Search for $α$ condensed states in $^{13}$C using $α$ inelastic scattering. (11th August 2021) - Inaba, K; Sasamoto, Y; Kawabata, T; Fujiwara, M; Funaki, Y; Hatanaka, K; Itoh, K; Itoh, M; Kawase, K; Matsubara, H; Maeda, Y; Suda, K; et al.
Abstract: We searched for the $α$ condensed state in $^{13}$ C by measuring the $α$ inelastic scattering at $E_α = 388$ MeV at forward angles including 0$^°$ . We performed a distorted-wave Born approximation calculation with the single-folding potential and multipole decomposition analysis to determine the isoscalar transition strengths in $^{13}$ C. We found a bump structure around $E_x = 12.5$ MeV due to the isoscalar monopole ($IS0$ ) transition. A peak-fit analysis suggested that this bump consisted of several $1/2^-$ states. We propose that this bump is due to the mirror state of the 13.5 MeV state in $^{13}$ N, which dominantly decays to the $α$ condensed state in $^{12}$ C. It was speculated that the $1/2^-$ states around $E_x = 12.5$ MeV were candidates for the $α$ condensed state, but the $3α + n$ orthogonality condition model suggests that the $α$ condensed state is unlikely to emerge as the negative parity states. We also found two $1/2^+$ or $3/2^+$ states at $E_x = 14.5$ and 16.1 MeV excited with the isoscalar dipole ($IS1$ ) strengths. We suggest that the 16.1 MeV state is a possible candidate for the $α$ condensed state predicted by the cluster model calculations on the basis of the good correspondence between the experimental and calculated level structures. However, the theoretical $IS1$ transition strength for this state is significantly smaller than the measured value. Further experimental information is strongly desired to establish the $α$ condensed state in $^{13}$ C.