The triple alpha process is studied using indirect methods. The beta decays of 12N and 12B are used to probe the triple alpha continuum of 12C. Different independent breakup channels are identified, consistently showing that the 10 MeV strength is dominated by a 0+ state interfering with the Hoyle state ghost. The 13.14 MeV region on the other hand is dominated by a 2+ state. Present: National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan MI-48824, USA.</p

Boutami, R

Dendooven, P

Diget, C A

Eronen, T

Fox, S P

Fulton, B R

Fynbo, H O U

García-Borge, M J

Jeppesen, H B

Jokinen, A

Jonson, B

Kankainen, A

Moore, I

Nieminen, A

Pedersen, S G

Pentillä, H

Pucknell, V F E

Riisager, K

Rinta-Antila, S

Tengblad, O

Wang, Y

Wilhelmsen, K

Äystö, J

Diget, Christian Aa

Borge, Maria J.G.

Boutami, Rafik

Dendooven, Peter

Eronen, Tommi

Fox, Simon P.

Fulton, Brian R.

Fynbo, Hans O.U.

Jeppesen, Henrik B.

Jokinen, Ari

Jonson, Björn

Kankainen, Anu

Moore, Iain

Nieminen, Arto

Pedersen, Solveig G.

Penttilä, Heikki

Pucknell, Victor F.E.

Riisager, Karsten

Rinta-Antila, Sami

Tengblad, Olof

Wang, Youbao

Wilhelmsen, Katarina

Äystö, Juha

Dissertations of the University of Groningen

Influences on the triple alpha process beyond the Hoyle state

CERN Document Server

PoS(NIC-IX)025Inuences on the triple alpha process beyond theHoyle stateChristian Aa. Diget∗a, Maria J. G. Borgeb, Rafik Boutamib, Peter Dendoovenc,Tommi Eronend, Simon P. Foxe, Brian R. Fultone, Hans O. U. Fynboa, Henrik B.Jeppesen f , Ari Jokinend, Björn Jonsong, Anu Kankainend, Iain Moored, ArtoNieminend, Solveig G. Pedersena, Heikki Penttiläd, Victor F. E. Pucknellh, KarstenRiisager f , Sami Rinta-Antilad, Olof Tengbladb, Youbao Wangd, KatarinaWilhelmseng, Juha Äystöda Institut for Fysik og Astronomi, Aarhus Universitet, DK-8000 Århus, Denmarkb Instituto Estructura de la Materia, CSIC, E-28006 Madrid, Spainc KVI, Zernikelaan 25, 9747 AA Groningen, Netherlandsd Department of Physics, University of Jyväskylä, FIN-40014 Jyväskylä, Finlande Department of Physics, University of York, Heslington, YO10 5DD, UKf PH Division, CERN, CH-1211 Geneva 23, Switzerlandg Fundamental Physics, Chalmers Univ. of Technology, S-41296 Göteborg, Swedenh CCLRC Daresbury Laboratory, Daresbury Warrington, Cheshire WA4 4AD, UKE-mail: diget@nscl.msu.eduThe triple alpha process is studied using indirect methods. The beta decays of 12N and 12B areused to probe the triple alpha continuum of 12C. Different independent breakup channels areidentified, consistently showing that the 10 MeV strength is dominated by a 0+ state interferingwith the Hoyle state ghost. The 13–14 MeV region on the other hand is dominated by a 2+ state.International Symposium on Nuclear Astrophysics - Nuclei in the Cosmos - IX25-30 June 2006CERN∗Speaker.†Present: National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MichiganMI-48824, USA.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(NIC-IX)025Influences on the triple alpha process beyond the Hoyle state Christian Aa. Diget1. The triple alpha process at resonanceThe triple alpha process is the process where three alpha particles combine to form 12C. Inthe most important temperature range from 0.1 GK to 2 GK the reaction rate is dominated by the8Be ground state and of the Hoyle state [1] at 7.654 MeV in 12C. At this temperature range bothresonances are within the Gamow window, and since they are both narrow, the narrow resonancecase applies when calculating the triple alpha reaction rate. Because of this, the analytical expres-sion for the rate is very simple: it is proportional to the radiative width of the Hoyle state and thepopulation of the state.2. The triple alpha reaction rate at extreme temperaturesIn the extreme temperature regions outside the 0.1–2 GK range, the resonant reaction throughthe Hoyle state does not necessarily dominate the reaction rate.1 The important contributions inthese regions are of course still natural parity states and the corresponding direct reactions. Forthe high temperature region the importance of the individual contributions is determined by theavailable states in 12C and 8Be within the Gamow window. The different possible contributions are0+ and 2+ strength in 8Be and 0+, 1−, 2+ and 3− strength in 12C. These contributions are all listedand discussed by Buchmann and Barnes [2].When taking states other than the 8Be ground state and the Hoyle state into account, we needto know not only the resonance energy and the radiative width, but the total width as well. Thisis because the resonances are in general not narrow. It is crucial for the reaction rate at hightemperatures which of the states are included and what we assume about these states. This isexactly the reason why the two commonly used rates NACRE [3] and Caughlan and Fowler [4]differ at the high temperatures. In the first a relatively narrow 2+ resonance at low energy (9MeV) is included whereas in the other it is not. This state has been described theoretically byP. Descouvemont and D. Baye [5], following the ideas of Morinaga [6] in describing the Hoylestate as a prolate triple alpha cluster, and building a rotational band on this state. The 2+ statein this energy region is seen as the first such rotational excitation. Such a state however remainsundetected experimentally.Here we will not discuss all possible contributions, but focus only on a few. Firstly we shouldbe aware that because the states are very close to the threshold, we must take special care asthreshold effects can be of importance. One such threshold effect is the appearance of ghosts [7].A ghost of a narrow state arises when the width of the state is heavily energy dependent. So forexample the shape of the 8Be ground state is not a simple Breit-Wigner distribution. In the highenergy tail of this distribution (around 1 MeV above the state) the width of the state becomes verybig, so at these energies the high energy tail of the 8Be ground state is blown up. This is a generalthreshold effect and does also apply for the Hoyle state.Having said this let us focus on the important possibility of a 2+ state in 12C just above the7.275 MeV triple alpha threshold, and the properties of such a state. There have been two recentexperimental identifications of such a low energy 2+ continuum state: Bency John et al. [8] suggest1Note that these temperatures are mainly relevant for scenarios where the triple alpha process does not set thetemperature.2PoS(NIC-IX)025Influences on the triple alpha process beyond the Hoyle state Christian Aa. Digeta 2+ contribution at 11.46(20) MeV with a width of 0.43(10) MeV probing the states by inelasticalpha scattering on 12C. Itoh et al. [9] in a similar experiment suggest a 1 MeV wide 2+ statearound 10.5 MeV. The main difficulty in these experiments is that the selectivity of this approachis limited, and therefore a lot of other states are populated in the same energy region.3. Beta decay experiment at IGISOLAs mentioned before alpha scattering experiments are limited by the population of manystates in the region of interest around 10 MeV. In order to avoid this background during the lastyears we have performed a series of experiments at the ISOLDE-CERN (Switzerland) and IGISOL(Jyväskylä, Finland) facilities to probe the triple alpha continuum. Here beta decays of 12N and12B have been used. These decays only populate 0+, 1+ and 2+ states in 12C due to the beta decayselection rules, which avoids most of the background from other resonances. Results of the firstexperiments have already been published, see [10 – 12].We will here present a new set of data, taken at the IGISOL separator in Jyväskylä [13] wherethese two isotopes are produced in the Ion Guide Isotope Separator. The 12B or 12N nuclei wereimplanted in a thin foil. The foil was surrounded by three Double Sided Silicon Strip Detectorsallowing us to detect all three alpha particles of the beta delayed triple alpha breakup. With thesetriple coincidences we are able to distinguish between and analyze data through the decay channels:8Be(0+gs); 8Be(0+ghost) and 8Be(2+) as shown in the following.4. Triple coincidence dataA scatter plot of the complete set of triple coincidence data (16k events) taken during about 5days of 12N beam time is shown in figure 1. Vertically we have the sum energy of the three alphaFigure 1: Triple coincidence data, beta delayed triple alpha breakup from 12N. Two channels: Breakupthrough 8Be ground state (left) and higher energies in 8Be.particles, or equivalently the 12C excitation energy. On the horizontal axis we have for any suchevent, the three individual alpha energies [14]. That is, one breakup event corresponds to threedots on a horizontal line. As can be seen to the right for the 12.7 MeV state, this can be three very3PoS(NIC-IX)025Influences on the triple alpha process beyond the Hoyle state Christian Aa. Digetdifferent energies. Or as seen to the left, one very high energy and two alpha particles sharing theremaining energy.This shows directly some information on the breakup channel, since a narrow state—in thiscase the 8Be ground state—determines the breakup directly by two body kinematics. The linesuperimposed on the data is exactly the line corresponding to the breakup through the 8Be groundstate just above the threshold, allowing us to look at these two breakup channels separately. Inthe right plot the situation is much more complicated, since it is not a clean sequential breakup.Furthermore this plot allows us to distinguish between the 0+ or 2+ states on the one hand and 1+states on the other, since a 1+ state cannot breakup through the ground state of 8Be because of itsunnatural parity, as is clearly seen for the 12.7 MeV 1+ state in 12C.5. The 8Be ground state channelLet us first look at the breakup through the 8Be ground state: The spectra are fitted to an R-Matrix model, as shown in figure 2. A three level model turns out to be essential to get a good fit.Figure 2: Measured spectra and R-Matrix fit for breakup through the 8Be ground state, where 0+ and 2+contributions to the fits are shown. 12N and 12B beta delayed breakup.The three states corresponding to these three levels are: A high energy 2+ state at 13.61(14) MeVof width 1.7(2) MeV dominating the upper energy region of the spectrum; a 0+ state at an energyof 11.47(16) MeV and of width 3.4(4) MeV; and the Hoyle state contributing with its ghost inthis energy region, making interference between the two 0+ states essential for understanding thespectrum.2 The two decay spectra are distorted by different beta decay phase space factors, and areinfluenced by the triple coincidence detection efficiency, however after correcting for these effectsthe two spectra are consistent and a combined fit of the two data sets is reasonable. Furthermore,the fit is consistent with our previously published data [11, 12] and is not consistent with a narrow2+ state at low energy.6. The 8Be excited state channelIn case of a broad exit channel as for the higher energy region of 8Be, the situation is a bitmore complicated. Here the efficiency dependens not only on the total energy of the three alphaparticles, but on the way the three share the total energy. Since an analytical form of this detectionefficiency is not available, it must be estimated using a Monte-Carlo simulation.2As in [12] the small contribution to the widths from the breakup through higher energies of 8Be is neglected.4PoS(NIC-IX)025Influences on the triple alpha process beyond the Hoyle state Christian Aa. DigetThe kinematics of the breakup are now determined not only by the energy in 12C but as wellby the line shape of the intermediate state of 8Be and of the angular momentum in the breakupsα +8 Be and α + α . In figure 3 the kinematics of the breakup at two different 12C energies areFigure 3: Dalitz plots for 12N data at two different sum energies. Simulated distributions for breakupthrough 8Be 2+ state and 8Be 0+ ghost. Two different possible spins (J) of the involved 12C state, twodifferent angular momenta (L) for the 8Be(2+)+ α intermediate system, where applicable. In addition tothe simulations shown here, J = 0,L = 2 and J = 2, L = 4 breakups through the 8Be (2+) state were as wellsimulated. These contributions however were easily excluded.shown. The Dalitz plots [15] shown here are in fact only one sixth of a full Dalitz plot and rangesfrom 0 to 1 on the horizontal axis and from −0.5 to 0.5 on the vertical axis. These axis values aredefined from the individual three alpha energies as:√3(E1−E3)/Esum and (2E2−E1−E3)/Esumrespectively. The plots are shown for the 12N data as well as for Monte-Carlo simulations aimedat reproducing the observed distributions from a symmetrized R-Matrix description of the breakup[10].The 8Be 0+ ghost channel is easily excluded for the high energy range as is the low energyJ = 2, L = 2 breakup through the 8Be 2+ state. For the remaining a statistical analysis must beapplied to discriminate between the different possibilities. With such an analysis, we can howeverconclude that at low energy the data is certainly dominated by breakup through the 8Be 0+ ghost,most likely from a 0+ state in 12C. At the high energies on the other hand, a 2+ state in 12C iscertainly dominating, and the breakup proceeds through the 8Be 2+ excited state, dominated by anorbital angular momentum of the first breakup of L = 2. These two conclusions are consistent withthose from the 8Be ground state breakup channel.7. Summary and outlookSummarizing, we have used beta decay of 12B and 12N to probe triple alpha continuum states.With the used detector set-up, we have been able to detect triple alpha breakups, not only throughthe 8Be ground state but through the ghost of this state as well as the excited 2+ state of 8Be.Also, we have been able to distinguish between the channels, even the latter two. From this wehave concluded that the 10 MeV strength in 12C is dominated by the interference between the 0+5PoS(NIC-IX)025Influences on the triple alpha process beyond the Hoyle state Christian Aa. DigetHoyle state and a wide 0+ state just above 11 MeV in 12C. Furthermore, the high energy region iscertainly dominated by a 2+ state in 12C.Regarding the possibility of a 2+ state, a narrow low energy (9 MeV) 2+ state is not consis-tent with the measured data. A wider state (1 MeV) at higher energies (e.g. 11 MeV) cannot becompletely excluded from the data, but it must contribute little to the total spectrum. Such a 2+state however would not dominate the triple alpha reaction rate at high temperatures, in contrast toa 2+ state at a lower energy. We will therefore conclude that for the high temperature range theCaughlan and Fowler rate should be recommended. At low temperatures however, we would stillrecommend use of either the NACRE rate or the rate that we published recently [11].It is worth noting that the data presented here were not sufficiently sensitive to the Hoyle statewidth to provide additional information on this. An intriguing outlook however is that if the 12Cspectrum (figure 2) had been measured with at least this precision at lower energies—if possibleall the way down to the Hoyle state—the fitting of such a spectrum could prove to be sensitive tothe Hoyle state width. This is because this width is not only determining the very narrow peak at7.654 MeV but as well determines the ghost of the state and through the interference with the 11.5MeV 0+ state influences the 12C spectrum. Such a spectrum has been measured recently and ispresented in these proceedings by S. G. Pedersen [16].References[1] F. Hoyle et al., A State in C12 predicted from Astrophysical Evidence, in proceedings of The AmericanPhysical Society, Physical Review 92 (1953) 1095.[2] L.R. Buchmann and C.A. Barnes, Nuclear reactions in stellar helium burning and later hydrostaticburning stages, Nuclear Physics A777 (2006) 254[3] C. Angulo et al., A Compilation of Charged-Particle Induced Thermonuclear Reaction Rates, NuclearPhysics A656 (1999) 3.[4] G.R. Caughlan and W.R. Fowler, Thermonuclear reaction rates, Atomic Data and Nuclear DataTables 40 (1988) 283.[5] P. Descouvemont and D. Baye, Microscopic theory of the 8Be(α ,γ)12C reaction in a three-clustermodel, Physical Review C36 (1987) 54.[6] H. Morinaga, Interpretation of Some of the Excited States of 4n Self-Conjugate Nuclei, PhysicalReview 101 (1956) 254.[7] F.C. Barker and P.B. Treacy, Nuclear levels near thresholds, Nuclear Physics, 38 (1962) 33.[8] Bency John et al., Isoscalar electric multipole strength in 12C, Physical Review C68 (2003) 014305.[9] M. Itoh et al., Study of the cluster state at Ex=10.3 MeV in 12C, Nuclear Physics A738 (2004) 268.[10] H.O.U. Fynbo et al., Clarification of the Three-Body Decay of 12C (12.71 MeV), Physical ReviewLetters 91 (2003) 082502.[11] H.O.U. Fynbo et al., Revised rates for the stellar triple-alpha process from measurement of 12Cnuclear resonances, Nature 433 (2005) 136.[12] C.Aa. Diget et al., Properties of the 12C 10 MeV state determined through β -decay, Nuclear PhysicsA760 (2005) 3.6PoS(NIC-IX)025Influences on the triple alpha process beyond the Hoyle state Christian Aa. Diget[13] J. Ärje et al., The ion guide isotope separator on-line, IGISOL, Nuclear Instruments and MethodsA247 (1986) 431[14] H.O.U. Fynbo et al., The β2p decay mechanism of 31Ar, Nuclear Physics A677 (2000) 38.[15] R.H. Dalitz, On the analysis of τ-meson data and the nature of the τ-meson, The PhilosophicalMagazine 44 (1953) 1068.[16] S.G. Pedersen, β -decay studies of states in 12C, in proceedings of International Symposium onNuclear Astrophysics - Nuclei in the Cosmos - IX PoS(NIC-IX)244.7

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Influences on the triple alpha process beyond the Hoyle state

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ARTS repository - University of Groningen