1. Extracting ANCs from elastic scattering data O. L. Ramírez Suárez and J-M. Sparenberg olramirez@ulb.ac.bejmspar@ulb.ac.be olramirez@ulb.ac.be and jmspar@ulb.ac.be Physique Nucléaire et Physique Quantique ATHENA Brussels workshop on Astrophysics January 27 - 28, 2014 Université Libre de Bruxelles - Belgium

2. Elastic scattering of 12 C +  12 C 16 O  http://www.tunl.duke.edu/nucldata/figures/16figs/16_08_1993.pdf

3. 12 C 16 O  Elastic scattering of 12 C +  (2 + wave) http://www.tunl.duke.edu/nucldata/figures/16figs/16_08_1993.pdf

4. 12 C 16 O  Elastic scattering of 12 C +  (2 + wave) 0 MeV -245 keV 2.68 MeV 4.35 MeV 4.97 MeV http://www.tunl.duke.edu/nucldata/figures/16figs/16_08_1993.pdf

5. Too difficult Exp. Elastic scattering of 12 C +  (2 + wave) 12 C 16 O  0 MeV -245 keV 2.68 MeV 4.35 MeV 4.97 MeV Possible Exp. ANC Phase shift

6. Elastic scattering of 12 C +  (2 + wave) 12 C  -245 keV 2.68 MeV 4.35 MeV Possible Exp. Too difficult Exp. 0 MeV 4.97 MeV E (MeV)  2 (rad)    We do not need just a parametrization we need a GOOD one!

7. Elastic scattering of 12 C +  (2 + wave) 12 C  -245 keV 2.68 MeV 4.35 MeV Possible Exp. Too difficult Exp. 0 MeV 4.97 MeV Key points: E (MeV)  2 (rad)    We do not need just a parametrization we need a GOOD one!

8. Elastic scattering of 12 C +  (2 + wave) 12 C  -245 keV 2.68 MeV 4.35 MeV Possible Exp. Too difficult Exp. 0 MeV 4.97 MeV E (MeV)  2 (rad)   

9. Elastic scattering of 12 C +  (2 + wave) 12 C  -245 keV 2.68 MeV 4.35 MeV Possible Exp. Too difficult Exp. 0 MeV 4.97 MeV E (MeV)  2 (rad)   

10. Elastic scattering of 12 C +  (2 + wave) 12 C  -245 keV 2.68 MeV 4.35 MeV Possible Exp. Too difficult Exp. 0 MeV 4.97 MeV E (MeV)  2 (rad)   

11. Elastic scattering of 12 C +  (2 + wave) E (MeV)  2 (rad)      Key points:

12. From physics S-matrix Effective range function (effective-range parameters) Cross sections: phase shifts Key points Errors Physical behaviors From mathematics Poles: Bound states and resonances (analytical continuation is not simple) Good analytical properties (especially at zero energy) Different kind of parametrizations (Taylor, Padé, …) Less free parameters Statistical analysis Filters The method in a simple way

13. Elastic scattering of 12 C +  (2 + wave)

20. Extracting the ANC ANC 

21. Extracting the ANC ANC  ANC = 99(9) x 10 3 fm -1/2

22. Summary and Conclusions New method to parameterize phase shifts To remark: Model independent - Input: from the experiment ANC extraction is possible (phase-shift errors are taking into account) For 16 O (2 + at 6.92 MeV) ANC = 99(9) x 10 3 fm -1/2 (97 to 147) x 10 3 fm -1/2