Fusion of Heavy IonsFusion of Heavy Ions

Students: Paduraru Catalin Students: Paduraru Catalin (Univ. of Bucharest, RO)(Univ. of Bucharest, RO)

Sporea Ciprian Sporea Ciprian (West Univ. of Timisoara, RO)(West Univ. of Timisoara, RO)

Pasca Horia Pasca Horia (“Babes-Bolyai” Univ., RO)(“Babes-Bolyai” Univ., RO)

Supervisors: Supervisors: Dr. Alexander Karpov Dr. Andrey Denikin

ObjectivesObjectives

Data analysis ofData 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 The influence of vibration and rotation degrees of freedom on fusion probability degrees of freedom on fusion probability

Experimental dataExperimental dataReaction 1: Reaction 1: 4848Ca + Ca + 154154Sm Sm

G. N. Knyazheva et al., Physical Review C 75 (2007) 064602G. N. Knyazheva et al., Physical Review C 75 (2007) 064602

Reaction 2: Reaction 2: 3636S + S + 9090ZrZrA.M. Stefanini et al., Physical Review, C 62 (2000) 14601A.M. Stefanini et al., Physical Review, C 62 (2000) 14601

Reaction 3: Reaction 3: 3434S + S + 168168ErErC.R. Morton et al., Physical Review, C 62 (2000) 24607C.R. Morton et al., Physical Review, C 62 (2000) 24607

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

One dimensional barrier One dimensional barrier The potential energy (consisting of long range Coulomb repulsive The potential energy (consisting of long range Coulomb repulsive

term and short range attractive nuclear term) can be approximated by term and short range attractive nuclear term) can be approximated by a parabolic shaped barrier. a parabolic shaped barrier.

)()12(2

)(0

2

ETlE

E ll

fus

One dimensional barrierOne dimensional barrier Experimental data can not be correctly fitted at low energy using Experimental data can not be correctly fitted at low energy using

this simplified potential this simplified potential more degrees of freedom must be more degrees of freedom must be taken into account. taken into account.

Empirical:Empirical: semi-classical model

Channel coupling:Channel coupling: quantum model

Empirical modelEmpirical model It takes into account the deformation It takes into account the deformation

and orientation degrees of freedomand orientation degrees of freedom

Orientation Deformation

Empirical modelEmpirical model The cross section The cross section σσ depends on the T(l,E) depends on the T(l,E)

(penetration probability) which depends on (penetration probability) which depends on F(B) (the barrier distribution function)F(B) (the barrier distribution function)

dBElllR

BEl

BFElTBB

1

2

2

]))1()(2

[),(

2exp(1)(),(

2

0exp)(E

BBNBF

)()12(2

)(0

2

ETlE

E ll

fus

Empirical model experimental dataEmpirical model experimental data

4848Ca + Ca + 154154SmSm3636S + S + 9090ZrZr

Pro

xim

ity p

oten

tial

9090ZrZrr0coul =1.16 fmb = 1.2 fm

Target: vibrationTarget: vibrationλ = 2hω = 2.18 MeVc = 20.12 Mev/fm2

154154SmSmr0coul =1.16 fmb = 1.06 fm

Target: rotationTarget: rotationβ2 = 0.29β4 = 0.068

Empirical model - experimental dataEmpirical model - experimental data

3434S + S + 168168Er Er Proximity potential: Proximity potential: r0coul = 1.16 b=1.2

Traget (rotation):Traget (rotation): β2= 0.294 β4= -0.007

3434SS

168Er

Channel coupling Channel coupling (quantum model)(quantum model)

The Hamiltonian of two interacting deformable The Hamiltonian of two interacting deformable nuclei gives coupled radial wave functionsnuclei gives coupled radial wave functions

"y

Cipi

Ey

r

lly ll [

2)1("

2,2,

0

,)(j

jET l

l

Channel coupling experimental dataChannel coupling experimental data

3636S + S + 9090ZrZrWood-Saxon volume Wood-Saxon volume potentialpotentialV0 = -125 MeVr0vol = 1.16 fmavol = 0.65 fm

Projectile: inertProjectile: inertTarget: vibrationTarget: vibrationλ = 2hω = 2.18 MeVβ0 = 0.205

4848Ca + Ca + 154154SmSmWood-Saxon volume potentialWood-Saxon volume potentialV0 = -199 MeVr0coul = 1.048 fmavol = 0.865 fm

Projectile: inertProjectile: inertTarget: rotationTarget: rotationE2+ = 0.082 MeVβ2 = 0.31 MeVβ4 = 0. 05 MeVNumber of levels = 5

Wood-Saxon volume potential

Channel coupling experimental dataChannel coupling experimental data 3434S + S + 168168ErEr

Projectile: vibrationProjectile: vibrationλ = 5hω = 2.128 MeV ß0 = 0.252 number of phonons = 5

Target: rotationTarget: rotationE2 = -0.007 MeV ß2 = 0.294 ß4 = -0.007 Nr. levels = 4

Wood-Saxon vol potentialWood-Saxon vol potentialV0 = -392.5 MeVr0vol = 0.800 ( 7.006) fmavol = 1.290 fmr0coul = 1.16

horica

ConclusionsConclusionsSemi-classical model gives good results but Semi-classical model gives good results but

a better approach is to use the channel a better approach is to use the channel coupling model.coupling model.

We have observed the need of taking into We have observed the need of taking into account all degree of freedom.account all degree of freedom.

We have learned how different potential We have learned how different potential parameters influence the fusion cross parameters influence the fusion cross section.section.

We have learned how to analyze We have learned how to analyze experimental data with the use of NRV experimental data with the use of NRV website (website (http://nrv.jinr.ru/nrv/http://nrv.jinr.ru/nrv/). ).

sherpica

MulMulţţumesc!umesc!

Спасибо!Спасибо!

Thank Thank you!you!

Especially to Dr. Alexander Karpov and Dr. Andrey DenikinEspecially to Dr. Alexander Karpov and Dr. Andrey Denikin