9/2/2013PHY 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.
9/2/2013PHY 711 Fall Lecture 32
9/2/2013PHY 711 Fall Lecture 33 Scattering geometry:
9/2/2013PHY 711 Fall Lecture 34 Relationship between scattering angle and impact parameter b for interaction potential V(r):
9/2/2013PHY 711 Fall Lecture 35 Example of cross section analysis
9/2/2013PHY 711 Fall Lecture 36 Hard sphere scattering: Example of cross section analysis
9/2/2013PHY 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 U2U2 V1V1 V2V2 m1m1 m2m2
9/2/2013PHY 711 Fall Lecture 38 Relationship between center of mass and laboratory frames of reference V1V1 V CM v1v1 U1U1 u1u1
9/2/2013PHY 711 Fall Lecture 39 Relationship between center of mass and laboratory frames of reference -- continued
9/2/2013PHY 711 Fall Lecture 310 V1V1 V CM v1v1 Relationship between center of mass and laboratory frames of reference For elastic scattering
9/2/2013PHY 711 Fall Lecture 311 Digression – elastic scattering Also note:
v1v1 V1V1 V CM 9/2/2013PHY 711 Fall Lecture 312 Relationship between center of mass and laboratory frames of reference – continued (elastic scattering)
9/2/2013PHY 711 Fall Lecture 313 Differential cross sections in different reference frames
9/2/2013PHY 711 Fall Lecture 314 Differential cross sections in different reference frames – continued:
9/2/2013PHY 711 Fall Lecture 315 Example: suppose m 1 = m 2
9/2/2013PHY 711 Fall Lecture 316 Example of cross section analysis – CM versus lab frame