Shell model determining spin and parity

1. Nov 20, 2008

Confundo

shell model determining spin and parity - urgent

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

Find the spin and parity of $$_{20}^{41}Ca$$ and $$_{20}^{40}Ca$$

2. Relevant equations

http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/shell.html

3. The attempt at a solution

For $$_{20}^{41}Ca$$we've an odd number of neutrons which will lie in 1f(7/2) level
so we have spin 7/2 and parity -

For $$_{20}^{40}Ca$$ both the unpaired neutron and proon will be in the 1d(3/2) level which has parity +, do I need to add together the two spins in this level. So I'd get spin 3 with parity +.

Last edited: Nov 20, 2008
2. Nov 20, 2008

Confundo

Thinking about it since the shell is full it can't contribute to spin.

3. Nov 20, 2008

malawi_glenn

Ca-40 has two closed shells, and since then it should have 0+ according to the shell model, right?

4. Nov 20, 2008

Confundo

Yes, I think.

If we had something like $$_{21}^{42}X$$. Then we'd have an odd neutron and odd proton in the $$1f_{7/2}$$, the spins would add and we'd have spin 7 and parity -1?

5. Nov 20, 2008

malawi_glenn

why negative parity?

6. Nov 20, 2008

Confundo

Oh yeah. Should multiply the parities and thus get positive parity right? Basically the angular momentums are "parallel".

7. Nov 21, 2008

malawi_glenn

You can also have J_tot = 6,5,4,3,2,1,0.

Remember how to add two angular momenta.