Nuclear Resonance: Effects of Width

[6Stang7]

Homework Statement

The greater the width of the nuclear resonance,...
a) the greater the rest energy of the resonance
b) the greater the lifetime of the resonance
c) the lower the rest energy of the resonance
d) the shorter the lifetime of the resonance
e) nothing

Homework Equations

Can't find any

The Attempt at a Solution

I've looked all over the internet to try to find what is meant by width for nuclear resonance. The only thing I have found is with T2, where a larger T2=>sharp signal and T1=>broad signal, so from that, I assume the width of the wave, i.e. the wavelength. So a greater width means a greater wavelength which means the greater the lifetime of the resonance, so b. But this is purely a guess; I'd like to understand the physics here.

 

[malawi_glenn]

Heisenberg uncertainty relation.

If E is larger what must happen to t (time) ?

 

[lalbatros]

"rest energy of a resonance": could that even have a meaning ?

 

[malawi_glenn]

"rest energy of a resonance": could that even have a meaning ?

If the width, i.e the uncertainty of energy is greater, that implies that t, lifetime, is lower?

nuclear resonance - the resonance absorption of a gamma ray by a nucleus identical to the nucleus that emitted the gamma ray
resonance - an excited state of a stable particle causing a sharp maximum in the probability of absorption of electromagnetic radiation

 

[lalbatros]

I think d is correct.
But the most important think, I believe, is to be able to explain it clearly.
A clear explanation should start with a good description of what a resonance is.
...

 

[Sojourner01]

'Resonance' is a terrible name for the phenomenon that's going on. What is actually happening is that the energies of the particles produced are varying due to the varying energy of the virtual particle interactions between them. Nuclear reactions occur due to i) the weak force ii) the strong force, both of which are communicated by virtual particles materialising from the vacuum a la Heisenberg. The longer duration they must exist for in order to travel the distance between the two interacting parent particles, the more tightly confined their spectrum of possible energies must be. Conversely, a virtual particle traveling a very short distance can have a (relatively) wide range of energies. The strong force interacts over a very, very short range, so generally their resonances are wider than interactions taking place through the weak force.

 

[6Stang7]

Ok, then a greater width would imply a shorter distance; however, I don't see how any of the answers relate to distance.

 

[malawi_glenn]

Think of lifetime. The smaller lifetime, the short distance the Virtual particle can travel.

But can you please tell us more about this resonance, there are several concepts in nuclear physics that uses terms as reconances.

What i mean in my first answer is that resnances are the "energy peaks" that a nuclues can absorb (compare to atomic spectrum). And the shorter the life time of a certain state/resonance, the more uncertainity in the energy (width of peak).

 

[6Stang7]

I talked with some fellow students, and the problem has been cleared up a little bit.

What is meant by width is the width of a peak in a probability function. I made this graph to help.

In this graph, P represents the probability of a particle being created, and E is the amount of energy that is placed in. the width that is in the question is the value W on the graph.

However, I am still lost here...