  In many-body theory of particles with long range interaction potential, such
as the potential of Newtonian gravity and its relativistic generalization,
Newton-Birkhoff theorem plays a very important role. This theorem is violated
in the case of short range interaction potential, such as the Yukawa potential
in nuclear physics. We discuss the relevance of this in the many-body treatment
of heavy nuclei. In particular, using techniques similar to those in Newtonian
gravity, we calculate analytically the mean-field potential in heavy nuclei.
The mean-field potential thus calculated depends on well known quantities such
as the pion-nucleon coupling constant, inverse pion mass, nuclear radius and
density. The qualitative features of the mean-field potential thus obtained is
similar to the well known phenomenological Wood-Saxon potential.
