1. Slide 1 of 14 2008-09-09 Woonyoung So International Workshop on e-Science for Physics 2008 Extended Optical Model Analyses for the 9 Be+ 144 Sm System at Near-Coulomb-Barrier Energies Department of Radiological Science, Catholic University of Pusan

2. Slide 2 of 14Motivation 1. We would like to compare our result with Camacho’s one for 9 Be + 144 Sm systems by using the Woods-Saxon potential. The extended optical model analyses for the 9 Be+ 144 Sm system considered The extended optical model analyses for the 9 Be+ 144 Sm system considered in the present study was already performed by using the folding potential in the present study was already performed by using the folding potential and Woods-Saxon potential as the bare potential. and Woods-Saxon potential as the bare potential. Folding potential : W. Y. So et al., submitted to the Phys. Rev. C Folding potential : W. Y. So et al., submitted to the Phys. Rev. C Woods-Saxon potential : A. G. Camacho et al., Phys. Rev. C 77, 054606 (2008) Woods-Saxon potential : A. G. Camacho et al., Phys. Rev. C 77, 054606 (2008) However, we become to face two important problems.

3. Slide 3 of 14Motivation ① First, the extracted total reaction cross section obtained from Camacho becomes to overestimate about 10%-40% with respect to our results. to overestimate about 10%-40% with respect to our results. ⇒ In order to investigate this discrepancy, we extracted χ 2 value obtained from χ 2 fitting on the elastic scattering data for both our study and Camacho's work. χ 2 fitting on the elastic scattering data for both our study and Camacho's work. As a result, we get χ 2 value 0.63, 0.92, and 0.97 for our work and 2.46, 1.57, and As a result, we get χ 2 value 0.63, 0.92, and 0.97 for our work and 2.46, 1.57, and 1.49 for Camacho's work at E lab = 34, 35, and 37MeV, respectively. 1.49 for Camacho's work at E lab = 34, 35, and 37MeV, respectively.

4. Slide 4 of 14Motivation This implies that χ 2 fitting by This implies that χ 2 fitting by Camacho et al. do not be enough Camacho et al. do not be enough carried out. carried out. Actually, we can see it through the plot of Actually, we can see it through the plot of the ratio of the elastic cross section the ratio of the elastic cross section to the Rutherford cross section obtained to the Rutherford cross section obtained by using χ 2 fitting by using χ 2 fitting χ 2 We can see that χ 2 fitting do not be enough performed betweenθ c.m. =70 o and θ c.m. =120 o at all energies.

5. Slide 5 of 14Motivation ② Secondly, the dispersion relation for the potential strength parameters used by Camacho becomes no longer valid. Camacho becomes no longer valid. Camacho used the energy dependent geometric parameters, a F and r D. But, we cannot see any energy dependency to the geometric parameters in the dispersion relation. Thus, Camacho should consider the extended dispersion relation taking into account the energy dependence of a F and r D.

6. Slide 6 of 14Motivation In order to overcome two problems, we have to perform again the extended optical In order to overcome two problems, we have to perform again the extended optical model analyses for the 9 Be+ 144 Sm system with Woods-Saxon potential model analyses for the 9 Be+ 144 Sm system with Woods-Saxon potential

7. Slide 7 of 14Motivation 2. We would like to study two competing physical effects of DR on fusion. 0.980.982.20 6 He 3.701.481.90 6 Li 1.671.571.80 9 Be 15.77.161.65 16 O SnSnSnSn SαSαSαSα dIdIdIdI E c.m. (MeV)

8. Slide 8 of 14Calculation U(r; E)=V C (r)-[V 0 (r) + U F (r;E)+ U D (r;E)]. The extended optical potential U (r; E) has the following form: V 0 (r)=V 0 f(X 0 ), f(X i )=[1+exp(X i )] -1 with X i =(r-R i )/a i (i = 0, 1, D, and F) Woods-Saxon potential

9. Slide 9 of 14Procedure Elastic DR Fusion extract U F and U D 4 parameters search, V F, W F, V D, and W D Threshold anomaly χ 2 -fitting Dispersion relation Optical model U i = V i + i W i (i = F or D) U = V c + V 0 + U F + U D σ F = 2 ħv σ D = ħv 2 Competition Between fusion and DR

10. Slide 10 of 14 Results and Discussion 1. Elastic and Reaction cross section

11. Slide 11 of 14 Results and Discussion 2. Two competing physical effects of DR on fusion R V = σ F ( V D ≠ 0, W D =0) σ F ( V D = W D =0) V D – lowers Coulomb barrier ; W D - moves the flux from elastic into DR ; ↓ σFσF ↑ σFσF R VW = σ F ( V D ≠ W D ≠0) σ F ( V D = W D =0) R W = σ F ( V D =0, W D ≠0) σ F ( V D = W D =0)

12. Slide 12 of 14 Results and Discussion

13. Slide 13 of 14Summary 1. We performed again the extended optical model analyses for the 9 Be+ 144 Sm system with Woods-Saxon potential for the 9 Be+ 144 Sm system with Woods-Saxon potential 2. The suppression of the fusion cross section in the above barrier seems to occur because the contribution of the flux loss into DR is larger than that of the barrier lowering.

14. Slide 14 of 14 International Workshop on e-Science for Physics 2008

15. Slide 15 of 14Contents1Motivation2Calculation 3Procedure 4 Results and Discussion 5Summary

16. Slide 16 of 14Motivation 1. 1.We would like to know why the threshold anomaly for loosely bound nuclei does not appear by using the extended optical model. The strength of optical potential varies very rapidly near Coulomb barrier energy V B, and then falls off almost zero at the threshold energy E 0. Loosely bound nucleiTightly bound nuclei

17. Slide 17 of 14 Results and Discussion 1. Threshold anomaly

18. Slide 18 of 14 Results and Discussion