$^{15}$C inelastic $1/2^+ \rightarrow 5/2^+$ excitation: A single-particle versus a collective process

Background: The excitation of one-neutron halo nucleus $^{15}$C from the $1/2^+$ ground state to the $5/2^+$ first excited state was measured at Argonne National Laboratory by impinging $^{15}$C on a deuterated target at $7.1 A$ MeV. This data was then analyzed in the Distorted Wave Born Approximation using a rigid rotor model for the excitation. Purpose: Being a one-neutron halo, we expect a single-particle excitation to better represent the excitation of $^{15}$C rather than a collective process. We expect the breakup of $^{15}$C to influence the reaction mechanisms because of the low one-neutron separation threshold, which is close in energy to $^{15}$C's first excited state. The goal of this work is to explore various the reaction mechanisms to reinterpret the data of Ref.[1] for the inelastic excitation of $^{15}$C. Method: We solve the scattering problem assuming a three-body model $^{14}$C$+n+d$. We use the Continuum Discretized Coupled Channel method (CDCC) and compare the results with those obtained assuming 1-step DWBA with quadrupole deformation, as done in the original experimental analysis. We also use Bayesian uncertainty quantification to estimate the uncertainties in our predictions coming from the $n$-$d$ interaction. Results: We analyze both the elastic and inelastic angular distributions for $^{15}$C(d,d')$^{15}\text{C}^*$ at $7.1 A$ MeV. Our results show that $^{15}$C breakup effects are important. Conclusions: While CDCC predicts the elastic angular distribution correctly, it is not able to fully describe the experimental inelastic angular distribution. We discuss additional effects that may be responsible for the remaining discrepancy.