1. 9/2/2013PHY 711 Fall 2013 -- Lecture 31 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 3: Chapter 1 – scattering theory continued; center of mass versus laboratory reference frame.

2. 9/2/2013PHY 711 Fall 2013 -- Lecture 32

3. 9/2/2013PHY 711 Fall 2013 -- Lecture 33 Scattering geometry:

4. 9/2/2013PHY 711 Fall 2013 -- Lecture 34 Relationship between scattering angle  and impact parameter b for interaction potential V(r):

5. 9/2/2013PHY 711 Fall 2013 -- Lecture 35 Example of cross section analysis

6. 9/2/2013PHY 711 Fall 2013 -- Lecture 36 Hard sphere scattering: Example of cross section analysis

7. 9/2/2013PHY 711 Fall 2013 -- Lecture 37 The results above were derived in the center of mass reference frame; relationship between normal laboratory reference and center of mass: Laboratory reference frame: Before After u1u1 u 2 =0 v1v1 v2v2   m1m1 m2m2 Center of mass reference frame: Before After U1U1 U2U2 V1V1 V2V2  m1m1 m2m2 

8. 9/2/2013PHY 711 Fall 2013 -- Lecture 38 Relationship between center of mass and laboratory frames of reference V1V1 V CM v1v1  U1U1 u1u1

9. 9/2/2013PHY 711 Fall 2013 -- Lecture 39 Relationship between center of mass and laboratory frames of reference -- continued

10. 9/2/2013PHY 711 Fall 2013 -- Lecture 310 V1V1 V CM v1v1  Relationship between center of mass and laboratory frames of reference For elastic scattering

11. 9/2/2013PHY 711 Fall 2013 -- Lecture 311 Digression – elastic scattering Also note:

12. v1v1 V1V1 V CM   9/2/2013PHY 711 Fall 2013 -- Lecture 312 Relationship between center of mass and laboratory frames of reference – continued (elastic scattering)

13. 9/2/2013PHY 711 Fall 2013 -- Lecture 313 Differential cross sections in different reference frames

14. 9/2/2013PHY 711 Fall 2013 -- Lecture 314 Differential cross sections in different reference frames – continued:

15. 9/2/2013PHY 711 Fall 2013 -- Lecture 315 Example: suppose m 1 = m 2

16. 9/2/2013PHY 711 Fall 2013 -- Lecture 316 Example of cross section analysis – CM versus lab frame