The potential energy surfaces are calculated for $N=Z,$ ${}^{72}\mathrm{Kr}$ to ${}^{92}\mathrm{Pd}$ nuclei in an axially deformed relativistic mean field approach, using a quadratic constraint scheme. The NL3 and TM1 parameter sets are used to see the dependence of our results on force parameters for a wide range of quadrupole deformation. The ground-state solutions as well as some excited state solutions for the binding energies and quadrupole deformations are deduced. Interestingly enough, more than two shapes at about the same binding energy are found to exist for all the $N=Z$ nuclei, which is perhaps the reason for a drastic change of shape with the addition of only two protons or two neutrons in the mass region $A\approx 80\pm 10.$ This new result of multiple low-lying spherical or deformed states, suggesting a “dynamically” variable nature of nuclear shapes in the neutron-deficient $N=Z$ exotic nuclei, needs an immediate experimental verification. For the ground state, our calculated results compare nicely with the experimental data and other theoretical works, wherever available.

• Received 18 June 2001

DOI:https://doi.org/10.1103/PhysRevC.65.054323