Correlation in formation of ^{8}Be nuclei and α-particles in fragmentation of relativistic nuclei
A.A. Zaitsev, D.A. Artemenkov, V.V. Glagolev, M.M. Chernyavsky, N.G. Peresadko, V.V. Rusakova, P.I. Zarubin
aa r X i v : . [ nu c l - e x ] F e b Correlation in formation of Be nuclei and α -particles infragmentation of relativistic nuclei A.A. Zaitsev,
1, 2
D.A. Artemenkov, V.V. Glagolev, M.M. Chernyavsky, N.G. Peresadko, V.V. Rusakova, and P.I. Zarubin
1, 2, ∗ Joint Institute for Nuclear Research, Dubna, Russia Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia (Dated: February 19, 2021)
Abstract
In the events of peripheral dissociation of relativistic nuclei in the nuclear track emulsion, itis possible to study the emerging ensembles of He and H nuclei, including those from decays ofthe unstable Be and B nuclei, as well as the Hoyle state. These extremely short-lived statesare identified by invariant masses calculated from the opening angles in 2 α -pairs, 2 αp - and 3 α -triplets in the approximation of conservation of momentum per nucleon of the primary nucleus.In the same approach, it is possible to search for more complex states. This paper explores thecorrelation between the formation of Be nuclei and the multiplicity of accompanying α -particlesin the dissociation of relativistic O, Ne, Si, and
Au nuclei. On this basis, estimates of sucha correlation are presented for the unstable B nucleus and the Hoyle state. An enhancement inthe Be contribution to dissociation with the α -particle multiplicity is found. Decays of B nucleiand Hoyle states follow the same trend.
PACS numbers: 21.60.Gx, 25.75.-q, 29.40.Rg ∗ email: [email protected] . INTRODUCTION The analysis of fragmentation of relativistic nuclei in a nuclear track emulsion (NTE)makes it possible to study internally non-relativistic ensembles of H and He nuclei startingwith produced in decays of the unstable Be and B nuclei and up to the most complexones [1–3]. NTE layers with a thickness of 200 to 500 µ m, longitudinally exposed to thenuclei under study, make it possible to determine with full completeness and resolution of0.5 µ m the angles between the directions of emission of relativistic fragments in the conesin θ fr = P fr / P , where P fr = 0.2 GeV/ c is the characteristic Fermi momentum of nucleonsin a projectile nucleus with a momentum per nucleon. The most valuable in this aspect arethe events of dissociation which are not accompanied by fragments of the target nuclei andgenerated mesons. They are called coherent dissociation or “white” stars.Despite the fact that coherent dissociation C → α and O → α is only 1–2% ofinelastic interactions, a targeted search performed by transverse scanning made it possibleto investigate by the invariant mass method 310 3 α and 641 4 α “white” stars [4, 5] andestablish in both cases the contributions of 3 α -decays of the Hoyle state (HS) [6, 7]. Ingeneral, the invariant mass Q = M ∗ - M is given by the sum M ∗ = Σ( P i · P k ), where P i,k are 4-momenta of fragments, and M is their mass. To calculate the invariant masses of2 α -pairs Q α and 3 α -triplets Q α in the approximation of conservation of momentum pernucleon by α -particles of the primary nucleus, only measurements of their emission anglesare used. The correspondence between He - He and H - H is assumed, since in the caseof extremely narrow decays of Be and B, the measured contributions of He and H aresmall. The initial portions of the event distributions over the variables Q α and Q α containpeaks corresponding to Be and HS for both C and O. Since the decay energy valuesare noticeably lower than the nearest excitations, the selection Q α ( Be) ≤ Q α (HS) ≤ Be (HS) 45 ±
4% (11 ± C and 62 ±
3% (22 ± O.The invariant representation makes it possible to identify among the relativistic fragmentsthe decays Be, B, and HS, including cascade ones, regardless of the initial collision energy.It becomes possible to establish a connection with the low energy studies [9–11]. The effectof relativistic collimation makes it possible not only to study the generation of Be, B andHS, but also to search for unstable states of increasing complexity decaying through them212–14].Earlier, the contribution of Be and B decays to the dissociation of few light, middle(Ne, Si) and heavy (Au) nuclei were estimated in a similar way (review [8]). Each of theseextremely unstable states has low decay energy and lifetime (inversely proportional to thedecay width) is several orders higher than the characteristic time of generating reactions.They are predicted to be unusually large in size (example in [12]). One can assume thepresence of these unstable states as virtual components in parent nuclei, which manifestthemselves in relativistic fragmentation. However, maintaining such universality with anincrease in the mass number of nuclei under study seems to be more and more problematic.An alternative consists in the Be formation during the final state interaction of theproduced α -particles and the subsequent pick-up of accompanying α -particles and nucleonswith the emission of the necessary γ -quanta. The consequence of such a scenario would bean increase in the Be yield with a multiplicity of α -particles n α in the event, and possibly Band HS decaying through Be. The purpose of this study is to identify a possible relationshipbetween the formation of the unstable sates and accompanying multiplicity.The smaller the difference between the charges and mass numbers of the parent nucleusand the reconstructed unstable state, the easier they are identified (for example, Be → Beand C → B [8]), since the distortions in determining the fragment emission angles, whichtend to increase in the transition from track to track, are minimized. In addition, in thestudied region of invariant masses, the combinatorial background from the accompanyingmultiplicity is minimized. However, this limitation is holding back testing the universalityand correlations in the unstable state production and the search for more complex statesof this kind. NTE layers exposed to heavy nuclei make it possible to radically expand themultiplicity of the studied fragments, which demands to study in practice identificationconditions with increasing n α .A primary track scanning in NTE allows one to find interactions without sampling, inparticular, with a different number of relativistic fragments of He and H. The data obtainedin this approach allow tracing the contribution of the unstable states and provide support inadvancing to greater statistics and more complex states by the transverse scanning method.Although the multiple channel statistics of turns out to be radically lower but its evolutioncan be followed. Further, overview measurements gathered by the emulsion collaborationat the JINR Synchrophasotron in the 80s and EMU collaboration at the AGS (BNL) and3PS (CERN) synchrotrons in the 90s on the fragmentation of relativistic nuclei O, Ne, Si and
Au are mainly used [15–19]. Photos and videos of characteristic interactions areavailable [1, 20].Large-scale and uniform, this data retains its uniqueness in terms of relativistic nuclearfragmentation. Among the many results obtained the conclusion about the limiting frag-mentation regime in the widest possible range of nuclei and primary energy values, which isexpressed by the invariability of the charge composition of fragments and the scale-invariantbehavior of their spectra, remains of fundamental value. At the same time, despite thediversity of the results obtained, fine effects associated with angular correlations within theensembles of fragments remained unexplored. In addition to the actual interest in the topic,they require a targeted build-up of statistics in multiple channels. Owing to the use of NTElayers exposed at that time, the statistics of the measured interactions Si → n α ( ≥
3) isstarted to be supplemented in the framework of our BECQUEREL experiment at JINR.All these measurements, uniformly represented in the variable of invariant mass, make itpossible to assess the role of unstable states in nuclear fragmentation and formulate thefurther study tasks.
II. O FRAGMENTATION
There are measurements for inelastic interactions at four energy values of O nuclei foundwhen tracing primary tracks including 2823 at 3.65 GeV/nucleon (JINR Synchrophasotron,80s), 689 at 14.6 GeV/nucleon (BNL AGS, 90s), 885 at 60 GeV/nucleon and 801 at 200GeV/nucleon (CERN SPS). The distributions of all 2 α -pair combinations from these inter-actions N (2 α ) over the invariant mass Q α ≤ O → α [8], a peak is observed at the origin, and the condition Q α ( Be) ≤ Be decay candidates.Table I shows the number of events N nα ( Be) containing at least one Be decay candidatesatisfying the condition Q α ( Be) ≤ N nα with the relativistic α -particle multiplicity n α . In the covered range of initial energy the distributions N nα and N nα ( Be) show similarities, which corresponds to the concept of the limiting nuclearfragmentation regime. As n α increases, the fraction of events with Be decays increases.The invariability of the composition of relativistic fragmentation from the initial energy4
MeV α Q / . M e V ) α ( N FIG. 1. Distribution of 2 α -pairs N (2 α ) over invariant mass Q α ( ≤ O nuclei (solid line); data for 15 (long dotted line), 60 (dotted line) and 200(short dotted line) GeV/nucleon O are added sequentially.TABLE I. Statistics N nα ( Be) among n α events of O dissociation; percentage of N nα ( Be) among N nα is indicated. n α N nα ( Be)/ N nα (%) 15 GeV/nucleon N nα ( Be)/ N nα (%) 60 GeV/nucleon N nα ( Be)/ N nα (%) 200 GeV/nucleon N nα ( Be)/ N nα (%) All N nα ( Be)/ N nα (%)2 32/390 (8 ±
2) 6/95 (6 ±
3) 9/97 (9 ±
3) 3/56 (5 ±
3) 50/638 (8 ± ±
4) 13/51 (26 ±
8) 12/64 (19 ±
6) 8/29 (28 ±
11) 73/320 (23 ± ±
15) 1/4 (25) 2/2 (100) 0/1 (0) 16/35 (46 ± gives grounds to summarize the statistics, confirming the contribution of Be, which growswith n α (right column of Table I). 13 4 α -events are “white” stars, and 6 of them contain Bedecays. This number makes it possible to relate the “white” 4 α -star statistics mentionedabove with the other O dissociation channels.Only the N nα ( Be) statistics at 3.65 GeV/nucleon correspond to the level expected forthe B and HS decays. The number of 2 αp triplets N αp ( Be) under the condition Q α ( Be) ≤ Q αp ( B) ≤ ABLE II. Statistics of N nαmp ( B) and N nαmp ( Be) decays in the fragmentation channels N nαmp ( Be) of O and Ne nuclei with a multiplicity of α -particles n α and protons m p . N nαmp O N nαmp ( B)/ N nαmp ( Be) (%) N nαmp Ne N nαmp ( B)/ N nαmp ( Be) (%)338 2 α + (1-4) p ±
14) 429 2 α + (1-6) p ± α + (1,2) p ±
13) 203 3 α + (1-4) p ± α + (1,2) p ± , MeV p α Q B e ) / . M e V ( ) p α ( N FIG. 2. Distribution of 2 αp triplets N (2 αp ) ( Be) over invariant mass Q αp ≤ O (solid) and 3.22 GeV/nucleon Ne fragmentation (added by dashed line). Dotsmark N (2 αp ) ( Be) distribution in coherent dissociation C → α p (normalized to O and Nestatistics). is adopted for the B decays N αp ( B). It coincides with the precipitation of 54 B decays inthe most convenient of coherent dissociation C → α p at 1.2 GeV/nucleon (Fig. 2) [8].In the channels n α with a multiplicity of protons mp , on going from n α = 2 to 3, thenumber N nαmp ( B) increases relative to N nαmp ( B) proportionally to N nαmp ( Be) (Table II).At n α = 3, one HS decay is identified and 5 at n α = 4. In the latter case, N α (HS)/ N nα ( Be)= 0.4 ± α stars.6 II. FRAGMENTATION OF O ON PROTONS
The accepted approximations can be verified using the data obtained in exposure to2.4 GeV/nucleon O nuclei of the JINR 1-meter hydrogen bubble chamber (VPK-100),placed in a magnetic field [21]. The dataset includes full solid angle measurements of themomentum vectors of the O + p reaction products in 11104 collisions of all kinds. Inthis case, there is also a peak in the initial part of the angle distribution of 2 α -pairs Θ α ,corresponding to Be decays [21]. As noted [8], when momenta of relativistic He fragmentsreconstructed with insufficient accuracy are used in the Q α calculation, the Be signalpractically disappears. There remains the possibility of moment fixing as in the NTE case,and using the measured values when normalized to the value of the initial momentum pernucleon for the identification of He and H isotopes.In Fig. 3, the invariant mass distributions of all 2 α -pairs Q α , 2 αp -triplets Q αp , and3 α -triplets Q α calculated from the angles determined in the VPK-100, are superimposed.In the presented range, the Q α distribution is normalized to the Q αp statistics with adecreasing factor of 25. Directly depending on Θ α , the Q α variant with fixed momentademonstrates the Be peak. According to the measured momenta of fragments, the condition Q α ( Be) ≤ He contribution, and the contribution of protons is 90%among H.The peak in the Q αp distribution shown in Fig. 3 with the condition Q α ( Be) ≤ B decays to Q αp ( B) ≤ h Q αp i (RMS) = 271 ±
15 (120) keV corresponds to the NTE result [6]. Similarly,the peak in the distribution Q α (HS) ≤ Q α ( Be) ≤ h Q α i (RMS) = 322 ±
25 (180) keV[9]. In the statistics, there are four events with a 2 Be formation and one with coincidentcandidates B and HS.Table III shows the data reflecting the change in contributions from unstable state decaysin events with the α -particles multiplicity n α (in this case, identified He nuclei). Withincreasing n α , the Be detecting probability increases rapidly. An increase in n α leads to arelative decrease in N nα ( B), which can be explained by a decrease in the number of protonsavailable for the B formation. On the contrary, N nα (HS) increases due to an increase in thenumber of α -particles available for the HS formation. In the coherent dissociation O → ABLE III. Statistics of events containing at least one Be decay candidate N nα ( Be), B, or HSunder the condition Q α ( Be) ≤ N nα events of fragmentation of O nuclei onprotons with multiplicity n α . n α N nα ( Be)/ N nα (% N nα ) N nα ( B)(% N nα ( Be)) N nα (HS)(% N nα ( Be))2 111/981 (11 ±
1) 29 (26 ±
6) -3 203/522 (39 ±
3) 31 (15 ±
3) 36 (18 ± ±
11) - 11 (41 ± , MeV Q / . M e V N FIG. 3. Distribution of 2.4 GeV/nucleon O fragmentation events on protons over invariant massesof all 2 α -pairs Q α (dots), 2 αp -triplets Q αp (dashed line) and 3 α -triplets Q α (solid). α , the fraction of HS decays relative to Be is 35 ± n α = 4 in the generally more severe O + p interaction (Table III). These factsindicate the universality of the appearance of Be and HS.8
MeV α Q / . M e V ) α ( N FIG. 4. Distribution of 2 α -pairs N (2 α ) over invariant mass Q α ( ≤ Ne (solid line) and 14.6 GeV/nucleon Si nuclei (added by dotted line).
IV. NE AND SI FRAGMENTATION
Measurements carried out in NTE layers exposed to Ne nuclei at 3.22 GeV/nucleon(4308 events, JINR Synchrophasotron) and Si at 14.6 GeV/nucleon (1093 events, BNLAGS) further expand the n α range. In both cases, no change in the condition Q α ( Be) ≤ N nα and N nα ( Be) statistics are presented in Table. IV.Recently, the Si statistics n α ≥ Be contribution also increases with the n α multiplicity. Be nuclei can arise both directly in fragmentation and via B and HS decays. Only the Ne statistics makes it possible to estimate the contributions of B and HS based on theinvariant masses Q αp and Q α . The distribution N (2 αp ) ( Be), added in Fig. 2 for the Necase, contains 2 αp triplets Q αp ( B) ≤ N (3 α ) ( Be) distribution shown in Fig.5, contains 3 α triplets Q α (HS) ≤ C → α from the N (3 α ) ( Be) distributionin Fig. 4. Similarly to the case of O, on going from n α = 2 to 4 for B, N nαmp ( B) relativeto N nαmp increases (Table II). Transition from n α = 3 to 4 indicates a noticeable increase in9 ABLE IV. Statistics of events N nα ( Be) among N nα events in dissociation of Ne and Si nuclei;the percentage of N nα ( Be) among N nα is indicated. n α Ne 3.22 GeV/nucleon N nα ( Be)/ N nα (%) Si 15 GeV/nucleon N nα ( Be)/ N nα (%) Si 15 GeV/nucleon N nα ( Be)/ N nα (%)2 30/528 (6 ±
1) 5/164 (3 ± n α ≥
33 45/243 (19 ±
3) 10/75 (13 ±
5) 33/231 (14 ± ±
6) 11/25 (44 ±
16) 39/121 (32 ± ±
31) 8/17 (47 ±
20) 16/42 (38 ± ± N nα (HS) among events N nα in dissociation of Ne nuclei; thepercentage of N nα ( Be) among N nα is indicated. n α N nα (HS)/ N nα (% N nα ) N (HS)/ N nα ( Be), %3 3/243 (1.2 ± ±
44 10/80 (13 ±
5) 40 ±
155 1/10 17
HS, showing an analogy with the O data as well (Table V). V. AU FRAGMENTATION
There are similar measurements of 1316 interactions of
Au nuclei at 10.7 GeV/nucleon(BNL AGS, 90s). For this dataset, Fig. 6a shows the distribution of 2 α -pairs at small valuesof Q α . Due to the deteriorated resolution, the Be region expands, which requires softeningthe selection of Q α ( Be) ≤ N nα ( Be)correlation and minimize the background in N nα ( B) and N nα (HS), the condition Q α ( Be) ≤ αp -triplets, 3 α -triplets, and 4 α -quartets inthe small Q regions of events in which, according to these conditions, there is at least onecandidate for Be decay are also included in Fig. 6. Note that the distributions (b) and (c)contain 2 αp and 3 α triplets satisfying the conditions Q αp ( B) ≤ Q α (HS) ≤ MeV α Q B e ) / . M e V ( ) α ( N FIG. 5. Distribution of 3 α -triplets N (3 α ) ( Be) over invariant mass Q αp ( ≤ Ne fragmentation (solid line). Dots mark distribution N (3 α ) ( Be) in dissociation C → α normalized to Ne statistics. Q α ( Be) ≤ n α ≥
11 are summed to reduce errors. Theratio of the number of events N nα ( Be) including at least one Be decay candidate to thestatistics of the channel N nα , grows rapidly to n α = 10 to about 0.5. This trend persistswhen the condition is tightened to Q α ( Be) despite the decrease in statistics (Fig. 7).The ratio of the number of events N nα ( B) and N nα (HS) to the statistics N nα ( Be) showsno noticeable change with multiplicity n α (Table VI). The statistics of the identified decays of Be pairs N nα (2 Be) behave in the same way. In fact, these three ratios indicate an increase in N nα ( B), N nα (HS) and N nα (2 Be) relative to N nα . In these three cases, significant statisticalerrors make it possible to characterize only general trends. Summing the statistics on themultiplicity n α and normalizing to the sum N nα ( Be) leads to the relative contributions N nα ( B), N nα (HS), and N nα (2 Be) equal to 25 ± ± ± Q α (Fig.6d) indicates near-threshold 4 α -quadruples, in which thedecays of HS and 2 Be are reconstructed with the condition Q α ( Be) ≤ Q α = 1.0 (16 α , HS), 1.9 (11 α , HS), 2.1 (9 α , 2 Be), 2.2 (5 α , 2 Be), 2.4 (9 α , HS) MeV. The11 MeV α Q / . M e V ) α ( N a) , MeV p α Q / . M e V ) p α ( N b) , MeV α Q / . M e V ) α ( N c) , MeV α Q / . M e V ) α ( N d) FIG. 6. Distributions over invariant masses Q of 2 α -pairs (a) in fragmentation of Au nuclei, aswell as 2 αp -triplets (b), 3 α -triplets (c), and 4 α -quartets (d) in events with Be candidate selectedaccording to Q α ( Be) ≤ ≤ α n α n N B e ) / ( α n N FIG. 7. Dependence of relative contribution of N nα ( Be) decays to the statistics N nα of eventswith α -particle multiplicity n α in fragmentation of Au nuclei upon selection Q α ( Be) ≤ ≤ ABLE VI. Statistics of events containing at least one Be, B or HS decay, or at least two Beprovided Q α ( Be) ≤ N nα of Au fragmentation with multiplicity n α ; the total statistics of the channels n α ≥
11 are highlighted. n α N nα ( Be)/ N nα (% N nα ) N nα ( B)(% N nα ( Be)) N nα (HS)(% N nα ( Be)) N nα (2 Be)(% N nα ( Be))2 3/133 (2 ±
1) - - -3 14/162 (9 ±
3) 1 (7) - -4 25/161 (16 ±
4) 7 (28 ±
12) 2 (8 ±
6) -5 23/135 (17 ±
4) 5 (22 ±
11) - 1 (4)6 31/101 (31 ±
7) 9 (29 ±
11) 2 (6 ±
4) -7 31/90 (34 ±
7) 6 (19 ±
9) 2 (6 ±
4) 3 (10 ± ±
10) 8 (25 ±
10) 2 (6 ±
4) 2 (7 ± ±
13) 9 (31 ±
12) 3 (10 ±
6) 5(17 ± ±
15) 4 (18 ±
10) - 5(23 ± ± ± ± ± ± ± ±
12 2/5 1 - 113 2/4 1 - 114 3/3 1 - 115 1/1 - - -16 1/2 1 1 1 +6 excitation of the O nucleus at 660 keV above the 4 α -threshold is assumed to be a 4 α -condensate [12, 13]. It could decay in the sequence the decay of which could proceed alongthe chain O(0 +6 ) → C(0 +2 ) → Be(0 + ) → α or O(0 +6 ) → Be(0 + ) → α . Investigationof this problem requires a qualitatively different level of n α -ensemble statistics, which, inprinciple, is available in the transverse event search.13 I. SUMMARY
The preserved and recently supplemented data on the relativistic fragmentation of O, Ne, Si, and
Au nuclei in a nuclear track emulsion made it possible to identify decays of Be, B nuclei and Hoyle state in the invariant mass distributions of 2 α -pairs, 2 αp - and 3 α -triplets. The determination of the invariant mass from the angles of emission of fragmentsin the velocity conservation approximation turns out to be an adequate approximation.Starting with the O fragmentation, the presented analysis indicates a relative enhancementin the Be contribution with an increase in the number of relativistic α -particles per eventand the remaining proportional contributions of HS and B. In the
Au fragmentation,the tendency is traced up to at least 10 relativistic α -particles per event. This observationmakes it possible to propose a development of the theory of relativistic fragmentation ofnuclei taking into account the interactions of α -particles, which are characteristic of low-energy nuclear physics.It is obvious that it is necessary to increase the statistics of events with a high multiplicityof α -particles with special attention to the accuracy of measurements of the emission anglesof relativistic He and H fragments. An analysis of the data on the O fragmentationin the hydrogen bubble chamber confirms the approximations and conclusions made. Theapplication of this method would be productive for light isotopes, including radioactive ones.Unfortunately, it has gone down in history, and its renewal does not seem real. The feasibilityof this approach by other methods of high energy physics has not yet been demonstrated.Therefore, the use of the flexible method of nuclear track emulsion retains a prospect for thestudy of unstable states produced in a narrow cone of relativistic fragmentation by nuclei inthe widest range of mass numbers.New possibilities are contained in existing layers exposed to 800-950 A MeV Kr nuclei(SIS synchrotron, GSI, early 90s) that were already used for the reaction multiplicity survey[22]. To limit the uncertainty associated with the deceleration of the beam nuclei, theanalysis was performed on a small NTE section. In principle, the decrease in energy canbe calculated and taken into account in the calculation of the invariant masses. Thus, thecovered energy range and the viewed NTE area can be radically extended. This developmentis in the near future. Note that the reconstruction of Be and the Hoyle state in the presented14pproach was successfully performed in the 400 MeV/nucleon C case [6]. [1] P.I. Zarubin, Lect. Notes in Phys., 875, Clusters in Nuclei, Volume 3. Springer Int. Publ., 51 (2013); DOI: 10.1007/978-3-319-01077-9 3.[2] D.A. Artemenkov, A. A. Zaitsev, P. I. Zarubin, Phys. Part. Nucl. 48 147(2017); DOI: 10.1134/S106377961701002[3] D.A. Artemenkov et al. , Phys. At. Nucl. 80, 1126 (2017); DOI:10.1134/S1063778817060047.[4] V.V. Belaga, A.A. Benjaza, V.V. Rusakova, D.A. Salomov, G.M. Chernov, Phys. At. Nucl. 58, 1905 (1995); arXiv:1109.0817.[5] N.P. Andreeva et al. , Phys. At. Nucl. 59, 102 (1996); arXiv:1109.3007.[6] D.A. Artemenkov et al. , Rad. Meas. 119, 199 (2018); DOI: 10.1016/j.radmeas.2018.11.005.[7] D.A. Artemenkov et al. , Springer Proc. Phys. 238, 137 (2020); DOI: 10.1007/978-3-030-32357-8 24.[8] D.A. Artemenkov et al. , Eur. Phys. J. A 56, 250 (2020); DOI: 10.1140/epja/s10050-020-00252-3[9] B. Borderie et al. , Phys. Lett. B 755, 475 (2016) ; DOI: 10.1016/j.physletb.2016.02.061.[10] K. Schmidt et al. , Phys. Rev. C 95, 054618 (2017); DOI: 10.1103/PhysRevC.95.054618.[11] M. Barbui et al. , Phys. Rev. C 98, 044601 (2018); DOI: 10.1103/PhysRevC.98.044601.[12] A. Tohsaki, H. Horiuchi, P. Schuck and G. R¨opke, Rev. Mod. Phys. 89, 011002 (2017); DOI: 10.1103/RevModPhys.89.011002.[13] T. Yamada and P. Schuck, Phys. Rev. C 69, 024309 (2004); DOI: 10.1103/PhysRevC.69.024309.[14] LM. Satarov, R.V. Poberezhnyuk, I. N. Mishustin, and H. Stoecker Phys. Rev. C 103, 024301 (2021); DOI: 10.1103/PhysRevC.103.024301.[15] N.P. Andreeva et al. , Sov. J. Nucl. Phys. 47 102 (1988); Yad. Fiz. 47 157 (1988) and DubnaJINR - 86-828.[16] A. El-Naghy et al. , J. Phys. G, 14 1125 (1988); DOI: 10.1088/0305-4616/14/8/015[17] M.I. Adamovich et al. , Phys. Rev. C 40, 66 (1989); DOI: 10.1103/PhysRevC.40.66[18] M.I. Adamovich et al. , Z. Phys. A 351, 311 (1995); DOI: 10.1007/BF01290914.[19] M.I. Adamovich et al. , Eur. Phys. J. A 5, 429 (1999); DOI: 10.1007/s100500050306.[20] The BECQUEREL Project http://becquerel.jinr.ru/movies/movies.html.[21] V.V. Glagolev et al. , Eur. Phys. J. A 11, 285 (2001); DOI: 10.1007/s100500170067.[22] S.A. Krasnov et al. , Czechoslovak J. of Phys. 46 531 (1996); DOI: 10.1007/BF01690674, Czechoslovak J. of Phys. 46 531 (1996); DOI: 10.1007/BF01690674