Isotopic trends of nuclear surface properties of spherical nuclei

The density profiles of spherical nuclei are calculated with two methods based on the energy density functional approach. Isotopic trends are discussed in nuclear surface diffuseness. The simple parametrizations of the dependencies of nuclear diffuseness and radius on neutron number are suggested. The nucleus-nucleus potentials are calculated with the nucleon densities obtained and are compared with those resulting from the phenomenological treatment. The height of the Coulomb barrier is suggested to be used in the fit of the density-dependent nucleon-nucleon interaction.

Figure 1

The binding energies per nucleon for the Ni isotopic chain. The energy density functional results (solid squares connected by lines) are compared with the experimental data (solid circles) of Ref. [33].

Figure 2

The calculated radial distributions of the proton density ${\rho }_p$ for ${}^{58}\mathrm{Ni}$ (dotted line) and ${}^{64}\mathrm{Ni}$ (solid line) are compared with the experimental data [37] shown by open and solid symbols, respectively.

Figure 3

The nucleon-density distributions calculated with method I in indicated spherical nuclei are fit with Eq. (22). The results of the three-parameter fit are shown by red lines. The results of the two-parameter fit at ${\rho }_0$ defined from Eq. (23) are shown by green lines. The results of the one-parameter fit at fixed ${\rho }_0=0.16{\mathrm{fm}}^{-3}$ and $r_0=1.15$ fm are shown by blue lines.

Figure 4

The comparison of isotopic dependencies of diffuseness of Ni obtained with method I (solid line), method II (dotted line), and the approach of Ref. [21] (dashed and dash-dotted lines result from the SLy4 and SKMS interactions, respectively).

Figure 5

The same as in Fig. 4, but for Pb.

Figure 6

Comparison of isotopic dependencies of (a) proton (solid line) and neutron (dashed line) radii, and (b) proton (solid line) and neutron (dashed line) diffuseness obtained with method I for Ni isotopes with those calculated for protons (dotted lines) and neutrons (dash-dotted lines) with Eqs. (25).

Figure 7

The comparison of isotopic dependencies of diffuseness of spherical Mg obtained with method I (solid line) and method II (dotted line). The values of $a$ are obtained at ${\rho }_0=0.16{\mathrm{fm}}^{-3}$.

Figure 8

The same as in Fig. 7, but for spherical Ni. The fit of the solid line with Eq. (26) at $N_0=28$ is presented by dash-dotted line. The isotopic dependence of $a$ calculated with Eqs. (25) is presented by dashed line.

Figure 9

The same as in Fig. 7, but for spherical Sn. The fit of the solid line with Eq. (26) at $N_0=50$ is presented by dash-dotted line.

Figure 10

The same as in Fig. 7, but for spherical Pb.

Figure 11

The same as in Fig. 7, but for spherical Ds.

Figure 12

Comparison of nucleus-nucleus potentials calculated with Eq. (27) and using nucleon densities of method I (solid lines), and with Eq. (31) and adopted $\rho$ (dashed lines) for the reactions indicated. The parameters are given in the text.

Figure 13

The same as in Fig. 12, but for the asymmetric reactions indicated. The dotted line is obtained with the same parameters as the solid line, but with $a=0.39$ fm for ${}^4\mathrm{He}$.