We have performed systematical calculations on multifragmentation picture for peripheral 84Kr+112,124Sn collisions at an incident beam energy of 35MeV/nucleon. In order to investigate the Coulomb and angular momentum effects for these reactions, the calculations are performed to reproduce the data for charge distributions of the fragments, on the basis of the microcanonical Markov chain approach within the statistical multifragmentation model

Botvina, A. S.

Buyukcizmeci, N.

Ogul, R.

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DOI 10.1393/ncc/i2016-16410-yColloquia: IWM-EC 2016IL NUOVO CIMENTO 39 C (2016) 410Theoretical analyses of FAZIA data with a statistical approachN. Buyukcizmeci(1), R. Ogul(1) and A. S. Botvina(2)(3)(1) Department of Physics, Selcuk University - 42079 Kampus, Konya, Turkey(2) Frankfurt Institute for Advanced Studies, J. W. Goethe University - D-60438 Frankfurt amMain, Germany(3) Institute for Nuclear Research, Russian Academy of Sciences - 117312 Moscow, Russiareceived 10 January 2017Summary. — We have performed systematical calculations on multifragmenta-tion picture for peripheral 84Kr+112,124Sn collisions at an incident beam energy of35 MeV/nucleon. In order to investigate the Coulomb and angular momentum ef-fects for these reactions, the calculations are performed to reproduce the data forcharge distributions of the fragments, on the basis of the microcanonical Markovchain approach within the statistical multifragmentation model.1. – IntroductionIn this short communication, we shall discuss the influence of angular momentum andCoulomb interactions between projectile and target like nuclei on the charge yields offragments for peripheral 84Kr+112,124Sn collisions at 35 MeV/nucleon for FAZIA exper-iment [1]. To simulate the peripheral 84Kr+112,124Sn reactions, we consider the break-up of a single source 84Kr in the neighborhood of a secondary source 112,124Sn. Thecalculations were carried out within the Markov chain version of the statistical multi-fragmentation model (SMM), which is designed for a microcanonical simulation of thedecay modes of nuclear sources [2-4]. This model version contains also ingredients takenfrom the standard SMM version developed in refs. [5]. We use the Markov chain ofpartitions to characterize the whole statistical ensemble. The individual fragment parti-tions and coordinate positions of fragments in the freeze-out volume are generated withinthis method. Partitions are selected according to the Metropolis algorithm. The decaychannels are generated by the Monte Carlo method according to their statistical weightsover 105 events. Thus, we take into account the influences of angular momentum andCoulomb interactions for each spatial configuration of primary fragments in the freeze-out volume in the same way used in refs. [3, 4, 6, 7]. In this work we have used thevalue of the freeze-out density as ρ = ρ0/6 (here ρ0 is the normal nuclear matter den-sity) for better evaluation of Coulomb and angular momentum effects. These kinds ofinvestigations are also important for construction of a reliable EoS of nuclear matter atsubnuclear densities. One may expect that similar conditions occur during the collapseand explosion of massive stars and in the crust of neutron stars [8,9], where the CoulombCreative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 N. BUYUKCIZMECI et al.Table I. – Values for the sources assumed to be formed according to the peripheral collisions for84Kr + 112,124Sn reactions.Ex Zs As As Weight Ang. Mom.(MeV/n) (112Sn) (124Sn) 2 34 77 82 0.13 303 33 75 80 0.19 304 32 73 77 0.32 405 30 68 73 0.25 406 29 66 70 0.08 407 28 64 68 0.03 40interactions of the dense electron environment make the fragmentation picture fluctuate.In our previous studies, isospin composition of the produced fragments [10], charge andisotope yields, and correlations of various fragment properties were successfully describedand compared with ALADIN data by the statistical ensemble approach [11-14] withinSMM [5]. The results of our analysis of the experimental data of the MSU experimentsat 50 MeV/nucleon [15] were given in refs. [16, 17]. In the following section, we willshow the results of our new calculations together with angular momentum and Coulombinteraction effects between the projectile- and target-like sources.2. – The angular momentum and Coulomb interaction effects for projectilefragmentation in peripheral collisions at Fermi energiesWe study peripheral nucleus-nucleus collisions at 35 MeV/nucleon with the corre-sponding relative velocities between the projectile and target around 45–70 mm/ns. Theprojectile nucleons can interact with target nucleons at the initial dynamical stage ofcollision, as a result, pre-equilibrium particles can be observed due to this interaction ofenergetic products. The excitation energy of projectile and target residues may changeand the relative velocity between the residues decreases as well. Later on, these excitedtarget- and projectile-like sources decay. Since a characteristic time is around 100 fm/c fornuclear multifragmentation, projectile- and target-like sources will not be far (≈ 15 fm)from each other before disintegration. At these short distances the long-range Coulombfield of one of the sources influences the break-up of the other one. In this situation,we suppose that the multifragmentation of a double nuclear system is a new physicalsituation with respect to the standard multifragmentation of a single isolated source.Two excited sources in such a double system are determined by the short-range nuclearforces. The presence of an external Coulomb field may affect the composition of the pro-duced fragments and their relative positions. An additional Coulomb barrier will preventdisintegration of the sources into many small pieces. In addition, we include the angularmomenta (rotation) of the separate sources, which can be transferred after the collision.It will also influence the positions and sizes of the fragments at the freeze-out [2, 6]. Inour approximation, we consider the sources obtained from 84Kr projectile at differentexcitation energies: 2, 3, 4, 5, 6 and 7 MeV/n as shown in table I. Such a selection ofthe adequate ensemble of the sources is a quite effective way to describe the experimen-tal data and make important physical conclusions within the statistical approach (see,e.g., [11,12]). We have taken two sources with the same charge and the same excitationenergy, but with two different N/Z ratios corresponding to N/Z ratios of 84Kr+112Snand 84Kr+124Sn, as in experiments [1]. Then, firstly, we made SMM calculations forTHEORETICAL ANALYSES OF FAZIA DATA WITH A STATISTICAL APPROACH 3Fig. 1. – Comparison of the charge yield of fragments, in the case without (open circles) and withangular momentum (full circles). Red stars show FAZIA experimental data [1] for 84Kr+124Sn(top panel) and 84Kr+112Sn (bottom panel). These projectile-like sources are assumed to beformed in the peripheral collisions at 35 MeV/nucleon, and their disintegration are affected bythe Coulomb field of the target source as shown in table I. The distributions are normalized inthe region Z = 18–28 as in ref. [1].each source and found charge and isotope distributions, N/Z ratio of fragments in thepresence of second source (112,124Sn) without and with angular momentum. In our previ-ous theoretical study, we selected angular momentum values with a randomly increasingorder (see table 1 in ref. [3]). In this study we have selected angular momentum valuesas average values (see table I). Afterwards, we have taken a mixture of all sources withweights (as shown in table I) corresponding to their excitation energies, which are relatedto the impact parameters. After this mixture was done, we directly compared with ex-perimental data as shown in fig. 1. We show the total charge yields of cold fragments inthe case with and without angular momentum conservation in fig. 1. Angular momentumvalues are selected as shown in table I. It is seen that the angular momentum favors theemission of large nearly symmetric fragments (like a nuclear fission) since the system inthe freeze-out stage needs to have a large moment of inertia in order to minimize therotational energy and to maximize the entropy. It is in a competition with the secondsource through the Coulomb interaction which prevents from emitting an IMF with alarge charge number. We have found very good agreement of experimental data with ourpredictions including Coulomb and angular momentum effects for 112,124Sn. We do notconsider small excitation energies (Ex < 2MeV/n) since the detection of big projectile-like fragments is affected by a narrow acceptance angle of the apparatus. The grazingangle should be simulated within a dynamical approach, that is beyond the present work.Therefore, there are no peaks for Z > 34 in our calculations. Moreover, we think thatthis acceptance angle is also the reason of a strongly disturbed U-shape distribution of4 N. BUYUKCIZMECI et al.detected charges (in comparison with the typical smooth U-shapes observed in other ex-periments), and this cause us to decrease the weights of low excitations in our ensembleof the sources to reproduce the data.3. – ConclusionsAs a result, we have found that conservation of angular momentum and complicatedCoulomb interactions caused by the proximity of target- and projectile-like sources in thefreeze-out stage produce significant changes in the multifragmentation picture. We alsoobserved new fragment formation trends, such as an asymmetry of IMF emission andincreasing the neutron content of light IMFs. These features are demonstrated after thesecondary excitation of hot fragments for the cold fragments, similar to the previouslyanalyzed reactions leading to the production and decay of the single isolated sources. Upto now, we have reported some preliminary encouraging results obtained with the helpof the ensemble of residual sources in refs. [3,4]. The present study is still in progress forvelocity distributions of fragments and for the possibility to apply this new approach forthe analyses of the experimental data at intermediate peripheral collisions such as theFAZIA data [1]. These investigations are important since they point out a new connectionbetween dynamical and statistical phenomena in nuclear reactions. In the light of ourtheoretical results, we plan to construct a connection between the results of dynamicalprocesses and statistical approach and we are willing to analyze the future experimentsas well.∗ ∗ ∗This work was supported by TUBITAK with project no. 113F058. The authorsare grateful to G. Casini, S. Piantelli and FAZIA group for fruitfull discussions. NBacknowledges the partial support by GANIL and by Scientific Research Coordination ofSelcuk University (BAP) under grant SU-14611118-14601100 to participate in IWM-EC2016.REFERENCES[1] Barlini S. et al., Phys. Rev. C, 87 (2013) 054607.[2] Botvina A. S. and Mishustin I. N., Phys. Rev. C, 63 (2001) 061601(R).[3] Buyukcizmeci N. et al., Nucl. Sci. Tech., 26 (2015) S20507.[4] Ergun A. et al., Phys. Rev. C, 92 (2015) 014610.[5] Bondorf J. P. et al., Phys. Rep., 257 (1995) 133.[6] Botvina A. S. and Gross D. H. E., Nucl. Phys. A, 592 (1995) 257.[7] Gross D. H. E., Phys. Rep., 279 (1997) 119.[8] Botvina A. S. and Mishustin I. N., Nucl. Phys. A, 843 (2010) 98.[9] Buyukcizmeci N. et al., Nucl. Phys. A, 907 (2013) 13.[10] Le Fèvre A. et al., Phys. Rev. Lett., 94 (2005) 162701.[11] Ogul R. et al., Phys. Rev. C, 83 (2011) 024608.[12] Imal H. et al., Phys. Rev. C, 91 (2015) 034605.[13] Buyukcizmeci N., Ogul R. and Botvina A. S., Eur. Phys. J. A, 25 (2005) 57.[14] Botvina A. S. et al., Phys. Rev. C, 74 (2006) 044609.[15] Liu T. X. et al., Phys. Rev. C, 69 (2004) 014603.[16] Ogul R. et al., J. Phys. G: Nucl. Part. Phys., 36 (2009) 115106.[17] Buyukcizmeci N. et al., J. Phys. G: Nucl. Part. Phys., 39 (2012) 115102.

Theoretical analyses of FAZIA data with a statistical approach

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Theoretical analyses of FAZIA data with a statistical approach

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