Re: forces

[DSCHROEDER@cc.weber.edu]

> >  ..... compute the cross-section for your desired process and quit 
> >   asking questions.
>
> How can Rutherford cross section (elastic scattering of alpha particles on 
> gold, for example) be calculated without knowing the force law of Coulomb?
> A question about a force (or its potential) must be asked before the 
> corresponding cross section can be evaluated. Is this wrong in general?
>
>                                                 Ludwik Kowalski

My comment was made mostly in jest.  But in answer to your perfectly
fair question, one can compute an awful lot about scattering processes
without knowing whether the force is attractive or repulsive.  The
Rutherford cross-section formula is the same in both cases!  In the
usual experimental situation we look at what goes in and we look at
what comes out and we have no way of following trajectories or seeing
what happened during the interaction itself.  In quantum mechanical
scattering calculations we normally use plane wave functions, and in
this picture there is no trajectory; the "particles" completely overlap
each other during the interaction.  There are some minus signs in the
scattering amplitudes that can, with care, be interpreted as telling
you whether the interaction is attractive or repulsive.  But the
cross-section is proportional the the square of the scattering
amplitude, so I'm in the habit of generally ignoring these minus signs.

-dan