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Homework Statement
A certain odd-parity shell-model state can hold up to a maximum of 4 nucleons. What are its values of J and L? What about an odd-parity shell-model state with a maximum of 6 nucleons?
Homework Equations
Parity = (-1)L
J = L+S
Total angular momentum, J, is equal to orbital angular momentum, L, plus spin, S.
Nucleons are both fermions and have spin = 1/2
Therefore, J = L + 1/2
The Attempt at a Solution
Parity is odd ∴ L has to be an odd number (Parity = (-1)L)
maximum of 4 nucleons: 1s1/2 shell is full for either protons or neutrons. 1p3/2 shell is not full.
∴ J= 3/2
3n + 1p OR 1n + 3p
J = L ± 1/2 = 1 + 1/2 → J = 3/2, L=1
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maximum of 6 nucleons
Parity is odd ∴ L has to be an odd number (Parity = (-1)L)
1s1/2+1p3/2 shells have maximum of 6 nucleons. ∴ L = 1
With 6 nucleons: 1s1/2 shell is full for both protons and neutrons. 1p3/2 shell is not full.
L=1
J = L ± 1/2 = 1 + 1/2 → J = 3/2, L=1