Why Don't Neutron-Neutron States Exist?

• Mr T
In summary, the reason why Neutron-Neutron or P-P states do not exist is due to the spin-dependent nature of the nucleon-nucleon force, which favors parallel spins. Additionally, the spins in a proton-proton or neutron-neutron system would have to be anti-parallel, making it energetically unfavorable. While there is no first principles calculation showing this, it can be approximated through QCD, gravity, and other factors. Gravity plays a crucial role in the existence of bound states, such as neutron stars.
Mr T
Hey all,

My year 13 physics students stumped me with this one: Why don't Neutron-Neutron (or P-P for that matter) states exist?

Thanks in anticipation...

Mr T

It would be really nice to have a first principles calculation showing this, but I'm fairly sure such a thing does not exist.

The textbook argument is this: the nucleon-nucleon force is spin dependent; specifically, parallel spins are favoured. If you had a proton-proton or neutron-neutron system, then due to them being fermions, the spins would have to be anti-parallel. Deuterium can be spin-parallel, and the nucleon-nucleon force is only just enough to hold it together (for instance, no excited bound state of it exists).

For NN you could just look at the potentials holding it to gether vs pushing it apart.
I think you can do some first order approximations for QCD (say, a heavy and light meson exchange yukawa potential) + gravity (very very weak) + spin+etc.

I think you can show that there should be no bound states. The reason I mention gravity is that there IS a bound state for a neutron particle, its called a neutron star. Gravity is finally large enough at that level to pull in the same amount that the repulsive forces (degeneracy pressure+temp) are pushing out.

1. Why is it impossible for two neutrons to form a stable state?

Two neutrons cannot form a stable state because they both have a negative charge, making them repel each other. This repulsive force is stronger than the strong nuclear force that holds the nucleus of an atom together.

2. Can other particles, such as protons, form a stable state with neutrons?

Yes, other particles can form stable states with neutrons. Protons, which have a positive charge, can form stable states with neutrons due to the attractive force of the strong nuclear force.

3. Are there any exceptions to the rule that neutron-neutron states do not exist?

There are a few rare and short-lived exceptions to this rule, such as in certain nuclear reactions or in the extreme conditions of neutron stars. However, in general, neutron-neutron states do not exist.

4. How does the presence of neutrons affect the stability of an atom?

The presence of neutrons in an atom can affect its stability in several ways. Extra neutrons can make the nucleus more unstable, leading to radioactive decay. However, in some cases, adding more neutrons can actually increase the stability of an atom by balancing out the repulsive forces between protons.

5. What implications does the absence of neutron-neutron states have in nuclear physics?

The absence of neutron-neutron states has significant implications in nuclear physics. It plays a crucial role in understanding and predicting the behavior of atomic nuclei, as well as the processes of nuclear fusion and fission. It also helps explain why certain elements are more stable than others and the limits of nuclear stability.

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