Structure of the ${}^{10}\mathrm{Li}$ nucleus investigated via the ${}^9\mathrm{Li}{\mathrm{}(d,p)\mathrm{}}^{10}\mathrm{Li}$ reaction

The structure of the particle unbound nucleus ${}^{10}\mathrm{Li}$ was investigated in a kinematically complete experiment using the ${}^9\mathrm{Li}{\mathrm{}(d,p)\mathrm{}}^{10}\mathrm{Li}$ reaction in inverse kinematics at an incident ${}^9\mathrm{Li}$ energy of 20 MeV/nucleon. The experiment utilized the S800 Spectrograph at the National Superconducting Cyclotron Laboratory to measure the outgoing ${}^9\mathrm{Li}$ from the breakup of ${}^{10}\mathrm{Li}$ in coincidence with the recoiling protons from the $\mathrm{}(d,p)\mathrm{}$ reaction which were measured using an array of silicon detectors. Based on the kinematics of the recoiling protons from the ${}^9\mathrm{Li}\mathrm{}(d,p)\mathrm{}$ reaction, we measured a lower limit of $\Delta =33.10\mathrm{}\pm 0.08$ MeV (i.e., $\Delta >33.02\mathrm{}$ MeV) for the mass excess of ${}^{10}\mathrm{Li}$ which is consistent with previous measurements. Through the complete reconstruction of the breakup kinematics, the structure of ${}^{10}\mathrm{Li}$ associated with a ground state ${}^9\mathrm{Li}$ core was distinguishable from structure associated with a ${}^9\mathrm{Li}$ core in its first excited state. The observed ratio of ${}^9{\mathrm{Li}}^{*}$ core events to the total number of ${}^{10}\mathrm{Li}$ events that were detected in the experiment was $0.10\pm 0.04$ at forward center of mass angles $(2.7\mathrm{}°$ to $9.5°),$ and $0.24\pm 0.03$ at more backward center of mass angles $(11\mathrm{}°$ to $26°).\mathrm{}$ The resulting Q-value spectra was best fit with either a single resonance located at $Q=-2.58\left(11\right)\mathrm{}$ MeV [corresponding to a neutron separation energy $S_n=-0.35\left(11\right)\mathrm{}$ MeV] or two resonances located at $Q=-3.00\left(24\right)\mathrm{}$ MeV $[S_n=-0.77(24)\mathrm{}$ MeV] and $Q>\mathrm{}-2.43$ MeV ${(S}_n>-0.2$ MeV).