# Spin and parity for nuclear shell model

1. Apr 9, 2012

### dingo_d

1. The problem statement, all variables and given/known data
I have an element: ${}^{207}Pb$, with Z=82, and A=125, and I need to find spin and parity of it.

2. Relevant equations
The angular momentum is determined by the angular momentum of the last nucleon that is odd, in this case it will be one unpaired neutron.

Now what confuses me is that the last neutron is in $3p_{1/2}$ shell, but when I look at the picture:

and start to fill the shells, how do I know that it must be $3p_{1/2}$ and not $2f_{5/2}$? Is it because of the energy difference? That is I take the one that is the closest to the filled shell?

That is basically what bothers me a bit. The spin and parity is easy once I know this. Since the protons are all paired I only need to look at this unpaired neutron, and the answer is $J^{\pi}=\frac{1}{2}^-$

EDIT: I totally misunderstood this magic stuff xD I need to fill each shell so that in the end I have all paired up, and if I have unpaired it needs to be in the next shell (if it is energy efficient ofc)! That's why I have it in $3p_{1/2}$!

:D

Last edited: Apr 9, 2012