Shell Model: Filling g9/2 Shell w/ 5 Protons

[eXorikos]

Homework Statement

How do 5 protons fill a g9/2 shell in the shell model?
There are 10 spots in the g9/2 shell.

Homework Equations

The Attempt at a Solution

Pauli principle dictates the first four to be in anti-parallel pairs. But the last can be either up or down. Am I missing something or is this really all there is to it?

 

[eXorikos]

I will try to go a little further in hope that someone picks it up and can help me.
I think I need to find the state of minimal energy for the last neutron. What are the assumptions I need to make to calculate this? Is it good enough to assume the complete independent particle model?

I really could use some help on this one. I can do the opposite, get total spin of nucleus in the groundstate by the nucleonconfiguration, but the reverse is not so clear for me...

 

[eXorikos]

I am still wondering btw... :p