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I have some problems concerning one of the exercises I got last week

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

List the quantum numbers J,S,L (in spectroscopic notation [tex]^{2S+1}L_J[/tex] for partial waves of the n + p systemup to total angular momentum J=2

The quantum numbers J, S and L represent the total angular momentum, the total spin, and the relativ orbital momentum, repectively.

b) Repeat for the n+n system

c) Use the above information, together with the known spectroscopy of the deuteron, to explain why there are no bound states of two neutrons

3. The attempt at a solution

Ok first of all we can have S=0 or S=1. Then we go through the different L states.

With L=0: S L=1 : P L=2: D

S=0:

L=0: [tex]^1S_0[/tex]

L=1: [tex]^1P_1[/tex]

L=2: [tex]^1D_2[/tex]

Now I have some problems with the S=1 states. Lets assume we have L=1 and S=1. What values can J have. Is it the same as I learned for the electron orbits [tex]J=|L-S|..L+S[/tex]? So can J be in the example be 0,1 and 2?

When yes then I get 7 additional cases

S=1

L=0: [tex]^3S_1[/tex]

L=1: [tex]^3P_0 ^3P_1 ^3P_2[/tex]

L=2: [tex]^3D_1 ^3D_2[/tex]

L=3: [tex]^3F_2[/tex]

I have really no idea if this is correct or not. But when this is true I am not sure about the second part. Now we have a n+n system, this means we have to consider the Pauli principle. Which of the combination is than not allowed any longer? Of course the [tex]^3S_1[/tex] one, because then both have same spin. But are all S=1 states forbidden, even when they have a relative angular momentum?

In the last part the question about a bound state of 2 neutrons. I know that the ground state in the deuteron is the [tex]^3S_1[/tex] state. This one is not allowed in the 2 neutron system, but why not the next higher state is the ground state for the 2 neutrons?(e.g. the first excited state of the deuteron)

Would be really nice if you could help me

Best regards

Fluffy

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# Homework Help: Quantum Numbers J,S and L in p+n and n+n system

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