# Neutron's life time

1. Mar 5, 2006

### antoon

The neutron decey is proceeded bij the weak force.
Therefore I would expect a lifetime of $$10^{-10}$$ second

But it is about 15 minutes,

Why does it take so long? is it because of the proton and neutron do not have a big mass difference ?

2. Mar 5, 2006

### mathman

On what basis did you expect it to be so short?

3. Mar 5, 2006

### Astronuc

Staff Emeritus
What is the basis of this expectation?

Actually about 10.2-10.3 minutes.

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/proton.html#c3

Last edited: Mar 5, 2006
4. Mar 6, 2006

### Meir Achuz

About 10 minutes is the half-life, not what a physicist usually calls the lifetime. It does take so long compared to other baryon beta decays because of the small mass difference.

5. Mar 6, 2006

### Astronuc

Staff Emeritus
Yeah, thanks for making that point! It is certainly more stable than mesons.

Of what other baryon beta decays is one thinking?

6. Mar 6, 2006

### antoon

I have learned that the lifetime of the particle is determinded by the force where by the decay is proceeded. A particle like the Pi menson, decay's very rapidy because of it is proceeded by the strong force. the lifetime is in the range of $$10^{-24}$$ second.

for Particle's witch decays by the weak force, the lifetime lays in the range of $$10^{-10}$$ second, But the neutron forms an exeption.

So it is the small (rest)mass diference between the neutron and proton?

sorce:
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/parint2.html#c2"

Last edited by a moderator: Apr 22, 2017
7. Mar 6, 2006

### Astronuc

Staff Emeritus
Ah, OK, I see now.

The short lifetimes cited would certainly apply to mesons and leptons.

I suspect that the stability of the neutron arises from the fact that it has 3 quarks instead of 2. This is strictly an opinion on my part.

8. Mar 6, 2006

### arivero

Hmm. One way to think is that the electroweak decays proceeds according the "espectator model", where one of the components (a down quark in this case) decays and the others just see the espectacle. In this model the decay rate depends of the quintic power of the mass of the decaying particle, m^5. Neutron decay proceeds via a down quark, so its width -inverse lifetime- should be very small compared to decays of strange and charm. This is a way to look at it, and it works, except that one can enter in discussions about if the appropiate mass to work with is the dressed one or the naked one... and that after all the mass of the quarks do not enter in the exact calculation, only the mass difference, so the expectator approximation is valid only when this difference is huge.

On other hand, and as in charged pion decay, you have a dependence on the mass of the electron, and in this case the neutron can not decay to muon. This helps a lot; you can see the formula in our thread on decays
https://www.physicsforums.com/showpost.php?p=922614&postcount=13

$$\Gamma={1 \over 4 \pi^3} ({g_w\over 2 M_W})^4 m_e^5 [function({m_n-m_p\over m_e})]$$

but you must to go to the book to check which the correction function is, I did not copied it :uhh:

Last edited: Mar 6, 2006
9. Mar 6, 2006

### Meir Achuz

There are several measured baryon berta decays listed
at pdg.lbl.gov. They are \Lambda --> p e nu,
\Xi^- --> \Lambda e nu, \Sigma^- --> n e nu,
\Sigma^+ --> \Lambda e^+ nu, \Xi^0 --> \Sigma^+ e nu.
Beta decay is not the primary decay mode.
For instance, for the \Lambda it occurs about 0.1% of the decays.
If beta decay were the only \Lambda decay mode, the lifetime would be
would be about 3X10^{-7} sec.

10. Mar 7, 2006

### arivero

Well, beta decay is the primary decay mode for the baryons you have listed, it is only that they can beta decay to quarks instead of leptons, as well as to second and third generation leptons.

Another very interesting baryon is Sigma0, the only one whose primary decay is electromagnetic.

There is a criterium in the nomenclature: if the main decay mode is strong, then the name of the particle has the mass following it, between parenthesis.

Last edited: Mar 7, 2006
11. Mar 7, 2006

### arivero

For neutron lifetime, you could be interested on the graphic in page three of http://arxiv.org/abs/hep-ex/0504034 where an history of this measurement is developed. Threre is some subtle systematic effect that clusters the lifetime in two different values, separated four or five seconds. This can be other reason explaing why so few books work out the calculation of neutron decay.

Last edited: Mar 7, 2006
12. Mar 7, 2006

### Meir Achuz

13. Mar 7, 2006

### Astronuc

Staff Emeritus
According to my old texts,

the $$\Lambda$$ particle decays according to $p\,\pi^-$ about 64.2% of the time, and $n\,\pi^o$ about 35.8% of the time, with small probablities of $p\,e^-\,\nu\,,\,p\,\mu^-\,\nu$,

and similarly

$$\Sigma^+$$ -> $p\,\pi^o$ (51.6%) and $n\,\pi^+$ (48.4%) and other rare modes,

$$\Sigma^o$$ -> $\Lambda\,\gamma$ (~100% eff.) and rarely $\Lambda\,e^+\,e^-$,

$$\Sigma^+$$ -> $n\,\pi^-$ (~100% eff.) and other rare modes

$$\Xi^o$$ -> $\Lambda\,\pi^o$ (~100% eff.) and other rare decay modes

$$\Xi^-$$ -> $\Lambda\,\pi^-$ (~100% eff.) and other rare decay modes

14. Mar 8, 2006

### arivero

I think that Meir Achuz calls beta decay to the lepton modes, while I call beta decay to any mode involving a W or Z in the decay process.

If it violates isospin and/or strange, charm, bottom numbers, then it is not strong decay; so to me it is beta decay. Call it electroweak decay if you prefer, and reserve beta for electron+neutrino. I think it is clearer to call all the electroweak not photon modes, "beta decays" but people used to "beta rays" could sustain the contrary opinion.

15. Mar 8, 2006

### Meir Achuz

I have never (until now) seen your useage. All hyperon decays are weak.
That is why they were called "strange" at one time.
Put "hyperon beta decay" into the arxiv and all you get is
Y-->Y' e nu.
I don't fence. Pistols?

16. Mar 8, 2006

### Astronuc

Staff Emeritus
:rofl: I am old and more or less set in my ways (unless there is a compelling reason to change), so beta decay to me means emission of e-, the beta particle. I don't even use the term 'positive beta decay', but rather I refer to 'positron emission'.

Pistols!? :surprised How about particles?

17. Mar 8, 2006

### arivero

Given the facts and the consensus, I can not take offense, and I hope you shall not take it neither, as you can see also my argument: I was using the emission of W particles as a criterium to call them "beta", where you -and common usage- say "weak", I thought it was more didactical.

(actually I have never fired a duel pistol -a friend has one and fires it, but not a pair of equal ones- so the proposal is interesting by itself, but we could wait for a more rabious offense . Mussolini sword duelling rules are also funny: disinfected blades, each time one blade touchs something the duel stops and the assistent wash it with alcohol)

In the other thread I have collected a log logplot of lifetimes against mass for all the non strongly decaying particles. If someone has missed it, it is also (even prettier) at

http://dftuz.unizar.es/~rivero/research/nonstrong.jpg [Broken]

It is funny to play with the parameters, for instance asking for what value of M_W should weak decays proceed with the same width than electromagnetic (photon) ones, or how should the plot vary if we vary the fundamental couplings.

Last edited by a moderator: May 2, 2017
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