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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: 1s

^{1/2}shell is full for either protons or neutrons. 1p

^{3/2}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})

1s

^{1/2}+1p

^{3/2}shells have maximum of 6 nucleons. ∴ L = 1

With 6 nucleons: 1s

^{1/2}shell is full for both protons and neutrons. 1p

^{3/2}shell is not full.

L=1

J = L ± 1/2 = 1 + 1/2 → J = 3/2, L=1