How to calculate the nuclear repulsive force?

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Discussion Overview

The discussion revolves around the calculation of nuclear repulsive force between a proton and neutron, particularly at a specified distance of 0.5 femtometers (fm). Participants explore the complexity of deriving a simple formula for this force and the methods used to understand nuclear interactions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about a simple formula for calculating nuclear repulsive force at a specific distance.
  • Another participant asserts that no simple formula exists for this calculation.
  • A third participant explains that the nuclear force becomes repulsive at distances less than approximately 0.8 fm and mentions two standard methods for quantitatively addressing the problem: one based on nuclear potentials and the other derived from chiral symmetry in QCD.
  • Some participants note that nuclear potentials are complex and do not lend themselves to simple formulas, with one specifically pointing out that even graphical representations do not provide straightforward equations.
  • A later reply expresses agreement with the complexity of the topic, indicating a shared understanding among participants regarding the challenges in finding a simple formula.
  • One participant expresses satisfaction with the information received, suggesting they found what they needed despite the complexity discussed.

Areas of Agreement / Disagreement

Participants generally agree on the complexity of deriving a simple formula for nuclear repulsive force, with multiple competing views on the methods available to address the problem. The discussion remains unresolved regarding the existence of a straightforward calculation method.

Contextual Notes

Limitations include the lack of a simple formula, the dependence on complex nuclear potentials, and the unresolved nature of the mathematical representations of nuclear forces.

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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Likes   Reactions: Jan Nebec
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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Likes   Reactions: berkeman

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