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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

PHY 7 11 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. Scattering geometry:.

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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

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  1. 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. PHY 711 Fall 2013 -- Lecture 3

  2. PHY 711 Fall 2013 -- Lecture 3

  3. Scattering geometry: PHY 711 Fall 2013 -- Lecture 3

  4. Relationship between scattering angle q and impact parameter b for interaction potential V(r): PHY 711 Fall 2013 -- Lecture 3

  5. Example of cross section analysis PHY 711 Fall 2013 -- Lecture 3

  6. Example of cross section analysis Hard sphere scattering: PHY 711 Fall 2013 -- Lecture 3

  7. 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 m1 m2 v1 u1 y u2=0 z v2 Center of mass reference frame: Before After m1 m2 V1 U1 U2 q q V2 PHY 711 Fall 2013 -- Lecture 3

  8. Relationship between center of mass and laboratory frames of reference VCM V1 v1 q y U1 VCM u1 PHY 711 Fall 2013 -- Lecture 3

  9. Relationship between center of mass and laboratory frames of reference -- continued PHY 711 Fall 2013 -- Lecture 3

  10. Relationship between center of mass and laboratory frames of reference VCM V1 v1 q y For elastic scattering PHY 711 Fall 2013 -- Lecture 3

  11. Digression – elastic scattering Also note: PHY 711 Fall 2013 -- Lecture 3

  12. Relationship between center of mass and laboratory frames of reference – continued (elastic scattering) VCM V1 v1 y q PHY 711 Fall 2013 -- Lecture 3

  13. Differential cross sections in different reference frames PHY 711 Fall 2013 -- Lecture 3

  14. Differential cross sections in different reference frames – continued: PHY 711 Fall 2013 -- Lecture 3

  15. Example: suppose m1 = m2 PHY 711 Fall 2013 -- Lecture 3

  16. Example of cross section analysis – CM versus lab frame PHY 711 Fall 2013 -- Lecture 3

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