# Predicting spin and parity of excited states from shell mode

1. May 14, 2016

### pondzo

1. The problem statement, all variables and given/known data

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.

Ground state:
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)^+

First excited state: 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)^+.

Second excited state: 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.

2. May 19, 2016