1. ERNA: Measurement and R-Matrix analysis of 12 C(  ) 16 O Daniel Schürmann University of Notre Dame Workshop on R-Matrix and Nuclear Reactions in Stellar Hydrogen and Helium Burning La Fonda, Santa Fe, NM April 21 – 23, 2008

2. 12 C(  ) 16 O „The holy grail of nuclear astrophysics“ (W. Fowler) Cascades E1,E2,E0 ? 6.05? ERNA  -measurements

3. Recoil Separator ERNA: an alternative approach to measure the reaction 12 C(  ) 16 O Requirements angular / energy acceptance knowledge of charge state distribution high purity of incoming 12 C beam suppression of 12 C beam ion source dynamitron tandem accelerator ion beam purification Gastarget & Post-Stripper singlet 60° magnet  E - E telescope recoil separation doublet analysing magnet recoil focussing Wien filter magnetic qu adrupole multiplets triplet side FC Advantages high efficiency ~p q measure  tot independent of  ‘s (mostly) background free  -ray coincidences possible N recoils detected = N projectiles  n target    T ERNA  p q

4. Recoil Separator ERNA: an alternative approach to measure the reaction 12 C(  ) 16 O Requirements angular / energy acceptance knowledge of charge state distribution high purity of incoming 12 C beam suppression of 12 C beam ion source dynamitron tandem accelerator ion beam purification Gastarget & Post-Stripper singlet 60° magnet  E - E telescope recoil separation doublet analysing magnet recoil focussing Wien filter magnetic qu adrupole multiplets triplet side FC Advantages high efficiency ~p q measure  tot independent of  ‘s (mostly) background free  -ray coincidences possible N recoils detected = N projectiles  n target    T ERNA  p q

5. Density Determination Energy Loss (Stopping Power) 7 Li(  ) 11 B 7 Li(  ´) 7 Li *Gastarget

6. Recoil Separator ERNA: an alternative approach to measure the reaction 12 C(  ) 16 O Requirements angular / energy acceptance knowledge of charge state distribution high purity of incoming 12 C beam suppression of 12 C beam ion source dynamitron tandem accelerator ion beam purification Gastarget & Post-Stripper singlet 60° magnet  E - E telescope recoil separation doublet analysing magnet recoil focussing Wien filter magnetic qu adrupole multiplets triplet side FC Advantages high efficiency ~p q measure  tot independent of  ‘s (mostly) background free  -ray coincidences possible N recoils detected = N projectiles  n target    T ERNA  p q

7. Charge State Distribution

8. Charge State Distribution electron loss calculated q recoil = q carbon measured q recoil = q carbon +2 12 C 3+  16 O 6+ Ecm=3.2 MeV integrate Solution: post-target stripper

9. Recoil Separator ERNA: an alternative approach to measure the reaction 12 C(  ) 16 O Requirements angular / energy acceptance knowledge of charge state distribution high purity of incoming 12 C beam suppression of 12 C beam ion source dynamitron tandem accelerator ion beam purification Gastarget & Post-Stripper singlet 60° magnet  E - E telescope recoil separation doublet analysing magnet recoil focussing Wien filter magnetic qu adrupole multiplets triplet side FC Advantages high efficiency ~p q measure  tot independent of  ‘s (mostly) background free  -ray coincidences possible N recoils detected = N projectiles  n target    T ERNA  p q

10. Acceptance Bad tuning Good tuning Matrix calculations: COSY INFINITY These just give STARTING values: Tune Separator with 16 O pilot beam!

11. Angular acceptance E cm = 2.4 MeV q rec = 6+

12. Angular Acceptance B ext. Triplet changed by 0.7% !

13. Energy Acceptance transmission  E / E 0 [ % ] experimental calculated by variation of beam energy

14. Recoil Separator ERNA: an alternative approach to measure the reaction 12 C(  ) 16 O Requirements angular / energy acceptance knowledge of charge state distribution high purity of incoming 12 C beam suppression of 12 C beam ion source dynamitron tandem accelerator ion beam purification Gastarget & Post-Stripper singlet 60° magnet  E - E telescope recoil separation doublet analysing magnet recoil focussing Wien filter magnetic qu adrupole multiplets triplet side FC Advantages high efficiency ~p q measure  tot independent of  ‘s (mostly) background free  -ray coincidences possible N recoils detected = N projectiles  n target    T ERNA  p q

15. Typical  E-E Spectra E cm = 2.2 MeV suppression ~ 1·10 11 E cm = 4.4 MeV suppression ~ 3·10 9

16. 12 C(  ) 16 O total cross section

17. Comparison ERNA Calculation Kunz. et al. (Kunz R. et al., ApJ 567, 643-650 2002)  Basic resonance properties well reproduced  Clear need for improved (new) R-Matrix calculation

18. New R-Matrix code rewritten from scratch rewritten from scratch utilizing classical formalism OR C. Brune’s alternative parameterization utilizing classical formalism OR C. Brune’s alternative parameterization all relevant channels included  -decay ( 16 N), (  ), ( ,  ) [external (direct) capture] all relevant channels included  -decay ( 16 N), (  ), ( ,  ) [external (direct) capture]

19. 16 N decay Fit to E1 groundstate data Assuncao et al. Scattering data taken from: D’Agostino Bruno M. et al., Nuovo Cimento A27, 1 (1975) Plaga R. et al., Nucl. Phys. A465, 291 (1987) Calculation with parameters from: Tischhauser P. et al., Phys. Rev. Lett. 88, 072501 (2002)

20. Results  (E)=S(E)·E -1 · e -2  Compare to old R-Matrix calculation [Kunz et al., APJ 567, 643-650 (2002)] New data available: capture to E x =6.05 MeV Level (DRAGON) No sign of „missing amplitude“

21. total cross section data available in broad energy range  fit needs improvements  fit to total data should correlate different amplitudes Monte Carlo Error Estimate Normalization (e.g. different E1 GS data sets) Outlook

22. ERNA Collaboration Bochum A. Di Leva R. Kunz D. Rogalla C. Rolfs F. Schümann D. Schürmann F. Strieder H.-P. Trautvetter Naples & Caserta N. De Cesare L. Gialanella A. D’Onofrio G. Imbriani C. Lubritto A. Ordine V. Roca M. Romano F. Terrasi Thank you!