Extended optical model analyses of elastic scattering and fusion cross sections for 6, 7 Li Pb systems at near-Coulomb-barrier energies by using a folding potential W. Y. So, T. Udagawa (University of Texas at Austin) K. S. Kim (Hankuk Aviation University) B. T. Kim, S.W.H (Sung Kyun Kwan University) International Nuclear Physics Conference June 6, 2007

Normalization of folding potential for elastic scattering G. R. Satchler and W. G. Love, Phys. Lett. B76, 23 (1978).

7 Li 6 Li G. R. Satchler and W. G. Love, Phys. Rep. 55, 183 (1979). Normalization of Double Folding Potential Breakup threshold energies MeV for 6 Li MeV for 7 Li

Breakup effect in elastic scattering Coupled Discretized Continuum Channel (CDCC) By including breakup channel ( 6 Li  + d) and using folding potential, it was shown 1. Normalization of folding potential is no longer needed. 2. Breakup coupling is repulsive at the surface causing N ~ Li Pb E B = 30 MeV Sakuragi, Phys. Rev. C35, 2161 (1987)

Normalization of folding potential and threshold anomaly An experiment done at near-barrier energies. 6 Li Pb 7 Li Pb N. Keeley et al, Nucl. Phys. A571, 326 (1994) Threshold anomaly No threshold anomaly

Simultaneous χ 2 analyses using extended optical model Simultaneous: - elastic scattering, - semi-experimental direct reaction, - fusion cross section data Extended optical model: two types of complex polarization potentials; DR and fusion potentials Folding potential will not be adjusted. (N=1)

 el /  R  F  DR Search 4 parameters V F, W F, V D, and W D (in U F and U D ) χ 2 -fitting Extended optical model U = V c – [V 0 + U F + U DR ] U i = V i + iW i (i = F or DR)  F = 2/(h v)  DR = 2/(h v) Search 2 parameters V F, W F χ 2 -fitting Dispersion relation r F =1.4 fm, r D =1.47 fm Semi-experimental  DR is obtained by a preliminary OM calculation Energy dependency of DR and fusion potentials separately

(1) V F, W F, V D, W D : Dispersion relation is satisfied for DR and fusion potentials. Results Repulsive DR potential

(2) Elastic cross sections 6 Li Pb 7 Li Pb Data: Keely et al, Nucl Phys A571, 326 (1994)

(3) Reaction and fusion cross sections Experimental  F exp taken from 6 Li Pb: Wu et al, PRC68, (2003) 7 Li Bi : Dasgupta et al, PRC66, (2002), PRC70, (2004)

Real potential for 6 Li Pb -Reduction of folding potential-

Disappearance of threshold anomaly(T.A.)? Weak T.A. in (dominating) DR potential Strong T.A. in (small) fusion potential Apparent disappearance of T.A. in total potential with loosely bound projectile. Separation of potential to DR and fusion parts shows T.A. (particularly in fusion). Imaginary potentials at strong absorption radii

The physical origin of the normalization factor for the folding potential is the repulsive DR dynamic polarization potential. The repulsive DR potential is consistent with CDCC calculations. Separation of the potential is needed to see the weak T.A. of dominating DR potential and strong T.A. of small fusion potential. Dispersion relation is satisfied for both DR and fusion potentials. Summary