Nucleosynthesis. at MAGIX/MESA. Stefan Lunkenheimer MAGIX Collaboration Meeting 2017

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1 Nucleosynthesis 12 C(α, γ) 16 O at MAGIX/MESA Stefan Lunkenheimer MAGIX Collaboration Meeting 2017

2 Topics S-Factor Simulation Outlook 2

3 S-Factor 3

4 Stages of stellar nucleosynthesis Hydrogen Burning (PPI-III & CNO Chain) Fuel: proton T K Main product: 4 He Helium Burning Fuel: 4 He T K Main product: 12 C, 16 O 4

5 Helium Burning in red giants Main reactions: 3α 12 C + γ 12 C α, γ 16 O 12 C/ 16 O abundance ratio Further burning states Nucleosynthesis in massive stars Cp. Hammache: 12 C α, γ 16 O in massive star stellar evolution 5

6 Gamow-Peak Fusion reaction below Coulomb barrier kt 15 T = K Transmission probability governed by tunnel efffect Gamow-Peak E 0 Convolution of probability distribution Maxwell-Boltxmann QM Coulomb barrier transmission Depends on reaction and temperature Cp. Marialuisa Aliotta: Exotic beam studies in Nuclear Astrophyiscs 6

7 S-Factor Nonresonant Cross section σ E = 1 1Z 2 αc E e 2πZ v S(E) e Factor = probability to tunnel through Coulomb barrier v = velocity between the two nuclei α = fine structure constant Z 1, Z 2 = Proton number of the nuclei S E = Deviation Factor from trivial model 7

8 Gamow-Peak for 12 C α, γ 16 O S E = E e b/ E σ(e) Gamow-Peak (T K) E 0 = 1 2 b k T kev k = Bolzmann constant b = παz 1 Z 2 2μc 2 μ = M 1M 2 M 1 +M 2 reduced mass Gamow Width Δ = 4 E 0 kt/3 8

9 Cross section σ(e 0 )~10 17 barn Precise low-energy measurements required MAGIX@MESA Direct measurements never < 0.9 MeV Cp. Simulation of Ugalde

10 Measurement of S-Factor Approximate S(300 kev) Buchmann (2005) kev b Caughlan and Fowler (1988) kev b Hammer (2005) 162 ± 39 kev b 10

11 Measurement at Time reverted reaction 16 O(γ, α) 12 C Cross section gain a factor of 100 Inelastic e scattering on oxygen gas Measurement of coincidence (e, α) suppress background α-particle with low energy High Luminosity 11

12 Inverse Kinematik Time reversed reaction: σ(e 0 )~10 15 barn High Energy resolution required MAGIX E 0 Cp. Simulation of Ugalde

13 Simulation 13

14 Introduction MXWare (see talk Caiazza) Monte Carlo Integration Fix Beam Energy Target at Rest Simulation acceptance 4π 14

15 Kinematik Momentum transfer q 2 = 4EE sin 2 θ 2 Photon Energy ν = W2 M 2 q 2 with 2M W 2 = p γ μ + p O μ 2 invariant mass of photon and oxygen M = Oxygen mass Inelastic scattering cross section d 2 σ dωde = 4α2 E 2 q 4 W 2 q 2, ν cos 2 θ 2 + 2W 1 q 2, ν sin 2 θ 2 15

16 Virtual Photon flux Relation beween structural functions and the transversal / longitudinal part of the virtual photon cross section σ T, σ L W 1 = κ σ 4π 2 α T W 2 = κ 4π 2 α 1 ν2 q 2 1 (σl + σ T ) with κ = W2 M 2 2M So we get with d 3 σ dωde = Γ σ T + εσ L Γ = ακ 2π 2 q 2 E E 1 1 ε ε = 1 2 ν2 q 2 q 2 tan 2 θ 2 1 For q 2 0 : σ L vanish and σ T σ tot γ + 16 O X d 5 σ dω e de dω = Γ dσ v dω Cp. Halzen & Martin: Quarks and Leptons 16

17 Time reversal Factor Direct cross section -> Measurement Compare with inverse cross section -> extract the S-Factor Calculate time reversal factor 17

18 Time reversal Factor Phase space examination under T-symmetry invariance Spinstatistic: σ i f = (2I 3+1)(2I 4 +1) p 2 f σ f i (2I 1 +1)(2I 2 +1) p 2 i I=0 for even even nuclides ( 4 He, 12 C, 16 O) in ground state 2I γ + 1 = 2 for photon. So we get σ( 16 O γ, α 12 C) = 1 2 W 2 m He + m C 2 W 2 m O 2 W 2 m He m C 2 W 2 m O 2 σ( 12 C(α, γ) 16 O) Cp. Mayer-Kuckuk Kernphysik: Chapter

19 Result of first simulations Nonresonant cross section σ( 16 O(γ, α) 12 C) Simulation correlate to the results of Ugalde 4π Simulation 0.1 mhz Reaction Rate by E 0 with L cm 2 s 1 Worst case Luminosity (see later talks) Now simulation with e, α Acceptance needed. 19

20 Outlook 20

21 Simulation Finish simulation electron acceptance α-particle acceptance Preliminary results Need measurement on angles smaller than Spectrometer coverage 0 degree scattering -> New Theoretic calculations 21

22 α-detection Low kinetic energy 20 MeV Needs specialized detector Silicon-Strip-Detector Choose and Test Silicon-Strip-Detectors in the Lab 22

23 THANK YOU FOR YOUR ATTENTION!

24 BACKUP

25 Production factor Waver and Woosley Phys Rep 227 (1993) 65 25

26 Two-Body Reaction In the center of mass frame 16 O(γ, α) 12 C E 3 = W2 +m 3 2 m 4 2 2W E 4 = W2 +m 4 2 m 3 2 2W p = E 2 m 2 = W2 m 3 +m 4 2 W 2 m 3 m 4 2 2W 26

27 Electron scattering Cross section inelastic scattering (cp. Chapter 7.2) d 2 σ dωde = dσ dω Mott With structural functions W 1, W 2 And Mott crossection (in this case) dσ dω Mott We get (cp. Halzen & Martin Chapter 8) W 2 q 2, ν + 2W 1 q 2, ν tan 2 θ 2 = 4α2 E 2 q 4 cos 2 θ 2 d 2 σ dωde = 4α2 E 2 q 4 W 2 q 2, ν cos 2 θ 2 + 2W 1 q 2, ν sin 2 θ 2 27

28 Basic of Simulation Connection between count rate and cross section With L : Luminosity N = Ω N : Number of counts A Ω dσ dω dω Ldt + N BG A Ω Acceptance (1 full accepted, 0 not detected) 28

29 Monte Carlo Integration Definition of mean value in volume V: f = 1 V V f x d n x Estimator for mean value: N f 1 N i=1 f(x i ) Monte-Carlo Integration: f x d n x = f V V N i=1 Strategies for numerical improvements: Improve convergence 1/ N Improve variance f 2 f 2 N f x i ± V N f2 f 2 29

30 Cross section simulation dσ dω e de e dω dω ede e dω Transform Ω, E W, 1/q 2, φ with det J = q 4 W 2MEE With Monte-Carlo Integration: dσ dω e de e dω dω ede e dω = V N i det J dσ dω e de e dω W, 1/q 2, φ, Ω Define ω i = V det J So we get dσ dω e de e dω ω i = q 4 W 2MEE v Δφ ΔW Δ cos θ Δφ Γ dσ v dω 30