Probing the quadrupole transition strength of C15 via deuteron inelastic scattering

Deuteron elastic scattering from $^{15}\mathrm{C}$ and inelastic scattering reactions to the first excited state of $^{15}\mathrm{C}$ were studied using a radioactive beam of $^{15}\mathrm{C}$ in inverse kinematics. The scattered deuterons were measured using HELIOS. The elastic scattering differential cross sections were analyzed using the optical model. A matter deformation length ${\ensuremath{\delta}}_{d}=1.04(11)\phantom{\rule{0.16em}{0ex}}\mathrm{fm}$ has been extracted from the differential cross sections of inelastic scattering to the first excited state. The ratio of neutron and proton matrix elements ${M}_{n}/{M}_{p}=3.6(4)$ has been determined from this quadrupole transition. Neutron effective charges and core-polarization parameters of $^{15}\mathrm{C}$ were determined and discussed. Results from ab initio no-core configuration interaction calculations were also compared with the experimental observations. This result supports a moderate core decoupling effect of the valence neutron in $^{15}\mathrm{C}$ similarly to its isotone $^{17}\mathrm{O}$, in line with the interpretation of other neutron-rich carbon isotopes.