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Advanced Physics Homework Help
Predicting spin and parity of excited states from shell mode
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[QUOTE="pondzo, post: 5473742, member: 321434"] [h2]Homework Statement [/h2]Consider the following example from a previous exam. We are to predict the spin and parity for F(A=17,Z=9), Florine, in the ground state and the first two excited states using the shell model. [B]Ground state:[/B] Neutrons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^2 Protons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^2 (1d 5/2)^1 Thus J^P = (5/2)^+ [B]First excited state:[/B] Promote one proton from the (1p 1/2) level Neutrons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^2 Protons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^1 (1d 5/2)^2 Does the spin and parity come from (a) the hole created or (b) the new filled level. If (a) then J^P = (1/2)^-. If (b) then J^P = (0)^+. [B]Second excited state: [/B]Promote one neutron from the (1p 1/2) level Neutrons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^1 (1d 5/2)^1 Protons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^2 (1d 5/2)^1 Does the spin and parity come from (a) the hole created or (b) the new filled level. If (a) then the possible J values range from |1/2 - 5/2| to (1/2 + 5/2) in steps of one, so J=2 or 3. The parity multiplies so we have a minus from the l=1 neutron and a positive from the l=2 proton thus parity is minus and J^P = (2)^- or (3)^-. If (b) then J ranges from |5/2 - 5/2| to (5/2 + 5/2) in steps of one so J = 0,1,2,3,4 or 5. The parities both come from the same l level (d) so is positive. Thus J^P = (0)^+, (1)^+, (2)^+, (3)^+, (4)^+ or (5)^+. So how do we get the spin's and parities from the excited states? Is it determined by the hole created or the new excited level? Also how do I know which would be the first excited level and which would be the second? And is there a way to figure out which levels get filled up first when calculating the ground state, or should I just remember the order of the levels? We are not expected to know the Nordheim rules. [/QUOTE]
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Predicting spin and parity of excited states from shell mode
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