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

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 degrees. We performed the distorted-wave Born-approximation calculation with the single-folding potential and the 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.

arXiv comment24 pages, 12 figures, published in PTEP

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