Nuclear Stability Calculations

[gildomar]

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.

 

[mfb]

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.

 

[gildomar]

Thanks! I had somehow managed to forget about that formula. :P

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?

 

[eys_physics]

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.

 

[mfb]

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.