Discussion of free neutron lifetime

[Vanadium 50]

TL;DR Summary

Discussion of free neutron lifetime, branched off from proton radius thread

The neutron lifetime? It's not settled even now ;-)). I think it's also in the above quoted history plots in the PDG Review of Particle Physics.

I'm splitting this off the proton radius thread.

The first measurements of the neutron lifetime worked as follows: you get a nuclear reactor as a neutron source and open a port in it to get a beam of neutrons. You count the number of neutrons in the beam and the number of protons (from neutron decay) in the beam and from that infer the neutron lifetime. Because you don't see every proton produced in neutron decays, the key to this measurement is understanding how many protons you saw vs. how many you missed. In 1951 the technique was refined by looking at proton-electron coincidences, and the first measurements came out around 1100 +/- 200 s.

The next major improvement was Christensen et al. in 1971, which used a clever geometry to reduce the acceptance systematic errors of the earlier generation. They got 918 +/- 14s. You can see the error bars (and central value) drop like a stone in 1971.

Since then, these experiments have gotten more and more sophisticated. To avoid gamma ray backgrounds, which are a problem in Christiansen-type measurements, protons are trapped and then counted. Lifetimes for the best of the measurements are around 888 +/- 2.something s. They are limited not so much by the counting of protons, but by the counting of neutrons in the beam.

That's the "beam" method.

The "bottle" method is conceptually simpler. You get some ultracold neutrons. You count them and put them in a container. You wait. You count them again. Now calculate the lifetime. Instead of a proton appearance experiment, you have a neutron disappearance experiment. Perhaps more importantly, you are fairly immune to miscounting, since the numbers cancel in the ratio. The world average for such measurements is about 880 +/- 1 second. However, later measurements are higher and have larger errors: this is really driven by the 2005 measurement at NIST.

The problem with this kind of experiment is neutrons "leaking" out of your bottle. They can interact with the bottle walls, or thermal motion can cause them to go out the top, and so on. Experiments work hard to minimize this, count what they can't minimize and adjust their geometries and extrapolate to a "perfect" one to make sure all these effects are accounted for.

From a theoretical point of view, Grinstein et al. made the observation that if a neutron had a decay channel that did not involve a proton, it would give you exactly the effect seen: proton appearance experiments would give a longer lifetime the neutron disappearance experiments. The 1% discrepancy we see could be accounted for by having 99% of the neutrons decaying normally and 1% decaying through a proton-free process. That number is small enough not to be excluded by other measurements.

From an experimental point of view, if there is some mistake, where is it likely to be? In the beam experiments, it's losing a proton with noticing, and it the bottle experiments its losing a neutron without noticing. Those would tend to bias the beam experiments high and the bottle experiments low. That's what we see.

 

[mfb]

There is an approach to combine both measurements. Count neutrons, put them in a bottle, measure decays, then count neutrons again. If that gives inconsistent results it still doesn't tell you what goes wrong, of course: It could still be neutrons getting absorbed by the walls, neutrons decaying to something else, or protons that you miss.
If you can measure the decay rate over time via detected decays then you can rule out neutrons decaying to something else as reason for a discrepancy.

 

[Vanadium 50]

Count neutrons, put them in a bottle, measure decays, then count neutrons again.

That is possible, and there is a Los Alamos experiment and two European experiments that attempt to do just that. There are several challenges created by that approach:

• These are tough measurements to begin with, and a detector that has to do two things is harder to build than a detector that just does one. How do you optimize it? For appearance? For disappearance? Compromise?
• You need almost-unprecedented accuracy. The discrepancy is 8 seconds; an uncertainty of more than 3 seconds will just add to the noise. It's not enough to combine the approaches. Both approaches need to be best-in-class. As mentioned above, compromises will have to be made.
• How do you blind the analysis? If the whole point is to do two experiments at once because doing them one at a time leads to discrepancies, you really want blinding. The natural common factor to blind is the time base, which would work if the experiment were not on human timescales. But it is.

The people doing these measurements really have their work cut out for them.

 

[Buzz Bloom]

in 1971, which used a clever geometry to reduce the acceptance systematic errors of the earlier generation. They got 918 +/- 14s.

Lifetimes for the best of the measurements are around 888 +/- 2.something s

The world average for such measurements is about 880 +/- 1 second.

Hi Vanadium:

I found the following in Wikipedia.
https://en.wikipedia.org/wiki/Free_neutron_decay

Outside the nucleus, free neutrons are unstable and have a mean lifetime of 881.5±1.5 s (about 14 minutes, 42 seconds). Therefore, the half-life for this process (which differs from the mean lifetime by a factor of ln(2) ≈ 0.693) is 611±1 s (about 10 minutes, 11 seconds).[1]​

The [1] reference is

J. Beringer et al. (Particle Data Group), Phys. Rev. D86, 010001 (2012)​

http://pdg.lbl.gov/2012/tables/rpp2012-sum-baryons.pdf​

The following aspects puzzle me.
1. The first of your examples give values that do not overlap the [1] values. The difference between means is 27 s, and the sum of error ranges is 15.5 s. If the +/- error ranges are 1 σ, then if these values are increased to 2 σ then the ranges would overlap by 4 s. This suggests that the 2 σ overlap implies that to achieve a suitable 95% confidence level, the +/- values should be doubled.

2. The second of your examples also gives non-overlapping value with [1], but if the +/- values are again doubled, then the two ranges just touch each other. This again suggests +/- values should be doubled.

3. Your third example has values that overlap the [1] values quite well. What puzzles me in this case is the fact that the +/- value of 1 s is derived by averaging "world" values of multiple experiments. I would appreciate your explaining how the +/- value is calculated for such an average. I intuitively would expect it to require that some of the +/- values must be less than 1 s, and that the corresponding experiments took place more recently than 2012. If this is correct, I would appreciate your giving a few dated examples (or references to them) where such examples have a error range less than 1 s.

Regards,
Buzz

 

[Vanadium 50]

The first of your examples give values that do not overlap the [1] values.

That's not what error bars mean. This is probably not the right thread to explain error bars.

 

[Vanadium 50]

There is a new "bottle" measurement https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.162501?ft=1 and (non-paywalled) https://arxiv.org/abs/2106.10375

It is the most accurate bottle measurement, 877.75 +/- 0.27 +0.22-0.16 seconds. This actually makes the discrepancy worse. I think many people felt that the problem was in the bottle measurements with neutron-wall interactions being the culprit. This measurement has the neutrons confined largely by magnetic and gravitational fields, so this is now unlikely.

Also, the window for new physics discussed in the OP is now 6x smaller. Bill Marciano and collaborators show in PRD 100 073008 that the maximum deviation possible from an unknown invisible neutron decay is 1/6 seconds, and the measurements are 9 seconds apart.

 

[Astronuc]

Brookhaven (BNL, NNDC) reports a half-life of 613.9 s, or mean lifetime of 885.7 s (~ 877.75 s + 8 s). I recall a half-life of something like 10.2 min or 10.23 min.
https://www.nndc.bnl.gov/nudat2/reCenter.jsp?z= 0&n= 1 (use Zoom 1)

I however wasn't trying to calculate the primordial abundances of light element in the beginning.

 

[Vanadium 50]

Looks like they are picking a number between the two values with an error bar to cover the difference. The PDG has adopted the approach of declaring the one set (in this case, bottle) of experiments to be definitive. Both are reasonable, but I would personally favor the NNDC approach.