# Can we Calculate Radioactive Decays?

Q:
Does there exist a model or a theory of atomic nuclei which would enable physicists to calculate the rate of radioactive decay of a particular isotope (as a function of the number of protons and neutrons contained in the nucleus) so that they could arrive at a theoretical half-life for that isotope, which could then be compared to its measured half-life? My point is the half-life of an isotope should not be just a natural constant, but should be calculable, it the theory is good enough, should it not?
- Jaakko Oksa (age 46)
Vantaa, Finland
A:

Hi Jaakko,

The decay of excited atomic energy states to lower energy states is fairly easy. For any individual atom, we can't say exactly when the decay will occur, since the event is spontaneous. Nonetheless, the decay rate of the transition can be calculated with high precision using standard quantum mechanics with a quantized electric and magnetic field. (Actually, we just did such a calculation as a homework problem for graduate quantum two at UIUC. We found a theoretical decay rate from the 2P to the 1S state of hydrogen to happen at 627 MHz, which agrees very closely with the experimental result of 627 MHz.)

As for nuclear decays, the same principle applies, except the interactions insides a nucleus are very difficult to calculate.  In early days, physicists studied forces between nucleons (neutrons and protons), and found out that the interactions are not just between two nucleons,  but also between three or even more nucleons.   We now understand that the interactions between nucleons are residual forces from the strong interactions between quarks inside the nucleons.  Strong force has the unusual property that it becomes stronger as quarks are moved away from each other.  The approximation methods used for calculating the atomic structure do not work in this situation.   New calculation methods with the help of super-computers are making headway in our understanding of nuclear structure.   We hope that one day the theory will be good enough to predict the nuclear decay half-lives, as you correctly pointed out.

Cheers,

David Schmid,  Liang Yang

(published on 02/18/2014)

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