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

Abstract

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.