1. Experimental investigation of stellar 12 C+ 12 C fusion toward extremely low energies by direct and indirect methods Xiao Fang University of Notre Dame The 11 th International Conference on Nucleus-nucleus Collisions (NN2012) San Antonio, Texas, May 31, 2012

2. Indirect method: 24 Mg(a,a’) inelastic Search the possible Resonances which can’t be directly measured 12 C+ 12 C Cross section within Gamow window (1 ~ 3MeV) 10 -22 b ~10 -7 b Cross section within Gamow window (1 ~ 3MeV) 10 -22 b ~10 -7 b 12 C+ 13 C 13 C+ 13 C 12 C+ 13 C 13 C+ 13 C 12 C+ 13 C 13 C+ 13 C Set upper limit for possibly existed resonances of 12 C+ 12 C SN 1987, Type II supernova SN 1994D, a type Ia supernova SN 1604 Carbon fusion project at Notre Dame Direct Measurement: 1.Efficient thick target 2. Solenoid spectrometer Verify old resonances and find new resonances

3. Below the barrier Above the barrier A simple pattern for complicated resonances For most energies, the 12 C+ 12 C cross sections are suppressed! Only at resonant energies, the 12 C+ 12 C cross sections matches with those of 12 C+ 13 C and 13 C+ 13 C!

4. Upper limit for 12 C+ 12 C fusion reaction Zickefoose (2010) ?? Spillane (2007) Cooper resonance (2009) H. Esbensen et al., Phys. Rev. C 84, 064613 (2011) M. Notani et al., Phys. Rev. C 85, 014607 (2012) 13 C+ 13 C 12 C+ 13 C 12 C+ 12 C Notre Dame Becker Esbensen

5. Efficient Thick target method 12 C p E’ reaction = E beam – ΔE beam 12 C( 12 C, p) 23 Na E reaction Q, E proton, θ Q=2.24 MeV - E excited ( 23 Na) E proton (MeV) Angle (deg) P 0 : protons with 23 Na at ground state P 1 : protons with 23 Na at first excited state P0P0 P1P1

6.  Only measure proton channel  Two YY1 silicon detectors at backward angle, covered with Aluminum foil to stop scattered 12 C and produced alpha particles  Use thick target of thickness 1mm  Detector resolution for 5.486 MeV alpha particles is 40 keV(FWHM). 0.5 p  A 12 C beam from FN tandem target YY1 detector The backward angle θ Lab : 113.5° - 163.5° θ cm : 122.5° - 166.3° Solid angle calibrated by mixed alpha source 2.59% Focus on: 12 C( 12 C, p) 23 Na Efficient Thick target measurement

7. Scan resonances in a wide range of 3 MeV<E cm <5.3 MeV p0 p1 S* factor (MeV) Ecm (MeV) New thick target quick-scan method − Thick target − Thin target − Thick target − Thin target

8. Ecm (MeV) S* factor (MeV b) 60 nb 40 nb 0.4 mb Covers 4 orders of magnitude ! p0 p1 Combined S* factor from a series of thick target measurements(primary results) Background

9. ND-IU-ANL-CIAE collaboration: Particle-Gamma coincidence GEORGINA array at ND The New 5MV Accelerator at ND Silicon Array at Notre Dame (SAND), (chamber and detector frame are being build at IU; ASIC readout from WUSL) Tuesday, Session 14: Measurement of fusion cross sections in 12C + 12C at Low beam energies using a particle-gamma coincidence technique C.L. Jiang, ANL

10. Capture the channels without  -ray Solenoid Spectrometer for Nuclear Astrophysics (SSNAP) Disadvantage of Particle-gamma technique: not work for the channels without  -ray (p0 and a0) which potentially have large decay branching ratios. Recent experimental results from HELIOS Alan Wuosmaa Western Michigan University, USA Recent experimental results from HELIOS Alan Wuosmaa Western Michigan University, USA

11. Z(m) E(MeV) E cm =6.0 MeV, No degrader, B=3.96 T p2 p3 P4,p5 p6 p7 P8, p9 p10 α0α0 α1α1 p11 α2α2 α3α3 12 C( 12 C,p) 23 Na (Q=2.24 MeV) 12 C( 12 C,  ) 20 Ne (Q=4.62 MeV)

12. 60 keV apart Excitation energy in 23 Na Resolution : 65 keV (FWHM) Resolution of HELIOS spectrometer: ~80 keV(FWHM) Energy resolution

13. p2 p3 P4,p5 p6 p7 P8, p9 p10 Z(m) E(MeV) p0 p1 E cm =5.0 MeV, Al-foil 5.8um, B=3.96 T α0α0 α1α1 xsec(p0): 1 mb Beam: ~80 pnA Duration: 6 hr 12 C( 12 C,p) 23 Na 12 C( 12 C,  ) 20 Ne

14. After energy loss correction Z(m) E(MeV) Z(m) E(MeV) E cm =5.0 MeV

15. p2 p3 P4,p5 p6 p7 P8, p9 p10 Z(m) E(MeV) p0 p1 E cm =4.0 MeV, Al-foil 5.8um, B=3.96 T α0α0 α1α1 Xsec(p0): 0.01 mb Beam: ~30 pnA Duration: 8 hr 12 C( 12 C,p) 23 Na 12 C( 12 C,  ) 20 Ne

16. Simulation: E cm =2.0 MeV, Al-foil 5.8um Z(m) E(MeV) α0α0 α1α1 p2 p3 P4,p5 p6 p0 p1 Xsec(p0): 1 pb

17. Estimation of event rate Table 1 Comparisons among different experiments studying the 12 C+ 12 C fusion Experiment Beam intensit y (p  A) Detector efficiency Event Rate (evt/day) E cm =2.1 MeV Naples (world record) 1 101.5% 0.5 (proton only) ND SAND4045% 120 =120*2*0.5 ND SAND + Gamma 2 40 45%(SAND)*8% (Gamma) 10 =10*2*0.5 ND SAND + Gamma 3 40 45%(SAND)*32% (Gamma) 38 =38*2*0.5 ND SSNAP4030% 80 =80*2*0.5 1.J. Zickefoose, U. Conn. Thesis (2010). 2. Only took the photopeak efficiency (440 keV and 1630 keV) 3. Used all the gamma energy > 0.1 MeV 2.1 MeV: ~10 -11 b 1.7 MeV: ~10 -13 b

18. Search of the potential resonances in the 12 C+ 12 C fusion reaction using the 24 Mg( ,  ’) reaction  Establish correlation between the two reactions at higher energies  Provide prediction at lower energies with 24 Mg( ,  ’) Grand Raiden at RCNP, Osaka University Precise energy calibration (<20 keV)  confirm the correlation Excellent energy resolution (<50 keV)  Resolving states Measurement of angular distribution  Check spin assignment (Nov. 2011) 24 Mg( α, α’ ) measurement at RCNP 16 O   12 C AMD+GCM calculation by Y. Kanada-Enyo

19. 0 1 2 3 4 5 6 7 E c.m. ( 12 C+ 12 C) Black: 12 C( 12 C, α) 20 Ne Red: 12 C( 12 C,p) 23 Na Black: 4.5 deg Blue: 0 deg Preliminary result Red: 0+ Blue: 2+ Mint: 4+ S* factor Strength Counts 0+0+ 4+4+ 2+2+ 2+2+ 2+2+ 2+2+ 12 C( 12 C,p 0,1 ) 24 Mg( ,  ’)

20. Summary  Set an upper limit for potential existed resonances in 12 C+ 12 C fusion  Silicon Array at Notre Dame (SAND), efficient thick target method:  to measure cross section of 12 C+ 12 C precisely (3MeV – 6MeV)  Disadvantage: suffer from background at lower energies  Particle-Gamma coincidence method:  to obtain reliable experimental data at lower energies (1.7MeV – 3MeV)  Disadvantage: not be able to detect p 0 and α 0  Solenoid spectrometer:  to obtain data of p 0 and α 0 channels  Indirect method:  To search potential resonances of 12 C+ 12 C fusion by studying 24 Mg(α,α’)

21. Collaborators Efficient thick target method (University of Notre Dame) Brian Bucher, S. Almaraz-Calderon, A. Alongi, D. Ayangeakaa, A. Best, Craig Cahillane, E. Dahlstroma, Q. Li, S. Lyons, N. Paul, M. Smith, Wanpeng Tan, and Xiao-Dong Tang ND-IU-ANL-CIAE carbon fusion project (SAND,SSNAP) University of Notre Dame: B. Bucher, A. Howard, J. Kolata, A. Roberts, W.P. Tan, X.D. Tang China Institute of Atomic Energy: X.X. Bai, B. Guo, Y.J. Li, W.P. Liu Argonne National Laboratory: H. Esbensen, C.L. Jiang, K.E. Rehm Indiana University Bloomington: R.de Souza, S. Hudan 24 Mg(α, α’) measurement at RCNP University of Notre Dame: B. Bucher, G.Berg, R. DeBoer, U. Garg, J. Goerres, A. Long, R. Talwar, X.D. Tang, M. Wiescher Kyoto University: T. Kawabata, N. Yokota, K. Tomosuke, Y. Matsuda, T. Kadoya Osaka University: A. Tamii, H. Fujita, Y. Fujita, K. Hatanaka, B. Liu, K. Miki Niigata University: T. Itoh Texas A&M University: Y.-W. Lui University of Birmingham: M. Freer

22. 24 Mg

23. 12 C+ 12 C Fusion 12 C( 12 C,p) 23 Na (Q=2.24 MeV) 12 C( 12 C,  ) 20 Ne (Q=4.62 MeV) 12 C( 12 C,n) 23 Mg (Q=-2.62MeV) Light particle: , p, n Gamma: 440 keV (p channel) 1634 keV ( channel) Fusion residue: 20 Ne, 23 Na … no success under barrier 23 Mg: decay spectroscopy Light particle: , p, n Gamma: 440 keV (p channel) 1634 keV ( channel) Fusion residue: 20 Ne, 23 Na … no success under barrier 23 Mg: decay spectroscopy Range investigated E c.m. =1 – 3MeV

24. Naples : 10 puA beam; 1.5% efficiency, 0.5 evt/day ( proton channel only ); ND-ANL-IU: ~ 40 puA beam; 45% efficiency, 120 evt/day (proton and alpha); If add particle + gamma coincidence: 120 *8%= 9.6 evt/day Naples : 10 puA beam; 1.5% efficiency, 0.5 evt/day ( proton channel only ); ND-ANL-IU: ~ 40 puA beam; 45% efficiency, 120 evt/day (proton and alpha); If add particle + gamma coincidence: 120 *8%= 9.6 evt/day A 5 MV Pelletron with ECR source in terminal is being built. It is expected to provide beam in the summer of 2012. Estimation of energy limit

25. [Costantini et al., Rep. Prog. Phys. 72, 086301 (2009)] Astrophysical important energy range: 1-3 MeV Large uncertainties in extrapolation Need better data at lower energies! 12 C+ 12 C fusion at low energies 12 C( 12 C,p) 23 Na 12 C( 12 C,  ) 20 Ne 12 C( 12 C,n) 23 Mg  ~10 -11 b @ 2.1 MeV Cooper resonance (2009)

26. Beam energy Reconstructed reaction energy: E reaction (MeV) Count Red: Q(p 0 )=2.24 MeV Black: Q(p 1 )=1.80 MeV With knowing the exact reaction Q value (Q)  Good reaction energy determination (90 keV for Elab  45 keV for Ecm). Determination of reaction energy 12 C( 12 C, p) 23 Na E reaction Q, E proton, θ Q=Qvalue-E excited ( 23 Na) E proton (MeV) Angle (deg) P 0 : protons with 23 Na at ground state P 1 : protons with 23 Na at first excited state P0P0 P1P1 P0P0 p1p1

27. S* factor extracted from E beam =8.2 MeV p0p0 P1P1 Simulation with a constant S* Ecm (MeV) S* factor (MeV b) E cm =0.5*E beam S* factor from a thick target measurement Ecm = 4.1 MeV

29. Lab Angle (deg) E cm (MeV) Angular distribution for the 12 C( 12 C, p 0 )and 12 C( 12 C,p 1 ) d  /d  *E*exp(87.21/sqrt(E)+0.46*E) Zickfoose only measure d  /d  at 135 deg in the lab frame. Zickfoose, Ph.D. Thesis, U. Conn 2010

30. P 0 angular distribution at E cm =5 MeV P 1 angular distribution at E cm =5 MeV P 3 angular distribution at E cm =5 MeV

31. P 0 angular distribution at E cm =4.1 MeV P 1 angular distribution at E cm =4.1 MeV P 3 angular distribution at E cm =4.1 MeV

32. The fractions for the gamma-decay channels 440 keV for 23 Na1634 keV for 20 Ne Proton and alpha channel data taken from Mazarakis