Physics 195bProblem set number 17Due 2 PM, Thursday, February 27, 2003Notes about course:• Homework should be turned in to the TA’s mail slot on the first floorof East Bridge.• Collaboration policy: OK to work together in small groups, and to helpwith each other’s understanding. Best to first give problems a good tryby yourself. Don’t just copy someone else’s work – whatever you turnin should be what you think you understand.• There is a web page for this course, which should be referred to for themost up-to-date information. The URL:http://www.hep.caltech.edu/˜fcp/ph195/• TA: Anura Abeyesinghe, [email protected]• If you think a problem is completely trivial (and hence a waste of yourtime), you don’t have to do it. Just write “trivial” where your solutionwould go, and you will get credit for it. Of course, this means you arevolunteering to help the rest of the class understand it, if they don’tfind it so simple. . .READING: Read the “Identical Particles” course note.PROBLEMS:80. High energy limit: Do Exercise 7 of the Scattering course note.81. Consider the graph in Fig. 1.Assume that the other phase shifts are negligible (e.g.,“lowenergy”is reasonably accurate). The pion mass and energy here are suffi-ciently small that we can at least entertain the approximation of aninfinitely heavy proton at rest – we’ll assume this to be the case,in any event. Note that Tπis the relativistic kinetic energy of theπ+: Tπ=P2π+ m2π− mπ.46050 100 20015004080120160T(MeV)PhaseShift(degrees)πFigure 1: Made-up graph of phase shifts δ0and δ1for elastic π+p scattering(neglecting spin).(a) Is the π+p force principally attractive or repulsive (as shown inthis figure)?(b) Plot the total cross section in mb (millibarns) as a function ofenergy, from Tπ=40 to 200 MeV.(c) Plot the angular distribution of the scattered π+at energies of120, 140 and 160 MeV.(d) What is the mean free path of 140 MeV pions in a liquid hydrogentarget, with these “protons”?82. Inelastic scattering: Do Exercise 8 of the Scattering course note.83. Exclusion principle and atomic states: Do Exercise 1 of the IdenticalParticles course