# Predicting Half-lives of Radioactive decays

As I understand it, it's not yet possible to predict/calculate, from first principles, the half-lives of radiactive decays corresponding to any particular type of atomic isotope. Can anyone confirm this? I would also be interested to know the difficulties involved in achieving this goal. Finally, what would the theoretical and practical implications of this achievement amount to?

## Answers and Replies

Yes, the half-life cannot be predicted based upon first principles, as far as we know. In general, the more the n/p ratio diverges from the line of stability, the shorter the half-life, but this isn't always the case. For example, helium-5 (T1/2 = 7E-22 s, how in blazes they managed to measuer that small a half life I'll never know!) actually has shorter half life than helium-8 (T1/2 = 119ms).

phyzguy
Science Advisor
The strong interaction is really complicated, so I don't think anyone can predict these half-lives from first principles. There is a branch of study called lattice QCD, where people are working to simulate the properties of hadrons (quark containing particles) by solving quantum field theory on a discrete lattice of spacetime points, then take the limit as the spacing between the points goes to zero. In principle they could simulate atomic nuclei, but it currently takes a supercomputer to simulate a pion, which contains only two quarks, so simulating a large nucleus is a ways off.

Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
I disagree with the idea "we can't calculate these". Of course some input from experiment is always needed. You need some input parameters for the calculation.

I just calculated the tritium half life using only the masses of the triton, 3He nucleus and electron. Doing so, I get a half-life of 16.8 years. That's about 37% high. If I drop the point-like assumption for the triton, use measured charge distributions, and correct for the effects of electron binding on the effective masses, I get numbers much closer to the measured value.

Of course some decays are more complicated than others. and these are harder to calculate. Calculation is not a binary thing; the more inputs you can include, the more accurate the output.

mathman
Science Advisor
Yes, the half-life cannot be predicted based upon first principles, as far as we know. In general, the more the n/p ratio diverges from the line of stability, the shorter the half-life, but this isn't always the case. For example, helium-5 (T1/2 = 7E-22 s, how in blazes they managed to measuer that small a half life I'll never know!) actually has shorter half life than helium-8 (T1/2 = 119ms).

An aside: I remember in graduate school a friend of mine was working on a PhD thesis which was studying Li5 and He5 (they are very similar from a nuclear physics point of view).

With respect to using Lattice QCD to simulate the properties of hadrons, I would like to enquire if it's necessary to make any novel inventions before simulations of a large nucleus can be performed? From what I have gathered so far, the limitations only appears to be, ultimately, a matter of economics. More importantly, I want to know what use it would be to be able to calculate half-lives of isotopes that haven't even been discovered yet.

@New Physicist. Suppose there's a short-lived fissile isotope with a much higher cross section than the currently popular U-235 and Pu-239. It would be of enormous benefit in nuclear power to be able to breed this short-lived isotope as fuel, so having a formula for the half-lives of all the isotopes would greatly shorten a search for such a species.

Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
Except that we already know the fissile isotopes, their cross-sections, and lifetimes.

I assume, the term "cross section" in this context refers to a measure of the probability of a nuclear fission process taking place under a unit neutron flux. How can all the fissile isotopes be known already? In any case, I don't understand how a formula for the half-lives of spontaneous nuclear decay would aid in breeding short-lived isotopes.
Also, considering that there is more than one type of nuclear decay, wouldn't there be a need for several formulas?

bcrowell
Staff Emeritus
Science Advisor
Gold Member
As I understand it, it's not yet possible to predict/calculate, from first principles, the half-lives of radiactive decays corresponding to any particular type of atomic isotope.

It is certainly possible to calculate alpha, beta, gamma, and fission half-lives. There are many different techniques. Not all techniques are practicable in all cases. For example, in a rotational band of a deformed nucleus, it's possible to make quite accurate estimates of the gamma-decay lifetimes. Fission half-lives can be estimated with WKB tunneling in a potential-energy landscape determined through techniques such as Strutinski smearing. For spherical nuclei, calculating beta-decay half-lives is one of the classic applications of the nuclear shell model.

Question: Stimulate Beta Decay

As an engineering problem, I'm trying to figure out if it is possible to stimulate beta decay in a nucleus (of, say, a Lithium 7, a relatively stable and abundant isotope). The natural decay path would be to Beryllium, but giving off an electron, we could generate power directly from this decay.

The question then is can this decay be stimulated?
1. Can we orient the nucleus in a specific direction via a high magnetic field, so where we could reasonably count on the neutrons to be more probably in the center (like a hamburger with the protons on top/bottom)... ?

2. Is it possible to calculate the amount of energy required to push the nucleons into an excited state such that a negative beta decay is induced? Or, is this unknowable? I would suspect the lower bound to be slightly below the energy given off by the electron during the beta decay. If it's a lot lower, we can extract energy from the process, correct?

Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
Lithium 7 is stable. You cannot get energy out of it.

If you apply energy to "induce" a decay, you will always get less energy out than you put in, because the daughters are heavier than the parent. Which is why Li-7 is stable.