Extended optical model analyses of elastic scattering and fusion cross sections

1. Extended optical model analyses of elastic scattering and fusion cross sections for 6, 7 Li + 208Pb systems at near-Coulomb-barrier energies by using a folding potential International Nuclear Physics Conference June 6, 2007 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)

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

3. Normalization of Double Folding Potential 7Li 6Li Breakup threshold energies - 1.48 MeV for 6Li - 2.47 MeV for 7Li G. R. Satchler and W. G. Love, Phys. Rep. 55, 183 (1979).

4. Breakup effect in elastic scattering Coupled Discretized Continuum Channel (CDCC) By including breakup channel (6Li  + 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 causingN ~ 0.5. 6Li + 208Pb EB = 30 MeV Sakuragi, Phys. Rev. C35, 2161 (1987)

5. 6Li + 208Pb 7Li + 208Pb Normalization of folding potential and threshold anomaly • An experiment done at near-barrier energies. Threshold anomaly No threshold anomaly N. Keeley et al, Nucl. Phys. A571, 326 (1994)

6. Simultaneous χ2 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)

7. Procedure Model Input data Extended optical model U = Vc – [V0 + UF + UDR ] Ui = Vi + iWi (i = F or DR) F= 2/(h v)< (+) | WF | (+) > DR= 2/(h v)< (+) | WDR | (+) > el/ R F DR rF=1.4 fm, rD=1.47 fm χ2-fitting Semi-experimental DR is obtained by a preliminary OM calculation Search 4 parameters VF,WF , VD,and WD (in UF and UD) χ2-fitting Dispersion relation Search 2 parameters VF,WF Energy dependency of DR and fusion potentials separately

8. Results (1) VF, WF, VD, WD: Dispersion relation is satisfied for DR and fusion potentials. RepulsiveDR potential

9. (2) Elastic cross sections 6Li + 208Pb 7Li + 208Pb Data: Keely et al, Nucl Phys A571, 326 (1994)

10. (3) Reaction and fusion cross sections Experimental Fexp taken from 6Li + 208Pb: Wu et al, PRC68, 44605 (2003) 7Li + 209Bi : Dasgupta et al, PRC66, 41602 (2002), PRC70, 24606 (2004)

11. Real potential for 6Li + 208Pb-Reduction of folding potential-

12. Disappearance of threshold anomaly(T.A.)? Imaginary potentials at strong absorption radii • 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).

13. Summary • 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.