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

In summary: Thank you.In summary, the conversation is about using nuclear potentials for solving the energies of 2 nucleon systems. The person is trying to use a Yukawa potential, but is unsure of the value of the scaling constant. They have searched for sources mentioning the natural units, but have not found any. Another person suggests checking a source which provides numerical values for the constant, and the original person expresses gratitude. They also ask for help with citing the source, which the other person offers to do.
  • #1
Phi6er
4
0
Links for context:
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?
 
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  • #2
Phi6er said:
Links for context:
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:

http://rickbradford.co.uk/CCC_AppF_StrongCouplinggs.pdf
 
  • Like
Likes Phi6er
  • #3
nrqed said:
See for example page 3 of the following source for numerical values:

http://rickbradford.co.uk/CCC_AppF_StrongCouplinggs.pdf

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.
 
  • #4
Phi6er said:
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.
 

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

The value of the pion-nucleon coupling constant, also known as gπN, is a dimensionless quantity that describes the strength of the interaction between a pion (π) and a nucleon (N). It is a fundamental parameter in the theory of strong interactions, also known as quantum chromodynamics (QCD).

Why is the pion-nucleon coupling constant important?

The pion-nucleon coupling constant is important because it governs the strength of the interaction between pions and nucleons, which are the building blocks of atomic nuclei. This interaction is crucial for understanding the structure and behavior of nuclei, as well as for studying the properties of the strong nuclear force.

How is the value of the pion-nucleon coupling constant determined?

The value of the pion-nucleon coupling constant is determined through experiments, specifically by measuring the cross section of pion-nucleon scattering. This involves colliding pions with nucleons and observing the resulting particles and their energies. The value of gπN can then be extracted from these measurements using theoretical models.

What is the current accepted value of the pion-nucleon coupling constant?

The currently accepted value of the pion-nucleon coupling constant is gπN = 13.3 ± 0.3, as determined by the Particle Data Group in 2018. This value has been refined over several decades of experiments and is considered to be very accurate.

Could the value of the pion-nucleon coupling constant change in the future?

While the current value of the pion-nucleon coupling constant is well-established, it is always subject to refinement as new experiments and techniques are developed. Additionally, theoretical models of QCD are constantly evolving and may provide new insights into the value of gπN. Therefore, it is possible that the value of the pion-nucleon coupling constant could change in the future, but any changes are expected to be small.

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