Nuclear Stability Calculations

In summary, the conversation discusses the equations that detail the stability of nuclei against beta decay and whether this can be derived from first principles using laws and nucleon counts. The semi-empirical mass formula is mentioned as a good approximation for a large range of nuclei, but deriving nuclear energies of heavier nuclei from first principles is a challenging task. The process of proton and neutron emission is also discussed, as well as the need for good nuclear-structure models and the impact of kinematics on half-life calculations. The conversation concludes by mentioning that these calculations are done and there are publications describing them.
  • #1
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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  • #2
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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  • #3
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?
 
  • #4
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.
 
  • #5
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.
 

Related to Nuclear Stability Calculations

1. What are nuclear stability equations?

Nuclear stability equations are mathematical equations used to predict the stability of atomic nuclei. These equations take into account the number of protons and neutrons in a nucleus to determine if it is stable or unstable.

2. How are nuclear stability equations used?

Nuclear stability equations are used by scientists to understand and predict the behavior of atomic nuclei. These equations help to determine the likelihood of nuclear reactions and the stability of different isotopes.

3. What factors affect nuclear stability?

The main factors that affect nuclear stability are the number of protons and neutrons in the nucleus. The ratio of protons to neutrons determines if a nucleus is stable or unstable. Other factors, such as nuclear spin, also play a role in nuclear stability.

4. Can nuclear stability equations predict nuclear reactions?

Yes, nuclear stability equations can predict the likelihood of nuclear reactions. By analyzing the stability of a nucleus and the energy required for a reaction, scientists can determine the probability of a nuclear reaction occurring.

5. Are there any limitations to nuclear stability equations?

While nuclear stability equations are a useful tool for understanding atomic nuclei, they have some limitations. These equations do not take into account the effects of nuclear forces and do not accurately predict the stability of very heavy or unstable nuclei.

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