# On the weak force and beta decay

• I

## Summary:

We know that beta decay is and ejection of an electron from nucleus, making a proton turn into a neutron (and a neutrino). Is it correct to say that is the weak force responsible for the increasing in the distance between electron and proton during this process (since the feel atracked by each other)?

## Main Question or Discussion Point

Hi All

We know that beta decay is and ejection of an electron from nucleus, making a proton turn into a neutron (and a neutrino).

Is it correct to say that is the weak force responsible for the increasing in the distance between electron and proton during this process (since the feel atracked by each other)?

Best regards,
DaTario

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Orodruin
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No, I would not put it like that.

Weak interactions (the term "force" is not really applicable over the distances where weak interactions are relevant) are responsible for changing an up quark do a down quark or vice versa depending on whether you have beta+ or beta- decay. In this process the weak force also creates the electron/positron and the accompanying neutrino and some energy is additionally available to be put into kinetic energy of the decay products. It is this kinetic energy that ensures that the electron in beta- decay escapes the Coulomb attraction of the positive the nucleus.

We know that beta decay is and ejection of an electron from nucleus, making a proton turn into a neutron (and a neutrino).
The process as you describe it would violate charge conservation by two units. The process where a proton turns into a neutron is beta+ decay, i.e., it emits a positron, not an electron. On the other hand, in beta- decay, a neutron turns into a proton, an electron, and an anti-neutrino.

Sorry, of course. My mistake.

So, this fliping of an up quark to a down quark is all accomplished by the weak interaction, is it?
Do you agree that this makes weak interaction rather vague and hard to understand for those who doesn't have any ideia about the internal structures of quarks?
Is there any way of putting weak interaction in the same ground of eletromagnetism ?
I have heard about the fusion betweem EM and weak interaction - it seems to happen at energies of around 450 GeV.
Weak interaction can be explained with a vector field?

jtbell
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Do you agree that this makes weak interaction rather vague and hard to understand for those who doesn't have any ideia about the internal structures of quarks?
What internal structure of quarks? In the standard model, quarks are fundamental particles.

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Do you agree that this makes weak interaction rather vague and hard to understand for those who doesn't have any ideia about the internal structures of quarks?
Yes, this is hard to understand if you don't put enough effort in. Lots of things are like this, not just in physics. "Enough effort" in this case, I'm afraid is years of study.

Is it correct to say that is the weak force responsible for the increasing in the distance between electron and proton during this process (since the feel atracked by each other)?
As mentioned earlier, at these scales "force" is not a particularly useful concept. But in any event, the answer is "no" because if force were a useful concept, at least three nuclei that undergo beta+ emission (K-40, Sr-83 and I-124) would have an attractive weak force, not repulsive.

Yes, jtbell. I must appologize for my apparent ignorance in this subject. And I must also say that behind this apparent ignorance there seems to exist a real ignorance. But I am trying to grasp what is meant by sentences like:

"The weak force manifests itself in certain forms of radioactive decay and in the nuclear reactions that fuel the Sun and other stars. " (Enciclopediae Britannica)
https://www.britannica.com/science/atomic-weight

the above sentence seems to be the only information one can make available to general public. It seems to be rather vague. One should not define a force this way. Imagine if I tried to define gravitational force like this:

"The gravitational force manifests itself in certain forms of tumbles and in the celestial dynamics that can be observed by eyes or by telescopes." (Enciclopediae Brutannica)

I have almost 30 years of study of physics and I still have many doubts. I have asked many physicist what is the weak force (or interaction) and I have never got an answer which I would call satisfactory. I would appreciate answers like: " To understand the weak force one has to feel very confortable with group theory in physics, otherwise all definitions will sound vague." This I would call an honest answer. But I don't know if it is true.

Vanadium50, thank you for trying hard to be delicate. Would you have a nice reference to suggest in this topic? And your last sentence was not clear, why would these atoms have attractive weak force instead of repulsive? Is the weak force repulsive???? (many q-marks = interested) :)

It is very frustrating to teach introduction to particle physics at graduation level and have almost nothing to say about the action of this interaction. A video showing Bubka, the pole vaulter , in action should not be presented as the only reference in the definition of the actin-myosin interaction. The video is noisy in the pedagogical respect. So is the beta-decay.

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mfb
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I would appreciate answers like: " To understand the weak force one has to feel very confortable with group theory in physics, otherwise all definitions will sound vague."
Well, that is easy: To understand the weak force one has to feel very comfortable with quantum field theory, otherwise all definitions will sound vague.

Without quantum field theory we can list things the weak interaction can do - like transforming one type of particle into another - but you can only accept that as a list without understanding why it is this list and not something else.

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To understand the weak force one has to feel very comfortable with quantum field theory,
And before you can understand quantum field theory, you need to understand quantum mechanics. Before you understand quantum mechanics, you need to understand classical mechanics. Somewhere in there you should understand electromagnetism.

why would these atoms have attractive weak force instead of repulsive
They aren't atoms. they are nuclei. This is why you need to start from the beginning. Otherwise when I say things like "weak isospin doublet" and "neutron-rich nuclei" you won't see how this fits in the bigger picture.

It is very frustrating to teach introduction to particle physics at graduation level and have almost nothing to say about the action of this interaction.
Are you teaching a course in particle physics?

Ok, Vanadium50, again my mistake with taking atom by nuclei, I am sorry. But I am aware that this interaction has not the reach to produce observable phenomena in electrons orbiting the nucleus. I think I can say that I have some understanding of classical physics, quantum physics and relativity (special).

My point with weak interaction now is that, considering the sentence of Orodruin:
"Weak interactions are responsible for changing an up quark to a down quark or vice versa depending on whether you have beta+ or beta- decay. "

is that it seems to be represented by some operator which annihilates an up quark and creates a down quark.
Is it correct?
In case of a "yes" it seems much more like a thumb rule than an explanation.
Is suppose that the idea of a potential V(r) has no sense to this interaction. Is it correct?

I am teaching Modern Physics III this semester, which corresponds to the last chapters of the book of Tipler-Llewellyn. You seemed shocked by seeing a physicist who doesn't know some of the physics he teaches. Am I correct?

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mfb
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But I am aware that this interaction has not the reach to produce observable phenomena in electrons orbiting the nucleus.
It does. Electron capture is an example. It doesn't need a long range, the electron wave functions are present inside the nucleus, too.
is that it seems to be represented by some operator which annihilates an up quark and creates a down quark.
That is only "one half" of the interaction. The other half is the creation of electron+neutrino or the transition electron<->neutrino (particles and antiparticles not explicitly distinguished here). In some cases you can also make another quark transition, but that is not something you'll find naturally on Earth.
Is suppose that the idea of a potential V(r) has no sense to this interaction. Is it correct?
Not in a way that would be helpful here at least.
You seemed shocked by seeing a physicist who doesn't know some of the physics he teaches. Am I correct?
I'm not V50 but I'm skeptical as well.

Concerning prerequisites.... (click on the image to go to the next one)

Lovely, mfb, the cartoon. Very pertinent. Thank you. I am probably a physicist that earned the titles of graduation, master degree and doctorate by means of some strange process. It would not be exactly a rare event in our planet. Perhaps I must appologize for asking questions in this forun. Perhaps I should appeal only to my colleagues and to books. I don't know. But anyway thank you V50 and mfb for the contributions.

I have just found in my Feynman Lectures a very small section on nuclear forces. He says: "So far as they are understood today, the laws of nuclear force are very complex; we do not understand them in any simple way, and the whole problem of analysing the fundamental machinery behind nuclear forces is unsolved."

This book seems to have been writen around 1977 (its sixth printing)...

I am skeptical with students saying they have understood quantum mechanics.

Best Regards to all.

Orodruin
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In case of a "yes" it seems much more like a thumb rule than an explanation.
It is not just a ”rule of thumb”, it is well described (along with electromagnetism) as a quantised and spontaneously broken Yang-Mills theory based on the symmetry group U(1)xSU(2) where the left-handed quarks and leptons form doublets under SU(2). This makes precise and testable predictions. Calling it a ”rule of thumb” is not really giving it the credit it deserves.

Ok, Orodruin, I guess I can understand the part of my not being fair with the model. But what kind of predictions this model does specifically related to beta decay ?

Just checking: beta decay is a process that happens inside the nucleus and can be described as a system of annihilations and creations of particles with some extra energy released in the kinetic form.
Another way of trying to understand it is by showing an specific example its nuclear reaction:
$n \rightarrow p^+ + e^- + \bar \nu_e$.

For instance, does the model predict the frequency with which a certain nucleus undergoes beta decay?

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Orodruin
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It gives rise to (among other things) an operator that indeed annihilates a down quark and creates an up quark (and creates the electron-neutrino pair). This can be used along with nuclear physics to compute decay rates. Generally, the errors coming from the nuclear physics side are much larger.

The spontaneous symmetry breaking (through the Higgs mechanism) also describes why the mediators of the weak interactions are massive and leads to the existence of fermion masses.

The understanding of the electroweak interactions is fundamental in our understanding of high-energy physics and the construction of the Standard Model - one of the mos successful and precise theories ever in physics.

In some sense I regret not having studied quantum field theory. The abundancies of infinites in the theory made me keep a safe distance to those classes . Recently I have heard that within the frame work of some related theory (string theory) the sum of all positive integers is remarkably taken to be -1/12.

But let me ask you just one more thing, when you say (I think you just said that) that nuclear physics in some sense contaminates the quality of the theoretical results, are you saying that the entanglement (not quantum) betweem these two theories allows us to verify the correctness of each one of them in this specific case?

Orodruin
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Beta decay predictions are not the best test of weak interactions. It is just the most apparent consequence that can be presented on an introductory level.

the sum of all positive integers is remarkably taken to be -1/12.
There is nothing ”taken to be” about this result. It is the result of a particular type of regularization of the sum, which obviously is divergent in itself.

Are you also worried about the infinities appearing in classical electrostatics?

Yes, I have been allways worried with infinites in nature. But I didn't want to attack this theory. I would need arguments and I don't have any. It is merely a subjective position, result of my limitations. It was more like "this theory is not the one I would prefer to spend time thinking about it."

But I think you gave me wonderful starting points to better my understanding. In the course I teach, the teacher is not expected to give but a notion of this processes and I was very displeased with the available information regarding the weak force and the mechanism of beta decay. Perhaps now I have an idea of the height of the mountain I would have to climb to understand these things better.
I am very grateful to you all.

Orodruin
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It was more like "this theory is not the one I would prefer to spend time thinking about it."
In all honesty, personal preference with regards to how a theory is formulated is not very useful in science. What is relevant is whether or not a theory makes verifiable testable predictions and whether those predictions are corroborated by experiment or not. Of course you can worry about such things and try to find a better description that does not involve the same sort of issues, but ignoring important parts of physics because it does not aesthetically appease you is invariably going to leave you behind in terms of knowledge.

mfb
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For instance, does the model predict the frequency with which a certain nucleus undergoes beta decay?
It can be complicated for larger nuclei, but in general: Yes. But it does more than that. It also predicts the energy distribution of the electron and neutrino and it predicts the angular distribution of them and how their spin will look like.
It also predicts the lifetime of tens of other particles and their decay probabilities, again together with the energy/angular distributions and spins. And many more things we have verified experimentally (and also many things we couldn't measure yet).

Thank you, mfb. I guess the term frequency is not correct in my question. I think average time would be more suitable. I think of an ensemble of identical nuclei, all created at a certain time $t_0$ and experimentally we collect the time it takes for each nucleus to suffer this process. Then the average is the reasonable parameter. But I guess you understood what I had in mind. Sorry, anyway. And thank you gain. Among this things we could not measure yet, do you have some which has pedagogical appeal (a measurement to be explained in an introductory course)?

What is relevant is whether or not a theory makes verifiable testable predictions and whether those predictions are corroborated by experiment or not.
Maybe I am of an old school, but I respectfully disagree with you. I consider relevant in a theory the story it tells. The possibility of interpretation and understanding of elementary units of context. I believe this is possible for the atomic and subatomic scale. Besides, having all physicists glued together in the same theory seems not to be productive. It seems to me essential that some of us decide to wonder about different possibilities of explanation and modeling.

mfb
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Among this things we could not measure yet, do you have some which has pedagogical appeal (a measurement to be explained in an introductory course)?
I don't see one. It is mainly about very rare processes like $B^0 \to e^- e^+$, the decay of a neutral B meson to electron and positron.

Orodruin
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Besides, having all physicists glued together in the same theory seems not to be productive.
I never said this. Do not put words in the mouths of others.

I appoligize, Orodruin, you have said two things which sounded a bit contradictory to me. The first one was:

"personal preference with regards to how a theory is formulated is not very useful in science. "

in this part I had the impression that you were trying to induce a physicist to basically follow the mainstream.
Nevertheless you also said in the same post that:

"Of course you can worry about such things and try to find a better description that does not involve the same sort of issues "

And this stablishes a pro freedom point of view, with which I agree. Please believe I was not intentionally trying to put words in anyone's mouth. I guess I am satisfyied with all contributions. Thank you all a lot, Orodruin, mfb, jtbell and V50.

I just would like to put one thing clear, regarding my post bellow.

Maybe I am of an old school, but I respectfully disagree with you. I consider relevant in a theory the story it tells. The possibility of interpretation and understanding of elementary units of context. I believe this is possible for the atomic and subatomic scale. Besides, having all physicists glued together in the same theory seems not to be productive. It seems to me essential that some of us decide to wonder about different possibilities of explanation and modeling.
I understand the fundamental role played by the experimental corroboration and verification of theoretical results in science.

Best wishes,