Neutron skin thickness and its volume and surface contributions

TL;DR

This work analyzes neutron skin thickness $ΔR_{ m np}$ in transuranium Berkelium isotopes using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). It decomposes $ΔR_{ m np}$ into volume and surface contributions via two-parameter Fermi fits to DRHBc densities, and examines anisotropy by fitting densities along and perpendicular to the symmetry axis. The study finds that the volume term typically dominates $ΔR_{ m np}$ (up to ~68%), deformation mainly enhances the surface component through increased diffuseness, and prolate deformations yield strong anisotropy with larger skins perpendicular to the symmetry axis. Comparisons with spherical RCHB show deformation amplifies skin thickness, while shell closures at $N=184$ and $N=258$ induce anti-kinks in $ΔR_{ m np}$. These results illuminate the interplay between deformation, shell structure, and neutron skins, with implications for constraining the density dependence of the symmetry energy.

Abstract

Accurate determination of the neutron skin thickness ($ΔR_{\mathrm{np}}$) in finite nuclei is crucial for constraining the density dependence of the nuclear symmetry energy. In this work, we systematically investigate $ΔR_{\mathrm{np}}$ in the transuranium berkelium (Bk) isotopic chain using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). Our results reveal a general increase of $ΔR_{\mathrm{np}}$ with neutron number $N$, which exhibits anti-kinks at the shell closures $N = 184, 258$ due to the shell effects. By decomposing $ΔR_{\mathrm{np}}$ 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 $68\%$ 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 $ΔR_{\mathrm{np}}$ that is largely driven by the surface term. Moreover, by extracting 2pF parameters along the symmetry axis ($θ= 0^\circ$) and perpendicular to it ($θ= 90^\circ$), we examine the anisotropy of $ΔR_{\mathrm{np}}$. In prolate deformed nuclei, a pronounced directional dependence emerges: although the nucleus elongates along the symmetry axis, $ΔR_{\mathrm{np}}$ is substantially larger in the perpendicular direction. This anisotropy is weak for oblate nuclei near shell closures. The anisotropy of $ΔR_{\rm np}$ 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.

Figures (10)

• Figure 1: (Color online) Evolution of the quadrupole deformation $|\beta_2|$ for the Bk isotopes in ground states as a function of the neutron number $N$ obtained by the DRHBc calculations with PC-PK1 density functional. The solid circles denote prolate shapes with positive $\beta_2$ while the open circles denote oblate shapes with negative $\beta_2$.
• Figure 2: (Color online) (a) Rms radius for neutrons $(r_{\rm n})$ and protons $(r_{\rm p})$, and (b) neutron skin thickness $\Delta R_{\rm np}$, as functions of the neutron number $N$ in Bk isotopes, obtained by the self-consistent DRHBc calculations. Spherical RCHB results ADNDT2018Xia_121_1 are included for comparison. The dashed line in panel (b) linking the values of the proton and neutron drip-line nuclei is given to guide the eye.
• Figure 3: (Color online) Neutron density distribution in $^{317}$Bk. The black solid line denotes the angle-averaged DRHBc result, while the red dashed line represents the corresponding 2pF fit. For comparison, sharp surface density profiles characterized by the central radius $C$, the equivalent sharp radius $R$, and the equivalent rms radius $Q$ are also included.
• Figure 4: (Color online) Proton and neutron 2pF parameters in Eq. (\ref{['Eq:rho_2pF']}), radius $R_{c}$, diffuseness $a$, and central density $\rho_0$, obtained by fitting the density distributions from (a-c) angle-averaged DRHBc and (d-f) RCHB calculations under charge number constraints. Solid symbols mark the nucleus at the shell closure $N=184$, and dashed lines indicate its parameter values.
• Figure 5: (Color online) Ratios of DRHBc to RCHB results for the (a) radius $R_{c}$, (b) diffuseness $a$, and (c) central density $\rho_0$. Circles and triangles represent results for neutrons and protons, respectively.