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The differential cross-sections of the elastic and inelastic α +11B scattering was measured at E(α) = 29 MeV. The analysis of the data by Modified Diffraction Model (MDM) showed that the root-mean- square (RMS) radius of the 11B state 3/2-, E* = 8.56 MeV is ~ 0.5 fm larger than that of the ground state. It is found that the radius of 3/2- (8.56 MeV) state in the 11B nucleus is close to the radii of the Hoyle state in 12C.

We present the results of measurements and analysis of the differential cross sections of the 11B(d, p)12B reaction leading to formation of the 1+ ground state and the 0.953-MeV 2+, 1.674-MeV 2−, 2.621-MeV 1−, 2.723-MeV 0+, 3.389-MeV 3− excited states of 12B at Ed = 21.5 MeV. The analysis of the data was carried out within the coupled-reaction-channels method for the direct neutron transfer and the Hauser-Feshbach formalism of the statistical compound-nucleus model. We deduced the spectroscopic factors, asymptotic normalization coefficients, and rms radii of the last neutron in all states studied. The existence of the neutron halos in the 1.674-MeV 2− and 2.621-MeV 1− states was found in consistence with the earlier published data. New information about the enlarged rms radii (6.5 fm) of the last neutron in the unbound 3.389-MeV 3− states of 12B was obtained, which may indicate the evidence of the neutron halo with the orbital momentum of the last neutron equal to two.

Differential cross-sections of 11B+α inelastic scattering at E(α) =65 MeV leading to most of the known 11B states at excitation energies up to 14 MeV were measured [1]. The data analysis was done using Modified diffraction model (MDM) [2] allowing determining radii of excited states. Radii of the states with excitation energies less than ∼ 7 MeV coincide with the radius of the ground state with an accuracy not less than 0.1 - 0.15 fm. This result is consistent with traditional view on shell structure of low-lying states in 11B. Most of the observed high-energy excited states are distributed among four rotational bands. Moments of inertia of band states are close to the moment of inertia of the Hoyle state of 12C. The calculated radii, related to these bands, are 0.7 - 1.0 fm larger than the radius of the ground state, and are close to the Hoyle state radius. These results are in agreement with existing predictions about various cluster structure of 11B at high excitation energies.

Differential cross-sections of the elastic and inelastic 13C + α scattering were measured at E(α) = 90 MeV. The root mean-square radii() of 13C nucleus in the states: 8.86 (1/2−), 3.09 (1/2+) and 9.90 (3/2−) MeV were determined by the Modified diffraction model (MDM). The radii of the first two levels are enhanced compared to that of the ground state of 13C, confirming the suggestion that the 8.86 MeV state is an analogue of the Hoyle state in 12C and the 3.09 MeV state has a neutron halo. Some indications to the abnormally small size of the 9.90 MeV state were obtained.

The differential cross-sections of the elastic and inelastic 11B + α scattering was measured at E(α) = 65 MeV. The analysis of the data by Modified diffraction model (MDM) showed that the RMS radii of the 11B state 3/2-, E* = 8.56 MeV is ~ 0.6 fm larger than that of the ground state. The 12.56 MeV state was not observed contrary to the predictions of the α-condensate model. The 13.1 MeV state was excited with the angular momentum transfer L = 4 confirming its belonging to the rotational band with the 8.56 MeV state as a head.

α + 12C inelastic differential cross-sections were measured at the energies 65 and 110 MeV. A new broad state at 13.75 MeV was observed. Its spin-parity has been determined as 4+ and the diffraction radius of the corresponding L = 4 transition is ~ 0.8 fm larger than that of the excitation of the 4+, 14.8 MeV level. The 13.75 MeV state was considered to be the third member of the rotational band based on the Hoyle state.

α + 12C elastic and inelastic to the Hoyle state (0+2, 7.65 MeV) differential cross-sections were measured at the energies 60 and 65 MeV with the aim of testing the microscopic wave function [1] widely used in modern structure calculations of 12C. Deep rainbow (Airy) minima were observed in all four curves. The minima in the inelastic angular distributions are shifted to the larger angles relatively those in the elastic ones, which testify the radius enhancement of the Hoyle state. In general, the DWBA calculations failed to reproduce the details of the cross sections in the region of therainbow minima in the inelastic scattering data. However, by using the phenomenological density with rms radius equal 2.9 fm, we can reproduce the Airy minimum positions.

The differential cross sections of the 9Be + α inelastic scattering at 30 MeV were measured at the tandem of Tsukuba University. All the known states of 9Be up to energies ~ 12 MeV were observed and decomposed into three rotational bands, each of them having a cluster structure consisting of a 8Be core plus a valence neutron in one of the sub-shells: p3/2−, s1/2+ and p1/2−. Existence of a neutron halo in the positive parity states was confirmed.

The differential cross-sections of the elastic and inelastic 13C + α scattering were measured at E(α) = 65 MeV. The radii of the states: 8.86 (1/2−), 3.09 (1/2+) and 9.90 (3/2−) MeV were determined by the Modified diffraction model (MDM). The radii of the first two levels are enhanced relatively that of the ground state of 13C, confirming the suggestion that the 8.86 MeV state could be an analogue of the Hoyle state in 12C and the 3.09 MeV state has a neutron halo. No enhancement of the radius of the 9.90 MeV state was observed.