  A consistent theory is developed of the volume energy oscillations of
spherical nuclei due to sharpness of the Fermi distribution boundary for
quasiparticles. The lowest value of the oscillating part of the energy
corresponds to a magic nucleus. A formula is obtained for the corresponding
limiting momentum of a quasiparticle and it is shown that we have here an
isolated point of a temperatureless second-order phase transition. An
expression for the discontinuity of the derivative of the energy of the body
with respect to the number of particles is obtained in the case of a sharp
(step-like) Fermi distribution limit. Comparison with experimental nuclear-mass
data permits some conclusions to be drawn regarding the true structure of the
boundary layer of the Fermi distribution and regarding its variation with
increasing nuclear size. In the region of magic nuclei actually accessible up
to the present time, apparently no signs are observed of any appreciably
expressed residual phenomenon, such as the Cooper phenomenon, which would
result in instability of the energy spectrum of infinite nuclear matter with an
absolutely sharp Fermi limit for quasiparticles.
