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 = N

_{0 e}^{-dt}Where N

_{0} 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.