Chemical freeze-outs of strange and non-strange particles and residual chemical non-equilibrium
K. A. Bugaev, D. R. Oliinychenko, V. V. Sagun, A. I. Ivanytskyi, J. Cleymans, E. G. Nikonov, G. M. Zinovjev
CChemical freeze-outs of strange and non-strangeparticles and residual chemical non-equilibrium
K. A. Bugaev , D. R. Oliinychenko , , V. V. Sagun , A. I. Ivanytskyi , J. Cleymans , E. G. Nikonov andG. M. Zinovjev Bogolyubov Institute for Theoretical Physics, Metrologichna str. 14 B , Kiev 03680, Ukraine FIAS, Goethe-University, Ruth-Moufang Str. 1, 60438 Frankfurt upon Main, Germany Department of Physics, University of Cape Town, Rondebosch 7701, South Africa Laboratory for Information Technologies, JINR, Joliot-Curie str. 6, 141980 Dubna, Russia
We propose an elaborate version of the hadron resonance gas model with the combined treatment of separatechemical freeze-outs for strange and non-strange hadrons and with an additional γ s factor which accounts forthe remaining strange particle non-equilibration. Two sets of chemical freeze-outs parameters are connectedby the conservation laws of entropy, baryonic charge, isospin projection and strangeness. The developedapproach enables us to perform a high-quality fit of the hadron multiplicity ratios for AGS, SPS and RHICenergies with total χ /dof (cid:39) p , ¯Λ and ¯Ξ selective suppression problem is also discussed. Relativistic A+A collisions are an important source of experimental information about the QCD phase diagramand the strongly interacting matter properties. The last stage of such collisions is traditionally analyzedwithin the statistical approach which gives us an excellent opportunity to reveal the parameters of chemicalfreeze-out. This approach is based on the assumption of the thermal equilibrium existence during the laststage of reaction. Such an equilibrium can be reached due to intensive particle scattering. The stage of thesystem evolution when the inelastic reactions between hadrons stop is referred to as a chemical freeze-out (FO).Particle yields are determined by the parameters of FO, namely by chemical potentials and temperature. Thisgeneral picture is a basis of the Hadron Resonance Gas Model (HRGM) [1] which is the most successful onein describing the hadronic yields measured in heavy-ion experiments for energies from AGS to LHC. Despitea significant success of the HRGM in the experimental data analysis there are a few unresolved problems. Ingeneral they are related to the description of hadron yields which contain (anti)strange quarks. Especially theenergy dependence of K + /π + and Λ /π − ratios was out of high quality description. Excess of strange hadronsyields within the HRGM led physical community to ponder over strangeness suppression. The first receipt toresolve this problem was to introduce the strangeness suppression factor γ s which should be fitted in order todescribe the experimental data [2]. However, such an approach is not supported by any underlying physicalmodel and the physical meaning of γ s remains unclear [3, 4, 5, 6, 7]. In addition the strangeness suppressionapproach in its original form does not contain a hard-core repulsion between hadrons, while the latter is animportant feature of the HRGM. A significant role of the hard-core repulsion was demonstrated once more inRefs. [5] where the global fit of hadron yield ratios was essentially improved (to χ /dof (cid:39) R b and R m ,respectively. At the same time the kaon and the pion radii R K and R π are fitted independently in orderto provide the best description of K + /π + ratio [5]. This is an important finding since the non-monotonicenergy dependence of K + /π + ratio may indicate some qualitative changes of the system properties and mayserve as a signal of the deconfinement onset. This is a reason why this ratio known as the Strangeness Hornis of a special interest. Note, that the multi-component approach substantially increased the StrangenessHorn description quality, without spoiling the other ratios including Λ /π − one. However, even this advancedapproach does not reproduce the topmost point of the Strangeness Horn indicating that the data descriptionis still not ideal. In order to resolve this problem in Ref. [6] the γ s factor was considered as a free parameterwithin the HRGM with multi-component repulsion. Although the γ s data fit improves the Strangeness Horndescription quality sizably, it does not seem to be useful for the description of other hadron multiplicities [6].1 a r X i v : . [ h e p - ph ] D ec urthermore, in contrast to the claims established on the low-quality fit [10], at low energies it was found [6]that within the error bars in heavy ion collisions there is an enhancement of strangeness and not a suppression.However, the effect of apparent strangeness non-equilibration can be more successfully explained by thehypothesis of separate chemical FO for all strange hadrons. Since all the hadrons made of u and d quarks areunder thermal equilibration whereas the hadrons containing s quark are not, then it is reasonable to assumetwo different FOs for these two kinds of particles. Following this conclusion in Ref. [6, 7] a separate strangenessFO (SFO) was introduced. Note, that according to [6] both FO and SFO parameters are connected by theconservation laws of entropy, baryonic charge and isospin projection, while the net strangeness is explicitlyset to zero at FO and at SFO. These conservation laws are crucial elements of the concept of separate SFOdeveloped in [6] which allows one to essentially reduce the number of independent fitting parameters. Anotherprincipal element that differs the HRGM of [6] from the ideal gas treatment used in [7] is the presence ofmulti-component hard-core repulsion.Using the HRGM of [6] it was possible to successfully describe all hadron multiplicities measured in A+Acollisions at AGS, SPS and RHIC energies with χ /dof (cid:39) K + /π + ratio energy dependence was rather good except for the upper point.Since an introduction of the γ s factor demonstrated a remarkable description of all points of the StrangenessHorn, whereas the separate SFO led to a systematic improvement of all hadron yields description, we decidedto combine these elements in order to describe an experimental data with the highest possible quality. Thisambitious task is the main aim of the present paper. In addition, the problem of residual strangeness non-equilibration should also be clarified due to its importance from the academic point of view. Evidently, thebest tool for such a purpose is the most successful version of the HRGM, i.e. the HRGM with the multi-component hadronic repulsion and SFO. As it will be shown below, such an approach makes it possible todescribe 111 hadron yield ratios measured for 14 values of the center of mass collision energy √ s NN in theinterval from 2.7 GeV to 200 GeV with the highest quality ever achieved.The paper is organized as follows. The basic features of the developed model are outlined in Section 3. InSection 4 we present and discuss the new fit of hadronic multiplicity ratios with two chemical freeze-outs and γ s factor, while Section 5 contains our conclusions. In what follows we treat a hadronic system as a multi-component Boltzmann gas of hard spheres. The effects ofquantum statistics are negligible for typical temperatures of the hadronic gas whereas the hard-core repulsionbetween the particles significantly affects a corresponding equation of state [5, 8]. The present model is dealingwith the Grand Canonical treatment. Hence a thermodynamical state of system under consideration is fixedby the volume V , the temperature T , the baryonic chemical potential µ B , the strange chemical potential µ S and the chemical potential of the isospin third component µ I . These parameters control the pressure p of thesystem. In addition they define the densities n Ki of corresponding charges Q Ki ( K ∈ { B, S, I } ). Introducingthe symmetric matrix of the second virial coefficients B with the elements b ij = π ( R i + R j ) , we can obtainthe parametric equation of state of the present model in a compact form pT = N (cid:88) i =1 ξ i , n Ki = Q Ki ξ i ξ T B ξ N (cid:80) j =1 ξ j , ξ = ξ ξ ...ξ N . (1)The equation of state is written in terms of the solutions ξ i of the following system ξ i = φ i ( T ) exp (cid:34) µ i T − N (cid:80) j =1 ξ j b ij + ξ T B ξ (cid:34) N (cid:80) j =1 ξ j (cid:35) − (cid:35) , (2) φ i ( T ) = g i (2 π ) (cid:90) exp (cid:32) − (cid:112) k + m i T (cid:33) d k . (3)It is worth to note, that quantities T ξ i have a meaning of i th sort of hadrons partial pressure. Each i th sort is characterized by its full chemical potential µ i = Q Bi µ Bi + Q Si µ Si + Q I i µ I i , mass m i and degeneracy g i .Function φ i ( T ) denotes the corresponding particle thermal density in case of ideal gas. Finally, the superscript T here is the symbolic notation for operation of a column transposition which yields a row of quantities ξ i .The obtained model parameters for two freeze-outs and their dependence on the collision energy are shownin Figs. 1-3. 2n order to account for the possible strangeness non-equilibration we introduce the γ s factor in a conven-tional way by replacing φ i in Eq. (2) as φ i ( T ) → φ i ( T ) γ s i s , (4)where s i is a number of strange valence quarks plus number of strange valence anti-quarks.The principal difference of the present model from the traditional approaches is that we employ an inde-pendent chemical FO of strange particles. Let us consider this in some detail. The independent freeze-out ofstrangeness means that inelastic reactions (except for the decays) with hadrons made of s quarks are switchedoff at the temperature T SF O , the baryonic chemical potential µ B SFO , the strange chemical potential µ S SFO ,the isospin third projection chemical potential µ I SFO and the three-dimensional emission volume V SF O . Ingeneral case these parameters of SFO do not coincide with the temperature T SF O , the chemical potentials µ B SFO , µ S SFO , µ I SFO and the volume V SF O which characterize the freeze-out of non-strange hadrons. Theparticle yields are given by the charge density n Ki in (1) and the corresponding volume at FO and at SFO.At the first glance a model with independent SFO contains four extra fitting parameters for each energyvalue compared to the traditional approach (temperature, three chemical potentials and the volume at SFOinstead of strangeness suppression/enhancement factor γ s ). However, this is not the case due to the conserva-tion laws. Indeed, since the entropy, the baryonic charge and the isospin third projection are conserved, thenthe parameters of FO and SFO are connected by the following equations s F O V F O = s SF O V SF O , (5) n BF O V F O = n BSF O V SF O , (6) n I F O V F O = n I SF O V SF O . (7)The effective volumes can be excluded, if these equations are rewritten as sn B (cid:12)(cid:12)(cid:12)(cid:12) F O = sn B (cid:12)(cid:12)(cid:12)(cid:12) SF O , n B n I (cid:12)(cid:12)(cid:12)(cid:12) F O = n B n I (cid:12)(cid:12)(cid:12)(cid:12) SF O . (8)Thus, the baryonic µ B SFO and the isospin third projection µ I SFO chemical potentials at SFO are now definedby Eqs. (8). Note, that the strange chemical potentials µ S FO and µ S SFO are found from the condition ofvanishing net strangeness at FO and SFO, respectively. Therefore, the concept of independent SFO leads toan appearance of one independently fitting parameter T SF O . Hence, the independent fitting parameters arethe following: the baryonic chemical potential µ B , the chemical potential of the third projection of isospin µ I , the chemical freeze-out temperature for strange hadrons T SF O , the chemical freeze-out temperature forall non-strange hadrons T F O and the γ s factor.An inclusion of the width Γ i of hadronic states is an important element of the present model. It is dueto the fact that the thermodynamical properties of the hadronic system are sensitive to the width [5, 6, 11].In order to account for the finite width of resonances we perform the usual modification of the thermalparticle density φ i . Namely, we convolute the Boltzmann exponent under the integral over momentum withthe normalized Breit-Wigner mass distribution. As a result, the modified thermal particle density of i th sorthadron acquires the form (cid:90) exp (cid:32) − (cid:112) k + m i T (cid:33) d k → (cid:82) ∞ M dx ( x − m i ) +Γ i / (cid:82) exp (cid:16) − √ k + x T (cid:17) d k (cid:82) ∞ M dx ( x − m i ) +Γ i / . (9)Here m i denotes the mean mass of hadron and M stands for the threshold in the dominant decay channel.The main advantages of this approximation is a simplicity of its realization and a clear way to account forthe finite width of hadrons.The observed hadronic multiplicities contain the thermal and decay contributions. For example, a largepart of pions is produced by the decays of heavier hadrons. Therefore, the total multiplicity is obtained as asum of thermal and decay multiplicities, exactly as it is done in a conventional model. However, writing theformula for final particle densities, we have to take into account that volumes of FO and SFO can be different: N fin ( X ) V F O = (cid:88) Y ∈ F O BR ( Y → X ) n th ( Y ) + (cid:88) Y ∈ SF O BR ( Y → X ) n th ( Y ) V SF O V F O . (10)Here the first term on the right hand side is due to decays after FO whereas the second one accounts for thestrange resonances decayed after SFO. The factor V SF O /V F O can be replaced by n BF O /n BSF O due to baryoniccharge conservation. BR ( Y → X ) denotes the branching ratio of the Y-th hadron decay into the X-th hadron,with the definition BR ( X → X ) = 1 used for the sake of convenience. The input parameters of the presentmodel (masses m i , widths Γ i , degeneracies g i and branching ratios of all strong decays) were taken from theparticle tables of the thermodynamical code THERMUS [12].3igure 1: (Colour on-line) Chemical freeze-outs parameters in the model with two freeze-outs and with the γ s fit. Baryonic chemical potential dependence of the chemical freeze-out temperature for SFO (marked withtriangles) and for FO (marked with circles). The solid black curves correspond to the isentops s/ρ B = const ,on which the FO and the SFO points are located. Data sets and fit procedure . The present model is applied to fit the data. We take the ratios of particlemultiplicities at midrapidity as the data points. In contrast to fitting multiplicities themselves such anapproach allows us to cancel the possible experimental biases. In this paper we use the data set almostidentical to Ref. [6]. At the AGS energies ( √ s NN = 2 . − . E lab = 2 − . π data are also available for Λ hyperons [17] and forΞ − hyperons (for 6 AGeV only) [18]. However, as was argued in Ref. [3], the data for Λ and Ξ − should berecalculated for midrapidity. Therefore, instead of raw experimental data we used the corrected values from[3]. Next comes the data set at the highest AGS energy ( √ s NN = 4 . E lab = 10 . √ s NN = 9 . √ s NN = 62 . √ s NN = 130 GeV [27, 28, 29, 30] and 200 GeV [30, 31, 32].The criterion to define the fitting parameters of the present model is a minimization of χ = (cid:80) i ( r theri − r expi ) σ i ,where r theori and r expi are, respectively, the theoretical and the experimental values of particle yields ratios, σ i stands for the corresponding experimental error and a summation is performed over all available experimentalpoints. Combined fit with SFO and γ s factor . Recently performed comprehensive data analysis [6] for twoalternative approaches, i.e the first one with γ s as a free parameter and the second one with separate FOand SFO, showed the advantages and disadvantages of both methods. Thus, the γ s fit provides one with anopportunity to noticeably improve the Strangeness Horn description with χ /dof = 3 . /
14, comparably tothe previous result χ /dof = 7 . /
14 [5], but there are only slight improvements of the ratios with strangebaryons (global χ /dof : 1 . → . p/π − , ¯Λ / Λ, ¯Ξ − / Ξ − and ¯Ω / Ω. Althoughthe overall χ /dof (cid:39) .
06 is notably better than with the γ s factor [5, 6], but the highest point fitting ofthe Horn got worse. These results led us to an idea to investigate the combination of these two approachesin order to get the high-quality Strangeness Horn description without spoiling the quality of other particleratios.For 14 values of collision energy √ s NN = 2.7, 3.3, 3.8, 4.3, 4.9, 6.3, 7.6, 8.8, 9.2, 12, 17, 62.4, 130, 200 GeVthe best description with two separate freeze-outs and the γ s fit gives χ /dof = 42.96/41 (cid:39) χ /dof =58.5/55 (cid:39) χ itself, not divided by number of degrees of freedom, has improved notably, although the4igure 2: (Colour on-line) The behavior of the model parameters: chemical freeze-out temperature T vs. √ s NN (left panel) and the freeze-out baryonic chemical potential µ B vs. √ s NN (right panel).Figure 3: (Colour on-line) √ s NN dependence of the γ s factor in the model with two freeze-outs and the γ s fit. 5igure 4: (Colour on-line) √ s NN dependences of K + /π + ratio. The solid line corresponds to the results of[5]. Horizontal bars correspond to the present model with SFO+ γ s fit, while the diamonds correspond to theresults previously obtained for SFO [6].deviation of the γ s factor from 1 does not exceed 27 % (see Fig. 3). These findings motivate us to study whatratios and at what energies are improved.As we mentioned earlier, at each collision energy there are five independent fitting parameters in theconsidered model with the simultaneous SFO and the γ s fit, while for some collision energies the number ofexperimental ratios is lower or equal to the number of parameters. For example, for the energies √ s NN =2.7,3.3, 3.8, 4.3, 9.2, 62.4 GeV the number of available ratios is small (4, 5, 5, 5, 5, 5, respectively) from whichonly kaons and Λ contain strange quarks. Therefore, for these energies we obtained a perfect data descriptionsince we had to solve the above equations. As a result for these energies the relative deviation of the fit isalmost a zero, but it gives us somewhat larger uncertainties for the fitting parameters.For the energies √ s NN = 17, 130 GeV we observed that the resulting fit quality became better comparedto the work [6]. The most significant improvements correspond to the collision energies √ s NN = 6.3, 7.6, and12 GeV, that are plotted in Fig. 5. Fig. 5 demonstrates very nice fit quality, especially for such traditionallyproblematic ratios as K + /π + , π − /π + , ¯Λ /π − and ϕ/K + . For √ s NN = 7.6 GeV the seven ratios out of tenare improved.A special attention in our consideration was paid to the Strangeness Horn, i.e. to K + /π + ratio. Anotherreason for a through study of the Strangeness Horn is a traditional problem of the HRGM to fit it. As onecan see from Fig. 4, the remarkable K + /π + fit improvement for √ s NN = 2.7, 3.3, 4.3, 4.9, 6.3, 7.6, 12 GeVjustifies the usage of the present model. Quantitatively, we found that χ /dof improvement due to SFO+ γ s introduction is χ /dof =1.5/14, i.e. even better than it was done in [6] with χ /dof =3.3/14 for the γ s fittingapproach and χ /dof =6.3/14 for SFO and γ s = 1.In addition, in Fig. 6 we give the Λ /π − and ¯Λ /π − ratios to show that two separate freeze-outs inclusionwith the γ s fit still does not improve these ratios. The Λ /π − fit quality, for instance, is ( χ /dof =10/8).Hence, up to now the best fit of the Λ /π − ratio was obtained within the SFO approach with γ s = 1. As it wasmentioned in [3, 4, 5] a too slow decrease of model results for Λ /π − ratio compared to the experimental datais typical for almost all statistical models. Evidently, the too steep rise in Λ /π − behavior is a consequence ofthe ¯Λ anomaly [3, 33]. Similar results are reported in Refs. [34, 35, 36] as the ¯ p , ¯Λ and ¯Ξ selective suppression.Since even an introduction of the separate strangeness freeze-out with the strangeness enhancement factordoes not allow us to better describe these ratios, we believe that there is an unclarified physical reason whichis responsible for it.Within the present model we also found a selective improvement and a certain degradation of the fitquality of various ratios for different collision energies. For instance, the π − /π + ratio is slightly increased for √ s NN = 6.3 and 7.6 GeV, but the situation drastically changes for √ s NN = 12 GeV. The same tendency istypical for ¯ p/p . On the contrary, for ¯Ξ − / Λ ratio there is a noticeably worse data description within SFO+ γ s approach at √ s NN = 6.3, 7.6 GeV, but for √ s NN = 12 GeV the fit quality is sizably better compared toall previous approaches. Thus, within the present model we reveal a noticeable change in the trend of someratios at √ s NN = 7.6-12 GeV . 6igure 5: (Colour on-line) Relative deviation of the theoretical description of ratios from the experimentalvalue in units of the experimental error σ . Particle ratios vs. the modulus of relative deviation ( | r theor − r exp | σ exp )for √ s NN = 6.3, 7.6, 12 and 130 GeV are shown. Solid lines correspond to the model with a single FO ofall hadrons and γ s = 1, blue dotted lines correspond to the model with SFO. The results of a model with acombined fit with SFO and γ s are highlighted by magenta dashed lines.7igure 6: (Colour on-line) √ s NN dependences of ¯Λ /π − (left panel) and Λ /π − (right panel) ratios. The solidline correspond to the results of [5]. Horizontal bars correspond to SFO+ γ s model, while green diamondscorrespond to the previously obtained results for the SFO model [6]. We have performed an elaborate fit of the data measured at AGS, SPS and RHIC energies within the multi-component hadron resonance gas model. The suggested approach to separately treat the freeze-outs of strangeand non-strange hadrons with the simultaneous γ s fitting gives rise for the top-notch Strangeness Horn de-scription with χ /dof =1.5/14. The developed model clearly demonstrates that the successful fit of hadronicmultiplicities includes all the advantages of these two approaches discussed in [6]. As a result for √ s NN =6.3, 7.6, 12, 130 GeV we found a significant data fit quality improvement. The achieved total value of χ /dof is 42 . / (cid:39) γ s values are consistent with the conclusion γ s (cid:39) γ s (cid:39) .
27, but with the large error bars. In addition, the description of ratios contain-ing the non-strange particles, especially such as π − /π + and ¯ p/p , gets better compared to previously reportedresults [5, 6]. At the same time the lack of available data at √ s NN =2.7, 3.3, 3.8, 4.3, 9.2, 62.4 GeV forcedus to solve the corresponding equations which in combination with the large experimental error bars led torather large uncertainties of the fitting parameters.From a significant improvement of the data description we conclude that the concept of separate chemicalfreeze-out of strange particles is an essential part of heavy ion collision phenomenology which should be takeninto account in further studies of strongly interacting matter properties. However, the remaining problemwith ¯ p , ¯Λ, ¯Ξ ratios led us to a conclusion that there is an unclarified physical reason which is responsiblefor them. The residual non-equilibration of strange particles found here seems to be weak and, perhaps, thebetter experimental data will help us to reduce it further.The obtained description of the hadron multiplicity ratios reached the highest quality ever achieved andthis fact demonstrates that the suggested approach is almost a precise tool to elucidate the thermodynamicsproperties of hadron matter at two chemical freeze-outs. The fresh illustrations to this statement can be foundin [11]. However, to get more reliable conclusions from this approach we need more experimental data withan essentially higher accuracy. Acknowledgments.
We would like to thank A. Andronic for providing an access to well-structured exper-imental data. The authors are thankful to I. N. Mishustin, D. H. Rischke and L. M. Satarov for valuablecomments. K.A.B., A.I.I. and G.M.Z. acknowledge a support of the Fundamental Research State Fund ofUkraine, Project No F58/04. K.A.B. acknowledges also a partial support provided by the Helmholtz Inter-national Center for FAIR within the framework of the LOEWE program launched by the State of Hesse.8 eferences [1] Braun-Munzinger P., Redlich K. and Stachel J., In *Hwa, R.C. (ed.) et al. : Quark gluon plasma* (2003) 491.[2] Rafelsky J., Phys. Lett. B (1991) 333.[3] Andronic A., Braun-Munzinger P. and Stachel J., Nucl. Phys. A (2006) 167 and references therein.[4] Andronic A., Braun-Munzinger P. and Stachel J., Phys. Lett. B (2009) 142.[5] Bugaev K. A., Oliinychenko D. R., Sorin A. S. and Zinovjev G. M., Eur. Phys. J. A (2013)30–1-8and references therein.[6] Bugaev K.A. et al., Europhys. Lett. (2013) 22002.[7] Chatterjee S., Godbole R. M. and Gupta S., Phys. Lett. B (2013) 554.[8] Zeeb G., Bugaev K. A., Reuter P. T. and St¨ocker H. Ukr. J. Phys. (2008) 279.[9] Oliinychenko D. R. , BugaevK. A. and Sorin A. S., Ukr. J. Phys. (2013) 211.[10] Becattini F., Manninen J. and Gazdzicki M., Phys. Rev. C (2006) 044905.[11] Bugaev K. A., Ivanytskyi A. I., Oliinychenko D.R., Nikonov E. G., Sagun V. V. and Zinovjev G. M.,arXiv:1311.4367 [nucl-th].[12] Wheaton S., Cleymans J. and Hauer M., Comput. Phys. Commun. (2009) 84.[13] Klay J. L. et al., Phys. Rev. C (2003) 054905.[14] Ahle L. et al., Phys. Lett. B (2000) 1.[15] Back B. B. et al.,
Phys. Rev. Lett. (2001) 1970.[16] Klay J. L. et al., Phys. Rev. Lett. (2002) 102301.[17] Pinkenburg C. et al., Nucl. Phys. A (2002) 495c.[18] Chung P. et al.,
Phys. Rev. Lett. (2003) 202301.[19] Afanasiev S. V. et al., Phys. Rev. C (2002) 054902.[20] Afanasiev S. V. et al., Phys. Rev. C (2004) 024902.[21] Anticic T. et al., Phys. Rev. Lett. (2004) 022302.[22] Afanasiev S. V. et al., Phys. Lett. B (2002) 275.[23] Alt C. et al.,
Phys. Rev. Lett. (2005) 192301.[24] Afanasiev S. V. et al., Phys. Lett. B (2000) 59.[25] Abelev B. et al.,
Phys. Rev. C (2010) 024911.[26] Abelev B. et al., Phys. Rev. C (2009) 034909.[27] Adams J. et al., Phys. Rev. Lett. (2004) 182301.[28] Adams J. et al., Phys. Lett. B (2003) 167.[29] Adler C. et al.,
Phys. Rev. C (2002) 041901(R).[30] Adams J. et al., Phys. Rev. Lett. (2004) 112301.[31] Adams J. et al., Phys. Lett. B (2005) 181.[32] Billmeier A. et al.,
J. Phys. G (2004) S363.[33] Back B. B. et al., Phys. Rev. Lett. (2001) 242301.[34] Becattini F. et al., Phys. Rev. C (2012) 044921.[35] Becattini F. et al., Phys. Rev. Lett.111