Neutron skin thickness and its volume and surface contributions

Accurate determination of the neutron skin thickness ($\mathrm{\Delta }{R}_{\mathrm{n}\mathrm{p}}$) in finite nuclei is crucial for constraining the density dependence of the nuclear symmetry energy. In this work, we systematically investigate $\mathrm{\Delta }{R}_{\mathrm{n}\mathrm{p}}$ in the transuranium berkelium (Bk) isotopic chain using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). Our results reveal a general increase of $\mathrm{\Delta }{R}_{\mathrm{n}\mathrm{p}}$ with neutron number $N$, which exhibits anti-kinks at the shell closures $N=184,258$ due to the shell effects. By decomposing $\mathrm{\Delta }{R}_{\mathrm{n}\mathrm{p}}$ into volume and surface contributions through two-parameter Fermi (2pF) fits to angle-averaged DRHBc densities, we find that the volume term accounts for as much as $68\mathrm{\%}$ in most nuclei, whereas the surface term dominates only near the proton drip line for $N<142$. Nuclear deformation is shown to slightly reduce the central radius $R_c$ while significantly enhancing the surface diffuseness $a$, resulting in a notable increase in $\mathrm{\Delta }{R}_{\mathrm{n}\mathrm{p}}$ that is largely driven by the surface term. Moreover, by extracting 2pF parameters along the symmetry axis ($\theta =0^{\circ }$) and perpendicular to it ($\theta ={90}^{\circ }$), we examine the anisotropy of $\mathrm{\Delta }{R}_{\mathrm{n}\mathrm{p}}$. In prolate deformed nuclei, a pronounced directional dependence emerges: although the nucleus elongates along the symmetry axis, $\mathrm{\Delta }{R}_{\mathrm{n}\mathrm{p}}$ is substantially larger in the perpendicular direction. This anisotropy is weak for oblate nuclei near shell closures. The anisotropy of $\mathrm{\Delta }{R}_{\mathrm{n}\mathrm{p}}$ is attributed mainly to the volume term, which remains the dominant contribution in most nuclei regardless of direction. These findings provide new insights into the interplay between deformation, shell structure, and the neutron skin in finite nuclei.