Oliver S. Kirsebom. Debrecen, 27 Oct 2012

Transcription

1 12 C and the triple-α reaction rate Oliver S. Kirsebom Debrecen, 27 Oct 2012 Aarhus University, Denmark & TRIUMF, Canada

2 Introduction

3 Astrophysical helium burning Red giant stars, T = GK Three reactions: (i) α + α + α 12 C (ii) α + 12 C 16 O (iii) α + 16 O 20 Ne Terminates with (iii) owing to lack of resonance in 20 Ne (i) known with 10% precision, whereas 5% desired (ii) known with 30% precision, whereas 10% desired

4 The triple-α reaction Hydrosta)c helium burning in red giant stars T = GK kt = kev F. Hoyle α 0 + α kev 92 kev 4 He 8 Be 12 C γ, e + e

5 Temperature regimes of the triple-α reaction T (GK) Burning Reaction mechanism Astrophysical sites hydrostatic s-wave resonances red giant stars < 0.1 hydrostatic direct three-body > 2 explosive higher-lying resonances early massive stars (to ignite CNO cycle) shock fronts of core-collapse SN X-ray bursts helium flashes during AGB phase

6 Reaction-rate formula (T = GK) R Γ α 0 Γ rad Γ ( T 3/2 exp Q ) kt Q = 92 kev kev = 380 kev Γ α0 = partial width for α decay to the ground state of 8 Be Γ rad = radiative width Γ = total width = Γ α + Γ rad Γ α (Γ rad /Γ = ) Γ α0 Γ rad Γ Γ α 0 Γ rad Γ α

7 Reaction-rate formula (T = GK) R Γ α 0 Γ rad Γ ( T 3/2 exp Q ) kt Q = 92 kev kev = 380 kev Γ α0 = partial width for α decay to the ground state of 8 Be Γ rad = radiative width Γ = total width = Γ α + Γ rad Γ α (Γ rad /Γ = ) Γ α0 Γ rad Γ Γ α 0 Γ rad Γ α = Γ rad An often overlooked assumption: Γ α = Γ α0

8 Uncertainty estimate Radiative width Γ rad = Γ γ + Γ π = Γ γ + Γ π Γ Γ Γ π Γ π

9 Uncertainty estimate Radiative width Γ rad = Γ γ + Γ π = Γ γ + Γ π Γ Γ Γ π Γ π Error budget Q = ± 0.20 kev (1.2%) [1] (Γ γ + Γ π )/Γ = (4.12 ± 0.11) 10 4 (2.7%) [2] Γ π /Γ = (6.8 ± 0.7) 10 6 (10%) [3] Γ π = 62.3 ± 2.0 µev (3.2%) [4] Experiments underway to reduce (Γ π /Γ) to 5% [1] Nolen and Austin, PRC 13 (1976) 1773 [2] Markham, Austin and Shahabuddin, NPA 270 (1976) 489 [3] Alburger, PRC 16 (1977) 2394 [4] Chernykh et al., PRL 105 (2010)

10 Direct breakup channels

11 Direct breakup channels Sequential and direct (non-sequential) breakup widths: Γ α = Γ α0 + Γ direct

12 Direct breakup channels Sequential and direct (non-sequential) breakup widths: Γ α = Γ α0 + Γ direct Upper limit due to Freer et al. (1996): Γ direct /Γ α < 0.04

13 Direct breakup channels Sequential and direct (non-sequential) breakup widths: Γ α = Γ α0 + Γ direct Upper limit due to Freer et al. (1996): Γ direct /Γ α < 0.04 Non-zero value due to Raduta et al. (2011): Γ direct /Γ α = 0.17(5)

14 Direct breakup channels SD = Sequential decay via the ground state of 8 Be DDE = Three α particle with equal energies DDL = One α particle at rest and the other two with equal energies BG = Background ( 40%) Ad.R. Raduta et al. / Physics Letters B 705 (2011) centage. Results of simulations in wh are plotted with dashed lines for the s may notice, they correspond to a wor particularly a sizeable underestimation events. In all cases, the amount of bac Finally we can now fully understan SD = 83.0 ± 5.0 % panel (c) of the figure presents also DDE = 7.5 Y corr ± (RMS)/Y 4.0 % uncorr (RMS) (thick lines). DDL = 9.5 region ± 4.0 around % E α = kev and corresponds to the sharing of the av Raduta ettwo al., α s PLBof705 8 Be (2011) and the65 remaining E α 130 kev and RMS = 90 kev cor of a linear chain. Though the CF show sitivity to the event selection or even pattern remains stable. Particularly th tematically shifted by about 20 kev w As early mentioned, a small shift of th tributed to the finite size of detection. 5. (Color online.) RMS spectra of experimental (solid points) and best χ 2 simu-

15 Astrophysical implications T = GK (s-wave resonance regime) rate reduced by 17% T < 0.1 GK (direct regime) rate enhanced by several orders of magnitude!

16 The experiment

17 The experiment 3 He + 11 B d + 12 C d + α + α + α (E beam = 8.5 MeV, Q = 3.2 MeV) Aarhus Madrid Göteborg York M. Alcorta et al., NIM A 605 (2009) 318

18 Data analysis and results

19 12 C excitation-energy spectrum Events / 20 kev , , , , , 2 (a) E x (MeV). units) 1

20 Dalitz plot ε 1 ρ ϕ ε 3 ε 2

21 Experimental data 0 max SD DDL DDE

22 Radial projection of the Dalitz plot 400 dn/dρ EXP DDE (7.5%) DDL (9.5%) SD (100%) DDΦ (100%) ρ

23 Upper limits At 95% confidence level: SD = 1 DDE < DDL < DDΦ < Kirsebom et al., PRL 180 (2012)

24 Upper limits At 95% confidence level: SD = 1 DDE < DDL < DDΦ < Kirsebom et al., PRL 180 (2012) SD = 1 DDE < DDL <... DDΦ < Manfredi et al., PRC 85 (2012)

25 Link to structure?

26 Structure of the Hoyle state l illustration Raduta et al. postulates connection between 12 C structure and 3α Dalitz-plot distribution DDE α-condensate structure DDL linear-chain structure Dalitz-plot distribution provides sensitive test of 12 C structure models if the latter is combined with a sophisticated 3α-breakup model

27 Three-body (α-cluster model) hyperspherical variables {ρ, α, Ω x, Ω y } expand wave function in hyperspherical harmonics Ω = {α, Ω x, Ω y } Ψ JM = ρ 5/2 n f n (ρ) Φ JM n (ρ, Ω) solve Faddeev equations in coordinate space phenomenological Ali-Bodmer α-α potential three-body short-range potential complex scaling method used to compute resonances x = ρ sin α y = ρ cos α R. Álvarez-Rodríguez et al., Eur. Phys. J. A 31 (2007) 303 and references therein

28 Importance of direct channels for the triple-α reaction rate at low temperatures?

29 Low-temperature triple-α reaction rate Assumption of statistical equilibrium leads to: R 3α (E) ( ) 2 Eγ σ γ (E γ ) E (non- resonant) 3α con3nuum state 3α threshold E g.s. 12 C γ E γ

30 Low-temperature triple-α reaction rate 3α threshold Hoyle state (resonance) (non resonant) 3α con6nuum state f > (I) g.s. 12 C i > (II) (I) resonant photo dissociation (II) direct photo dissociation For the resonant contribution (I): σ γ Eγ 2 Γ α Γ γ (E E R ) 2 + Γ 2 /4, Γ α = Γ α0 + Γ direct

31 Low-temperature triple-α reaction rate Partial α-decay widths: Γ α0 (E) P α0 (E) γ 2 α 0 Γ direct (E) P direct (E) γ 2 direct Hoyle state (a) sequential (b) direct 3α threshold E (a) 8 Be(gs) (b) (a) 3α E R =379 kev E 8Be =92 kev If the photo-dissociation process proceeds via the low-energy tail of the Hoyle state with E < E8 Be, then P α0 (E) 0 whereas P direct (E) remains sizeable

32 Low-temperature triple-α reaction rate Comparison of various theoretical models FIG. 1: (Color online) Different evaluations of the triplealpha reaction Nguyen rate: et al., comparing arxiv: v2 the Hyperspherical (2012) Harmonic R-matrix method (solid) with NACRE (dotted), CDCC (dashed) and the three-body Breit Wigner (dot-dashed). HHR: Nguyen et al., arxiv: v2 (2012) NACRE: C. Angulo et al., NPA 656 (1999) 3 CDCC: Ogata et al., PTP 122 (2009) 1055 BW(3B): Garrido et al., EPJA 47 (2011) 102

33 Summary

34 Some key points Complete-kinematics measurements of multi-particle final states are useful The Hoyle state decays sequentially (> 99.5%) The uncertainty on the triple-α reaction rate is 10% in the temperature regime of s-wave resonance dominance (T = GK); the dominating source of uncertainty is Γ π /Γ At low temperatures (T < 0.1 GK), the triple-α reaction is not sequential. Three-body models predict very different rates (important for evolution of early massive stars) Can the observation of direct-decay branches be used to test 12 C structure models? Yes, but only if the latter is combined with a sophisticated breakup model

35 The end Collaboration O. S. Kirsebom 1, M. Alcorta 2, M. J. G. Borge 2, M. Cubero 2, C. Aa. Diget 3, R. Dominguez-Reyes 2, L. M. Fraile 4, B. R. Fulton 3, H. O. U. Fynbo 1, D. Galaviz 2, S. Hyldegaard 1, B. Jonson 5, M. Madurga 2, A. Muñoz Martin 6, T. Nilsson 5, G. Nyman 5, A. Perea 2, K. Riisager 1, O. Tengblad 2 and M. Turrion 2 1 Department of Physics and Astronomy, Aarhus University, Denmark 2 Instituto de Estructura de la Materia, CSIC, Madrid, Spain 3 Department of Physics, University of York, UK 4 PH Department, CERN, Geneva, Switzerland 5 Fundamental Physics, Chalmers University of Technology, Goteborg, Sweden 6 CMAM, Universidad Autonoma de Madrid, Spain

36 Kinematic fitting ε i ρ ϕ (a) (c) ε k ε j 0 max (b) Kinematic fitting (d) SD DDL DDE