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   [re] Why do pure neutral nuclei NOT exist?

>>I wonder why pure small neutral nuclei (e.g. only 4 neutrons instead
>>of 2 protons and 2 neutrons like in He) seemed not to exist. I know
>>that giant stars can transform in so called "neutron stars", that
>>consist only of neutrons.
>>These kind of single neutral nuclei normally should be more likely and
>>even more stable, because there is no electromagnetical repulsive
>>forces between each other like in normal nuclei. It is clear that
>>single neutrons are not stable and decay within about 10 Min., but
>>bounded neutrons should exist. In standardmodel of particle physics
>>all quarks are equal to the strength of the strong interaction. The
>>strong force do not distinguish between the flavor, so there is no
>>sensible reason why neutral nuclei should not exist.
>>Maybe someone knows the answer...
>>Kind Regards!
>>Dorian Credé
>They decay for the same reason that the single neutron does.
>With strong interaction it wouldn't, but with weak interaction, it does.
>Arnold Neumaier

That's wrong, even if there was no weak and electromagnetic
interactions, there couldn't be bound states of two equal nucleons. The
reason is that the tensor force of the NN-potential is the binding
force, and it's only attractive enough if you are in the right
spin-isospin state, the deuteron state.

The deuteron bound state is S=1, T=0, and it's the only bound state of
the two-nucleon system. Since the spin-isospin part is odd under
particle exchange, the orbital part is also even, because the total
angular momentum is J=1. To be precise: it's a mixing of the orbital
angular momentum l=0 (s-wave) and l=2 (d-wave) states due to the tensor
force, which is crucial for the existence of the deuteron bound state.
The mixing of the d-state is experimentally proven by the fact that the
deuteron has indeed an electrical quadrupol moment.

Two neutrons cannot be in this state, because both have T_z=-1/2 which
cannot build the isospin-singulett state T=0, which is  the
antisymmetric combination of the two-isospin state.

Singulett isospin state: |up down>-|down up>
Triplett state: |up up>, |down down>, |down up+up down>




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