16. The range of the potential between two hydrogen atoms is approximately 4 °A. For a gas in…

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 (b–e) 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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