Shell model determining spin and parity

[Confundo]

shell model determining spin and parity - urgent

Homework Statement

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

Homework Equations

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

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 +.

 

[Confundo]

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

 

[malawi_glenn]

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

 

[Confundo]

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

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?

 

[malawi_glenn]

why negative parity?

 

[Confundo]

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

 

[malawi_glenn]

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

Remember how to add two angular momenta.