Cluster rotational bands in 11 B

Differential cross-sections of B+α inelastic scattering at E(α) = 65 MeV leading to most of the known B 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 B. 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 C. 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 B at high excitation energies.


Introduction
During long time 11 B nucleus was considered as a good example of shell effects in light nuclei. Up to excitation energies ∼ 7 MeV 11 B states were described by different variants of shell models. Recently, however, a number of theoretical and experimental works appeared [3][4][5] with predictions about cluster configurations of various types co-existed in 11 B.
Particular attention was drawn to the idea that there may be states in 11 B, which are analogs of the famous 0 + 2 state in 12 C nucleus (the socalled Hoyle state). The Hoyle state consists of three weakly interacting alpha -clusters and its properties were crucial for verification of the alphaparticle condensation theory [6]. One of the main suggestions of this theory is abnormally large radius of the Hoyle state. Accordingly, Hoyle state analogs in 11 B must also have increased size.
It was assumed [3] that the Hoyle state analog in 11 B is the state 3/2 − with excitation energy 8.56 MeV, which is not described by any variant of the shell model. The radius of 8.56 MeV state was considered to be abnormally large, and it was predicted that this state is a base for rotational band.
There are a lot of experimental studies of 11 B (see, e.g., [7] and references therein), but they did not affect the excitation energy region of interest for the problem. Due to the fact that many questions about 11 B states remained open, we have undertaken a new study of inelastic 11 B + α scattering at E(α) = 65 MeV [1]. Experimental results were analyzed using Modified diffraction model (MDM). In this article we discuss results for high-energy excited states and possible cluster rotational bands formed from them.
As seen from Fig. 2, increased radii were found, at least, for one of the members of each band, and in most cases they are about 0.7 -1.0 fm larger than the radius of the ground state of 11 B. This leads to the conclusion that all states belonging to the bands under consideration, have abnormal size. Theoretical works [3][4][5] suggest a significant deformation of the rotational states of 11 B with E * > 7 MeV and it allows the increase of their radii. The radii and moments of inertia of these states are close to the corresponding values of the Hoyle state in 12 C nucleus and the rotational band based on it. These facts indicate probable cluster nature of the 11 B states discussed. In particular, the 8.56 MeV state can be considered as an analog of the Hoyle state. But some open questions remain regarding the rotational band that is based on the 6.79 MeV state, including the very existence of band [1].