16. The range of the potential between two hydrogen atoms is approximately 4 _A. For a gas in thermal equilibrium, obtain a numerical estimate of the temperature below which the atom-atom scattering is essentially s-wave. 17. (a) If you remember it, write down the differential cross section for Rutherford scattering in cm2/sr. If you do not remember it, say so, and write down your best guess. Make sure that the Z dependence, energy dependence, angular dependence and dimensions are reasonable. Use the expression you have just given, whether correct

View complete question » 16. The range of the potential between two hydrogen atoms is approximately 4 _A. For a gas in thermal equilibrium, obtain a numerical estimate of the temperature below which the atom-atom scattering is essentially s-wave. 17. (a) If you remember it, write down the differential cross section for Rutherford scattering in cm2/sr. If you do not remember it, say so, and write down your best guess. Make sure that the Z dependence, energy dependence, angular dependence and dimensions are reasonable. Use the expression you have just given, whether correct or your best guess, to evaluate parts (be) below. An accelerator supplies a proton beam of 1012 particles per second and 200 MeV/c momentum. This beam passes through a 0.01-cm aluminium window. (Al density _ = 2.7 gm/cm3 , Al radiation length x0 = 24 gm/cm2 , Z = 13, A = 27). (b) Compute the differential Rutherford scattering cross section in cm2 /sr at 300 for the above beam in Al. (c) How many protons per second will enter a 1-cm radius circular counter at a distance of 2 meters and at an angle of 300 with the beam direction? (d) Compute the integrated Rutherford scattering cross section for angles greater than 50 . (e) How many protons per second are scattered out of the beam into angles > 50 ? (f) Compute the projected rms multiple Coulomb scattering angle for the proton beam through the above window. Take the constant in the expression for multiple Coulomb scattering as 15 MeV/c.

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