Fusion of Heavy Ions

1. Fusion of Heavy Ions Students: Paduraru Catalin (Univ. of Bucharest, RO) Sporea Ciprian (West Univ. of Timisoara, RO) Pasca Horia (“Babes-Bolyai” Univ., RO) Supervisors: Dr. Alexander Karpov Dr. Andrey Denikin

2. Objectives • Data analysis of specific experimental data on fusion cross sections of heavy ions • Use of the low-energy nuclear knowledge base (NRV http://nrv.jinr.ru/nrv) • The influence of vibration and rotation degrees of freedom on fusion probability

3. Experimental data Reaction 1: 48Ca + 154Sm G. N. Knyazheva et al., Physical Review C 75 (2007) 064602 Reaction 2: 36S + 90Zr A.M. Stefanini et al., Physical Review, C 62 (2000) 14601 Reaction 3: 34S + 168Er C.R. Morton et al., Physical Review, C 62 (2000) 24607

4. NRV: Low-energy nuclear knowledge basehttp://nrv.jinr.ru/nrv/

5. One dimensional barrier • The potential energy (consisting of long range Coulomb repulsive term and short range attractive nuclear term) can be approximated by a parabolic shaped barrier.

6. One dimensional barrier • Experimental data can not be correctly fitted at low energy using this simplified potential  more degrees of freedom must be taken into account. Empirical: semi-classical model Channel coupling: quantum model

7. Empirical model • It takes into account the deformation and orientation degrees of freedom Orientation Deformation

8. Empirical model • The cross section σ depends on the T(l,E) (penetration probability) which depends on F(B) (the barrier distribution function)

9. Empirical model experimental data Proximity potential 36S + 90Zr 48Ca + 154Sm 90Zr r0coul =1.16 fm b = 1.2 fm Target: vibration λ = 2 hω = 2.18 MeV c = 20.12 Mev/fm2 154Sm r0coul =1.16 fm b = 1.06 fm Target: rotation β2= 0.29 β4 = 0.068

10. Empirical model - experimental data 168Er • 34S + 168Er Proximity potential: r0coul = 1.16 b=1.2 Traget (rotation):β2= 0.294 β4= -0.007 34S

11. Channel coupling (quantum model) • The Hamiltonian of two interacting deformable nuclei gives coupled radial wave functions Cipi 

12. Channel coupling experimental data 48Ca + 154Sm Wood-Saxon volume potential V0 = -199 MeV r0coul = 1.048 fm avol = 0.865 fm Projectile: inert Target: rotation E2+ = 0.082 MeV β2 = 0.31 MeV β4 = 0. 05 MeV Number of levels = 5 Wood-Saxon volume potential 36S + 90Zr Wood-Saxon volume potential V0 = -125 MeV r0vol = 1.16 fm avol = 0.65 fm Projectile: inert Target: vibration λ = 2 hω = 2.18 MeV β0 = 0.205

13. Channel coupling experimental data • 34S + 168Er Projectile: vibration λ = 5 hω = 2.128 MeV ß0 = 0.252 number of phonons = 5 Target: rotation E2 = -0.007 MeV ß2 = 0.294 ß4 = -0.007 Nr. levels = 4 Wood-Saxon vol potential V0 = -392.5 MeV r0vol = 0.800 ( 7.006) fm avol = 1.290 fm r0coul = 1.16 horica 

14. Conclusions • Semi-classical model gives good results but a better approach is to use the channel coupling model. • We have observed the need of taking into account all degree of freedom. • We have learned how different potential parameters influence the fusion cross section. • We have learned how to analyze experimental data with the use of NRV website (http://nrv.jinr.ru/nrv/). sherpica 

15. Mulţumesc! Спасибо! Thank you! Especially to Dr. Alexander Karpov and Dr. Andrey Denikin