Understanding Alpha Particle Bombardment: Scattering, Resonance, and Capture

[jimmy p]

When alpha particles are fired at a nucleus (eg. like in the Rutherford experiment) do they actually collide with the nuclei if fired head on, or is it the repulsion of the protons in each that causes them to fly off in different directions?

I ask because i have to work out the "path of closest approach" which is kinda when an alpha particle gets near to a nuclei, what is the minimum distance before a force is observed on them...or something like that, and I am having trouble picking up a lead..

 

[Njorl]

I believe that you are probably not interested in a collision. You are probably doing electric fields, right? A collision would mean you are really dealing with the nuclear strong force. This is the case if the alpha particle gets close enough for the strong force to be significant. Scattering usually implies only electric fields at work.

Dealing with just electric fields, the alpha particle can never hit the nucleus. If it did, it would have infinite potential energy. The "straight on" approach, where we don't have to worry about the particle flying off to the side, is really just a conservation of energy problem.

Assume, at an arbitrarily far distance the alpha particle has no potential energy, it is just flying in with kinetic energy. As it flies in, it converts kinetic energy to potential energy. When all kinetic is converted to potential, it comes to a stop and turns around. This is it's closest point.

So, set up a formula to give potential energy of an alpha article in proximity of a nucleus, and set that equal to the kinetic energy of your alpha particle, and solve for the distance, and that is your closest point.

Njorl

 

[Deeviant]

If the inertial forces in the particle being fired is greater than that of the coulomb force repulsion(like charges repel), the particles will collide and produce nuclear reactions(in this case fusion).

If the inertial forces our less they will simply repel each other.

As far as the smallest distance that a force would be observered between the particles, you may want to look up the range of the strong nuclear force, and find the range in which the electro-magnetic repulsion is strong enough to effect the particles trajectories in any meaningful way.

 

[jimmy p]

im not studying electric fields but I am sure the equations link. I am studying nuclear physics at the moment but its a little wishy washy. i don't know where i stand in my module. Does anyone have any equations that could start me off. books and the internet have failed me, and i can't see a way of working it out with the equations i know.

 

[Njorl]

It is a very complicated topic. It is not as simple as the electric field problem. There are quite a few different scenarios, all of them requiring quite a bit of work to explain the details.

There is the low-energy case resulting in only scattering, and the high energy case that has more complex possibilities.

At low energy, there are two possibilities:
Elastic scattering, like a baseball bouncing off a basketball. You treat both the alpha particle and the nucleus as rigid spheres.

Inelastic scattering - At certain resonant energies, the particles will stop acting like monolithic entities, and will instead act like collections of waves. The energy levels of the nuclear shells become perturbed as the nucleons of each system react with each other on an individual level rather than as a unit. Energy is released, usually as gamma rays I think, and kinetic energy is lost.

At higher energies, you also introduce the possibility of capture. Capture can result in re-emission or reorganisation to a new element.

Rather than start with an alpha particle and a nucleus, how about starting with a neutron. That is the usual first step.

Njorl

[Editted - sorry, I seem to have started typing and entirely forgotten your original post. Hope I didn't waste too much of your time]