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

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

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

Standard approach to transfer Oak Ridge, Oct 2006 Overlap functions Spectroscopic factor Experimental xs related to DWBA xs DWBA transition matrix element  Validity of DWBA  Optical pot (U opt-in & U opt-out )  Single particle parameters for I AB (r)

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

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

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

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

The question: Oak Ridge, Oct 2006 Are the analyses of transfers to extract SF consistent with independent ANC measurements? 14 C(d,p) 15 MeV 16 O(d,p) MeV 40 Ca(d,p) MeV 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 Q=+1.9 MeV Q=+6.1 MeV BE=1.2 MeV BE=4.1 MeV BE=8.4 MeV

Independent ANC Oak Ridge, Oct 2006 Sub-Coulomb heavy ion transfer reactions can be used to extract ANCs Pb( 17 O, MeV C 2 (exp) =0.67(05) fm -1 Franey et al., NPA324 (1979) O( 17 O, 16 O) MeV C 2 (exp) =0.69(03) fm -1 Burzynski et al., NPA399 (1983) 230. Knockout data on 9 Be and 12 C ~50 MeV/u was used to extract the 15 C ANC Sauvan et al., PRC 69 (2004) Maddalena et al., NPA 682 (2001) 332. C 2 (exp) =1.48(18) fm -1 Only 40 Ca(d,p) 41 MeV to extract ANC C 2 (exp) =8.36(42) fm -1 Kocher et al., NPA172 (1971) 652.

Global optical potentials Oak Ridge, Oct 2006 U in =Perey&Perey; U out =CH89 16 O(d,p) MeV 40 Ca(d,p) MeV C 2 (exp) =0.67(5) fm -1 C 2 (exp) =8.36(42) fm -1 r 0 =1.2 fm C 2 =0.75 fm -1 r 0 =1.2 fm C 2 =5.0 fm -1 Values consistent with SF=1 Procedure: keep a=0.65, vary r 0 to obtain a range of ANCs

Global optical potentials Oak Ridge, Oct 2006 U in =Perey&Perey; U out =CH89 16 O(d,p) MeV 40 Ca(d,p) MeV r 0 =1.5 fm C 2 =0.81 fm -1 r 0 =1.35 fm C 2 =5.1 fm -1 C 2 (exp) =0.67(5) fm -1 C 2 (exp) =8.36(42) fm -1 Values consistent with SF=0.7

Global optical potentials Oak Ridge, Oct 2006 U in =Perey&Perey; U out =CH89 14 C(d,p) 15 MeV r 0 =1.7 fm C 2 =2.66 fm -1 C 2 (exp) =1.48(18) fm -1 Value consistent with SF=1 r 0 =1.2 fm C 2 =2.54 fm -1 SF=1.27 Standard s.p. parameters

Fitting elastic Oak Ridge, Oct 2006 r 0 =1.1 fm C 2 =0.62 fm -1 C 2 (exp) =0.67(5) fm -1 r 0 =1.1 fm C 2 =2.7 fm -1 C 2 (exp) =8.36(42) fm -1 r 0 =1.65 fm C 2 =2.65 fm -1 C 2 (exp) =1.48(18) fm -1 Values consistent with SF=1 14 C(d,p) 15 MeV 16 O(d,p) MeV 40 Ca(d,p) MeV

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

fit to elastic+transfer Oak Ridge, Oct 2006

deuteron breakup Oak Ridge, Oct 2006 U in =Johnson and Soper r 0 =1.2 fm C 2 =0.77 fm -1 C 2 (exp) =0.67(5) fm -1 r 0 =1.15 fm C 2 =4.2 fm -1 C 2 (exp) =8.36(42) fm -1 r 0 =1.5 fm C 2 =2.38 fm -1 C 2 (exp) =1.48(18) fm C(d,p) 15 MeV 16 O(d,p) MeV 40 Ca(d,p) MeV Values consistent with SF=1 increase ~ 3% reduction ~ 10% reduction ~ 15%

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

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

summary Oak Ridge, Oct )Global pot 2)Fit to elastic SF=1.0(1)SF=0.7(1)

summary Oak Ridge, Oct 2006 SF=1.0(1)SF=0.7(1) 1)Global pot 2)Fit to elastic 3)Deuteron breakup

summary Oak Ridge, Oct 2006 SF=1.0(1)SF=0.7(1) 1)Global pot 2)Fit to elastic 3)Deuteron breakup 4)Couplings

summary Oak Ridge, Oct 2006 SF=1.0(1)SF=0.7(1) 1)Global pot 2)Fit to elastic 3)Deuteron breakup 4)Couplings 5)Overall estimate

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

The end Oak Ridge, Oct 2006