The Ground State Aspects and the Impact of Shell Structures on the Stability of Es-Isotopes

In this work, we have analyzed the nuclear structure and several prospective decay characteristics of the $^{240-259}$Es$_{99}$ isotopes. For this we use Relativistic Mean Field model (RMF) with NL-SH and NL3* force parameter in an axially deformed oscillator basis. In structural properties, we have analyzed binding energy (B.E.), skin thickness ($r_{np}$) , charge radius ($r_c$), one neutron separation energy ($S_{1n}$), two neutron separation energy ($S_{2n}$), differential variation of two neutron separation energy ($dS_{2n}$), the single particle energy and its variation with quadrupole deformation parameter of Es isotopes. We have also estimated the $\alpha$-decay, $\beta$-decay and cluster decay half lives of Es isotopes to analyze the shell structure and also to predict the suitable decay mode among them. The $\alpha$-decay half-life periods are calculated using the MUDL and AKRE formulae using both our calculated Q-values and empirically assessable Q-values. In a similar manner, we have computed the half-lives of cluster decay using Universal Decay Law and HOROI formula. A longer decay half-life indicates a shell stabilized parent nucleus, while a small parent half-life suggests the shell stability of the daughter. This study provides us the insights regarding the structural changes with the change in neutron number enabling us to predict shell closures and nuclear stability. We found a shell/sub-shell closure at N = 154 for the NL-SH parameter set. This research aids in our comprehension of Es isotopes' shell structure and decay mechanism.