Charge and matter distributions and form factors of light, medium, and heavy neutron-rich nuclei

Results of charge form factors calculations for several unstable neutron-rich isotopes of light, medium, and heavy nuclei (He, Li, Ni, Kr, Sn) are presented and compared to those of stable isotopes in the same isotopic chain. For the lighter isotopes (He and Li) the proton and neutron densities are obtained within a microscopic large-scale shell-model, while for heavier ones Ni, Kr, and Sn the densities are calculated in deformed self-consistent mean-field Skyrme HF+BCS method. We also compare proton densities to matter densities together with their rms radii and diffuseness parameter values. Whenever possible comparison of form factors, densities and rms radii with available experimental data is also performed. Calculations of form factors are carried out both in plane wave Born approximation (PWBA) and in distorted wave Born approximation (DWBA). These form factors are suggested as predictions for the future experiments on the electron-radioactive beam colliders where the effect of the neutron halo or skin on the proton distributions in exotic nuclei is planned to be studied and thereby the various theoretical models of exotic nuclei will be tested.

Figure 1

Thin lines are LSSM point proton densities of ${}^{4,6,8}\mathrm{He}$ compared to the “experimental” charge density for ${}^4\mathrm{He}$ from “model-independent” analyses [54, 59]. Thick lines are LSSM matter densities of ${}^{4,6,8}\mathrm{He}$ compared to matter density of ${}^8\mathrm{He}$ deduced from the experimental proton scattering cross section data in Ref. 25 (grey area).

Figure 2

Thin lines are LSSM point proton densities of ${}^{6,11}\mathrm{Li}$ compared to the point-proton density of ${}^6\mathrm{Li}$ extracted from the “experimental” charge density in a “model-independent” analysis [61]. Thick lines are LSSM matter densities of ${}^{6,11}\mathrm{Li}$ compared to matter density of ${}^{11}\mathrm{Li}$ deduced from the experimental proton scattering cross section data in Ref. 25 (grey area).

Figure 3

(a) Charge form factors of ${}^6\mathrm{He}$, ${}^8\mathrm{He}$, and ${}^{11}\mathrm{Li}$ calculated in PWBA (thin lines) and in DWBA (thick lines) using LSSM densities; (b) charge form factors in DWBA for ${}^4\mathrm{He}$ (calculated by using “experimental” charge density [59] and the LSSM density) and of ${}^{6,8}\mathrm{He}$ (using the LSSM densities); (c) charge form factor in DWBA for ${}^6\mathrm{Li}$ (using the “experimental” charge density [59] and the LSSM densities) and for ${}^{11}\mathrm{Li}$ (using the LSSM densities).

Figure 4

(a) Charge form factors for the unstable doubly-magic ${}^{56}\mathrm{Ni}$, stable ${}^{62}\mathrm{Ni}$, and unstable ${}^{74}\mathrm{Ni}$ isotopes calculated by using the HF+BCS densities and the DWBA; (b) HF+BCS proton densities of ${}^{56}\mathrm{Ni}$, ${}^{62}\mathrm{Ni}$, and ${}^{74}\mathrm{Ni}$.

Figure 5

(a) Charge form factors for the stable isotope ${}^{82}\mathrm{Kr}$ and for the unstable ${}^{92}\mathrm{Kr}$ and ${}^{94}\mathrm{Kr}$ isotopes calculated by using the HF+BCS densities and the DWBA; (b) HF+BCS proton densities of ${}^{82}\mathrm{Kr}$, ${}^{92}\mathrm{Kr}$, and ${}^{94}\mathrm{Kr}$.

Figure 6

(a) Charge form factors for the stable isotope ${}^{118}\mathrm{Sn}$, unstable ${}^{126}\mathrm{Sn}$, and unstable doubly-magic ${}^{132}\mathrm{Sn}$ isotopes calculated by using the HF+BCS densities and the DWBA; (b) HF+BCS proton densities of ${}^{118}\mathrm{Sn}$, ${}^{126}\mathrm{Sn}$, and ${}^{132}\mathrm{Sn}$.

Figure 7

Charge form factors for the stable isotopes ${}^4\mathrm{He}$ and ${}^6\mathrm{Li}$ calculated using LSSM densities in PWBA and in DWBA in comparison with the experimental data.

Figure 8

Charge form factors for the stable isotopes ${}^{58}\mathrm{Ni}$ and ${}^{62}\mathrm{Ni}$ calculated by using the HF+BCS densities and the PWBA and DWBA in comparison with the experimental data.

Figure 9

Charge form factors for the stable isotopes ${}^{116}\mathrm{Sn}$, ${}^{118}\mathrm{Sn}$, and ${}^{124}\mathrm{Sn}$ calculated by using the HF+BCS densities and the PWBA and DWBA in comparison with the experimental data.

Figure 10

(a) Charge form factors for the stable isotope ${}^{118}\mathrm{Sn}$ calculated by using the DWBA (thick solid line), PWBA (dashed line), and PWIA with $q_{\mathrm{eff}}$ given in the text (thin solid line); (b) Charge form factor for the unstable doubly-magic ${}^{132}\mathrm{Sn}$ isotope calculated by using the DWBA and corresponding to Eq. (1) (solid line) and to the proton contribution only [i.e., to the first term of Eq. (1)] (dashed line).

Figure 11

Charge ($R_{\mathrm{ch}}$) (solid lines to guide the eye) and matter ($R_m$) (dashed lines) rms radii calculated in this work as a function of the relative neutron excess $(N-Z)/Z$ of He and Li isotopes (full symbols) (a) and Ni, Kr, and Sn isotopes (open symbols) (b).