Deformation, orientation, and medium effects in16,19C+Creactions

Abstract

The shape, deformation, and orientation dependence as well as in-medium effects are investigated for the reaction cross sections of ${}^{16,19}\text{C}+\text{C}$ systems within the optical Glauber theory, which is currently used to deduce information about the structure of exotic nuclei. A density- and energy-dependent effective nucleon-nucleon reaction cross section is used locally to study in-medium effects. The projectile deformation is treated by a deformed Fermi shape with quadrupole and hexadecapole deformations, where the deformation parameters of ${}^{16}\text{C}$ and ${}^{19}\text{C}$ are calculated from the Lagrangian density of the relativistic mean-field (RMF) model. A strong prolate deformation is predicted for ${}^{16}\text{C}$ while a more stronger oblate shape is predicted for ${}^{19}\text{C}$. Medium effects are found to be important for extracting reliable information about the nuclear densities and radii. The deformations and orientations strongly affected the reaction cross section. The difference in the reaction cross section calculated at orientation angle $\ensuremath{\pi}/2$ and at zero degree is of the order of 400 mb. The integrated reaction cross section over all orientation angles (angle average), including in-medium effects, predicted the experimental reaction cross section of ${}^{19}\text{C}+{}^{12}\text{C}$. For ${}^{16}\text{C}+{}^{12}\text{C}$ the rms radius of ${}^{16}\text{C}$ is increased to about $7%$ than that predicted by the RMF model in order to predict the experimental data. This greater increase in the rms radius of ${}^{16}\text{C}$, to about 3 fm, indicates a neutron halo structure for this nucleus. The deduced spherical Fermi distributions which fit the experimental data of ${}^{16,19}\text{C}+{}^{12}\text{C}$ systems are in fact a prediction of the angle average cross sections.