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I'm trying to understand the role of Yukawa potential, and it seems to describe the nuclear force. But at the top of the article it says:

This article is about the force that holds nucleons together in a nucleus. For the force that holds quarks together in a nucleon, see Strong interaction.
Not to be confused with weak nuclear force.

So it seems that it's neither strong interaction nor weak interaction? So what is it? Or is it actually electromagnetic interaction in the case of nuclear? I have a feeling that strong interaction is more likely to be correct.

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Behind the scenes, it is the strong force. But on the nuclear scale, it looks quite different, and is mediated by pions (composed of two quarks) rather than gluons. Sometimes the resulting force is called the residual strong force.

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  • $\begingroup$ I see. So the Yukawa potential is the unification between strong force and electromagnetic force? I thought we need to combine EM with weak force first before combining the two with strong force? $\endgroup$ – Ooker Nov 10 '19 at 15:52
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    $\begingroup$ The Yukawa potential is a simple potential that is not necessarily just applicable for the nuclear force, or even the Standard Model. Basically, it describes any force mediated by a massive boson (including as a special case $m = 0$, as for photons, giving the Coulomb potential). But you can use it for a simple model of the nuclear force where the massive bosons are pions. In this case, the underlying fundamental physics is just the strong force (electromagnetism is not important). $\endgroup$ – Elias Riedel Gårding Nov 10 '19 at 17:19
  • $\begingroup$ I see. So the reason the nuclear force is used in the Wikipedia article is because it's the simplest and historic case? So it is the one that unify all forces in one formula? $\endgroup$ – Ooker Nov 10 '19 at 18:13
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    $\begingroup$ Yes, the Yukawa potential was historically invented to explain the nuclear force, so that is probably the most famous application of it. But it doesn't really relate to unification. Unification doesn't mean showing that "two different forces behave the same", but rather that "two forces with different behaviour have the same origin". For example, the electroweak theory shows that the photon and Z boson have a common origin. Any similarity in their behaviour is not the point. $\endgroup$ – Elias Riedel Gårding Nov 11 '19 at 1:17
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    $\begingroup$ No. Just think of Newton's law of gravitation and Coulomb's force law. These look the same (both are $1/r$ potentials). But they are both approximations of very different underlying theories (GR and QED). While the similarity is interesting, it doesn't necessarily imply a connection between them. Similarly, the nuclear Yukawa potential is an approximation that you get by replacing very complicated QCD processes (that were not known in Yukawa's time) by a simplified "effective theory". It is not a fundamental law. The fundamental law (as far as we know today) is the Standard Model Lagrangian. $\endgroup$ – Elias Riedel Gårding Nov 11 '19 at 8:59

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