Study of heavy ion elastic scattering within quantum optical model - - PowerPoint PPT Presentation

Study of heavy–ion elastic scattering within quantum

• ptical model

Caracaș Ioana–Alexandra Dinuț Claudiu Ionuț

University of Bucharest, Department of Physics Supervisors: Vladimir Rachkov, Mikhail Naumenko

Flerov Laboratory of Nuclear Reactions

Contents

Introduction

• Project description
• Cross section
• I. Theoretical Part
• Optical model of the elastic scattering of nuclei
• The optical aspects of quantum scattering
• Fresnel diffraction
• Fraunhofer diffraction
• II. Practical part
• NRV knowledge base
• Description of the elastic scattering of 4He + 58Ni and 4He + 209Bi at different

energies

Conclusions

Project description

• Aim of the project:

Study of the behavior of the elastic scattering differential cross section for different energies and different projectile-target combinations

• Steps:

1. Studying of the elastic scattering theory and quantum optical model 2. Derivation of expressions for

• partial wave expansion of a plane wave
• relation between the elastic cross section and phase shifts
• a relation between the scattering amplitude and the phase shifts

3. Digitizing experimental data from the graphs of articles using GSYS program 4. Checking the correctness of digitizing by comparing the results with the experimental graphs 5. Importing data in the NRV optical model codes 6. Determining the parameters of the optical model potential 7. Interpreting the results

Cross section

• Interaction of particles is usually described by the

cross section s : effective area of interaction Typical units: 1 barn = 10-28 m2 = 100 fm2

Typical units: barn/steradian

Optical model (OM) of the elastic scattering of nuclei

• OM is based on solution of time-independent Schrӧdinger equation:

with phenomenological Optical Potential: and boundary condition at infinity:

2 2 ( ) ( )

( , ) ( , ) 2

OM k

V r k E r k 

 

           

Ek > 0

Scattering amplitude

Optical model (OM) of the elastic scattering of nuclei

• 1. Partial wave decomposition:
• 2. Numerical solution of the radial Schrodinger equation (Numerov method) with

certain boundary conditions for calculation of partial wave functions and differential cross section.

Coulomb (Rutherford) Scattering: VOM = VC

Coulomb scattering amplitude: Rutherford law

Coulomb + Nuclear Scattering: VOM = VC + VN

The optical aspects of quantum scattering

Fresnel scattering

• Bombarding energy around the Coulomb barrier
• Coulomb interaction dominates (η > >1)
• “Illumination region”: interference pattern
• “Shadow region”: strong absorption

dominates negligible

The optical aspects of quantum scattering

Fraunhofer scattering

negligible dominates

Practical part

NRV knowledge base

The NRV web knowledge base is a unique interactive research system:

• Allows to run complicated computational codes
• Works in any internet browser
• Has graphical interface for preparation of input parameters and analysis of
• utput results
• Combines computational codes with experimental databases on properties of

nuclei and nuclear reactions

• Contains detailed description of models

http://nrv.jinr.ru

Practical part

Optical Model calculation with NRV OM code

Main steps of calculation:

Physical

• Set projectile and target parameters (mass, spin, etc)
• Set the incident energy
• Set the parameters of the OM potential

http://nrv.jinr.ru

Practical part

Optical Model calculation with NRV OM code

Main steps of calculation:

Numerical

• Set the radial step for integration
• Set the maximum radius R for integration
• Set the maximum angular momentum L

http://nrv.jinr.ru

OM potential parameters

System Elab (MeV) V0 (MeV) rV (fm) aV (fm) W0 (MeV) rw (fm) aw (fm)

4He + 58Ni

8.1

• 75

0.9 0.49

• 8.5

1.37 0.75 9.6

• 75

0.96 0.49

• 23.5

1.37 0.583 25

• 75.3

1.051 0.655

• 9.5

1.2 0.75

4He + 209Bi

12

• 69.805

0.902 0.7

• 8.535

1.666 0.48 22

• 74

1.1 0.68

• 19.55

1.2 0.6 69.5

• 72.151

1.091 0.626

• 10.562

1.257 0.818

Practical part

Description of the elastic scattering of

4He + 209Bi at different energies

Fraunhofer scattering η = 6,27 Fresnel scattering η = 11,145 Pure Rutherford scattering η = 15.09 Transition from classical (optical) picture to quantum picture

*) Experimental data from 1) P. Sighn et al., Phys. Rev. C 43 (1993), 1867; 2) A.R. Barnett, J.S. Lilley, Phys. Rev. C 9 (1974), 2010.

Practical part

Description of the elastic scattering of 4He + 58Ni at different energies

Fresnel scattering η = 5,692 Close to Rutherford Scattering η = 6,196 Fraunhofer scattering η = 3,527 Transition from classical (optical) picture to quantum picture

*) Experimental data from 1) L.R. Gasques et al., Phys. Rev. C 67 (2003), 024602 ; 2) F. Ballester et al., J. Phys. G 13 (1987), 1541.

Conclusions

• We studied the elastic scattering theory and the Optical Model.
• We derived the expressions for

– partial wave expansion of a plane wave, – a relation between the elastic cross section and phase shifts – a relation between the scattering amplitude and the phase shifts

• We applied the NRV OM code to study elastic scattering of 4He

+ 58Ni and 4He + 209Bi at different energies

• Good agreement between calculation results and experimental

data was achieved.

• Correctness of the results is also justified by their correlation

with optics.