Re: [Phys-l] Electron vs. Alpha particle...

[John Denker <jsd@av8n.com>]

On 01/12/2011 03:38 PM, Jeff Loats wrote:

> This term a curious student asked some great questions about what would
> happen when such a collision took place.

>         What would happen if an alpha particle was fired head-on at an
> electron.

I would tell the student:  That's a great question, and I even
know the answer, but you're not going to like it.  Even though
the question is simple, the answer is very, very complicated.
By way of analogy, note that the laws of chess are rather simple,
but the situations that arise during a chess game can be quite
complex.  This is like chess, only more so.  The rules are even
simpler, and the consequences are very, very complicated.

If you study real hard for the next several years you can get to the
point where you actually understand the answer to this question.

It's called Coulomb scattering.
  http://www.google.com/search?q=coulomb+scattering+wave-function+site%3A.edu

Here is a highly condensed summary of part of the answer:
  http://hitoshi.berkeley.edu/221b/scattering4.pdf

Actually, strictly speaking, those Berkeley lecture notes don't answer 
the question, in the sense that they punt on the exact head-on case.  
In that case you need
  http://www.google.com/search?q=coulomb-scattering+forward-scattering+optical-theorem+site%3A.edu

Note that the so-called poles in the Coulomb scattering correspond 
to bound states ... i.e. atoms and ions.  The solution for the bound
states was worked out a while back by some guy named Schrödinger.
An accessible discussion can be found in Feynman volume III.  For
the next level of detail, consult Baym and then Sakurai.

On 01/12/2011 07:52 PM, Richard Tarara wrote:
> > there is also the 'clean miss' possibility--after all the
> > electron may not be there any longer once the alpha gets there!

Actually, of all the weird things that might happen, that's 
the one thing that cannot happen.  The Coulomb interaction has
infinite range.  It's almost like trying to shoot a barn ... 
from inside the barn.  You can't miss.