Unstable states in dissociation of relativistic nuclei. Recent findings and prospects of researches
D.A. Artemenkov, V. Bradnova, M.M. Chernyavsky, E. Firu, M. Haiduc, N.K. Kornegrutsa, A.I. Malakhov, E. Mitsova, A. Neagu, N.G. Peresadko, V.V. Rusakova, R. Stanoeva, A.A. Zaitsev, I.G. Zarubina, P.I. Zarubin
aa r X i v : . [ nu c l - e x ] A p r Unstable states in dissociation of relativistic nuclei.Recent findings and prospects of researches.
D.A. Artemenkov , V. Bradnova , M.M. Chernyavsky , E. Firu , M. Haiduc ,N.K. Kornegrutsa , A.I. Malakhov , E. Mitsova , A. Neagu , N.G. Peresadko ,V.V. Rusakova , R. Stanoeva , A.A. Zaitsev , , I.G. Zarubina , P.I. Zarubin , ∗ Joint Institute for Nuclear Research, Dubna, Russia Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia Institute of Space Science, Magurele, Romania Southwestern University, Blagoevgrad, Bulgaria
Abstract
The invariant mass method is used to identify the Be and B nuclei and Hoyle state formedin dissociation of relativistic nuclei in a nuclear track emulsion. It is shown that to identify theseextremely short-lived states in the case of the isotopes Be, B, C, C, C, and O, it issufficient to determine the invariant mass as a function of the angles in pairs and triples of Heand H fragments in the approximation of the conservation of momentum per nucleon of the parentnucleus. According to the criteria established in this way, the contribution of these three unstablestates was evaluated in the relativistic fragmentation of the Si and
Au nuclei.
PACS numbers: 21.60.Gx, 25.75.-q, 29.40.Rg ∗ Electronic address: e-mail: [email protected] . INTRODUCTION The fragmentation of relativistic nuclei observed in nuclear track emulsion (NTE) servesas a source of ensembles of the lightest nuclei of interest to modern nuclear physics and nu-clear astrophysics. NTE allows one to study production of such ensembles in full with recordangular resolution and identification He and H isotopes. The first studies of interactions ofrelativistic nuclei took place in the late 1940s when analyzing NTE layers irradiated in thestratosphere [1]. On this basis, to describe the cross section for the interaction of primarynuclei with the nuclei of the NTE composition, a geometric overlap formula was proposed,called the Bradt-Peters formula. At the same time, break-up events of nuclei of cosmic origincontaining groups of tracks of relativistic α particles concentrated in a narrow angular conewere discovered. Manifesting as a natural phenomenon they reflect the α -particle clusteringin the nuclear structure which is the research subject to date.In the 70s exposures of NTE stacks to light nuclei at the Synchrophasotron (JINR) andBevalac (LBL) began, and in the 90s - medium and heavy ones at AGS (BNL) and SPS(CERN). The manifestation of the nuclear structure in the cone of limiting fragmentationwas noted [2]. However, electronic experiments in this direction run into fundamental diffi-culties due to the quadratic drop down of ionization on the charges of the nuclei, extremelysmall angular divergence of relativistic fragments, and, often, an approximate coincidence inmagnetic rigidity with the beam nuclei. Therefore, the NTE method retains its uniquenessas the composition analysis tool in the relativistic fragmentation cone. In this aspect, theresults obtained in the 7090s by NTE and the preserved data files have not lost their rele-vance, and the irradiated layers can be used for in-depth studies. It can be hoped that theprogress of image analysis will intensify the use of the NTE method in the not too distantfuture.Since the early 2000s the NTE method is used at the JINR Nuclotron in the BEC-QUEREL experiment to study the clustering in light stable and radioactive nuclei in therelativistic approach (reviews [3–5]). Known and new structural features revealed of theisotopes , Be, , , B, , C, and , N are revealed in the dissociation channel probabil-ities. B decays are identified in the dissociation B, C, and C. This fact indicatesthat apparently, the absence of a stable state of the B nucleus does not prevent its virtualpresence in the structure of these nuclei. Their synthesis could occur through the B +2 resonance along the chain Be( He, p ) B( p , γ ) C(e + , ν ) B( p , γ ) C(e + , ν ) B. As a result, B is “imprinted” in the formed nuclei, which is manifested in relativistic dissociation. Inthe Be fragmentation, Be → α + 2 p decays are identified. However, the Be signal wasnot detected in the C dissociation.The identification of the relativistic decays of Be and B pointed out the possibility tosearch for triples of α particles in the Hoyle state (HS) in the relativistic dissociation C → α [6] and then O → α [7]. HS is the second (and first unbound) C excitation 0 +2 .So far, the synthesis through an unstable nucleus is recognized only in the case of 3 α → α Be → C(0 +2 or HS) → C. The history of the discovery and status of the study of thisshort-lived state of three real α -particles are presented in the review [8].The unstable nucleus Be is an indispensable product of the decay of HS and B. Thedecay energy of Be is 91.8 keV, and the width is 5.57 ± C excitations, the extremely small values of the energy above the 3 α threshold (378keV) and the decay width (9.3 ± Be nucleus [9]. The B ground state is 185.1 keV higher than the threshold Be + p and its width is 0.54 ± C nucleus. Essentially,in the 3 α -process, HS manifests itself as an unstable nucleus, albeit of an unusual nuclear-molecular nature. HS is manifested in nuclear reactions as the universal object similar to Be and B [10–12]. Be and HS are considered as the simplest states of the α -particle Bose-Einstein conden-sate [13, 14]. The 6 th excited state 0 +6 of the O nucleus at 15.1 MeV (or 660 keV over the4 α threshold) is considered as a 4 α -condensate. Its decay could go in the sequence O(0 +6 ) → C(0 +2 ) → Be(0 +2 ) → α . Research in this direction is actively underway [10, 11].However, the contribution of 4 α ensembles above 1 MeV is dominant. The possibility ofmore complex α -condensate states up to 10 α -particle one with the decay energy of about4.5 MeV above the 10 α -threshold is assumed which leads to unprecedented experimentalrequirements including parent nucleus energy growth.In addition, the B and HS nuclei can serve as bases in the nuclear molecules B p , B α and C(0 +2 ) p . Like the α -condensing states the unstable states with an odd number of protonscan meet excitations immediately above the corresponding thresholds having electromagneticdecay widths. The excitation of the N nucleus at 15.1 ± ± α p is only 600 keV, B α
250 keV, and HS p
160 keV. At the same time,these channels are open and can appear as narrowest quartets 3 α p . The ratio of the decayprobabilities on the B α and HS p channels is of interest.All these states can be studied uniformly in the peripheral interactions of relativisticnuclei. According to the widths, Be, B, and HS nuclei are real fragments in relativisticdissociation. The products of their decay appear along ranges from several thousand ( Beand HS) to several tens ( B) atomic sizes, i.e., over a time many orders of magnitude longerthan the time of the appearance of other fragments. Not being directly observable, theyshould manifest themselves as pairs and triples of He and H nuclei with the smallest openingangles due to smallest decay energy.Next, the results of identification of the unstable states in the relativistic dissociation ofseveral light nuclei will be summarized. Being interesting with respect to the structure ofthe studied nuclei, these observations indicate the universal nature of the unstable states,and, therefore, the possibility of their manifestation of dissociation of medium and heavynuclei where it becomes possible to search for more complex states of this type. As a firststep, an analysis of the available measurements in NTE exposed in BNL to Si nuclei at14.5 A GeV and
Au at 10.7 A GeV will be presented.
II. THE NTE METHOD IN BRIEF
The NTE method was almost completely developed in that initial period (sometimescalled “romantic”) when fundamental discoveries in high-energy physics were made in cosmicrays studies. These achievements are presented in the classical textbook by C.H. Powell,P.H. Fowler and D.H. Perkins [15] along with developed analysis methods and photographsof characteristic events. The last chapter devoted to relativistic nuclei in cosmic radiationcontains a description and photographs of the first observed events of their fragmentation.In subsequent irradiations in accelerator beams, the type and energy of the studied nucleibecame determined. In such a “narrow” aspect, the use of NTE remains unsurpassed eversince.To be exposed in a directed beam of accelerated nuclei, NTE layers having a thicknessof 550 µ m and sizes of 10 × (10-20) cm are assembled in a stack. During exposure a stack4urface is oriented parallel to a beam direction. Fragments of interacted nuclei are centeredin the cone sinθ fr = p fr / P , where p fr = 0.2 GeV/ c – a quantity characterizing the nucleonFermi momentum in the projectile nucleus, and P – its momentum per nucleon. Typically,fragment tracks remain long enough in one layer to fully define their directions. Observedtraces fragments of target nuclei are classified as b -particle ( α -particles and protons below 26MeV) and g -particles (protons of over 26 MeV). The most peripheral interactions referred tocoherent dissociation or “white” stars are not accompanied by fragmentation of the targetnuclei and produced mesons ( s -particles). Videos of characteristic interactions are available[16].The mass number assignment to H and He fragment tracks is possible by total momentumvalues derived from the average angle of Coulomb scattering. The use of this laboriousmethod is justified in special cases for a limited number of tracks. In the case of dissociationof stable nuclei, it is often sufficient to assume the correspondence of He – He and H – Hsince the established He and H contributions do not exceed 20%. This simplification isespecially true in extremely narrow Be and B decays.The invariant mass an ensemble of several particles of 4-momenta P i,k having total mass M is Q = M ∗ – M , where M ∗ is defined via the sum of all products, i.e. M ∗ = Σ( P i · P k ).Subtraction of the total mass of the particles M is a matter of convenience. In the regionof limiting fragmentation of nuclei when the initial energy exceeds 1 A GeV, a reasonableapproximation is taken for the conservation of the fragment of the initial momentum pernucleon P (or the projectile velocity) demonstrated in experiments with magnetic analysis(for example, [17] and recently [18]). Then, Q is a function of the angles between fragmentemission directions.The most accurate measurements of the angles are provided with a KSM-1 (Carl Zeiss,Jena) microscope when using the coordinate method. Measurements are carried out in aCartesian coordinate system. The NTE layer unfolds in such a way that the direction of theanalyzed primary trace coincides with the microscope stage axis OX with a deviation notworse 0.1-0.2 µ m per 1 mm of track length. Then the axis OX coincides with the primarytrack projection on the layer plane, and the axis OY on it is perpendicular to the primarytrack. The axis OZ is perpendicular to the layer plane. The measurements along OX andOY are made with horizontal micro-screws, and along the OZ, the depth of field micro-screwis used. Three coordinates are measured on the primary and secondary tracks at lengths5rom 1 to 4 mm in increments of 100 µ m, according to a linear approximation of which theplanar and dip angles are calculated. Details and illustrations of measurements on the planeof the layer and its depth have recently been published [6].In the direct method, inter-track angles in the layer plane are determined directly onthe graduated scale observed in the eyepiece with the best coincidence of the guide linewith the measured track in the field of view. The advantage is an increase in the speed ofmeasuring planar angles, especially in events with a large multiplicity of fragments. Thismethod is used to obtain inclusive angular distributions in survey studies. Its accuracy inthe fragmentation cone is somewhat worse compared to the coordinate method.The coordinate method accuracy reaches 10 − rad, and the direct one – 3.6 × − rad. Themeasurements are accompanied by errors due to distortion, false scattering, grain noise, tablenoise, focusing, thermal noise and readout noise. These errors have different nature, sta-tistical properties and magnitude. When measuring relative angles, the coordinate methodallows one to compensate for local distortions by simultaneously measuring the coordinatesof nearby tracks. However, a significant amount of unique data has been obtained with thedirect method. The combination of the methods allows one to accelerate the selection ofcandidates for decays and measure them with the best accuracy. III. RELATIVISTIC DECAYS OF BE In the fragmentation of relativistic nuclei in NTE intense tracks are observed often thatbranch into pairs of He tracks with minimal opening angles which are attributed Be decays.Obviously, this definition, which depends directly on the initial energy, is inconvenient whenanalyzing a variety of data. Universal Be identification by the 2 α -pair invariant mass Q α is the first “key” to the problem of the unstable nuclear states.The distribution Q α is shown in Fig.1 for the coherent dissociation C → α and O → α at 3.65 A GeV. In the C case, measurements of polar and azimuthal angles of α -particles in 316 “white” stars made in the 90s by the groups of G. M. Chernov (Tashkent)[19] and A. Sh. Gaitinov (Alma-Ata) and recently supplemented by the FIAN and JINRgroups are used. In the O case, similar data is available for 641 “white” stars [20]. Forthese events, Fig.1 presents distributions of invariant mass in the region Q α <
10 MeVof all 2 α -pair combinations N α normalized to the corresponding number of “white” stars6 ABLE I: Q α , MeV N α (%) n g + n b + n s = 0 N α (%) n g + n b + n s > Q α ≤ ±
6) 103 (34 ± < Q α ≤ ±
6) 40 (13 ± < Q α ≤ ±
4) 108 (36 ± Q α > ±
2) 51 (17 ± N ws . In the insert these data are shown in the range Q α < Be, however, due to the presenceof “tails” caused by reflections of (3-4) α excitations the selection condition Q α ( Be) is notsufficiently defined.The angular measurements of Be → α at 1.2 A GeV makes it possible to possibleto refine the selection condition of Be decays by the invariant mass Q α (review [3]). Thedistribution over Q α of 500 2 α -pairs including 198 “white” ones presented in Fig.2 indicatesthe limit Q α ( Be) < Q α equal to 0.6 and3 MeV. The first reflects the Be excitation at 2.43 MeV [21], and the second one the Be2 + state [9]. The condition Q α ( Be) takes into account the accepted approximation, thekinematic ellipse of Be decay, and the resolution of angular measurements. Its applicationallows us to determine the contribution of Be decays to the statistics of “white” stars equalto 45 ±
4% for C → α and 62 ±
3% for O → α . A similar selection of C → α at0.42 A GeV gives 53 ±
11% [6, 7].Table 1 gives the distribution over the characteristic Q α intervals of the number of α -pairsin “white” stars and containing additional tracks. The bulk of the statistics corresponds todissociation through Be 0 + and 2 + states in a close ratio which is especially pronounced inthe case of the sample with additional tracks definitely referring to neutron removal. Thisfact corresponds to the description of Be, in which the Be core is presented as an equalmixture of the 0 + and 2 + states [22, 23]. The question of whether the contribution of the2.43 MeV excitation reflects the presence of the component α + α + n or whether it is areaction product requires theoretical consideration.7 MeV α Q / . M e V w s N / α N FIG. 1: Distribution of the number of 2 α -pairs N α over invariant mass Q α in coherent dissociation C → α (solid line) and O → α (dashed line) at 3.65 A GeV; the inset, enlarged part Q α < N ws . , MeV α Q / . M e V α N FIG. 2: Distribution of the number of 2 α -pairs of N α over the invariant mass Q α in 500 disso-ciation events Be → α (dots) at 1.2 A GeV including 198 “white” stars (solid line); in inset,enlarged part Q α < V. RELATIVISTIC DECAYS OF B The next “key” in the unstable state studies is the B nucleus. When studying thecoherent dissociation of the C isotope at 1.2 A GeV, the 2He + 2H dissociation channelappeared as the leading one (review [3]). The statistics of the 2He + 2H quartets in itamounted to 186 or 82% of the observed “white” stars. The distribution over the invariantmass of 2 αp triples Q αp presented in Fig.3 indicates the number of decays N ( B) = 54satisfying the condition Q αp ( B) < ±
4% of the events 2He + 2H.According to the condition Q α ( Be) < Be decays are also identified in all these2 αp triples and only in them. This fact indicates the dominance of the decay sequence B → Be + p and Be → α . The abundant formation of B nuclei in the dissociation of Cindicates its important role as the structural basis of this isotope.The confident identification of Be and B based on the C nucleonic composition allowsone to turn to their contribution to the B and C dissociation. Angular measurementsare performed in 318 events B → A GeV among which 20 decays B → Be + p were identified that satisfy the condition Q αp ( B) < C → A GeV N ( B) = 22 (Fig.3) are found. Thus, inthe dissociation of C, B and C, the universal condition Q αp ( B) was established. Inaddition, when identifying B → Be + p decays, the criterion Q α ( Be) is confirmed underthe purest conditions.
V. RELATIVISTIC DECAYS OF THE HOYLE STATE
Using the angular measurements of the “white” stars C → α and O → α theapplication of the invariant mass method can be easily extended to the identification ofrelativistic decays of the Hoyle state. In the latter case, HS decays can manifest themselvesin the dissociation O → O ∗ → C ∗ ( → α ) + α . Both distributions over the invariantmass of 3 α -triples Q α presented in Fig.4 show similarities. Their main parts in the region Q α <
10 MeV, covering the C α -particle excitations up to the nucleon separation thresholdare described by the Rayleigh distribution with parameters σ Q α ( C) = 3.9 ± σ Q α ( O) = 3.8 ± Q α < MeV p α Q / . M e V p α N FIG. 3: Distribution of the number of 2 αp triples N αp over invariant mass Q αp ( < C → C → B → , MeV α Q / . M e V α N / . M e V w s N / FIG. 4: Distribution of number of 3 α -triples N α over invariant mass Q α in 316 “white” stars C → α (solid) and 641 “white” stars O → α (dashed) at 3.65 A GeV; in inset, enlarged part Q α < N ws . MeV α Q / . M e V α N / . M e V α N FIG. 5: Distributions over invariant mass Q α in 641 “white” stars O → α at 3.65 A GeV ofall 4 α -quartets (dots) and α HS events (solid line); smooth line - Rayleigh distribution; the inset,enlarged part Q α < , MeV α Q / . M e V e v N FIG. 6: Distribution of events O → Be over invariant mass Q α . HS signal is expected. The statistics in the peaks minus the background is N HS ( C) =37 with an average value h Q α i (RMS) = 417 ±
27 (165) keV and N HS ( O) = 139 with h Q α i (RMS) = 349 ± C → α is 11 ± O → α , it is 22 ± α combinations in O → α leads to a noticeable increase in the contributionof HS decays. At the same time, the ratio of the Be and HS yields shows an approximateconstancy N HS ( C)/ N Be ( C) = 0.26 ± N HS ( O)/ N Be ( O) = 0.35 ± α decay of the 0 +6 excitation ofthe O nucleus. The distribution of “white” O → α stars over the invariant mass of 4 α -quartets Q α presented in Fig.5 in the main part is described by the Rayleigh distributionwith the parameter σ Q α = (6.1 ± α -triple with Q α (HS) <
700 keV in a 4 α -event ( α HS) shifts the distribution over Q α tothe low-energy side, and the parameter to σ Q α = 4.5 ± Q α presented in the inset in Fig.5 indicates 9 events satisfying Q α < h Q α i (RMS) = 624 ±
84 (252) keV. Then, thecontribution of the decays O(0 +6 ) → α + HS is estimated to be 1.4 ± N ws ( O) and 7 ±
2% for normalization to N HS ( O).33 events O → Be are identified, which is 5 ±
1% of the “white” stars O → α .Then, the statistics of coherent dissociation for the O → Be and O → α HS channelshas a ratio of 0.22 ± Q α of the events O → Be shown in Fig.6 indicates two candidates O(0 +6 ) → Be in the region of Q α < O(0 +6 ) → Be and O(0 +6 ) → α HS is 0.22 ± α “precursor” is possible in the relativistic dissociation of nuclei. Atthe same time, increasing the statistics of events O → α in the traditional way can beconsidered exhausted. There remains the possibility of studying (3-4) α -ensembles in thefragmentation of heavier nuclei. VI. SEARCH FOR UNSTABLE STATES IN THE FRAGMENTATION OF SIAND
AU NUCLEI
EMU collaboration data are available on 1093 interactions of Si nuclei at 14.6 A GeV[24] and 1316 ones of
Au at 10.7 A GeV [25] which contains measurements of the anglesof emission of relativistic fragments. Then the search for events was conducted on theprimary tracks without sampling. The number of events with the multiplicity of relativistic12
MeV p Be Q / . M e V p B e N , MeV α Be Q / . M e V α B e N
024 , MeV α Q / . M e V α N , MeV α Q / . M e V α N a) b)c) d) FIG. 7: Distributions of 2 α , 2 αp , 3 α and 4 α combinations from events of fragmentation of Sinuclei at 14.6 A GeV over the invariant masses Q α (a), Q αp (b), Q α (c) and Q α (d) in the theirsmall value regions according to data for without sampling (points) and recent measurements inaccelerated search (added by solid line). α particles N α > N α > ◦ . Thus, the analysis in the regionof interest of small invariant masses is radically accelerated. In a relatively short time, 133events N α > Q α , Q αp , Q α and Q α in the small value regions obtained on the basis of these data arepresented in Fig.7 and 8. According to the criteria described above, the numbers of decays Be ( N Be ), B ( N B ) and HS ( N HS ) are determined by them.For the Si interactions, N Be = 52 is obtained; N B = 8 with h Q αp i (RMS) = 246 ± N HS = 9 with h Q α i (RMS) = 405 ±
53 (160) keV at N α = 3(3), 4(3), 5(2) and6(1). N HS / N Be = 0.17 ± N α >
2. 4 α quartets are absent up to Q α < N Be = 143; N B = 38 with h Q αp i (RMS)= 320 ±
16 (116) keV; N HS = 12 with h Q α i (RMS) = 435 ±
29 (106) keV at N α = 4(2),13 MeV p Be Q / . M e V p B e N α Be Q / . M e V α B e N α Q / . M e V α N α Q / . M e V α N a) b)c) d) FIG. 8: Distributions of 2 α , 2 αp , 3 α and 4 α combinations from events of fragmentation of Aunuclei at 10.7 A GeV over the invariant masses Q α (a), Q αp (b), Q α (c) and Q α (d) in the theirsmall value regions. N HS / N Be = 0.08 ± N α >
2. There is one 4 α quartet including HS with Q α = 1 MeV at N α = 16. In 11 events, Be pair formation isidentified.Under the assumption of a power-law dependence on the charge of the parent nucleusZ, which determines the production of α particles, the Be and B yields nuclei growsapproximately as Z . . Such a behavior is close to volume type dependence. The ratio ofthese yields is approximately the same. Statistics of 3 α triples N HS is small for estimates.It can be concluded that in the both cases, Be and B decays are identified and indicationsof HS formation is obtained, and in the Au case, one candidate for 4 α decay of the O(0 +6 )state was found. Due to the fact that the measurements were made without sampling, theyallow one to plan searches for the unstable states. A set of statistics of events N α > II. CONCLUSION
Preserved and recently obtained data on interactions of light relativistic nuclei in a nucleartrack emulsion allowed to establish the contribution in their dissociation of unstable nuclei Be and B and the Hoyle state as well as to assess the prospects of such research in relationto medium and heavy nuclei. These three states are uniformly identified by the invariantmasses calculated from the measured angles of emission of He and H fragments under theassumption of conservation of the primary momentum per nucleon.The Be selection in dissociation of the isotopes Be, B, C, and C is determinedby the restriction from above of the invariant mass of 2 α -pairs up to 0.2 MeV, and the B2 α p -triple mass up to 0.5 MeV. The certainty in the Be and B identification of becamethe basis for the search for decays from the Hoyle state in the dissociation C → α . Inthe latter case, the 3 α triple invariant mass is set to be limited to 0.7 MeV. The choice ofthese three conditions as “cut-offs from above” is sufficient because the decay energy valuesof these three states are noticeably lower than the nearest excitations with the same nucleoncompositions, and the reflections of more complex excitations is small for these nuclei.Being tested in the studies of the light nuclei, a similar selection is applicable to thedissociation of heavier nuclei to search for more complex states. In turn, the products of α -partial or proton decay of these states could be the Hoyle state or B, and then Be. Apossible decay variant is the occurrence of more than one state from this triple. In anycase, the initial stage of searches should be the selection of events containing relativistic Bedecays.Dozens of Be and B decays are identified in the relativistic fragmentation cone of Si andAu nuclei. At the same time, the small number of 3 α triples attributable to the decay of theHoyle which requires increasing statistics to the current Be equivalent. Then, the search forthe excited state O(0 +6 ) will become feasible. There are no fundamental problems alongthis path since there are a sufficient number of earlier exposed NTE layers, with transversescanning of which the required α ensemble statistics is achievable. This whole complexof problems, united by questions of identification of unstable states, is in the focus of theapplication in the BECQUEREL experiment in the present time.The results obtained make it possible to assess the prospects of the presented approach inmodern problems of nuclear physics. Among the most important of them is the verification15f theoretical ideas about matter arising from the combination of nucleons in clusters thatdo not have excited states up to the coupling threshold [26]. These are the lightest Henuclei, as well as deuterons, tritons and He nuclei. The evolution of the composition ofthe lightest isotopes is predicted at a nuclear density less than normal and a temperature ofseveral MeV. Passing through such a phase may be necessary on the way to the synthesisof heavy nuclei. A look at the dissociation of relativistic nuclei with time reversal indirectlyindicates the feasibility of such a transition.In the parent nucleus reference system, their energy distributions cover the temperaturerange 10 -10 K corresponding to phases from the red giant to the supernova. In the disso-ciation of heavy nuclei, an unprecedented variety of coherent ensembles of the lightest nucleiand nucleons is available. The observations of unstable states presented here substantiatethe possibility of studying cluster matter up to the lower limit of nuclear temperature anddensity. Identification of , , H and , He isotopes by multiple scattering allows expandingthe analysis of cluster states in the direction of the properties of the rarefied matter. Thetransverse momenta of fragments are determined from the emission angles, which makes itpossible to isolate the temperature components. The practical feasibility of a detailed studyof relativistic cluster jets can serve as a motivation for assessing the applicability of therelativistic approach to the problem of the existence of cold and rarefied nuclear matter.In the relativistic dissociation of heavy nuclei, the formation of light fragments occurswith a greater ratio of charge to mass number than that of the primary nucleus, causingthe appearance of associated neutrons that manifest themselves in secondary stars. Thefrequency of such “neutron” stars should increase with an increase in the number of lightestnuclei in the fragmentation cone. The average range of neutrons in NTE is about 32 cm.Reaching dozens, the multiplicity of neutrons in an event can be estimated by proportionallydecreasing the average path to the formation of the “neutron” stars at paths of the order ofseveral centimeters. The accuracy of determining the coordinates of their vertices makes itpossible to restore the angles of neutron emission, and, therefore, the transverse momentain the approximation of the conservation of the initial velocity. Thus, it is possible to studythe effects of the neutron “skin”. Estimation of the yield of neutrons, as well as deuteronsand tritons binding neutrons, can be of applied value.It remains unclear why the peripheral dissociation of the nuclei corresponds to a suffi-ciently large cross section and a wide distribution over the multiplicity of fragments. This16
FIG. 9: Diagram of break up of C nucleus into three particles by relativistic muon. phenomenon may be based on the transition of virtual photons exchanged between the beamand target nuclei into pairs of virtual mesons. A critical test can be the fragmentation of theNTE composition nuclei under the action of relativistic muons [26, 27]. The combinationpresented in Fig.9 provides long-range interaction with effective nuclear destruction and canbe extended to peripheral interactions of relativistic nuclei. It was established that frag-mentation of the target nuclei under the action of muons is most likely for the breakup C → α . In these events, the α particle energy and emission angles are determined from theranges making it possible to obtain distributions over the invariant mass, as well as over thetotal momentum of pairs and triples of α particles. It has been preliminary established thatthe distribution over the total transverse momentum of the α -particle triples correspondsnot to electromagnetic, but nuclear diffraction. Note that the 3 α splitting cross section isimportant for geophysics, since it will allow testing the hypothesis of helium generation inthe earth’s crust by cosmic muons.It is hoped that the rapid progress in image analysis will give a whole new dimension tothe use of the NTE method in the study of nuclear structure in the relativistic approach.The solution of the tasks set requires investment in modern automated microscopes and thereconstruction of NTE technology at a modern level. At the same time, such a developmentwill be based on the classical NTE method, the foundations of which were laid seven decadesago in cosmic ray physics. 17
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