# Neutrons don't decay in nuclei because no available states incorrect?

• nonequilibrium
In summary: The electron in the ground state of an atom has a lower total energy than the atom itself, but it's not in an energy eigenstate.There's a difference between an electron in the ground state and a neutron in a nucleus. The electron is in a lower energy state, but it's still in an energy eigenstate. For a neutron, it's not because there are no available states, it's because it has a very low energy.Thanks for trying to help, but I don't think you're getting my point.
nonequilibrium
"Neutrons don't decay in nuclei because no available states" incorrect?

Hello,

If I understand correctly, the argument for a neutron (usually) not decaying when in a nucleus, is that the resulting proton would then have to occupy a high energy level, the lower levels already being occupied by the protons that are already there.

But that argument presupposes that a particle has to be in an energy eigenstate (or at least immediately after decaying). Is there any argument for this? There are an infinite number of states with average energies lower than that "high energy state" it would be obliged--according to the traditional argument--to occupy.

mr. vodka said:
Hello,

If I understand correctly, the argument for a neutron (usually) not decaying when in a nucleus, is that the resulting proton would then have to occupy a high energy level, the lower levels already being occupied by the protons that are already there.

But that argument presupposes that a particle has to be in an energy eigenstate (or at least immediately after decaying). Is there any argument for this? There are an infinite number of states with average energies lower than that "high energy state" it would be obliged--according to the traditional argument--to occupy.

The quantum mechanical bound state problem has a discrete set of bound states with energies below the configuration of free particles. The continuous spectrum is the free particle spectrum.

Stable nuclei and molecules are in the ground state of the bound state problem. Furthermore, stability requires that there are no configurations whatsoever that have lower energy, no matter what the individual particles might be able to decay into were they free. Any intermediate state should be well approximated by a linear combination of energy eigenstates, but there are none with an energy lower than that of the stable nucleus.

The "traditional argument" is nothing more than conservation of energy. It doesn't rely solely on the spectrum of intermediate states, but mainly on the energy of the ground state.

Thanks for trying to help, but I don't think you're getting my point. For example
The quantum mechanical bound state problem has a discrete set of bound states with energies below the configuration of free particles. The continuous spectrum is the free particle spectrum.
doesn't answer my question, it's only relevant if you presuppose the particles have to be in an energy eigenstate. So maybe I should rephrase my question like that, shortly put: why is it assumed that the nucleons are in energy eigenstates?

It isn't assumed. A nucleus has a total energy, therefore it is in a total energy eigenstate. It's a conclusion, not an assumption.

Okay, why does it have a total energy then?

mr. vodka said:
...doesn't answer my question, it's only relevant if you presuppose the particles have to be in an energy eigenstate.

You seem to have missed this crucial sentence:

fzero said:
Any intermediate state should be well approximated by a linear combination of energy eigenstates, but there are none with an energy lower than that of the stable nucleus.

So the argument does not rely on the nucleus actually being in an energy eigenstate.

Oh I indeed seem to have missed that part, my apologies. But either I'm misinterpreting it, or I don't understand why it's true: to me the quote
Any intermediate state should be well approximated by a linear combination of energy eigenstates, but there are none with an energy lower than that of the stable nucleus.
means that, for example, any superposition of the 1st and 2nd lowest energy eigenstates have a higher (average) energy than, for example, the 2nd lowest energy eigenstate itself.

With "stable nucleus", he means the ground state of the nucleus. And you agree that you can't find a linear combination with an average energy below the ground state? Sure, you can have all kinds of excited states, but eventually, they will decay into the ground state.

btw: this is nothing specific to nuclear physics. If your argument was true, it would also apply to electrons in atoms.

## 1. What is the significance of neutrons not decaying in nuclei?

The stability of neutrons in nuclei is essential for the stability of atoms and the existence of matter in the universe. If neutrons were to decay within nuclei, it would lead to the rapid disintegration of all elements, making life as we know it impossible.

## 2. Why do neutrons not decay in nuclei?

Neutrons do not decay in nuclei because there are no available energy states for them to decay into. In order for a particle to decay, there must be a lower energy state available for it to transition into. However, in the tightly bound environment of the nucleus, all possible energy states are already occupied by other particles, leaving no room for the neutron to decay.

## 3. Is it possible for neutrons to decay in nuclei?

No, it is not possible for neutrons to decay in nuclei. As mentioned before, all possible energy states within the nucleus are already occupied, leaving no room for the neutron to decay. Additionally, the strong nuclear force, which holds the nucleus together, is much stronger than the weak force responsible for neutron decay.

## 4. Does the stability of neutrons in nuclei have any implications in other fields of science?

Yes, the stability of neutrons in nuclei has implications in fields such as nuclear physics, astrophysics, and cosmology. It plays a crucial role in understanding the structure of atoms, the stability of elements, and the formation of stars and galaxies in the universe.

## 5. Are there any exceptions to neutrons not decaying in nuclei?

There are a few rare cases where neutrons can decay within nuclei, but these are highly unstable and short-lived isotopes that are not found in nature. They can only be created in laboratory conditions using particle accelerators.

• High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
• High Energy, Nuclear, Particle Physics
Replies
5
Views
2K
• High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
• High Energy, Nuclear, Particle Physics
Replies
15
Views
3K
• High Energy, Nuclear, Particle Physics
Replies
8
Views
3K
• High Energy, Nuclear, Particle Physics
Replies
4
Views
2K
• High Energy, Nuclear, Particle Physics
Replies
12
Views
3K
• High Energy, Nuclear, Particle Physics
Replies
8
Views
2K
• High Energy, Nuclear, Particle Physics
Replies
5
Views
4K
• High Energy, Nuclear, Particle Physics
Replies
2
Views
2K