9/3/2012PHY 711 Fall 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.

9/3/2012PHY 711 Fall Lecture 32

9/3/2012PHY 711 Fall Lecture 33 Scattering geometry:

9/3/2012PHY 711 Fall Lecture 34 Relationship between scattering angle  and impact parameter b for interaction potential V(r):

9/3/2012PHY 711 Fall Lecture 35 Example of cross section analysis

9/3/2012PHY 711 Fall Lecture 36 Hard sphere scattering: Example of cross section analysis

9/3/2012 PHY 711 Fall 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 U 2 =0 V1V1 V2V2  m1m1 m2m2 

9/3/2012PHY 711 Fall Lecture 38 Relationship between center of mass and laboratory frames of reference V1V1 V CM v1v1 

9/3/2012PHY 711 Fall Lecture 39 V1V1 V CM v1v1  Relationship between center of mass and laboratory frames of reference

9/3/2012PHY 711 Fall Lecture 310 Differential cross sections in different reference frames

9/3/2012PHY 711 Fall Lecture 311 Differential cross sections in different reference frames – continued:

9/3/2012PHY 711 Fall Lecture 312 Example: suppose m 1 = m 2