Answer Happy

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 gfactor 𝑔 = 1 2 (𝑔𝑝 + 𝑔𝑛) + (𝑔𝑝
− 𝑔𝑛)[𝑗𝑝(𝑗𝑝 + 1) − 𝑗𝑛 (𝑗𝑛 + 1)] 2𝐼(𝐼 + 1) (You could show this, but
I won’t make you!) Use this result to evaluate the magnetic moments
of the following nuclei in this simple model, and compare to the
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 I, and you should scale the single-particle proton and
neutron g factors as 0.6*𝑔𝑓𝑟𝑒𝑒, where 𝑔𝑓𝑟𝑒𝑒is 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
50 28 20 1. g9/2 -pl/2 15/2 -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 17/2 1 9=₂(9p+gn) +- (Ip − In)[jp(İp + 1) − İn(İn +1)] 21(1+1) d3/2 (You could show this, but I won't make you!) s1/2 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 I, 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 00