneria e Architettura, Università Kore - Enna, Italyreceived 10 January 2017Summary. — We report on the results obtained by studying nuclear reactionsbetween isotopes of Ca and Ti at 25MeV/nucleon. We used the multidetectorCHIMERA to detect charged reaction products. In particular, we studied twomain effects: the isospin diffusion and the isospin drift. In order to study theseprocesses we performed a moving-source analysis on kinetic energy spectra of theisobar nuclei 3H and 3He. This method allows to isolate the emission from the typ-ical sources produced in reactions at Fermi energy: projectile like fragment (PLF),target like fragment (TLF), and mid-velocity (MV) emission. The obtained resultsare compared to previous experimental investigations and to simulations obtainedwith CoMD-II model.1. – IntroductionIn the last twenty years a large attention has been devoted to the isospin physics, inorder to understand the role played by this degree of freedom in the nuclear reactionsdynamics. Among the possible effects linked to the N/Z gradient between the two in-teracting nuclei the main is the isospin equilibration. Indeed, the nuclear forces tend toCreative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 N. S. MARTORANA et al.restore a uniform distribution of N/Z ratio between the two nuclei in interaction. Inthis work we studied this phenomenon in nuclear collisions 40Ca + 40Ca, 40Ca + 46Ti,40Ca + 48Ca and 48Ca + 48Ca at 25 MeV/nucleon. The energy domain of these reac-tions is traditionally called Fermi energy domain. Several investigations show that, forsemi-peripheral reactions, this regime is characterized by the presence of three fragment-emitting sources: PLF, TLF and MV. Moreover, it is predicted that two main effectstake place in this energy domain: the isospin drift and the isospin diffusion [1-4]. Thefirst one is related to a density gradient, in the overlap region between the two nuclei,that causes a transition of neutrons towards the low-density region (MV), producing anincrease of neutron-rich fragment emitted in this region. The second one is related to anisospin gradient between projectile and target; this causes a net neutron flux from theneutron-rich partner to the neutron-poor one. Consequently, the N/Z ratio of emittedfragments is strongly linked to the entrance channel one. Assuming to have a peripheralcollision of an isospin asymmetric system, a di-nuclear transient system composed by thepartial overlap of projectile and target is formed. After a time-window of a few hundredfm/c, the PLF and TLF excited sources will re-separated and the N/Z ratio of the PLFwill be modified with respect to the ratio of the projectile P [5]. If a complete isospinequilibration is reached between the projectile and the target, the PLF source will showvalues of N/Z close to those of the total system. The total system, in this case, indicatesthe system which should be formed if the neutron excess is uniformly re-distributed be-tween the target and the projectile. Consequently, the N/Z ratio of this latter representsthe N/Z of a chemically equilibrated system. A common way to estimate the degree ofequilibration reached during the interaction relies on the use of the equilibration fractionfeq, defined as [6](1) feq =(NZ )PLF − (NZ )P(NZ )TOT − (NZ )P.In this equation the difference between the (NZ )PLF and the (NZ )P is scaled by the max-imum possible difference (neglecting, as a first approximation, pre-equilibrium effects),namely the difference between the value of N/Z of the total system and the N/Z ofprojectile one [6]. If this value is equal to 1, a complete equilibration is reached, if thisvalue is equal to 0 the equilibration is not reached. In order to investigate the abovementioned effect it is necessary to obtain information on the N/Z of emission sources;to obtain that, we used the isobaric ratio method [6] by detecting isobar nuclei 3H and3He, using the CHIMERA multidetector; for more details on the experimental set-upsee [7,8]. We employed the ΔE-E technique for the Z identification of fragments punch-ing through the silicon detectors and the Fast-Slow technique for energetic light chargedparticles stopped in CsI(Tl) detectors.2. – Data analysis and resultsIn order to extract detailed information on the N/Z sources, we analyzed the kineticenergy spectra of 3H and 3He by performing fit that used a Maxwellian moving sourceparametrization of the emitted particles [9]. To improve statistics, the fit was extendedto all the reaction data set considering that, for geometrical reasons, semi-peripheralcollisions prevail. From the fit we derived the emission yields of 3H and 3He for the PLFand MV sources, and we built the yield ratios r3 = σ(3H)/σ(3He). The obtained resultsSTUDY ON THE ISOSPIN EQUILIBRATION PHENOMENON IN NUCLEAR REACTIONS ETC. 3MV                                                              PLF  He)3 (σH)3 (σ= 3r123456789Ca48Ca+ 48Ca48Ca+ 40Ti46Ca+ 40Ca40Ca+ 40Fig. 1. – Trend of r3 obtained by the Maxwellian moving source analysis.for the PLF and MV sources are reported in fig. 1. Due to the detection thresholdsit was very difficult to have access to the TLF contribution. In fig. 1 we can observea MV emission characterized by r3 values higher than the PLF emission one, also forthe isospin symmetric reactions. This finding indicates that the isospin drift takes placeduring the collision. Moreover, the r3 increases with the N/Z of target nuclei also forreactions involving the same projectile, 40Ca. This shows that the isospin diffusion takesplace between projectile and target. It is also possible to note that there is a very smalldifference between the 40Ca + 40Ca and 40Ca + 46Ti; this confirms that a moderate sizedifference between systems with similar N/Z does not cause appreciable variations in theisobaric ratio. The obtained results are in agreement with a previous analysis performedon 7Li, 7Be [10,11] but in the present case we have lower statistical uncertainties, due tothe larger statistics of light isobars. In the present analysis the role played by symmetricreactions is of fundamental importance; indeed for these reactions just the effect ofisospin drift is predicted. For this reason these two reactions can be used as referencesystems to make a comparison with the mixed system 40Ca + 48Ca. Following statisticalmulti-fragmentation model it is possible to assume that the isobaric ratio is exponentiallylinked to the N/Z of a given source [6,12]. In fig. 2 it is reported the ln(r3) for the PLFsource as a function of the N/Z of the total system, for the two symmetric reactions.They can be seen as reference points because, being the isospin diffusion process absentby definition, the ln(r3) can be linearly related to the N/Z of a given source. The lineconnecting these points is the equilibration line. If a complete isospin mixing takes place,the point of isobaric ratio for PLF source, formed in the mixed system, should stay onN/Z1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4) 3ln(r-0.200.20.40.60.81Ca40Ca+40Ca48Ca+48Ca48Ca+40Fig. 2. – In figure is reported the ln r3 for the PLF source as function of N/Z of the total system.The dotted line is the equilibration line calculated by the symmetric reactions.4 N. S. MARTORANA et al.the equilibration line. On the contrary, if a complete isospin mixing is not reached,experimental point of mixed system would be distant from the equilibration line. Infig. 2 it is possible to observe that the point for the mixed system is distant from theequilibration line. This finding points out an incomplete isospin equilibration reachedby the mixed systems during the interaction phase. Following the procedure discussedin [10] we estimated a value of (NZ )PLF = 1.080±0.006, namely a value of feq = 40±5%.This value is slightly different with respect to that obtained from the previous analysisperformed on 7Li/7Be, indeed in this case the obtained value was feq = 63 ± 15%. Thisdiscrepancy could be attributed to different side feeding effects that involve mass 3 andmass 7 isobars and will be explored with detailed statistical model calculations. In anycase, it is interesting to observe that a theoretical calculation performed with the CoMD-II [13] shows a (N/Z)PLF value equal to 1.07, in good agreement with the one obtainedusing the r3 values reported in the present analysis.3. – Conclusions and outlooksWe studied the phenomenon of isospin equilibration, by using the method of isobaricratio. We observed a strong neutron enrichment for the MV region, for all studiedreactions. This enrichment can be explained through the isospin drift phenomenon.We observed also the presence of the isospin diffusion for the mixed system, with afeq = 40 ± 5%. These results are slightly different with respect to the ones obtainedby using mass 7 isobars, pointing out a possible role played by statistical decay effectson the yields of fragment of different masses. This finding deserves further analysis andcomparisons with dynamical and statistical models that are currently ongoing [14]. Animprovement of the present results will be obtained with a selection in centrality ofthe events, that is currently under investigation. Using the FRIBs facility we have thepossibility to study a wide range of N/Z ratios and proton-rich systems, moreover usingthe FARCOS multidetector [15] and the GET electronics we can obtain informationon TLF.REFERENCES[1] DeFilippo E. et al., Phys. Rev. C, 86 (2012) 014610.[2] Lombardo I. et al., Phys. Rev. C, 84 (2011) 024613.[3] DiToro M. et al., Eur. Phys. J. A, 30 (2006) 65.[4] Cardella G. et al., Phys. Rev. C, 85 (2012) 064609.[5] Shetty D. V. et al., Phys. Rev. C, 76 (2007) 024606.[6] Keksis A. et al., Phys. Rev. C, 81 (2010) 054602.[7] Pagano A. et al., Nucl. Phys. A, 734 (2004) 504.[8] DeFilippo E. and Pagano A., Eur. Phys. J. A, 50 (2014) 32.[9] Awes T. C. et al., Phys. Rev. C, 25 (1982) 2361.[10] Lombardo I. et al., J. Phys.: Conf. Ser., 420 (2013) 012094.[11] Lombardo I. et al., Phys. Rev. C, 82 (2010) 014608.[12] Su J. et al., Phys. Rev. C, 84 (2011) 047601.[13] Papa M. and Giuliani G., Eur. Phys. J. A, 117 (2009) 054602.[14] Papa M. et al., Phys. Rev. C, 91 (2015) 041601(R).[15] Pagano E. V. et al., Status and perspective of FARCOS: A new correlator array fornuclear reaction studies, in Conference Proceedings, 109(2) (SIF, Bologna) 2016, p. 1077,EPJ Web of Conferences, 117 (2016) 10008 (online version).

Study on the isospin equilibration phenomenon in nuclear reactions 40Ca + 40Ca, 40Ca + 46Ti, 40Ca + 48Ca, 48Ca + 48Ca at 25 MeV/nucleon by using the CHIMERA multidetector

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Study on the isospin equilibration phenomenon in nuclear reactions 40Ca + 40Ca, 40Ca + 46Ti, 40Ca + 48Ca, 48Ca + 48Ca at 25 MeV/nucleon by using the CHIMERA multidetector

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