Atomic and Nuclear Physics [Phys 433/ Gsci 593]            Fall, 2003 Assignment 10, due in class Friday, October 24. [1] Read sections 9.1 and 9.2 in Dunlap.  The questions below, of course, are completely unrelated to this reading. [2] Work out the problem below, which details some of the true trials and tribulations of a neutrino detector. A common reaction used to detect neutrinos from the sun is the inverse beta-decay reaction:  íe + 37Cl ? e- + 37Ar.  The number of solar neutrinos produced may be estimated from the solar constant (1350 W/m2).  Assume that 10% of the thermonuclear energy is carried by neutrinos of mean energy 1 MeV each.  Only about 1% of the neutrinos are energetic enough to convert 37Cl to 37Ar.  If a detector containing 400 m3 of tetrachloroethylene (C2Cl4) is used, estimate the average number of 37Ar nuclei produced in a day if the density of C2Cl4 is 1.5 g/cm3 and about a quarter of the chlorine is 37Cl.  The cross section for the reaction may be taken to be 10-49 m2 (ahh…that's the killer). [3] One of the things that a Ä++ particle really likes to do is to decay to a proton plus a ð+.    (a) If angular momentum is to be conserved, what possible values can the orbital angular momentum quantum number, l, between the proton and pion have?  (b)  Which of these l values do you expect to be most common? [4] Suppose that a spin 2 particle and a spin 3/2 particle are combined to form a state with overall spin j = 5/2 and overall z-component of spin m = -1/2.  If we were to measure the z-component of the spin of the spin-2 particle, what possible values could we obtain, and with what probabilities?