What is the spin and parity of the nucleus 15N in the shell model?

[Zit501]

Hi all,

Homework Statement

In this question consider the nucleus 15N (The 15 is the atomic mass, so superscript top left of N), and refer to the shell model diagram.
(a) Predict the ground state spin and parity, J^pi.
(b) Write out the relevant odd particle configuration in the form: p (or n): (nl_j)^a (n'l_j')^a'...
where (nl_j) denotes the sub-shell and a the occupancy.

Homework Equations

The Attempt at a Solution

(a) Well from what I know there will be 7 protons, hence 1s will be filled, and 1p will have 5 out of 6 spaces filled. Do the positive spins get filled first? If so then it's a negative spin? Not sure about this parity thing... Wikipedia has an article that says both 1s and 1p filled gives odd parity, so does this mean that 7 protons is even?

(b) (1sl_j)² (1pl_j)⁷ ??

 

[malawi_glenn]

you have to differ between spin and spin. i.e. Spin of a nucleon and J, the total angular momentum (nuclear spin).

 

[Zit501]

Well, this is for a nuclear course.. I'm not sure the difference between the 2.

 

[malawi_glenn]

you have S, and J.

J = L + S

The spin (i.e the NUCLEAR spin, J) of the last unpaired nucleon determines the spin the the entire nucleus in the shell model.

And the parity of the nucleus is the parity of the last unpaired nucleon. Parity of a state is (-1)^L

Your notes on the Shell Model should say this.