Nuclear Stability Calculations

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Discussion Overview

The discussion revolves around the stability of atomic nuclei against beta decay, exploring whether the half-lives of isotopes can be derived from first principles using laws of physics and nucleon counts. It also touches on related processes such as proton and neutron emission, particularly in extreme isotopes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants inquire about equations that detail nuclear stability against beta decay and whether half-lives can be derived from first principles.
  • One participant mentions the semi-empirical mass formula as a good approximation for nuclear stability across a range of nuclei.
  • There is acknowledgment that deriving nuclear energies for heavier nuclei from first principles is challenging due to the complexity of many nucleons involved.
  • Participants note that beta decay is sensitive to the structure of nuclear states and that accurate predictions require good nuclear-structure models and consideration of phase-space factors.
  • It is suggested that while the semi-empirical mass formula can indicate stability against beta decay, computed half-lives are model dependent and not straightforward.

Areas of Agreement / Disagreement

Participants express a range of views on the feasibility of deriving half-lives from first principles, with some acknowledging the complexity involved and others emphasizing the need for specific models. No consensus is reached on the methods or models that should be used.

Contextual Notes

The discussion highlights limitations in deriving half-lives, including the dependence on nuclear structure models and the challenges posed by the interactions of multiple nucleons.

gildomar
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Are there equations that detail the stability of nuclei against beta decay? On a related point, I'm familiar with the chart that shows all the isotopes and their half-lives (with a good chunk undergoing beta decay), but I was wondering if that can be derived from first principles, just using the various laws and nucleon counts? And would it cover the likelihood of proton and neutron emission as well? Because I saw that those occur at the some of the extreme edges of the table.
 
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The semi-empirical mass formula gives a good approximation for a large range of nuclei.

Deriving nuclear energies of heavier nuclei from first principles is an extremely challenging task as there are many nucleons involved.

Proton and neutron emission is a process of the strong interaction, if it is energetically "reasonable" it is usually the faster process, but it needs large differences in binding energies.
 
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Thanks! I had somehow managed to forget about that formula. :P

mfb said:
Deriving nuclear energies of heavier nuclei from first principles is an extremely challenging task as there are many nucleons involved.

So that's what would be needed to do in order to help determine what the beta decay half-lives theoretically should be?
 
gildomar said:
Thanks! I had somehow managed to forget about that formula. :P
So that's what would be needed to do in order to help determine what the beta decay half-lives theoretically should be?

Beta decays are very sensitive to structure of the nuclear states which are involved. Therefore, one needs good nuclear-structure models. In addition the half-life depends on the phase-space factor (i.e. the kinematics). The semi-emperical mass formula can tell you whether a nucleus is stable against beta decay. But, the computed half-life is except for the simplest cases quite model dependent.
 
gildomar said:
So that's what would be needed to do in order to help determine what the beta decay half-lives theoretically should be?
The simple model, and then some additional effects like the nuclear shell structure. I'm not a nuclear physics expert, but I know those calculations are done, and there are publications describing how.
 

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