How to calculate the nuclear repulsive force?

In summary, the nuclear force between a proton and neutron becomes repulsive at short distances, with the critical distance being around 0.8 fm. There are two methods to quantitatively address this issue: using nuclear potentials based on phenomenology, or using chiral symmetry and hadrons as field-degrees of freedom. However, there is no simple formula for calculating nuclear repulsive force, as even the curves on Wikipedia do not have one associated with them.
  • #1
Jan Nebec
19
1
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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  • #2
There is not.
 
  • #3
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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  • #4
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.
 
  • #5
Well, that's indeed true. Sigh...
 
  • #6
Thank you for answer :)
I think I got what I needed!
 
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FAQ: How to calculate the nuclear repulsive force?

1. How do you calculate the nuclear repulsive force?

The nuclear repulsive force can be calculated using Coulomb's law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This can be expressed mathematically as F = (k * q1 * q2) / r^2, where F is the force, k is the Coulomb constant, q1 and q2 are the charges of the particles, and r is the distance between them.

2. What is the Coulomb constant?

The Coulomb constant, denoted by k, is a proportionality constant used in Coulomb's law to calculate the force between two charged particles. Its value is approximately 8.99 x 10^9 N*m^2/C^2.

3. Are there any other factors that affect the nuclear repulsive force?

Yes, the distance between the charged particles and the medium they are in can also affect the nuclear repulsive force. In a medium with a higher dielectric constant, the force will be weaker due to the polarization of the medium's molecules, which reduces the effective charge of the particles.

4. How does the nuclear repulsive force affect the stability of an atom?

The nuclear repulsive force plays a crucial role in determining the stability of an atom. If the repulsive force between protons in the nucleus is greater than the attractive force of the strong nuclear force, the nucleus can become unstable and undergo radioactive decay. This is why elements with a high number of protons tend to be less stable and have shorter half-lives.

5. Can nuclear repulsive force be manipulated or controlled?

As a scientist, it is not within our current capabilities to manipulate or control the nuclear repulsive force. However, through research and experimentation, we can better understand the factors that influence this force and potentially find ways to mitigate its effects on the stability of atoms.

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