Yb Isotope: Effect of deformation and isospin asymmetry on the depletion fraction and symmetry energy

Bubble structure is characterised by a reduction in the central density of a nucleus and is estimated through the depletion fraction, as defined in the literature [1]. The reduction in the central density is due to the vacancy in the l=0 orbital (s-orbital). The depletion fraction is affected by quadrupole deformation [2] and also by isospin asymmetry [2]. To study the depletion fraction, Yb isotopes of even-even nuclei with neutron numbers 60-130 covering the 3s-orbitals, including the low N/Z ratio to high, have been studied within axially deformed covariant density functional theory (CDFT) [3] using two classes of density-dependent interaction, DD-ME2 [4] and DD-PC1 [5]. Yb isotopes are found to have a deformed ground state, and N=70 is reported as a magic number [6]. Therefore, to examine the impact of deformation on the depletion fraction and symmetry energy, the Yb isotope is chosen as the best possible and least explored candidate for the study. The aforementioned isotopes are found to have a shape coexistence nature in the vicinity of the magic number, and oblate-shaped nuclei are found to have less depletion fraction than the prolate shape. The magic character is found at N=70, 82, 112, and 126. The depletion fraction decreases with an increase in the deformation in the vicinity of s-orbitals. Beyond this, it increases with an increase in asymmetry. The symmetry energy is found to be higher for the oblate-shaped nuclei than for the prolate ones. The present study aims to enhance our understanding of exotic nuclei.