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

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

Experimental data Reaction 1: 48Ca + 154Sm Reaction 2: 36S + 90Zr 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

NRV: Low-energy nuclear knowledge base http://nrv.jinr.ru/nrv/

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.

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

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

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

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

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

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

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

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 

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 

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