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Is it true that the nucleus of all atoms (including radioactive isotopes) contain at least one proton? Is there an atomic nucleus consisting entirely of neutrons? (Let's exclude neutron stars for the moment.) If so, how does one name them? (since Periodic Table starts from atomic number 1, not 0.)

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The question to ask yourself here is "What makes it a 'nucleus' instead of just a collection of protons and neutrons?" – dmckee May 17 '14 at 15:16
What you are looking at is a conjectured element called Neutronium:… – DarioP May 17 '14 at 15:17
Does a neutron star count as a nucleus? – Superbest May 18 '14 at 0:01
up vote 7 down vote accepted

Well, actually there exists a nucleus which contains no protons. It has the atomic number 0, the mass number 1, and consists of one neutron, zero protons and zero electrons. It is called neutron. It is an unstable nucleus which decays via beta decay.

If you think that calling the neutron a nucleus is not proper, then think of the following: The hydrogen nucleus is just a proton. And chemists have no problem to talk about $\mathrm{H}^+$ ions, which are also nothing but protons, without any electrons around them.

According to the Wikipedia page DarioP linked to, also a di-neutron ($Z=0$, $A=2$) has been observed, which is extremely unstable. While the decay channel is not stated there, I guess the two neutrons just separate from each other; whether you call that neutron emission of spontaneous fission is a question of semantics. I guess in principle there would be also the possibility of beta decay to deuterium, but I'd not expect that to happen in observable rates.

Higher isotopes have not been observed, and are not to expect from theory.

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Indeed you are right. But just to make things less trivial, let's assume more than one neutron. – ashpool May 17 '14 at 15:25
@ashpool: See my edit – celtschk May 17 '14 at 15:38
The instability of the dineutron and diproton is a consequence of isospin symmetry and is famously related to the spin of deuterium. – rob May 17 '14 at 18:53
The fact that there are no stable composite of neutrons seems to indicate that there is some sort of exclusion principle at work here? Probably something to do with spins as rob mentioned. – ashpool May 17 '14 at 19:38
I think the assumption for a nucleus containing only (multiple) neutrons is that they would be held together by the nuclear force, with no counter-electric force that would cause instability off the main "island". Can you explain why this would not be the case? – Michael Jan 22 '15 at 18:59

Such thing can exist. However, we call atoms the elementary particles of what we consider "matter", which have some physical and chemical properties.

Chemical properties are most important here, and they are defined by the atom's electron configuration — actually, everything chemical that happens in the entire world happens due to atoms interacting through their outer electron shells. "Nucleus" that consists only of neutrons has no charge and cannot hold any electrons, so it is really just a bunch of neutrons in space. Probably this is why people don't call a single neutron "nucleus" (which would imply that it is the inner part of "something", but there is no something for such nucleus). Not so say that free neutron decay (AFAIR, the half-life is about 10 minutes).

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