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
The influence of vibration and rotation degrees of freedom on fusion probability

3. Experimental data Reaction 1: 48Ca + 154Sm Reaction 2: 36S + 90Zr
G. N. Knyazheva et al., Physical Review C 75 (2007)
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 base http://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 = Mev/fm2
154Sm
r0coul =1.16 fm
b = 1.06 fm
Target: rotation
β2 = 0.29
β4 = 0.068

10. Empirical model - experimental data
34S + 168Er
Proximity potential: r0coul = b=1.2
Traget (rotation): β2=  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 = fm
avol = fm
Projectile: inert
Target: rotation
E2+ = MeV
β2 = 0.31 MeV
β4 = 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 = MeV
ß0 = 0.252
number of phonons = 5
Target: rotation
E2 = MeV
ß2 = 0.294
ß4 =
Nr. levels = 4
Wood-Saxon vol potential
V0 = MeV
r0vol = ( 7.006) fm
avol = 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 (
sherpica 

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