Nucleon Potential: Why 3D Harmonic Oscillator?

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    Nucleon Potential
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Discussion Overview

The discussion revolves around the potential energy of nucleons within a nucleus, specifically focusing on the approximation of a 3D harmonic oscillator potential and its relation to other potentials like the Yukawa and Hultén potentials. Participants explore theoretical frameworks, mathematical approximations, and the implications of different potential models in nuclear physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question why the potential energy of nucleons is approximated by a 3D harmonic oscillator potential, suggesting it may relate to the Yukawa potential experienced collectively by nucleons.
  • One participant notes that the harmonic oscillator potential can approximate any potential near its minimum due to the Taylor series expansion, emphasizing the mathematical aspect of this approximation.
  • Another participant argues that the effective potential is more similar to a rounded square well rather than a harmonic oscillator, and mentions the Pauli exclusion principle allowing nucleons to pass through the nucleus until they reach the edge.
  • Several participants discuss the Hultén potential as an analytical potential for the deuteron and clarify that it is not the potential seen by a nucleon in a nucleus.
  • There is a mention of the Woods-Saxon potential as another model for nucleons inside a nucleus, which some participants identify as similar to the rounded square well.
  • One participant asserts that the Yukawa potential does not act within the nucleus due to the Pauli exclusion principle, while another challenges this assertion and seeks clarification on the role of the Pauli exclusion principle and the concept of the nucleus's edge.
  • Discussions also touch on the quantized bound states of nucleons and the energy requirements for state changes, with one participant emphasizing the nucleus's radius and the conditions under which nucleons are affected by forces.
  • There is a query about recommended literature on nuclear physics, with a suggestion of Henley and Fraunfelder's book, and a discussion on the potential used to model neutron-proton interactions in the deuterium nucleus.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of the harmonic oscillator potential, the role of the Yukawa potential, and the nature of the effective potential in nuclear interactions. The discussion remains unresolved with multiple competing perspectives presented.

Contextual Notes

Participants note limitations in their discussions, such as the focus on the radial part of the potential and the complexity of nuclear interactions that include various components like spin-spin and tensor interactions.

quantumfireball
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Why is the potential energy of a nucleon within the nucleus approximated by 3D harmonic oscillator potential?
Is the 3D harmonic oscillator potential approximately equal to the yukawa potential experienced by the nucleon as a result of all the other nuclei(ie collectively) ?
 
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A harmonic oscillator has a potential that goes as ~x2. The Taylor series of any potential looks like x2 near the minimum. So you can always approximate with a harmonic oscillator. That's just mathematics.

How good this approximation is, that's physics.
 
The SHO is used because the many body wave functions are easier to work with.
The actual effective potential is more like a somewhat rounded square well.
The Yukawa potential does not act because the Pauli principle tends to let the nucleons pass freely through the nucleus until they near an edge.
 
The Hultén potential is an analytical potential for the deuteron, i.e the N-P force.

Remember also that we here only discuss the RADIAL part of the potential, there are SS parts, LS parts, etc. as well
 
malawi_glenn said:
The Hultén potential is an analytical potential for the deuteron, i.e the N-P force.

Remember also that we here only discuss the RADIAL part of the potential, there are SS parts, LS parts, etc. as well
The Hulthen potential is an approximate two-nucleon potential, it is not the potential seen by a nucleon in a nucleus.
 
clem said:
The Hulthen potential is an approximate two-nucleon potential, it is not the potential seen by a nucleon in a nucleus.

Yes, I have not stated anything else.

Another used potential for nucleons inside a nucleus which has not been mentioned is the wood saxon, which is the one you are referring to as "a rounded square well".

I am not familiar with the Yukawa potential when talking about the potential energy of a nucleon inside a nucleus, only when discussing the nucleon-nucleon force, since the yukawa potential arises due to scalar meson exchange.. that's why I mentioned the hulten potential.
 
The YP is due to pseudoscalar exchange.
The YP and HP are both used in the N-N interaction, but not in larger nuclei.
You are not "not familiar with the Yukawa potential when talking about the potential energy of a nucleon inside a nucleus", because as I said in my post, it does not act there.
You are right in identifying my simplification as the Woods-Saxon potential.
 
clem said:
The Yukawa potential does not act because the Pauli principle tends to let the nucleons pass freely through the nucleus until they near an edge.


What PEP has got to do?
Plz make it more clear.
What do you mean by edge?
 
The nucleons in a nucleus are all in quantized bound states.
In order for a nucleon to change its state due to interaction, it must be raised to a higher unoccupied state. Most of the interactions do not provide enough energy for that.
The nucleus is like a sphere of radius 1.2A^(1/3)fm. A nucleon does not get affected by the forces until it tries to leave the nucleus at its edge.
You should read a nuclear physics book instead of this forum.
 
  • #10
clem said:
You should read a nuclear physics book instead of this forum.

Which authors do you recommend??
BTW what potential is used to model the interaction between neutron and proton in deuterium nucleus?
should'nt it be the Yukawa potential.
If so does the equation admit solutions that are similar to that of electron in hydrogen atom for the theta-phi part .The radial part depending on the potential
 
  • #11
The Hulthen potential is a fairly simple for the deuteron.
The N-N potential has a hard core at small distance, which is lacking in the Yukawa potential.
The angular part for any spherically symmetric potential is the same (spherical harmonics).
However the N-N system has only one bound state, and it is sphericallly symmetric with no angular dependence.
I am not familiar with new books on nuclear physics, but Henley and Fraunfelder wrote a good book some time ago. You should know QM to read it.
 

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