Matter radii of light proton-rich and neutron-rich nuclear isotopes

We extract the matter root-mean-square (rms) radii of a wide range of light proton and neutron rich nuclear isotopes (He–Mg) by studying their interaction cross sections (${\sigma }_I$) on ${}^{12}\mathrm{C}$ at intermediate energies within the framework of the Glauber model. The calculations involve the nucleon densities obtained from harmonic-oscillator Slater determinants. The matter rms radii so obtained are compared with those available in the literature. It is demonstrated that the present description of matter densities can be conveniently used to explain the experimental values of ${\sigma }_I$, and the extracted matter rms radii may be considered an indication of the presence of halos and skins in proton- and neutron-rich nuclei.

Figure 1

Differential cross sections of $p-{}^4\mathrm{He}$ elastic scattering at 650 and 800 MeV, and $p-{}^{16}\mathrm{O}$ elastic scattering at 1000 MeV. The experimental data (dots) are taken from Aslanides et al. [36] for (a) and (c) and Courant et al. [35] for (b).

Figure 2

Proton (shown by solid lines) and neutron (shown by hatched area) density distributions in ${}^{4,6,8}\mathrm{He}$. The calculations use HO densities (given in the Appendix) which involve the values of oscillator constants for proton and neutron distributions as given in Table 2.

Figure 3

Same as in Fig. 2, but for ${}^{6\text{–}9,11}\mathrm{Li}$.

Figure 4

Same as in Fig. 2, but for ${}^{9\text{–}12,14}\mathrm{Be}$.

Figure 5

Same as in Fig. 2, but for ${}^{10\text{–}15,17,19}\mathrm{B}$.

Figure 6

Same as in Fig. 2, but for ${}^{12\text{–}20}\mathrm{C}$.

Figure 7

Same as in Fig. 2, but for ${}^{14\text{–}23}\mathrm{N}$.

Figure 8

Same as in Fig. 2, but for ${}^{16\text{–}24}\mathrm{O}$.

Figure 9

Same as in Fig. 2, but for ${}^{18\text{–}21,23\text{–}26}\mathrm{F}$.

Figure 10

Same as in Fig. 2, but for ${}^{20,21,23\text{–}26,28,29}\mathrm{Ne}$.

Figure 11

Same as in Fig. 2, but for ${}^{22,23,25\text{–}32}\mathrm{Na}$.

Figure 12

Same as in Fig. 2, but for ${}^{24,25,27,29\text{–}32}\mathrm{Mg}$.

Figure 13

Neutron density distributions (shown by symbols) in neutron-rich nuclei. The calculations use HO densities (given in the Appendix) which involve the values of oscillator constants for proton and neutron distributions as given in Table 2.

Figure 14

Proton (shown by solid lines) and neutron (shown by dotted lines) density distributions in proton-rich nuclei. The calculations use HO densities (given in the Appendix) which involve the values of oscillator constants for proton and neutron distributions as given in Table 4.

Figure 15

Same as in Fig. 14.