Question

H8 Hard Sphere Scattering The dlifferential cross-section in the CM frame is given in terms of the impact parameter b and the CM scattering angle 0" by: do b db sin () Two identical hard spheres of mass m and radius R scatter off each other. Find the differential cross-section in the CM frame, σ(F). (ii) Show that the relationship between the LAB and CMI scattering angles θ and for identical spheres can be written in the form: (ii) Use the result from (i) to convert the result from (i) into a differential cross- section in the LAB frame, σ(9). (iv) Show that the total cross-sections are the same in the CM and LAB frames. Evaluate / × F) . dS where s is the open hemispherical surface x2 +y2 + z-08, with z 2 0, and (i) By direct evaluation. Take the vector element of area dS to point away from (i) By using the divergence theorem applied to the vector field Y x P. (ii) By using Stokes' theorem applied to the vector field F. the origin. (Recall that the divergence theorem applies to a closed surface.)

Answer 1

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