Macroscopic-microscopic analysis of deformation energy, Q20 electric quadrupole moments, and equilibrium shapes in even-even barium and cerium isotopes

This study investigates the electric quadrupole moments (Q₂₀) and deformation energies of even-even nuclei within the mass range 114 ≤ A ≤ 140, focusing on Barium and Cerium isotopes. A macroscopic-microscopic approach is employed, combining the liquid drop model for macroscopic energy with Strutinsky shell corrections and BCS (Bardeen-Cooper-Schrieffer) pairing correlations for microscopic refinements. The shell corrections are derived by solving a Schrödinger equation with a deformed Woods–Saxon mean field. Numerical solutions, performed using an optimized FORTRAN program, identify equilibrium shapes by locating energy minima in deformation energy contour plots. From these equilibrium shapes, single-particle wave functions and the BCS approximation are used to calculate electric quadrupole moments. Theoretical results align closely with experimental data, confirming the robustness of the proposed model. This study advances our understanding of nuclear deformation and structure, particularly in isotopes far from spherical symmetry.