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In this paper, we analyze the structural properties of $Z=132$ and $Z=138$superheavy nuclei within the ambit of axially deformed relativistic mean-fieldframework with NL$3^{*}$ parametrization and calculate the total bindingenergies, radii, quadrupole deformation parameter, separation energies, densitydistributions. We also investigate the phenomenon of shape coexistence byperforming the calculations for prolate, oblate and spherical configurations.For clear presentation of nucleon distributions, the two-dimensional contourrepresentation of individual nucleon density and total matter density has beenmade. Further, a competition between possible decay modes such as$\alpha$-decay, $\beta$-decay and spontaneous fission of the isotopic chain ofsuperheavy nuclei with $Z=132$ within the range 312 $\le$ A $\le$ 392 and 318$\le$ A $\le$ 398 for $Z=138$ is systematically analyzed within self-consistentrelativistic mean field model. From our analysis, we inferred that the$\alpha$-decay and spontaneous fission are the principal modes of decay inmajority of the isotopes of superheavy nuclei under investigation apart from$\beta$ decay as dominant mode of decay in $^{318-322}138$ isotopes.

Structural and decay properties of $Z=132,138$ superheavy nuclei