I read that it is 10.5 minutes. Can this be artificially extended by, for example, acceleration in a particle accelerator or some other means? And since as I understand it, half-life is probabilistic, would not some neutrons just naturally remain intact for a long period, even many hours?
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4$\begingroup$ Not via acceleration, but if it is moving very fast at constant velocity, that would be enough to seem like it takes very long to decay. The other question is also a yes. $\endgroup$– naturallyInconsistentCommented Aug 6 at 4:05
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$\begingroup$ @naturallyInconsistent That sounds like it should be an answer rather than a comment. $\endgroup$– SebCommented Aug 6 at 15:28
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1$\begingroup$ Neutrons are not trivial to accelerate with existing particle accelerator technology. $\endgroup$– fraxinusCommented Aug 6 at 18:09
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2 Answers
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You can surround the neutrons with an ultra dense gas containing degenerate protons and electrons. Since the beta decay electron has a maximum energy, then if this maximum is less than the Fermi energy of the surrounding electrons, the decay is suppressed.
This is how neutron stars exist - the neutrons decay until the created electrons and protons attain Fermi energies that block further decay. The lifetime of a neutron in the interior of a neutron star could be as long as 1000 years.
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The half-life as measured in the rest frame cannot be changed. You could however make it appear longer with time dilation effects. A group of very fast neutrons would appear to you, in the lab frame, to last significantly longer than 10.5 minutes because of this.
The answer to the second question is 'yes'. Roughly half the neutrons decay in 10.5 minutes, so half are left. After 21 minutes, a quarter remain, and so on and so forth. The number remaining decays exponentially, but if you start with enough neutrons, you'll still have some left after a few hours.
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$\begingroup$ I agree that the answer to the second question is "yes" as a practical matter. I disagree with "you'll still have some left after a few hours". That is a probability, not a certainty. Nit-picking, I know. $\endgroup$– WastrelCommented Aug 6 at 15:42
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2$\begingroup$ @Wastrel: Isn't all (or much) of macrosopic physics just probability? But with such gigantic ensembles that we are happy to use phrases such as you'll still have some left after a few hours? $\endgroup$ Commented Aug 6 at 18:58
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$\begingroup$ @LeeMosher: Specifically, the probability that all of the initial $n$ neutrons have decayed after $𝜏$ half-lives is $(1-2^{-𝜏})^n = \exp(n \log(1-2^{-𝜏})) ≈ \exp(-n \, 2^{-𝜏}) = \exp(-2^{\log_2(n)-𝜏})$. This implies that, on average, the last neutron decays after about $\log_2(n)+0.83$ half-lives. A quick numerical solution also shows that after $\log_2(n)-3.8$ half-lives the probability of all neutrons having decayed is less than one in a million, whereas after $\log_2(n)+20$ half-lives the chance of there still being even a single neutron left is also less than one in a million. $\endgroup$ Commented Aug 8 at 8:34