# Nuclear fusion and strong force

## Main Question or Discussion Point

I want to know the work of strong force during fusion of two atoms (say hydrogen), It is known that atoms need to get close enough to fuse but what does strong force especially "color charges" or "gluon" perform which causes fusion?

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the nuclear force is always attractive.
it is thought that much of the mass of the particle is contained in the energy of the nuclear force. yet when particles annihilate that energy is liberated.
it is short ranged
it is thought to be a residual effect of the (color) force holding quarks together. Sort of like Van der Waals is a residual effect of the forces that hold atoms together.
it is 137 times stronger than the electromagnetic force. hence you cant have nuclei with more than 137 protons.
α=the speed of the electron in the bohr atom=1/137 (coincidence?)

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it is 137 times stronger than the electromagnetic force. hence you cant have nuclei with more than 137 protons.
α=the speed of the electron in the bohr atom=1/137 (coincidence?)
Just to clarify, yes that is a coincidence (and alpha is the dimensionless coupling constant for E&M, not the speed of the electron). The strong coupling "constant" is on the order of 1, but its not even a constant it's a function of energy. The importantce of it being ~1 is that its strong and QCD problems can't be solved perturbatively.

You may well be able to describe a "speed of the electron in the Bohr atom", but given that the Bohr atom is a terrible approximation to physical reality, such a quantity is entirely meaningless. Electrons in atoms don't have speeds!

I didnt say that the bohr model wasnt a poor model.

I seriously doubt that a coincidence like that can be entirely meaningless.
It must mean SOMETHING.

But to address the original question, the key is what michael879 pointed out: the strong nuclear force is a strong interaction, and it's not possible to describe it "perturbatively" in terms of individual color charges or gluons -- these are not well-defined degrees of freedom at low energies.

Once two nuclei are forced close enough to each other (which requires overcoming the electromagnetic repulsion between electric charges of the same sign), the short-range strong force can shove electromagnetism to the side and pull the two nuclei together into a single blob. If this blob has less mass=energy than the two original nuclei had separately, the excess energy will be released, and we'll end up with a single new nucleus (at least for a time). Fusion accomplished.

If the blob has more energy than the two original nuclei had separately, a new nucleus might still be formed, but it would absorb at least some of the energy you had to pump in to overcome the electromagnetic repulsion. Not much more than that can be said without going to lattice QCD, which is just now becoming computationally feasible.

I didnt say that the bohr model wasnt a poor model.

I seriously doubt that a coincidence like that can be entirely meaningless.
It must mean SOMETHING.
It means the fine structure constant appears in Bohr's model, which we already knew.

It means the fine structure constant appears in Bohr's model, which we already knew.
Yes. I know its part of Bohr's model. I was the one who pointed that out.
The point is that it is a very interesting part of the model.
Now I dont know exactly what to make of it but its clearly very interesting.
And its clearly not 'meaningless'.

In stoney scale units

http://en.wikipedia.org/wiki/Stoney_scale_units

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Bohr puts it in the model. We see that it's in the model. I don't see what's interesting about that.

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the nuclear force
it is 137 times stronger than the electromagnetic force. hence you cant have nuclei with more than 137 protons.
Hello granpa,your comment above took me rather by surprise one reason being that that the size of the forces depends upon the separation of the particles this needing to be accounted for when comparing the forces.The electric force varies inversely as the separation squared and I don't know how the strong force varies except that its range is very short and it acts only between adjacent nucleons.
Anyway,if your comment is correct I will be interested to find out more about this.I have already tried a google search and found one vague comment that the "strong force is a hundred times stronger than the electric force".My search so far hasn't been succesful so if you can point me in the right direction I will be very grateful.Thank you.

Thank you granpa.Your reference threw up a lot of information some of which looks quite good.When I get time I will go through it more thoroughly.What gets me is that the forces are different in nature and the relative magnitudes of the forces can't be pinned down to a number as is often seen because it depends on other factors.The strong force,for example might be about 137 times stronger than the electric force but for what particle separation?
I think it may be more useful to look at the concept of "coupling constants"

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I'm afraid that much of what granpa wrote is incorrect, s

the nuclear force is always attractive.
No, it's not.

it is 137 times stronger than the electromagnetic force. hence you cant have nuclei with more than 137 protons.
You can't compare two forces with different ranges.

tα=the speed of the electron in the bohr atom=1/137 (coincidence?)
Of course its not coincidence. It's alpha*c. Even ordinary Newtonian mechanics has a relationship between the strength of a force and how fast a body orbits under that force.

No, it's not.
So do an antiproton and a proton attract or repel? If they repel (by the nuclear force) then how do they annihilate?

moreover, if it can be repulsive then why was I told once before on this very forum that it is always attractive?

You can't compare two forces with different ranges.
I just know what I read. Apparently the point they are making is that you cant get more than 137 protons in one nucleus. (without it being unstable)

It's alpha*c.
duh

Even ordinary Newtonian mechanics has a relationship between the strength of a force and how fast a body orbits under that force.
I cant imagine what your point could possibly be.

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bcrowell
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So do an antiproton and a proton attract or repel? If they repel (by the nuclear force) then how do they annihilate?
Annihilation has nothing to do with repulsion or attraction.

moreover, if it can be repulsive then why was I told once before on this very forum that it is always attractive?
Probably because the person who said that was speaking loosely.

I just know what I read. Apparently the point they are making is that you cant get more than 137 protons in one nucleus. (without it being unstable)
No, that's incorrect. There is no relationship between 1/alpha and the maximum stable Z. One way to see this is that your arguments about the orbital speeds of electrons is all about *electrons*, and has nothing to do with *nuclear* stability.

Annihilation has nothing to do with repulsion or attraction.

Probably because the person who said that was speaking loosely.

No, that's incorrect. There is no relationship between 1/alpha and the maximum stable Z. One way to see this is that your arguments about the orbital speeds of electrons is all about *electrons*, and has nothing to do with *nuclear* stability.
If they cant come together then they cant annihilate.

I didnt say that the nuclear force was alpha times stronger than the electromagnetic. I said that I had read that it was 137 times stronger. I am not sure exactly what point they are making. I would be very surprised if alpha had anything to do with it. I would certainly be interested in learning more about it though.

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bcrowell
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Gold Member
If they cant come together then they cant annihilate.
Just because two things repel, that doesn't mean they can't come together.

Just because two things repel, that doesn't mean they can't come together.
that depends on how strongly they repel doesnt it? And the nuclear force is pretty darn strong.

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Probably because the person who said that was speaking loosely.

bcrowell
Staff Emeritus
Gold Member
FAQ: Is the force between nucleons always attractive?

Protons and neutrons are referred to collectively as nucleons. Nucleons interact via the strong nuclear force, and unlike the electric and gravitational interactions, this interaction can't be expressed by any simple equation. The reason is that nucleons are not fundamental particles. They're actually clusters of quarks. All we have are models of the force, and just because two models differ, we can't conclude that one is right and one is wrong. They are simply fits to the data, with their forms chosen for convenience for a certain purpose, and often with lots of adjustable parameters. The description of the strong nuclear force is also complicated because it depends on both the spins of the nucleons and on the particular combination of neutrons and protons (although it stays the same when the identities of neutrons and protons are swapped).

Since nuclei are bound, and the electrical interactions in a nucleus are repulsive, we conclude that the nuclear force is at least sometimes attractive. It is not possible, however, to infer simply from the fact that nuclei don't collapse that the nuclear force is sometimes repulsive. In fact the main reason that nuclei don't collapse is the zero-point motion required by the Heisenberg uncertainty principle; this is exactly analogous to the reason that the hydrogen atom doesn't collapse, even though the interaction between the proton and electron is purely attractive. There are some models of the nuclear force, such as the one-pion exchange potential (OPEP), that are purely attractive, and that predict roughly the right sizes for nuclei.

Relatively sophisticated models of the nucleon-nucleon interaction do usually include repulsion under certain circumstances, e.g., there may be a "hard core" in the potential at short ranges. The fact that all such models seem to do a better job of reproducing certain data when the repulsive features are turned on suggests that this repulsive feature is model-independent.

FAQ: Is the force between nucleons always attractive?

Protons and neutrons are referred to collectively as nucleons. Nucleons interact via the strong nuclear force, and unlike the electric and gravitational interactions, this interaction can't be expressed by any simple equation. The reason is that nucleons are not fundamental particles. They're actually clusters of quarks. All we have are models of the force, and just because two models differ, we can't conclude that one is right and one is wrong. They are simply fits to the data, with their forms chosen for convenience for a certain purpose, and often with lots of adjustable parameters. The description of the strong nuclear force is also complicated because it depends on both the spins of the nucleons and on the particular combination of neutrons and protons (although it stays the same when the identities of neutrons and protons are swapped).

Since nuclei are bound, and the electrical interactions in a nucleus are repulsive, we conclude that the nuclear force is at least sometimes attractive. It is not possible, however, to infer simply from the fact that nuclei don't collapse that the nuclear force is sometimes repulsive. In fact the main reason that nuclei don't collapse is the zero-point motion required by the Heisenberg uncertainty principle; this is exactly analogous to the reason that the hydrogen atom doesn't collapse, even though the interaction between the proton and electron is purely attractive. There are some models of the nuclear force, such as the one-pion exchange potential (OPEP), that are purely attractive, and that predict roughly the right sizes for nuclei.

Relatively sophisticated models of the nucleon-nucleon interaction do usually include repulsion under certain circumstances, e.g., there may be a "hard core" in the potential at short ranges. The fact that all such models seem to do a better job of reproducing certain data when the repulsive features are turned on suggests that this repulsive feature is model-independent.
So? Who cares? As I made clear in post 15, that isnt what i was talking about. I was talking about the nuclear force between protons and antiprotons. (or neutrons and antineutrons)

Annihilation has nothing to do with repulsion or attraction.

.
I think it possibly does with the annihilation of charged particles.Does not the Coulomb attraction play a big part in the electron positron annihilation event? With the proton and antiproton one might expect the strong force to feature in the event but does it?I think there is some evidence to give some description of the strong force between particles but how much do we know much about the strong force and how it interacts,if at all,between a particle and antiparticle?Just thinking out loud here and I will research it .Any pointers about where to look will be appreciated.

So? Who cares? As I made clear in post 15, that isnt what i was talking about. I was talking about the nuclear force between protons and antiprotons. (or neutrons and antineutrons)
These cases are the same as bcrowell describes. Note that all four systems you mention are color-neutral. The strong nuclear force treats protons, anti-protons, neutrons and anti-neutrons the same. Annihilation means that systems containing both nucleons and anti-nucleons don't exist in nature (at least not for very long), but this has nothing to do with the strong nuclear force.

FAQ: Is the force between nucleons always attractive?
Thanks for this thorough explanation.

I do want to add a brief postscript on an issue I mentioned earlier (in the seventh post in this thread): there is a bona fide theory of the strong force, quantum chromodynamics (QCD), which is not just a mere phenomenological model. It is, unfortunately, analytically incalculable at the energy scales of nuclear physics, but we can obtain predictions from this theory by performing large-scale "lattice QCD" calculations on computers. Computational power is only now reaching the level necessary to permit multi-nucleon calculations in lattice QCD, but reliable results are beginning to be obtained.

I'm not an expert in this field, but to my knowledge the main remaining ambiguity is how to define "the potential" from the QCD calculations being performed. Any reasonable scheme should reproduce the same physical features.

Those with a strong background in quantum field theory might find these lectures, or references therein, to be interesting:
http://arxiv.org/abs/1008.4427
Section 3.4 presents lattice QCD results indicating that the two-nucleon potential does indeed possess a repulsive core, "whose origin is still theoretically unclear". That quote comes from the first paragraph of section 4, which tries to explain these features in terms of a QCD operator product expansion.