Background: Experimental information on the structure of low-lying levels with isospin 3/2 in systems with 13 nucleons can be used to evaluate the quality of modern theoretical predictions for the light exotic systems. This level structure is poorly known at present. Purpose: Search for $T=3/2$ states in ${}^{13}\mathrm{C}$ was performed in this work. Method: These states were observed in the resonance elastic scattering of radioactive beam ${}^{12}\mathrm{B}$ on protons using the thick target inverse kinematics technique. Results: Six new states in ${}^{13}\mathrm{C}$ were identified as $T=3/2$ states. Tentative spin-parity assignments are suggested. Comparison to the previous knowledge of the level structure of $T=3/2$ $A=13$ system and to shell-model predictions is given. Conclusion: The elastic scattering of neutron-rich beams on proton target is a convenient tool for isobaric analog states search. The observed ${}^{12}\mathrm{B}$$+p$ excitation function is determined by the $T=3/2$ states and no features associated with $T=1/2$ states were found. Although the level scheme of $T=3/2$ states in $A=13$ systems is still far from being complete the emerging picture shows significant disagreements with predictions of contemporary shell models.

• Received 5 May 2008

DOI:https://doi.org/10.1103/PhysRevC.78.044603