  The microscopically constrained relativistic mean field theory is used to
investigate the superdeformation for Pb isotopes. The calculations show that
there exists a clear superdeformed minimum in the potential energy surfaces
with four different interactions NL3, PK1, TM1 and NLSH. The excitation energy,
deformation and depth of well in the superdeformed minimum are comparable for
four different interactions. Furthermore the trend for the change of the
superdeformed excitation energy with neutron number is correctly reproduced.
The calculated two-neutron separation energy in the ground state and
superdeformed minimum together with their differences are in agreement with the
data available. The larger energy difference appearing in superdeformed minimum
reflects a lower average level density at superdeformations for Pb isotopes.
