Neutron Death

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Neutron Death

Postby Event Horizon on March 6th, 2018, 4:17 pm 

I am interested to hear if anyone has yet worked out why Neutrons only survive on their own for about 8-12 minutes before they disintegrate, presumably into disparate quarks or something.
I was wondering why being in close proximity to protons gives them stability. I understand there are entire bodies in space that are nothing but Neutronium, the most explosive form of matter we know of. For a particle that we call neutral, well, it doesn't seem very neutral to me. If anyone could help me understand this, I would be very grateful.
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Re: A non-Binding Answer

Postby Faradave on March 6th, 2018, 6:08 pm 

Hi EV,

While I don't think we can yet truly know the answer as to why an isolated proton appears to be completely stable and an isolated neutron has a half life around 10-15 min., certain assumptions can be made. The masses of these particles is about 98-99% binding energy, with the remainder attributable to the rest masses of the comprising quark triplet for each.

A stable proton has a rest mass of 938.3 MeV/c2. A neutron has a rest mass of 939.6 MeV/c2. The higher energy state of the neutron is a reasonable guess as to why it's less stable. (But why so much more stable?) Then assume the neutron decay products (typically proton + electron + anti-neutrino)have a lower total binding energy than the parent particle.

"The decay of one of the neutron's down quarks into a lighter up quark can be achieved by the emission of a W boson. By this process, the Standard Model description of beta decay, the neutron decays into a proton (which contains one down and two up quarks), an electron, and an electron antineutrino." - Neutron Decay

In a neutron star, the reverse decay of proton + electron = neutron requires energy. This is supplied by the gravitational collapse to a more the dense state, and presumably the source of its stability, at least until enough mass accretes to cause a further degenerative collapse to a quark plasma and then to a black hole.
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Re: Neutron Death

Postby Event Horizon on March 9th, 2018, 1:49 pm 

I'm a little curious that the Universe does not appear to me to have a Neutron deficit. I would have expected all unbound neutrons to self destruct leaving only disparate component parts. I was wondering if perhaps there is a process capable of creating new neutrons, I don't personally know of one. I Know fission and fusion reactions often liberate huge amounts of neutrons, but I think those processes just liberate pre-existing bound or free neutrons.
If we wanted to create a new supply of virgin neutrons, how would we try that?
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Re: Shifting into Reverse

Postby Faradave on March 9th, 2018, 2:01 pm 

EH wrote:I was wondering if perhaps there is a process capable of creating new neutrons, ...


The "reverse decay" I referred to above is more properly called "electron capture" and gains a neutron at the expense of a proton.

If you count the ones in neutron stars, there may well be an excess of neutrons over protons in the universe. Overall, conservation of charge remains because of the involvement of electrons.

*Sorry about referring to you as "EV" above. In addition to laziness, I suffer chronic typo-rrhea.
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Re: Neutron Death

Postby Event Horizon on March 9th, 2018, 3:33 pm 

You are more than welcome to use the EV moniker. It's not a problem as far as I am concerned. Dare I say it's even a little comforting. Thanks for explaining the physics above. If there is/was such a surplus, it might suggest that they were easier than many other particles to condense out of the primordial universe, but I don't know why this should be. As much as we know about these particles, I still find them a bit odd. I apologize for my ignorance, I am not a physicist, I couldn't deal with the maths. I went into Biology, which I hadn't realised was mainly just number-crunching too!
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Re: Neutron Death

Postby JMP1958 on March 10th, 2018, 1:29 pm 

Event Horizon » March 6th, 2018, 1:17 pm wrote:I am interested to hear if anyone has yet worked out why Neutrons only survive on their own for about 8-12 minutes before they disintegrate, presumably into disparate quarks or something.
I was wondering why being in close proximity to protons gives them stability. I understand there are entire bodies in space that are nothing but Neutronium, the most explosive form of matter we know of. For a particle that we call neutral, well, it doesn't seem very neutral to me. If anyone could help me understand this, I would be very grateful.


An isolated neutron has a mean lifetime of ~14 min. However this does not result in any individual neutron living 14 min on average. In this case, the term mean lifetime has a specific meaning which is related to the half-life in exponential decay. It is the inverse of the decay rate.

The decay rate, in turn can be used in the following equation to determine the expected number of remaining particles from given sample after some time

N = N0 e-dt

Where N0 is the number of particles you started with
e is the base of natural logarithms
d is the decay constant
t is the time period.

The mean lifetime is also related to the half-life by a factor of ~0.693. Thus the half-life of a neutron is ~10 min 11 sec. The thing about mean lifetimes and half-lives is that they really only work with large populations of particles. The half-life of the neutron tells us that if you start with x neutrons, after 10 min 11 sec you would have x/2 neutrons and after 20 min 22 sec you would have x/4 neutrons, etc. But a single isolated neutron could decay in the next second or a billion years from now. (though more likely sooner than later)

Inside a nucleus are more complex. We know that being in the close presence of protons helps prevent this decay. Part of this might just be that the energy of decay is just not enough to overcome the strong nuclear binding force. But their are also "magic numbers" certain ratios of neutrons to protons are more stable than others. Thus while in general nuclei become more unstable the larger they are, there are exceptions.

Neutron stars remain stable because of the above mentioned energy of decay to binding energy issue.
When a neutron decays into a proton and electron, it does so through a decay energy. A Neutron alone takes up less volume than a proton/electron pair. Thus if the neutrons try to decay, the neutron star would have to expand to make room for them. This means raising some of its mass against its own pull of gravity increasing its gravitational potential. If this increase in gravitational potential is larger than the energy supplied by the neutron decay, then the neutron can't decay. In essence, the neutron star's own gravity prevents its neutrons from decaying.
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