A simple analytical calculation of mean-field potential in heavy nuclei

摘要

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