# How do physicists calculate half-lives?

1. Nov 17, 2008

### Petrix

Hello!

I have just been wondering if each of the isotopes of an atom is determined by its proton (Z) and neutron number (N), then wouldn't these two numbers be enough to calculate the half-lives of them (given of course the masses of the proton and neutron also)?

So, how does current nuclear physics determine the half-life of an isotope beforehand?

What actual equations and calculations do you have to do, if theoretically those two numbers (Z & N) would be enough to determine it?

Thank you.

Last edited: Nov 17, 2008
2. Nov 17, 2008

### malawi_glenn

oh dude, this is a very difficult subject!

Basically, you need initial state (wavefunction) and final state and the transition matrix element (The interaction wich takes you from inital to final state, i.e the abstract formulation of beta decay or alpha decay etc.)

So you need:
$$<\psi _{final } |H|\psi _{initial}>$$

All of these quantities are (often) very long equations, and are also model based, which are "approximations" for which the general and important feature of the underlying basic physics are included.

So you first need your potential, in which the nucleuses moves, in order to get the hamiltonian. Then you obtain all the wavefunctions from this. Then you must find an operator wich describes and represent the physical interaction of the decay.

Maybe you have no clue what I just wrote, since what I wrote require basic knowledge of quantum mechanics.

So instead of asking us all these questions, which all requires quantum physics as background, I suggest you first learn quantum mechanics formalism and so on. Otherwise I think it is a waste of time for us talking about stuff which you can't understand ;-)

3. Nov 17, 2008

### mgb_phys

Can you predict the half life an isotope given its mass and Z?
You can make estimates of it's stability but I don't think you can actualy calculate the half life or a real atom.

Half lifes are very easy to determine experimentally of course.

4. Nov 17, 2008

### hamster143

Theoretically speaking yes, practically speaking no. To do this computation exactly, one needs analytical expression of non-perturbative sector of QCD, which is not yet known to physicists at this time. Alternatively, one could try to use existing numerical non-perturbative methods (Lattice QCD), but required computational resources would be humongous and also out of reach.

The best thing we can do is to use approximate models of nucleus and semi-empirical formulas.

5. Nov 17, 2008

### vanesch

Staff Emeritus
Pfww! I don't think anybody has ever attempted (maybe I'm wrong, refs ?) to calculate one single nuclear property "ab initio" from QCD. With a lot of effort, one can calculate the mass of a pion or so, and then with less accuracy than the experimental result.