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The differential cross-sections of the elastic and inelastic d + $^{13}$C scattering were measured at E(d)=14.5 and 18 MeV on U150M cyclotron of Institute of Nuclear Physics (Almaty, Kazakhstan).
The first 3.09 MeV $(1/2^{+})$ excited state of $^{13}$C nucleus is of special interest because, it is a state with increased radius, where we can talk about a neutron halo-like structure.
The most probable candidate having the structure of $\alpha$-particle condensate is still considered a known Hoyle state of 7.65 MeV (0$^{+}_{2}$) in the $^{12}$C nucleus. In the context of $\alpha$-particle hypothesis, the level of 7.65 MeV in the $^{12}$C nucleus is the simplest example of $\alpha$-particle condensate state and plays an important role in Astrophysics problem. In the work [1], it is proposed that similar Hoyle state can be detected in some neighboring nuclei, such as excited state 8.86 MeV (1/2$^{-}$) in the $^{13}$C nucleus.
In this paper we show the results of the calculations of the radii of the excited states: 3.09 (1/2$^{+}$) and 8.86 (1/2$^{-}$) which were determined by the Modified diffraction model (MDM)[2] at E(d)=14.5 MeV.
[1] M. Milin and W. von Oertzen, EPJ A V 14 (2002);
[2] A.N. Danilov et.al. Phys.Rev. C 80 (2009);
