How to calculate the nuclear repulsive force?

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SUMMARY

The discussion centers on calculating the nuclear repulsive force between protons and neutrons at short distances, specifically at 0.5 femtometers (fm). It is established that there is no simple formula for this calculation. Two primary methods are highlighted: the traditional approach using nuclear potentials derived from nucleon-nucleon scattering and the modern method based on chiral symmetry, which utilizes Quantum Chromodynamics (QCD) and hadrons. Reference materials include Wikipedia and specific arXiv papers for further reading.

PREREQUISITES
  • Understanding of nuclear potentials and nucleon-nucleon scattering
  • Familiarity with effective field theories, particularly chiral symmetry
  • Knowledge of Quantum Chromodynamics (QCD)
  • Basic grasp of femtometer scale measurements in nuclear physics
NEXT STEPS
  • Research the Walecka model and its applications in nuclear physics
  • Study chiral perturbation theory and its implications for nuclear forces
  • Examine nucleon-nucleon scattering experiments and their results
  • Explore the latest arXiv papers on nuclear force calculations and methodologies
USEFUL FOR

This discussion is beneficial for nuclear physicists, researchers in particle physics, and students studying advanced concepts in quantum mechanics and nuclear interactions.

Jan Nebec
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Hello!

I'm wondering if there is a simple formula to calculate nuclear repulsive force at given distance between a proton and neutron? For example at 0,5 fm between them...

Thank you!
 
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There is not.
 
Sure, the nuclear force gets repulsive at short distances (for distances less than about 0.8 fm or so). Today there are two standard methods to quantitatively address this problem: One is decades old and uses nuclear potentials, which are based on detailed phenomenology on nucleon-nucleon scattering, sometimes derived from effective one- and/or multiple-boson-exchange models (like the Walecka model).

The other is more modern and has the ambitious goal to derive the potential from chiral symmetry, which is the appropriate effective low-energy theory of QCD using hadrons as the relevant field-degrees of freedom.

See, e.g.,

https://en.wikipedia.org/wiki/Nuclear_force
https://arxiv.org/abs/1105.2919
https://arxiv.org/abs/1001.3229
 
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Yes, but he asked for a simple formula. Even the curves on Wikipedia don't have a simple formula associated with them. Because nuclear potentials are not simple.
 
Well, that's indeed true. Sigh...
 
Thank you for answer :)
I think I got what I needed!
 
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