1. Cross Section

2. Two-Body Collision  Center of mass R  Neglect external force.  Motion is in a plane Reduced mass applies Compare to CM m2m2 r1r1 F 2 int r2r2 R m1m1 F 1 int r = r 1 – r 2

3. Frame of Reference  Two body interactions generally define a natural axis. One body at rest, so the moving body moves along xOne body at rest, so the moving body moves along x Objects as point masses, so use the axis connecting the points.Objects as point masses, so use the axis connecting the points. m1m1 m2m2 v x m1m1 m2m2 v1v1 x v2v2

4. Scattering Angles  Look only at one mass. Mass 2 at restMass 2 at rest  Compare to CM frame. Set up velocity triangle in the plane of the collisionSet up velocity triangle in the plane of the collision x  m1m1   The general solution is transcendental. Often special cases For m 2 >> m 1 (=  ) Or m 2 = m 1 (= 2  )

5. Elastic Scattering  Scattering angle measured in CM. Convert to lab frame.Convert to lab frame. Depends on mass ratio.Depends on mass ratio. x 

6. Impact Parameter  Two body results are kinematic, not dynamic.  Predict angle from dynamic variables. Angular momentum JAngular momentum J Kinetic energy TKinetic energy T  Define impact parameter b. For a given T, J(b)For a given T, J(b) recoil m1m1 m2m2 v x b scatter 

7. Differential Cross Section  Predict angles from a initial distribution. Force decreases with distanceForce decreases with distance Trajectory must be asymptotic.Trajectory must be asymptotic.  Start with incident flux I. Particles/time / area normal to beam.Particles/time / area normal to beam.  Number of interactions N per solid angle  that scatter at angle .

8. Axial Symmetry  Central forces are symmetric. Axis through force centerAxis through force center Integrate over azimuthal angleIntegrate over azimuthal angle  Particles scatter in an angular range. b  

9. Lab Scattering  The cross section can be determined in the CM or lab frame. Convert from CM to lab anglesConvert from CM to lab angles next