8/31/2015PHY 711 Fall 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.

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

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

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

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8/31/2015PHY 711 Fall Lecture 38

8/31/2015PHY 711 Fall Lecture 39

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

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8/31/2015PHY 711 Fall Lecture 314 From webpage: What happens as   0?

8/31/2015PHY 711 Fall 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 

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

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

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

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

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

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

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

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

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