# Help: Definition: 'decay width' for isotopes

1. Apr 26, 2010

### LaPaqueta

I have looked for a definition of 'decay width' on the internet and could only find articles that use the term, no definition. I first saw the term on a periodic table of elements showing information about different radioactive isotopes and their decay modes. Is 'resonance width' a synonym?

Thank you for any help.

2. Apr 27, 2010

### HotCells

Last edited: Apr 27, 2010
3. Apr 29, 2010

### LaPaqueta

Thank you for your help above.

In regard to those links above, an equation is good but that does not really tell me what 'resonance width' is. The 'definition' at that link is so short, it can hardly be a 'discussion'.

May be that the sort of definition I was looking for is wrong for this forum. Can you give me anything more? Also, what is 'decay width', if it is not a synonym for 'resonance width'?

Thanks

Last edited: Apr 29, 2010
4. Apr 30, 2010

### Staff: Mentor

Decay width, Γ, is simply the inverse of the mean lifetime, τ.

Γ = 1/τ

Is the question related to decay of particles or radionuclides?

Last edited: Apr 30, 2010
5. Apr 30, 2010

### HotCells

Take another look at http://www.nucleonica.net/wiki/index.php/Unbound_state. The definition has been updated to include an explanation including a diagram. Hope this is clearer now.

6. Apr 30, 2010

### LaPaqueta

Thank you very much to HotCells and Astronuc.

With above 2 posts and links, I think I can start to better understand 'decay width' now.

My question was originally related to radionuclides, but I like the particles too.

Thanks.

7. Apr 30, 2010

### Rajini

More news for you (especially to radioactive decay):
When a nucleus decays it follows a exponential decay function. When you make a FT of that exponential decay function you get a Lorentzian function. Now the FWHM of that Lorentzian is just the nuclear meanlife time. Got it?

8. May 2, 2010

### LaPaqueta

Thank you Rajini.

No, I havn't got it. I looked up 'Lorentzian function' on the internet and I see it involves a whole lot of math. I like math, but I was hoping for a more 'intuitive' definition for decay width. Or maybe better, words combined with equations to tie them to the concept. That sort of explanation would probably be found in text books I guess.

I will try to grapple with the Fourier transform of the Lorentzian function. This will take me a good amount of effort, but it also gives me some direction.

Thanks.

9. May 2, 2010

### Staff: Mentor

Perhaps it should be mentioned that for radioactive decay, where the decay is characterized by a half-life, t1/2, that the mean lifetime, τ, is given by

τ = t1/2/(ln 2) ~ t1/2/0.69315 = 1.4427 t1/2

The mean lifetime is also related to the decay constant, λ, by

τ = 1/λ, so λ is the same as decay width.

A nice explanation of mean lifetime is here:

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/halfli2.html (see panel 4)
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/halfli2.html#c4

10. May 2, 2010

### Rajini

Hi,
Sorry i notice a error in my post (after seeing Astronuc's post).
The FWHM of a Lorentzian is equal to:
$$\hbar/({\textrm {meanlife time}})$$.

11. May 2, 2010

### LaPaqueta

Thank you very much Astronuc.

I have a good ideal what ‘mean lifetime’ is now, a term new to me. The Wikipedia link you gave contained a good discussion about exponential decay and explained well the new term.

There is something strange though. I first encountered the term ‘decay width’ on a periodic table at this link: http://www.ptable.com/# On the isotopes tab page is listed some values for each isotope including ‘decay width’. Decay width is expressed in energy units, MeV (million electron volts), not time units like ‘mean lifetime’. (Of course mass can be expressed in energy units because m = E / c^2, so maybe the term is a mass.)

Also, thank you Rajini for addition bit of info.

12. May 3, 2010

### Rajini

Hi Lapaqueta,
Mass-energy is not applicable here!
Otherwise all isotope would have nonzero decaywidth.
So i think the decaywidth $$\Gamma$$ is expressed as follows (see my previous post or Astronuc's):
$$\Gamma=\hbar/\tau$$.
$$\tau$$ is meanlife time.
PS: but i don't why in that website they used this formula $$\Gamma=\hbar/(\tau\times 10^6)$$. And units in MeV?

Last edited: May 3, 2010
13. May 4, 2010

### LaPaqueta

Hello Rajini.

Yes, you are right. After converting MeV to Joules, I divided the values for ‘decay width’ into h-bar and got the ‘mean lifetime’ in seconds. So now I understand the mystery. Your last post clinched it for me. Thank you Rajini.

That periodic table at http://www.ptable.com/ is a very good one.

Thank you to all posters. All the posts were helpful to me.

14. May 4, 2010

### Rajini

Even more easy:
Instead of converting MeV to J, you can take hbar in eVs. Then meanlife in s.

15. May 4, 2010

### LaPaqueta

True . . . almost, Rajini. Instead of eV, take h-bar in MeV,
since Michael Dayah’s periodic table lists the values in MeVs.
Otherwise mean lifetime will come out in megaseconds, Ms. (Ms = million seconds)

Thank you Rajini.