From: luther@ohstpy.mps.ohio-state.edu
Newsgroups: sci.physics
Subject: Re: strong force
Date: 19 Aug 92 17:37:29 GMT

In article <1992Aug18.175554.18835@pellns.alleg.edu>,
 frisinv@alleg.edu(Vincent Frisina) writes:
> Is there a mathematical force law for the strong force? If so, what is it?
> If there is no exact formula, what's the closest we have from what's  
> known? Thanks.
> -----
> Vince

   Not a very easy question to answer.  In fact one of the basic goals of
nuclear theory is to understand the forces between "free" nucleons and then use
this to explain the behavior of many nucleon systems. (e.g. nuclei, nuclear
reactions, neutron stars...)
    Why is this so tough?

     1) The nuclear force is STRONG on the distance scales of interest. 
        Perturbation theory methods are probably not applicable, (though they
        are used all the time.)

     2) Finite nuclei are made up of a "few" nucleons (on the order of 100.) 
        This is too many to solve the equations of motion directly and too few
        to sucessfully apply statistical methods in most cases.

     3) Nucleons and mesons are composite objects.  Three-quark objects and
        quark-antiquark pairs most likely.  This means that forces between
        nucleons are complicated, containing many variables.  It also means
        that the derivation of "the nuclear force" is unclear, (i.e. exactly
        what causes it?)
 
   However despite all that no one is giving up.  The "Traditional
Non-relativistic" description of the Strong force is purely phenonmenological.
Important variables are space (r), spin (S=s1+s2), orbital angular 
momentum (L) and  isospin (t1,t2).  The potential then is 

V =  V0(r) + VL(r)*(s1.s2) + VT(r)*S12 + VSO(r)*(L.S)

     S12 = 3*(s1.R)*(s2.R) - (s1.s2)

     R = unit vector in direction of r1-r2

     r = magnitude of r1-r2

     (a.b) = dot product of a and b

Each V_i(r) = V_i(r) + V_it(r)*(t1.t2) and the r dependence of the V_i(r)'s is
usually determined by fits to data.  Sometimes the Yukawa potential and its
derivatives are used as a base to start from

   V(r) = c1*(1/r)*exp(-c2*r)

were c1 and c2 are parameters.  (This is part of the "One-Boson-Exchange
Potential.")  Of course the field has advanced much since this was developed
and a number of potentials have been developed that deal with (some) 
relativistic properties and fit the data extremely well.  Unfortunately these
still contain many parameters determined by fits to experimental data.  Two of
the most popular are the Bonn and Paris Potentials.

   Well, I'm sure that's completely obscured the issue so I'll stop there.  For
a much better explanation I recommend Preston and Bhaduri _Structure of the
Nucleus_.  

(My apologies to Dr. B.C. Clark who gave the lectures in which I supposedly
learned this material.  Whatever is right is due to her, all mistakes are mine
alone -- except typos which belong to The Ohio State University.)

____________________________________________________________________________
B. Luther                             |  
Internet: Luther@mps.ohio-state.edu   |  "Seek simplicity and distrust it"
Ohio State University Physics Dept.   |              -Whitehead
____________________________________________________________________________
Newsgroups: sci.physics