Shell Structure in Atomic Nucleus

[unscientific]

Homework Statement

(a) What shows the existence of shell structure? What are the other numbers?

(b) Deduce the spin and parities.

Homework Equations

The Attempt at a Solution

The shell model is given by:

So for Li, 3 protons pair up with 3 neutrons, leaving an unpaired neutron in $1p_{\frac{3}{2}}$. Thus S = 3/2. It's parity is odd.

For Oxygen, 8 protons pair up with 8 neutrons, leaving the unpaired neutron at $1d_{\frac{5}{2}}$. Thus S = 5/2. Parity is odd.

For Neon, 10 protons pair up with 10 neutrons. it's even-even. Parity is even.

For Aluminium, 13 protons pair up with 13 neutrons, leaving the unpaired neutron is in $1d_{\frac{5}{2}}$. Thus S = 5/2. Parity is odd.

For Nitrogen, 7 protons pair up with 7 neutrons. No unpaired?

For Potassium, 19 protons pair up with 19 neutrons, leaving unpaired neutron at $1d_{\frac{3}{2}}$.

For Scandium, 20 protons pair up with 20 neutrons, leaving unpaired proton at $1f_{\frac{7}{2}}$.

 

[mfb]

Protons don't pair up with neutrons, they are different particles. Protons can pair up with protons, and neutrons with neutrons.

 

[unscientific]

Protons don't pair up with neutrons, they are different particles. Protons can pair up with protons, and neutrons with neutrons.

OK, I got it. How do you determine the parity then? Say for Oxygen, there is 1 unpaired neutron in 1d(5/2). What is its parity?