C. Dash, A. Anupam, I. Naik, B. K. Sharma, B. B. Sahu
7 min
Abstract
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 $α$-decay, $β$-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 $α$-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.
Sam: Yes. They compute two-neutron separation energies, which drop around N=154, like a full backpack you can't easily stuff more into. Diagrams of single-particle levels show large energy gaps there too, confirming extra stability. With NL3*, Es-253 looks about twice as long-lived as neighbors.
Alex: That dip and gap at N=154 seems like a solid sign for better targets. Beyond separation energies, what other properties check the nucleus structure—like binding or size?
Sam: Binding energy per nucleon is the total glue energy divided by all particles—higher means tighter hold, like a packed suitcase. It peaks around N=144, and NL3* matches experiments closely. Neutron skin thickness—the extra neutron reach—grows with more neutrons, like frosting on a lopsided cake. Charge radius, from proton positions, shows odd-even staggering: odd-neutron nuclei puffier because the extra neutron disrupts pairing, like an uneven crowd.
Alex: So binding peaks at N=144, and skin plus radius trends support stability without big jumps. How does shape fit in?
Sam: Nuclei can stretch like a football due to how particles arrange. Quadrupole deformation measures this bulge. Both sets predict prolate shapes with odd-even staggering—odd neutrons pull it more. Deformation peaks early then eases to about 0.29 near N=154.
Alex: Prolate shapes with staggering match the pairing idea. How do shapes tie to those energy drops and gaps?
Sam: Single-neutron and two-neutron separation energies drop sharply at closures. Plots show plunges at N=148 and N=154, with Es-253 extra sticky. Single-particle diagrams versus stretch reveal wide gaps at N=154, like big spaces between stairs, confirming sub-shell strength—though another model sees it at 152.
Alex: Those plunges and gaps align on N=154. What about decay energies as another check?
Sam: Alpha decay spits out a helium chunk, with Q-alpha energy lowest at stable spots—harder to break off, like yanking from a solid wall. It dips at N=154 with NL-SH. Half-lives stretch longer there, formulas predicting peaks around N=154 for Es-253, about twice as stable. Alpha dominates for some isotopes like Es-253, matching experiments; beta for others.
Alex: A Q-alpha dip means resistance to decay at N=154. Does cluster decay add more?
Sam: Cluster decay ejects bigger chunks, sensitive to shells in parent and daughter. Plots show a deepening at N=158 for Es-257, hinting stability in the daughter at N=154.
Alex: Even rare decays echo N=154 stability. Pulling it together, what does this mean for superheavy hunts?
Sam: NL3* flags Es-253 at N=154 as tough against neutron loss and alpha decay. Gaps at N=154 reinforce this. It maps resilience to spotlight stable targets, though parameter differences and lack of direct experiments mean lab tests are needed.
Alex: Computations build a case for smarter Einsteinium targets in superheavy synthesis, like for element 119. Thanks, Sam—that maps the challenges clearly.
Sam: It advances actinide stability insights for better target design. Thanks for the discussion.