50 -- g9/2 1. (6 pts) In an odd-Z odd-N nucleus, we can treat the . p1/2 ground-state as the coupling between an odd proton and an odd f5/2 p3/2 neutron state, I = jp + in. If the proton and neutron states have g-factors gp and gn, we can show that the combination has a g- 28 17/2 factor 20 9 =7(9p + gn) + (9p - In) jp(jp + 1) - in(in + 1)] --- d3/2 21 (1 + 1) $1/2 (You could show this, but I won't make you!) d5/2 8 Use this result to evaluate the magnetic moments of the -- p1/2 following nuclei in this simple model, and compare to the - P3/2 experimental values. What do the deviations tell you about the structure of these nuclei? You'll need to use the shell model (orbitals provided to the left) to find the proton and neutron single-particle states (i.e. the configuration) that leads to the state /, and you should scale the single-particle proton and neutron g factors as 0.6*g free, where gfreeis the g-factor for the free proton and neutron provided in class. (a) 14N, I = 1+ . Experimental value / = 0.40UN (b) 60Co, 1 = 5+ . Experimental value u = 3.8 UN (c) 84Rb, 1 = 2- . Experimental value / = -1.3 UN