The Hoyle state in relativistic dissociation of light nuclei
aa r X i v : . [ nu c l - e x ] J u l The Hoyle state in relativistic dissociation of light nuclei ∗ A.A. Zaitsev
1, 2 and P.I. Zarubin
1, 2, ∗ Joint Institute for Nuclear Research (JINR), Dubna, Russia Lebedev Physical Institute, Russian Academy of science, Moscow, Russia
Abstract
In the context of the search for triples of relativistic α -particles in the Hoyle state, the analysisof available data on the dissociation of the nuclei C, O and Ne in the nuclear emulsion wascarried out. The Hoyle state is identified by the invariant mass calculated from pair angles ofexpansion in α -triples in the approximation of the conservation of the momentum per nucleon ofthe parent nucleus. The contribution of the Hoyle state to the dissociation of C → α is 11%. Inthe case of the coherent dissociation of O → α it reaches 22% when the portion of the channel O → Be is equal to 5%.
PACS numbers: 21.60.Gx, 25.75.-q, 29.40.RgKeywords: Hoyle state, relativistic nuclei, emulsion, invariant mass ∗ Submitted to Physics of Atomic Nuclei ∗ Electronic address: [email protected] . INTRODUCTION Irradiations of stacks of nuclear track emulsion (NTE) in beams of light relativistic nucleiwere performed in the 70-80s at the JINR Synchrophasotron and Bevalac (LBL, USA). Theuse of NTE to study the interactions of the gold and lead nuclei continued in the 80-90sat the AGS (BNL, USA) and SPS (CERN) accelerators. Observations in NTE of tracks ofcharged particles in a full solid angle and practically without a threshold made it possibleto determine the contours of a complex picture of the collision of relativistic nuclei. Specialattention was paid to central nuclear collisions. The subsequent development of this areaon the basis of large-scale electronic experiments is widely known. At the same time, theresults obtained by the NTE method as well as the irradiated layers themselves and the fileswith measurement results retain their uniqueness with respect to the structure of nuclearfragmentation.In peripheral interactions of nuclei, in which the charge of the incident nucleus is dis-tributed between its fragments, the individual features of the incident nuclei are reflected.They are observed in NTE as often and completely as central collisions, so there is a fun-damental possibility in the cone of relativistic fragmentation to study the nuclear structure.However, in this aspect, the use of traditional spectrometers was extremely limited. Thedifficulties encountered are of fundamental nature. They are caused by a dramatic decreasein the ionization of relativistic fragments in an extremely narrow fragmentation cone, and,often, by an approximate coincidence in the magnetic rigidity of fragments and beam nuclei.For these reasons, measurements were carried out with the registration of single relativisticfragments with charges close to the charge of the studied nucleus.The pause in obtaining data on the ”fine“ structure of relativistic fragmentation motivatedfurther NTE irradiations in beams of light nuclei of the JINR Nuclotron including radioactiveones. Since the early 2000s, the BECQUEREL experiment aimed at systematic study ofperipheral interactions of relativistic nuclei by the NTE method has been started. Theanalysis of peripheral interactions in longitudinally irradiated NTE layers allowed one tostudy cluster features of a whole family of light nuclei, including neutron-deficient ones, in asingle approach (reviews [1, 2]). The possibility of analyzing such ensembles is a prerequisitefor testing the concepts developed in nuclear physics and nuclear astrophysics. The role ofunstable cores Be and B in their structure was established. In the dissociation of the C2ucleus, an indication of the B p resonance at energy of about 4 MeV was found.The decisive factor for reconstructing the decays of Be and B nuclei among fragmentsof a relativistic projectile nucleus is the best spatial resolution (about 0.5 µ m) provided bythe NTE technique. Decays are identified by the invariant mass M ∗ , determined by thesum of all products of 4-momenta P i of relativistic fragments He and H. Subtraction of thesum of masses of fragments Q = M ∗ − M is a matter of convenience. The components P i of are determined from the angles of emission of He and H fragments assuming that theymaintain momentum per nucleon of the projectile (or its velocity). Then the invariant massof the considered ensemble of fragments is determined by the angles of their expansion. B → Be p decays can be considered as a pure source of Be nuclei. Their analysis allowed usto confirm the criterion Q α < Be which takes into accountthe adopted approximation and resolution of the method [3].The successful reconstruction of the Be and B decays allows one to take the next stepto search in relativistic dissociation C → α for triples of α -particles in the Hoyle state(HS). This state is the second and first unbound excitation 0 +2 of the C nucleus. Thesignificance of this short-lived state of three real α -particles and the status of its researchare presented in the review [4]. The HS features such as isolation in the initial part of the Cexcitation spectrum, lowest decay energy and its narrow width (378 keV and 8.5 eV) indicateits similarity with the 2 α -particle nucleus Be (91 keV and 5.6 eV). Be is an indispensableproduct of HS decays. It can be assumed that HS is not limited to C excitation but it canalso appear as a 3 α -partial analog of Be in relativistic fragmentation of heavier nuclei.Interest in HS is motivated by the concept of α -partial Bose-Einstein condensate (review[5]), the status of which is presented in [6]. As the simplest forms of such a condensatethe ground state of the unstable Be nucleus and, after it, HS are suggested. Continuingthe Be and HS branches, it is assumed that the condensate 4 α state is the 6th excitedstate 0 +6 of the O nucleus, located 700 keV above the 4 α threshold. Then, the condensatedecomposition could go in the sequence O(0 +6 ) → C(0 +2 ) → Be(0 +2 ) → α .The fact of HS generation may reflect both the presence of three weakly bound α -particlesin the 0S-state in the parent nucleus as well as arise through the excited fragment C ∗ ( → α )or be a product of the interaction of α -particles in the final state. These options require the-oretical consideration. Experimentally, the general question is as follows. Can the fragmen-tation of relativistic nuclei serve as a “factory” for the generation of ensembles of α -particles3f increasing multiplicity at the lower limit of nuclear temperature? Further, in the contextof the HS problem, distributions of invariant mass Q (2-4) α of α -partial pairs, triples andquartets born in the dissociation of nuclei C, O and Ne will be presented.
II. DISSOCIATION OF C NUCLEI
For the C nucleus at an energy of 3.65 A GeV there are measurements of emissionangles of α -particles made in the groups of G. M. Chernov (Tashkent) [7] at 72 and A. Sh.Gaitinov ( Alma-Ata) in 114 events coherent dissociation of C → α , not accompaniedby fragments of target nuclei or generated mesons, which are briefly referred to as “white”stars. The search for such events was carried out in an accelerated manner along transversestrips of NTE layers. Thus, the contribution of Be → α decays by the smallest anglesof scattering of α -particles was determined [7]. Figure 1 shows the distribution over theinvariant mass of α -pairs Q α . In the Q α < Bedecays is 17 ± α -stars, including 130 “white”, have been added. In addition, there are NTE layers irradiatedin the C beam of the booster of the Institute of High Energy Physics (Protvino) at 420 A MeV, which allow using an approach based on a variable invariant mass [5]. In the lattercase, emission angles are measured in 86 3 α -events found, including 36 “white” stars.The distribution Q α for all 510 stars is shown in Fig. 2. The region Q α <
10 MeVcovering the C α -particle excitations below the nucleon separation thresholds is describedby the Rayleigh distribution with the parameter σ Q (3 α ) = (3.9 ± Q α < A GeV contributed to this peak the average value h Q α i (RMS) is 397 ±
26 (166) keV, andat 420 A MeV, 346 ±
28 (85) keV, respectively. According to the condition Q α < A GeV can be attributed to HS decays, and 9 at 420 A MeV (outof 86) including 5 “white” stars (out of 36). As a result, the contribution of HS decays to C → α dissociation is 10 ± IG. 1: Distribution over invariant mass Q α of α -pairs in coherent dissociation C → α at 3.65 A GeV (hatched); in the inset, part of the distribution Q α < Q α of α -triples in the dissociation C → α at 3.65 A GeV (shaded) and 420 A MeV (added by a dotted line); line - Rayleigh distribution.
III. COHERENT DISSOCIATION OF O NUCLEI
The distribution Q α for all 2 α combinations in 641 “white” star O → α according tothe data [8] is presented in Fig. 3. As in the case C → α , for Q α < Be decays which manifests itself in 15 ±
1% of events.HS decays can manifest themselves in the dissociation O → C ∗ ( → α ) + α . Figure 4shows the Q α distribution of all 3 α combinations. As in the C case, its main part with Q α MeV α Q FIG. 3: Distribution of all α -pairs in “white” stars O → α at 3.65 A GeV over the invariantmass Q α ; in the inset, part of the distribution Q α < <
10 MeV is described by the Rayleigh distribution with the parameter σ ( Q α ) = (3.8 ± Q α <
700 keV. The condition Q α <
200 keV meaning at leastone Be decay in a 4 α event does not affect the statistics in this Q α range. The contributionto the peak of the combinatorial background estimated at 8% is excluded. The remaining139 events have an average value of h Q α i = (349 ±
14) keV corresponding to HS and RMS174 keV. In 9 events of them more than one 3 α -combination corresponds to the condition Q α <
700 keV. In sum, the contribution of HS decays to the coherent dissociation of O → α is 22 ± α -triples of HS over the total transverse momentum P T(HS) (Fig. 5) is described by the Rayleigh distribution with the parameter σ P T (HS) =(191 ±
8) MeV/ c the value of which is characteristic for nuclear diffraction.HS can arise as a product of the α decay of the excited state 0 +6 of the O nucleus [5, 6](by analogy with the decay of HS into Be + α ). In the 641 “white” star, the full distributionof α -quartets over Q α (Fig. 6) is described mainly by the Rayleigh distribution with theparameter σ ( Q α ) = (6.1 ± α -event ( α HS)of at least one α -triple with Q α <
700 keV changes toward the low-energy direction the Q α distribution (Fig. 6) and the value of the parameter σ Q α = (4.5 α α will be correlated in direction.Figure 7 shows the distribution of α HS over Q α and the azimuth angle ε ( α HS) between theHS directions and the α particle. It is worth noting that Q α and ε ( α HS) are functionally6
MeV α Q N FIG. 4: Distribution of all α -triples in “white” stars O → α at 3.65 A GeV over invariant mass Q α ; line - Rayleigh distribution. c (HS), MeV/ T P N FIG. 5: Distribution of α -triples Q α < O → α at 3.65 A GeVover total transverse momentum P T (HS); line - Rayleigh distribution. related. The condition ε ( α HS) < ◦ identifies 9 events that satisfy Q α < h Q α i = (624 ±
84) keV with RMS 252 keV (Fig. 6). On their basis, theassessment of the contribution of the 0 +6 state is 7 ± O → α , 33 events were selected, in which two Be fragments( Q α < ε (2 Be)show anti-correlation (Fig. 8) which indicates the binary formation of these fragments. In7
MeV α Q N FIG. 6: Distribution over invariant mass Q α of “white” stars O → α at 3.65 A GeV of all4 α -quartets (points), α HS events (dotted lines) and α HS events ε ( α HS) < ◦ (hatched); line -Rayleigh distribution. , MeV α Q H S ) , d e g α ( ε FIG. 7: Distribution of events O → α HS over invariant mass Q α and azimuth angle ε ( α HS).
31 events 2 Be there are no triples of α -particles that satisfy the condition HS ( Q α < O → Be channel is equal to 5 ± P T(2 Be) is describedby the Rayleigh distribution with the parameter σ PT (2 Be) = (161 ±
2) MeV/ c . Figure 9shows the distribution over Q α for 2 Be events for which the Rayleigh parameter is (4.3 ± O → α HS and O → Be has a ratio8 e), deg (2 ε ev N FIG. 8: Distribution of events O → Be over azimuth angle ε (2 Be) between Be fragments. , MeV α Q N FIG. 9: Distribution of events O → Be over invariant mass Q α ; line - Rayleigh distribution. ± IV. FRAGMENTATION NE The results of measurements of 4301 interaction of Ne nuclei at energy of 3.22 A GeVare available for analysis. The search for events was performed by scanning tracks of primarynuclei (that is, without sampling) providing an overview of the Ne fragmentation topology[9]. This set includes measurements of the angles of emission of relativistic α -particles for 5282 α , 243 3 α , 80 4 α , and 10 5 α events which allows analysis in variables of the invariant mass Q (2-5) α . It is worth noting that measurements of the angles of scattering of the fragments9 MeV α Q FIG. 10: Distribution over invariant mass Q α of all α -pairs in the fragmentation channels Ne → (2-5) α at 3.22 A GeV. , MeV α Q FIG. 11: Distribution over invariant mass Q α of all α -triples in 4 α channel in fragmentation of Ne nuclei at 3.22 A GeV; line - Rayleigh distribution. were made by the method that gives worse relative accuracy than in the cases presentedabove. Nevertheless, the Q α distribution allows one to isolate the Be signal in the region Q α < Q α for channel 4 α . In the region Q α < h Q α i = (557 ±
51) keV and RMS 195 keV which is close to the HSvalue. The values of the Rayleigh distribution parameters σ Q α in approximations of Q α distributions for channels 3 α , 4 α and 5 α in the region up to 10 MeV are (4.0 ± MeV α Q N FIG. 12: Distribution of all α -quartets in 4 α and 5 α channels over invariant mass Q α in thefragmentation of Ne nuclei at 3.22 A GeV 5 α (marked with hatching). ± ± C and O. In the Q α < α , 4 α and 5 α channels is 3 (1.2 ± ± α -channel there is a significant indication of HS. The shift h Q α i compared with casesof C and O requires better measurement accuracy.The distributions over Q α in channels 4 α and 5 α are presented in Figure 12. Its mainpart limited by Q α <
10 MeV is described by the Rayleigh distribution with the parameter σ Q α = (4.9 ± α channel there is a single event with the value Q α =791 keV in which all α -triples meet the condition HS Q α < α -quartet cancorrespond to the decay of the O 0 +6 state. Obvious interest is the increase in statisticsin channels 4 α and 5 α . An additional possibility is provided by the existing NTE layersirradiated with Si nuclei at 3.65 A GeV.
CONCLUSION
Based on the data obtained in the 1980s 1990s on dissociation of relativistic C, Oand Ne nuclei in the nuclear track emulsion, as well as of their modern complement in thecase of C a search for triples of relativistic α -particles in the Hoyle state was performed.Determining the invariant mass of the α -particle triples by their emission angles in the11pproximation of preserving the velocity of the parent nucleus ensures sufficient accuracy inidentifying the HS against the background of higher 3 α excitations of the C nucleus. Thecontribution of HS decays to C → α dissociation is 11 ± O → α , the contribution of HS decays is 22 ± α -particles leads to a noticeableincrease in the contribution of HS to the dissociation of O → α . An analysis of theinvariant masses of α -quartets gives an estimate of the contribution of the decays of thestate O 0 +6 to 7 ± α + HS dominates in the HSformation.Analysis of fragmentation of the Ne nucleus revealed the HS formation only in the 4 α channel for which the share of events with HS was 15 ± α -ensembles byaccelerating scanning over the area of nuclear NTE layers.In general, the HS feature as a universal and sufficiently long-lived object similar tothe unstable Be nucleus is confirmed. The closest source for verifying the HS universalityis peripheral dissociation of the N nucleus in which the 3He + H channel leads, with acontribution of Be decays of about 25% [10]. Analysis of the NTE layers irradiated in theearly 2000s with relativistic N nuclei was resumed in the context of the HS problem. Asimilar analysis will be carried out in the NTE layers which were irradiated by relativisticnuclei Ne and Si at the JINR Synchrophasotron in the late 80s and used for overviewanalysis. Despite the past decades this experimental material has retained the necessaryquality.
ACKNOWLEDGMENTS
The presented material is based on the analysis of experimental material and data ob-tained since the beginning of the 70s and up to the present. In itself, this fact demonstratesthe solidity of the method of the nuclear track emulsion and its ability to evolve. It is impos-sible to list all the participants in the emulsion cooperation at the JINR Synchrophasotronin analyzing the interactions of relativistic nuclei. Behind this entire scientific heritage therewas enormous work and the joy of being pioneers in. Therefore, we hope that citing pub-lications and the further use of materials and methods are not only useful in research but12lso serve to preserve the memory of the era of the emergence of research on relativisticnuclear physics. The authors are especially grateful to A.I. Lvov and E.P. Cherenkova forthe opportunity to present the results of the research at the Cherenkov Readings at FIAN.Held annually, this event was in 2019 already the 12th in a row. [1] Zarubin P.I. // Lect. Notes in Physics 2014, V. 875, Clusters in Nuclei, 3, P. 51, Springer Int.Publ.; arXiv:1309.4881.[2] Artemenkov D.A., Zaitsev A.A., Zarubin P.I. // Phys. Part. Nucl. 2017, V. 48, P. 147; DOI:10.1134/S1063779617010026 ; arXiv:1607.08020.[3] Artemenkov D.A., Bradnova V., Britvich G.I., Firu E., Haiduc M., Kalinin V.A., KharlamovS.P., Kornegrutsa N.K., Kostin M.Yu., Maksimov A.V., Mitseva E., Neagu A., Pikalov V.A.,Polkovnikov M.K., Rusakova V.V., Stanoeva R., Zaitseva, A.A., Zarubin P.I., Zarubina I.G.// Rad. Meas. 2018, V. 119, P. 199; DOI: 10.1016/j.radmeas.2018.11.005; arXiv:1812.09096.[4] Freer M., Fynbo H.O.U. // Prog, in Part. and Nucl. Phys. 2014, V. 78, P. 1; DOI:10.1016/j.ppnp.2014.06.001.[5] Tohsaki A., Horiuchi H., Schuck P. and Ropke G. // Rev. Mod. Phys. 2017, V. 89, 011002;DOI: 10.1103/RevModPhys.89.011002.[6] Schuck P. // arXiv:1811.11580.[7] Belaga V.V., Benjaza A.A., Rusakova V.V., Salomov D.A., Chernov G.M., Phys. Atom. Nucl.1995, V. 58, P. 1905; DOI: 10.1063/7788-1905(95)5811-5; arXiv:1109.0817.[8] Andreeva N.P. et al. Phys. Atom. Nucl. 1996, V. 59, P. 102; DOI: 10.1063/S5901-0102(96)7788-0; arXiv:1109.3007.[9] El-Naghy A. et al. J. Phys. G: Nucl. Phys. 1988, V. 14, P. 1125; DOI:10.1088/0305-4616/14/8/015.[10] Shchedrina T.V. et al. Phys. Atom. Nucl. 2007, V. 70, P. 1230; DOI:10.1134/S1063778807070149; arXiv:nucl-ex/0605022.[1] Zarubin P.I. // Lect. Notes in Physics 2014, V. 875, Clusters in Nuclei, 3, P. 51, Springer Int.Publ.; arXiv:1309.4881.[2] Artemenkov D.A., Zaitsev A.A., Zarubin P.I. // Phys. Part. Nucl. 2017, V. 48, P. 147; DOI:10.1134/S1063779617010026 ; arXiv:1607.08020.[3] Artemenkov D.A., Bradnova V., Britvich G.I., Firu E., Haiduc M., Kalinin V.A., KharlamovS.P., Kornegrutsa N.K., Kostin M.Yu., Maksimov A.V., Mitseva E., Neagu A., Pikalov V.A.,Polkovnikov M.K., Rusakova V.V., Stanoeva R., Zaitseva, A.A., Zarubin P.I., Zarubina I.G.// Rad. Meas. 2018, V. 119, P. 199; DOI: 10.1016/j.radmeas.2018.11.005; arXiv:1812.09096.[4] Freer M., Fynbo H.O.U. // Prog, in Part. and Nucl. Phys. 2014, V. 78, P. 1; DOI:10.1016/j.ppnp.2014.06.001.[5] Tohsaki A., Horiuchi H., Schuck P. and Ropke G. // Rev. Mod. Phys. 2017, V. 89, 011002;DOI: 10.1103/RevModPhys.89.011002.[6] Schuck P. // arXiv:1811.11580.[7] Belaga V.V., Benjaza A.A., Rusakova V.V., Salomov D.A., Chernov G.M., Phys. Atom. Nucl.1995, V. 58, P. 1905; DOI: 10.1063/7788-1905(95)5811-5; arXiv:1109.0817.[8] Andreeva N.P. et al. Phys. Atom. Nucl. 1996, V. 59, P. 102; DOI: 10.1063/S5901-0102(96)7788-0; arXiv:1109.3007.[9] El-Naghy A. et al. J. Phys. G: Nucl. Phys. 1988, V. 14, P. 1125; DOI:10.1088/0305-4616/14/8/015.[10] Shchedrina T.V. et al. Phys. Atom. Nucl. 2007, V. 70, P. 1230; DOI:10.1134/S1063778807070149; arXiv:nucl-ex/0605022.