# A What is the value of the pion-nucleon coupling constant?

#### Phi6er

1. https://en.wikipedia.org/wiki/Yukawa_potential
2. https://en.wikipedia.org/wiki/Yukawa_interaction#Classical_potential

I'm working on my BSc right now and I'm solving the energies of 2 nucleon systems (so basically just deuteron) by treating them as non-relativistic two particle systems where the potential only depends on distance. The 3D Schrödinger-equation reduces into a one dimensional one with an effective potential, which I then solve numerically.

But I need nuclear potentials to plug in, of course! I've already used a sort of square well type of potential, so I thought I'd plug in a Yukawa potential next. Here's where the problem arises: I don't know what to use as the value of the scaling constant. In link 1, the mystery constant is notated as g2 and in link 2 it is notated as g2/4π. The constant is apparently called the "gauge coupling constant" between the meson and fermion fields.

I've yet to find a single source that bothers to mention what kind of natural units they use, so all the numerical values I've found for the constant are useless to me. I know the units of the constant obviously have to be units of energy times units of length, as that way the potential function itself spits out units of energy. I've even tried to guess the units based on this, but every time I get a potential that is either way too deep or too shallow compared to the square well type of potential that I used and hence know is reasonably close to the truth.

So yeah, I have no idea where to find the value of this mysterious constant. Does anyone here know what it is?

#### nrqed

Homework Helper
Gold Member
1. https://en.wikipedia.org/wiki/Yukawa_potential
2. https://en.wikipedia.org/wiki/Yukawa_interaction#Classical_potential

I'm working on my BSc right now and I'm solving the energies of 2 nucleon systems (so basically just deuteron) by treating them as non-relativistic two particle systems where the potential only depends on distance. The 3D Schrödinger-equation reduces into a one dimensional one with an effective potential, which I then solve numerically.

But I need nuclear potentials to plug in, of course! I've already used a sort of square well type of potential, so I thought I'd plug in a Yukawa potential next. Here's where the problem arises: I don't know what to use as the value of the scaling constant. In link 1, the mystery constant is notated as g2 and in link 2 it is notated as g2/4π. The constant is apparently called the "gauge coupling constant" between the meson and fermion fields.

I've yet to find a single source that bothers to mention what kind of natural units they use, so all the numerical values I've found for the constant are useless to me. I know the units of the constant obviously have to be units of energy times units of length, as that way the potential function itself spits out units of energy. I've even tried to guess the units based on this, but every time I get a potential that is either way too deep or too shallow compared to the square well type of potential that I used and hence know is reasonably close to the truth.

So yeah, I have no idea where to find the value of this mysterious constant. Does anyone here know what it is?
See for example page 3 of the following source for numerical values:

#### Phi6er

See for example page 3 of the following source for numerical values:

You're a damn hero. Thank you so much.

One more question though: how do I cite something like this? Can you throw me a link to whatever that is an appendix to? That would help me cite it.

#### nrqed

Homework Helper
Gold Member
You're a damn hero. Thank you so much.

One more question though: how do I cite something like this? Can you throw me a link to whatever that is an appendix to? That would help me cite it.
You are very welcome. Good question.... I know that I have seen similar numbers in some book but I cannot remember which one, right now. I will try to find one and will get back to you.

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