Neutron-skin thickness determines the surface tension of a compressible nuclear droplet

Abstract

We systematically investigate the neutron-skin thickness of neutron-rich nuclei within a compressible droplet model, which includes several parameters characterizing the surface tension and the equation of state (EOS) of asymmetric nuclear matter as well as corrections due to the surface diffuseness. Such a systematic analysis helps towards constraining the EOS parameters of asymmetric nuclear matter and the poorly known density dependence of the surface tension; the latter is estimated with help of available experimental data for the neutron and proton density distributions and the nuclear masses. Validity of the present approach is confirmed by calculating realistic density distributions of Ca, Ni, Zr, Sn, Yb, and Pb isotopes within a microscopic Skyrme-Hartree-Fock+BCS method for various sets of the effective nuclear force. Our macroscopic model accompanied by the diffuseness corrections works well in the sense that it well reproduces the evolution of the microscopically deduced neutron-skin thickness with respect to the neutron number for selected sets of the effective nuclear force. We find that the surface tension of the compressible nuclear droplet is a key to bridging a gap between microscopic and macroscopic approaches.

Nuclear surface diffuseness revealed in nucleon-nucleus diffraction

“…We believe that this is very important, but leave it for our future studies [47]. The HF+BCS density distributions with the SkM* interaction [35,39] are used.…”

“…We calculate the first peak positions θ M and its magnitude of the elastic scattering differential cross section. The proton and neutron density distributions obtained by the HF+BCS method using the SkM* effective interaction [35,39] are employed. Figure 12 compares the results calculated with the pN [33] and averaged NN [32] profile functions at various incident energies.…”

“…As discussed in Ref. [39], the nuclear diffuseness is closely related to the width of the nuclear surface that determines the surface tension of the nuclear droplet. A systematic analysis of the surface widths clearly shows some exotic nuclear structure, such as nuclear deformation, and weakly bound orbits.…”

“…[35,39] (one can also take them from the theoretical database [40]). The calculation was performed self-consistently in a three-dimensional Cartesian mesh, in which any nuclear deformation can be taken into account.…”

Swelling of Doubly Magic Ca48 Core in Ca Isotopes beyond N=28

“…This anomalous phenomenon observed in Ca isotopes is stimulating further studies of nuclear charge radii in a wide mass region [8][9][10][11][12].In contrast, information on the evolution of the size of the neutron density distribution has not been obtained across N = 28. For example, nucleon density distributions ρ m (r) or point-neutron density distributions ρ n (r) for Ca isotopes have been deduced only for stable nuclei, 40,42,44,48 Ca, through the hadron elastic scattering [13][14][15][16][17][18][19][20][21][22][23].The experimental data for root-mean-square (RMS) radii of ρ m (r) or ρ n (r) for Ca isotopes beyond N = 28…”