NEEP 541 – Cross Sections

1. NEEP 541 – Cross Sections Fall 2003 Jake Blanchard

2. Outline • Cross Sections • Definitions • Scattering • Recoils • Mean energy transfer • Examples

3. CM System M1 u1F u10  M1 M2 u20  u2F M2

4. Results

5. Scattering Angle

6. Definitions Unit area Energetic particles N Particles per unit volume dx

7. Definitions Probability of collision between incident particle and target particle Probability that collision transfers energy between T and T+dT to target Probability that collision scatters incident particle into angle between  and +d total scattering cross section differential energy cross section Differential angular cross section

8. Recoil Production • Recoils are lattice atoms displaced by incident particles or by other lattice atoms • The number of recoils produced per unit volume per unit time with energy in the range T to T+dT= Number density particle flux

9. Cross Sections r 

10. Cross Sections

11. Mean Energy Transfer Isotropic scattering, incident energy E

12. Scattering Cross Section  p

13. Scattering Ions which enter between p and p+dp will scatter into energy T and T+dT

14. Approach • Choose potential • Find scattering angle as function of p • Determine differential cross section from

15. Hard Sphere Potential

16. Hard Sphere Potential

17. Coulomb Potential

18. Coulomb Potential