Abstract
Various shapes of Hg isotopes are calculated using a relativistic mean field theory. We observe shape transitions from oblate to prolate and prolate to oblate at A=178 and A=188, respectively. Both in the oblate and in the prolate solutions the sign of the hexadecupole moment changes from positive to negative values with increasing mass number. The predicted shape of the ground state agrees with the available data contrary to nonrelativistic calculations for neutron deficient isotopes. A low-lying superdeformed configuration is found in some isotopes, and found to be the ground state for $^{180}\mathrm{Hg}$. A possible discrepancy between the experimental data of the quadrupole deformation and those of the charge radii is pointed out.
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