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Spectroscopic factors and Asymptotic normalization coefficients

Spectroscopic factors and Asymptotic normalization coefficients. F.M. Nunes. NSCL, Michigan State University. in collaboration with D. Pang and A.M. Mukhamedzhanov. Oak Ridge, Oct 2006. Publications. Search for spectroscopic AND transfer reaction in PHYS journals.

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Spectroscopic factors and Asymptotic normalization coefficients

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  1. Spectroscopic factors and Asymptotic normalization coefficients F.M. Nunes NSCL, Michigan State University in collaboration with D. Pang and A.M. Mukhamedzhanov Oak Ridge, Oct 2006

  2. Publications Search for spectroscopic AND transfer reaction in PHYS journals Oak Ridge, Oct 2006

  3. Larger combination of initial and final states How to measure spectroscopic factors? For stable nuclei Knockout using stable beams (e,e’p) Transfer reactions using light beams (d,p), (3He,d) or using heavy ions (12C,13C) or (16O,17O) For radioactive beams Knockout using radioactive beams (12C,11B) Transfer reactions using exotic beams (inverse kinematics) Oak Ridge, Oct 2006

  4. Standard approach to transfer DWBA transition matrix element Overlap functions Experimental xs related to DWBA xs Spectroscopic factor • Validity of DWBA • Optical pot (Uopt-in &Uopt-out ) • Single particle parameters for IAB(r) Oak Ridge, Oct 2006

  5. Many Body approximation SF versus ANC Single Particle Oak Ridge, Oct 2006

  6. SF versus ANC: definitions r (fm) Oak Ridge, Oct 2006

  7. pinning down the single particle ANC extracting SF or ANCs? DWBA transition matrix element Mukhamedzhanov et al., PRC72 (2005) 017602 Oak Ridge, Oct 2006 Goncharov et al.,Sov. J. Nucl. Phys. 35 (1982) 383

  8. extracting SF or ANCs? DWBA transition matrix element Typically Mout is large so if ANC is unknown large error in SF If Min is negligible then one cannot extract SF unambiguously one can only extract ANC Mukhamedzhanov et al., PRC72 (2005) 017602 Oak Ridge, Oct 2006 Goncharov et al.,Sov. J. Nucl. Phys. 35 (1982) 383

  9. Requirements: • data for elastic+transfer at an energy above the barrier • data from which to extract ANC independently Three test cases: Q=-1.0 MeV BE=1.2 MeV 14C(d,p)15C @14 MeV BE=4.1 MeV Q=+1.9 MeV 16O(d,p)17O @ 15 MeV BE=8.4 MeV Q=+6.1 MeV 40Ca(d,p)41Ca @ 11 MeV The question: Are the analyses of transfers to extract SF consistent with independent ANC measurements? Oak Ridge, Oct 2006

  10. Sub-Coulomb heavy ion transfer reactions can be used to extract ANCs Pb(17O, 16O)Pb @ 67 MeV 16O(17O, 16O)17O @ 22 MeV C2(exp)=0.67(05) fm-1 C2(exp)=0.69(03) fm-1 Franey et al., NPA324 (1979) 193. Burzynski et al., NPA399 (1983) 230. Knockout data on 9Be and 12C ~50 MeV/u was used to extract the 15C ANC C2(exp)=1.48(18) fm-1 Sauvan et al., PRC 69 (2004) 044603. Maddalena et al., NPA 682 (2001) 332. Only 40Ca(d,p)41Ca@2.5 MeV to extract ANC C2(exp)=8.36(42) fm-1 Kocher et al., NPA172 (1971) 652. Independent ANC Oak Ridge, Oct 2006

  11. Values consistent with SF=1 r0=1.2 fm C2=5.0 fm-1 C2(exp)=8.36(42) fm-1 r0=1.2 fm C2=0.75 fm-1 C2(exp)=0.67(5) fm-1 Global optical potentials Procedure: keep a=0.65, vary r0 to obtain a range of ANCs 40Ca(d,p)41Ca @ 11 MeV 16O(d,p)17O @ 15 MeV Oak Ridge, Oct 2006 Uin=Perey&Perey; Uout=CH89

  12. Global optical potentials 40Ca(d,p)41Ca @ 11 MeV Values consistent with SF=0.7 16O(d,p)17O @ 15 MeV r0=1.35 fm C2=5.1 fm-1 C2(exp)=8.36(42) fm-1 r0=1.5 fm C2=0.81 fm-1 C2(exp)=0.67(5) fm-1 Oak Ridge, Oct 2006 Uin=Perey&Perey; Uout=CH89

  13. Standard s.p. parameters r0=1.2 fm C2=2.54 fm-1 SF=1.27 Global optical potentials 14C(d,p)15C @14 MeV Value consistent with SF=1 r0=1.7 fm C2=2.66 fm-1 C2(exp)=1.48(18) fm-1 Oak Ridge, Oct 2006 Uin=Perey&Perey; Uout=CH89

  14. Fitting elastic 14C(d,p)15C @14 MeV 16O(d,p)17O @ 15 MeV 40Ca(d,p)41Ca @ 11 MeV r0=1.65 fm C2=2.65 fm-1 r0=1.1 fm C2=0.62 fm-1 r0=1.1 fm C2=2.7 fm-1 C2(exp)=1.48(18) fm-1 C2(exp)=0.67(5) fm-1 C2(exp)=8.36(42) fm-1 Oak Ridge, Oct 2006 Values consistent with SF=1

  15. peripherality 14C(d,p)15C @14 MeV 16O(d,p)17O @ 15 MeV 40Ca(d,p)41Ca @ 11 MeV r R Oak Ridge, Oct 2006

  16. fit to elastic+transfer Oak Ridge, Oct 2006

  17. deuteron breakup 14C(d,p)15C @14 MeV 16O(d,p)17O @ 15 MeV 40Ca(d,p)41Ca @ 11 MeV r0=1.5 fm C2=2.38 fm-1 r0=1.2 fm C2=0.77 fm-1 r0=1.15 fm C2=4.2 fm-1 C2(exp)=0.67(5) fm-1 C2(exp)=1.48(18) fm-1 C2(exp)=8.36(42) fm-1 reduction ~ 15% reduction ~ 10% increase ~ 3% Values consistent with SF=1 Uin=Johnson and Soper Oak Ridge, Oct 2006

  18. CCBA results reduction ~20% reduction ~50% weak Target excitation 14C(d,p)15C 16O(d,p)17O 40Ca(d,p)41Ca CRC results reduction ~ 20% increase ~ 20% weak Oak Ridge, Oct 2006

  19. summary 1) Global pot SF=1.0(1) SF=0.7(1) SF=0.7(1) Oak Ridge, Oct 2006

  20. summary • Global pot • Fit to elastic SF=1.0(1) SF=0.7(1) SF=0.7(1) Oak Ridge, Oct 2006

  21. summary • Global pot • Fit to elastic • Deuteron breakup SF=1.0(1) SF=0.7(1) SF=0.7(1) Oak Ridge, Oct 2006

  22. summary • Global pot • Fit to elastic • Deuteron breakup • Couplings SF=1.0(1) SF=0.7(1) SF=0.7(1) Oak Ridge, Oct 2006

  23. summary • Global pot • Fit to elastic • Deuteron breakup • Couplings • Overall estimate SF=1.0(1) SF=0.7(1) SF=0.7(1) Oak Ridge, Oct 2006

  24. conclusions • Transfer reactions, even well above the Coulomb barrier, • have a very large contribution from large distances Important to pin down ANC independently Sub-Coulomb heavy ion transfer or breakup • ANC measurements for good test cases (closed shell nuclei) • to provide a handle on reaction theory limitations ANC for 41Ca • Solving the cases for stable nuclei is the first step to tackle exotic nuclei! Oak Ridge, Oct 2006

  25. The end Oak Ridge, Oct 2006

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