Interaction cross sections and matter radii of oxygen isotopes using the Glauber model

Using the Coulomb modified correlation expansion for the Glauber model $S$ matrix, we calculate the interaction cross sections of oxygen isotopes (${}^{16–26}\mathrm{O}$) on ${}^{12}\mathrm{C}$ at 1.0 GeV/nucleon. The densities of ${}^{16–26}\mathrm{O}$ are obtained using (i) the Slater determinants consisting of the harmonic oscillator single-particle wave functions (SDHO) and (ii) the relativistic mean-field approach (RMF). Retaining up to the two-body density term in the correlation expansion, the calculations are performed employing the free as well as the in-medium nucleon-nucleon ($NN$) scattering amplitude. The in-medium $NN$ amplitude considers the effects arising due to phase variation, higher momentum transfer components, and Pauli blocking. Our main focus in this work is to reveal how could one make the best use of SDHO densities with reference to the RMF one. The results demonstrate that the SDHO densities, along with the in-medium $NN$ amplitude, are able to provide satisfactory explanation of the experimental data. It is found that, except for ${}^{23,24}\mathrm{O}$, the predicted SDHO matter rms radii of oxygen isotopes closely agree with those obtained using the RMF densities. However, for ${}^{23,24}\mathrm{O}$, our results require reasonably larger SDHO matter rms radii than the RMF values, thereby predicting thicker neutron skins in ${}^{23}\mathrm{O}$ and ${}^{24}\mathrm{O}$ as compared to RMF ones. In conclusion, the results of the present analysis establish the utility of SDHO densities in predicting fairly reliable estimates of the matter rms radii of neutron-rich nuclei.

Figure 1

Point-proton SDHO and RMF density distributions in ${}^{16–26}\mathrm{O}$ isotopes. Squares (inverted triangles) and triangles show, respectively, SDHO and RMF densities. The calculations of SDHO densities, shown by squares and inverted triangles, correspond to the values of oscillator parameters for proton distributions as given in Tables 2 and 3, respectively.

Figure 2

Point-neutron SDHO and RMF density distributions in ${}^{16–26}\mathrm{O}$ isotopes. Squares (inverted triangles) and triangles show, respectively, SDHO and RMF densities. The calculations of SDHO densities, shown by squares and inverted triangles, correspond to the values of oscillator parameters for neutron distributions as given in Tables 2 and 3, respectively.

Figure 3

Interaction cross sections of ${}^{16–26}\mathrm{O}$ isotopes on a ${}^{12}\mathrm{C}$ target at 1.0 GeV/nucleon using SDHO (squares) and RMF (triangles) densities. The calculations using SDHO densities involve the values of oscillator parameters for proton and neutron distributions as given in Table 2. The experimental data (dots and open circles) are taken from Ozawa et al. [2] and Kanungo et al. [10].

Figure 4

Interaction cross sections of ${}^{16–24}\mathrm{O}$ isotopes on a ${}^{12}\mathrm{C}$ target at 1.0 GeV/nucleon using SDHO (inverted triangles) densities. The calculations using SDHO densities involve the values of oscillator parameters for proton and neutron distributions as given in Table 3. The experimental data (dots and open circles) are taken from Ozawa et al. [2] and Kanungo et al. [10].

Figure 5

Matter rms radii of ${}^{16–24}\mathrm{O}$ isotopes using SDHO (inverted triangles) and RMF (triangles) densities. The SDHO densities involve the values of oscillator parameters for proton and neutron distributions as given in Table 3. The inverted open triangles with uncertainties are the predicted SDHO matter rms radii of ${}^{23,24}\mathrm{O}$ that account for the interaction cross-section data on ${}^{23}\mathrm{O}$ and ${}^{24}\mathrm{O}$ employing the in-medium $NN$ amplitude (see the text).

Figure 6

Differential cross section of $p-{}^{16}\mathrm{O}$ elastic scattering at 200, 300, 600, and 1000 MeV. Squares, inverted triangles, and triangles represent the results using SDHO (Table 2), SDHO (Table 3), and RMF densities, respectively. The experimental data (dots) are taken from (a) Murdock et al. [25], (b) Abu-Ibrahim et al. [24], and [(c), (d)] Bruge [26].

Figure 7

Reaction cross sections of $p-{}^{16}\mathrm{O}$ scattering in the energy range 40–1000 MeV. Squares, inverted triangles, and triangles represent the results using SDHO (Table 2), SDHO (Table 3), and RMF densities, respectively. The experimental data (dots) are taken from Carlson [27].

Figure 8

Differential cross section of $p-{}^{16}\mathrm{O}$ elastic scattering at 1.0 GeV, showing the effects due to phase variation (PV) (inverted triangles), higher momentum transfer components (HMTC) (squares), and Pauli blocking (PB) (triangles) of the $NN$ amplitude. Open squares show the combined effect of PV, HMTC, and PB. The experimental data (dots) are taken from Bruge [26].

Figure 9

Interaction cross sections of ${}^{16–24}\mathrm{O}$ isotopes on a ${}^{12}\mathrm{C}$ target at 1.0 GeV/nucleon. Squares show the results using SDHO densities (involving the values of oscillator parameters for proton and neutron distributions as given in Table 2) and the free $NN$ amplitude. Open squares show the results using similar SDHO densities as used in obtaining squares, but involve the combined effect of the phase variation, higher momentum transfer components, and Pauli blocking of the $NN$ amplitude. The experimental data (dots and open circles) are taken from Ozawa et al. [2] and Kanungo et al. [10].