Search for $\alpha$ condensed states in $^{13}$C using $\alpha$ inelastic scattering

• Published in: Progress of theoretical and experimental physics Vol. 2021; no. 9
• Main Authors: Inaba, K, Sasamoto, Y, Kawabata, T, Fujiwara, M, Funaki, Y, Hatanaka, K, Itoh, K, Itoh, M, Kawase, K, Matsubara, H, Maeda, Y, Suda, K, Sakaguchi, S, Shimizu, Y, Tamii, A, Tameshige, Y, Uchida, M, Uesaka, T, Yamada, T, Yoshida, H P
• Format: Journal Article
• Language: English
• Published: Oxford University Press 07-09-2021
• Subjects: D05; D11; D22
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/ptab102

Abstract
We searched for the $\alpha$ condensed state in $^{13}$C by measuring the $\alpha$ inelastic scattering at $E_\alpha = 388$ MeV at forward angles including 0$^\circ$. 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 $\alpha$ condensed state in $^{12}$C. It was speculated that the $1/2^-$ states around $E_x = 12.5$ MeV were candidates for the $\alpha$ condensed state, but the $3\alpha + n$ orthogonality condition model suggests that the $\alpha$ 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 $\alpha$ 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 $\alpha$ condensed state in $^{13}$C.