Symmetry energy in nuclear physics

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Discussion Overview

The discussion revolves around the concept of symmetry energy in the semi-empirical mass formula, specifically questioning the absence of a linear term in the asymmetry parameter and exploring the implications of this formulation in nuclear physics.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why the symmetry energy term in the semi-empirical mass formula includes only the squared asymmetry parameter and not a linear term.
  • Another participant argues that the asymmetry parameter (N-Z) does not relate to symmetry as it can vary widely, suggesting that absolute values are unnecessary based on experimental evidence.
  • A different viewpoint suggests that using squared terms rather than absolute values is preferred for maintaining functional properties and aligns with experimental results.
  • One participant proposes a thought experiment involving potential energy calculations related to the height of bricks, aiming to explore the dependency of total energy on the asymmetry parameter.
  • A reference to a Wikipedia derivation of the symmetry-energy term is made, explaining the treatment of protons and neutrons as overlapping Fermi liquids and the resulting mathematical implications of using squared terms.
  • Concerns are raised about the mathematical properties of absolute-value functions, particularly their singularity at zero, which contrasts with the smoother behavior of squared functions.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and implications of including a linear term in the asymmetry parameter, with no consensus reached on the validity of the existing formulation or the proposed alternatives.

Contextual Notes

Participants highlight potential mathematical issues with absolute-value functions and the implications of using squared terms, but do not resolve these concerns or provide definitive conclusions about the symmetry energy formulation.

rahele
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I have a question about symmetry energy in semi-empirical mass formula,
According to semi-empirical mass formula as follows:
E=avA-asA2/3-acZ(Z-1)/A1/3-asym(N-Z)2/A
why in the symmetry energy only squared parameter symmetry are exist and there is not the first power of asymmetry parameter?
 
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(N-Z) would have nothing to do with symmetry, it would go from -infinity to +infinity (well, bounded by 0 neutrons and 0 protons of course). And the absolute proton and neutron numbers are in the total mass anyway (this is just the binding energy).

There could be |N-Z|, but experiments show this is not needed. And I don't see a physical reason for it.
 
I think absolute values are not so favored... :) they miss nice functional properties. So we wouldn't search for a fitting in | | but in ( )^2 if we knew a priori that something is happening, and see how that works
Also, I guess, it's because it fits the experiments as mfb said.
 
Calculate the average potential energy of a brick in a brick wall of height N. Calculate the same for a wall of height Z. Keep the sum of the height A = Z + N fixed but allow their difference (N - Z) to be a free parameter. Find out the dependency of the total energy on that free parameter.
 
Semi-empirical mass formula - Wikipedia has a derivation of the form of the symmetry-energy term. The derivation treats protons and neutrons as separate but overlapping Fermi liquids that both extend over the nucleus.

Ekinetic = EFermi/A2/3*(Z5/3 + N5/3)

One then sets Z = (A/2) + X and N = (A/2) - X and expands in X. The first term in X is a term in X2.

The absolute-value function has a problem: it has a singularity at 0. Its first derivative is a step function and its second derivative a Dirac delta function.

The square function does not have that problem.
 

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