1. 8/31/2015PHY 711 Fall 2015 -- Lecture 31 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 3: 1.Scattering theory – some more details 2.Rutherford scattering 3.Transformation between lab and center of mass reference frame.

2. 8/31/2015PHY 711 Fall 2015 -- Lecture 32 Scattering theory:

3. 8/31/2015PHY 711 Fall 2015 -- Lecture 33 Figure from Marion & Thorton, Classical Dynamics b

4. 8/31/2015PHY 711 Fall 2015 -- Lecture 34 r min r  

5. 8/31/2015PHY 711 Fall 2015 -- Lecture 35

6. 8/31/2015PHY 711 Fall 2015 -- Lecture 36

7. 8/31/2015PHY 711 Fall 2015 -- Lecture 37

8. 8/31/2015PHY 711 Fall 2015 -- Lecture 38

9. 8/31/2015PHY 711 Fall 2015 -- Lecture 39

10. 8/31/2015PHY 711 Fall 2015 -- Lecture 310 Relationship between  max and 

11. 8/31/2015PHY 711 Fall 2015 -- Lecture 311

12. 8/31/2015PHY 711 Fall 2015 -- Lecture 312

13. 8/31/2015PHY 711 Fall 2015 -- Lecture 313

14. 8/31/2015PHY 711 Fall 2015 -- Lecture 314 From webpage: http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/rutsca2.html#c3http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/rutsca2.html#c3 What happens as   0?

15. 8/31/2015PHY 711 Fall 2015 -- Lecture 315 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 

16. 8/31/2015PHY 711 Fall 2015 -- Lecture 316 Relationship between center of mass and laboratory frames of reference V1V1 V CM v1v1  U1U1 u1u1

17. 8/31/2015PHY 711 Fall 2015 -- Lecture 317 Relationship between center of mass and laboratory frames of reference -- continued

18. 8/31/2015PHY 711 Fall 2015 -- Lecture 318 V1V1 V CM v1v1  Relationship between center of mass and laboratory frames of reference For elastic scattering

19. 8/31/2015PHY 711 Fall 2015 -- Lecture 319 Digression – elastic scattering Also note:

20. v1v1 V1V1 V CM   8/31/2015PHY 711 Fall 2015 -- Lecture 320 Relationship between center of mass and laboratory frames of reference – continued (elastic scattering)

21. 8/31/2015PHY 711 Fall 2015 -- Lecture 321 Differential cross sections in different reference frames

22. 8/31/2015PHY 711 Fall 2015 -- Lecture 322 Differential cross sections in different reference frames – continued:

23. 8/31/2015PHY 711 Fall 2015 -- Lecture 323 Example: suppose m 1 = m 2

24. 8/31/2015PHY 711 Fall 2015 -- Lecture 324 Example of cross section analysis – CM versus lab frame