The spin-parities of the 13.35 MeV state and high-lying excited states around 20 MeV in ^12 C nucleus

study of the ^11 B( ^3 He,d) ^12 C reaction at incident ^3 He energy E_lab = 25 MeV has been performed at the K-130 cyclotron at the University of Jyväskylä, Finland. Differential cross sections have been measured for the 13.35 MeV state and for the states with excitation energy around 20 MeV in ^12 C. The data were analyzed with the DWBA method. A tentative assignment, 4 ^- , is given for the state at 13.35 MeV in a joint study of the reaction and inelastic scattering of α -particles with the energy of 110 MeV. For the state at 20.98 MeV, the possible spin-parity 3 ^- and the isospin T = 0 are assigned for the first time. Our model description of the broad state at 21.6 MeV is consistent with the previous assignments of isospin T = 0 and spin-parity of 2 ^+ or 3 ^- . The excited state at 22.4 MeV may have possible spin-parities of either 6 ^+ or 5 ^- . The collected statistics was insufficient to solve this question. Rotational bands which can exist in ^12 C were presented.