Abstract
We calculate the binding energy, root-mean-square radius, and quadrupole deformation parameter for the recent, possibly discovered superheavy element $Z=122$, using the axially deformed relativistic mean-field (RMF) and nonrelativistic Skyrme Hartree-Fock (SHF) formalisms. The calculation is extended to include various isotopes of $Z=122$ element, starting from $A=282$ to $A=320$. We predict highly deformed structures in the ground state for all the isotopes. A shape transition appears at about $A=290$ from a highly oblate to a large prolate shape, which may be considered as the superdeformed and hyperdeformed structures of the $Z=122$ nucleus in the mean-field approaches. The most stable isotope (largest binding energy per nucleon) is found to be $^{302}122$, instead of the experimentally observed $^{292}122$.
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