Measurement of Proton Transfer Reaction for Single-Particle States in $^{23}$F

We have studied excited states in neutron-rich $^{23}$F using a one-proton transfer reaction onto $^{22}$O at 35 MeV/nucleon. The experiment was performed at RIKEN Accelerator Facility, where an intense RI beam bombarded a liquid helium target in inverse kinematics. Incident and outgoing particles were identified for tagging the secondary reaction channel, and de-excitation $\gamma$ rays from reaction products were detected by an array of 150 NaI(Tl) scintillators (DALI2) surrounding a secondary target in order to identify excitated states of reaction products. In addition to the transfer reaction, we could simultaneously measure the inelastic scattering of $^{23}$F at 41.5 MeV/nucleon and the neutron-knockout reaction of $^{24}$F at 36 MeV/nucleon, because the RI beam contained several nuclei around $^{23}$F and induced several reactions which populated excited states in $^{23}$F. We identifiled proton single-particle states in $^{23}$F by comparing population strengths in the different reactions. In the present talk, we will report details of the experiment and discuss the proton shell structure in neutron-rich $^{23}$F.