- 50 G9 2 1 Pl 2 F5 2 P3 2 6 Pts In An Odd Z Odd N Nucleus We Can Treat The Ground State As The Coupling Between An Od 1 (136.61 KiB) Viewed 38 times
50 g9/2 1. pl/2 f5/2 p3/2 (6 pts) In an odd-Z odd-N nucleus, we can treat the ground-state as the coupling between an odd proton and an odd neutron state, I =jp+jn. If the proton and neutron states have g-factors gp and gn, we can show that the combination has a g- factor 28 f7/2 (9p - 9n) [jp (jp + 1) − İn(İn + 1)] 21(1+1) 20 9 = (9p+9₂) +- d3/2 s1/2 (You could show this, but I won't make you!) d5/2 8 Use this result to evaluate the magnetic moments of the following nuclei in this simple model, and compare to the pl/2 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*gfree, where g free is the g-factor for the free proton and neutron provided in class. (a) 14N, I = 1+. Experimental value μ = 0.40μN (b) 60Co, I = 5+. Experimental value μ = 3.8 μN (c) 84Rb, I = 2. Experimental value μ = -1.3 μN 2. (4 pts) Let's consider the two doubly-magic nuclei, 4ºCa and 56Ni. We discussed briefly in class that collective nuclear states can be expanded as a superposition of different shell model states. (a) (2 pts) List all the particle-hole excitations across the Z=N=20 and Z=N=28 shell gaps that could give rise to 3 states in 4ºCa and 56Ni, respectively. (b) (2 pts) Considering the number of ways that you can make 3 states, which of 4ºCa or 56 Ni will have the lower-lying octopole vibration?