Probing the quadrupole transition strength of $^{15}$C via deuteron inelastic scattering

Deuteron elastic scattering from $^{15}$C and inelastic scattering reactions to the first excited state of $^{15}$C were studied using a radioactive beam of $^{15}$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 δd = 1.04(11) 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 Mn/Mp = 3.6(4) has been determined from this quadrupole transition. Neutron effective charges and core-polarization parameters of $^{15}$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 $^{15}$C similarly to its isotone $^{17}$O, in line with the interpretation of other neutron-rich carbon isotopes.