Non-uniqueness theory of the Convergent Close-coupling method

1. Non-uniqueness theory of the Convergent Close-coupling method Connor Guilfoile, Curtin University Supervisor: Prof Igor Bray Curtin University

2. Background Theory • In atomic physics it is important to know how electrons interact with different atoms. • The simplest case of this is an electron interacting with Hydrogen. • This is known as e-H scattering.

3. Background Theory • An electron incident on a Hydrogen atom can cause several processes to occur: • These are: • Elastic scattering (No excitation) • Excitation of the bound electron to a higher energy state • Ionisation, ejection of the bound electron

4. Background Theory

5. Convergent close-coupling method • Early work in using close-coupling equations were done by Massey and Mohr back in 1932 [1] . • The purpose of the CCC method is to determine the relative probabilities (cross sections) of the processes. • Applications of the CCC method include: • Lighting (Fluorescent tubes) • Fusion • Astrophysics

6. Non-Uniqueness

7. Non-Uniqueness

8. Results • Using the optimal k-grid the TICS were plotted for different partial waves from J=0 to J=9 • Smooth results for higher partial waves • Poor results for lower partial waves especially J=2 and J=4

9. Results • Using the same k-grid, θ=1 was plotted • Much smoother results across low partial waves • Similar results for higher partial waves (as expected)

10. Results • Now the sum of all partial waves is plotted, comparing θ=1 and θ=0 to the experimental data (blue) • Slightly less magnitude, need to calculate more partial waves to add • θ=1 gave a better result than θ=0

11. References • [1] Igor Bray 2010, Curtin University, Western Australia, viewed 14 Feb 2014 http://atom.curtin.edu.au/igor/atom/atomic1.html • [2] Massey H S W and Mohr C B O 1932 Proc. Roy. Soc. A 136 289–311 • [3] Bray I and Stelbovics A T 1992 Phys. Rev. Lett. 69 53–56 • Special thanks to Igor Bray and Valerie Maxville • Thanks for listening 