Cluster rotational bands in 11B

This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Author(s): Title: Year: Version: Please cite the original version: All material supplied via JYX is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Cluster rotational bands in 11B Danilov, A.N.; Demyanova, A.S.; Ogloblin, A.A.; Belyaeva, T.L.; Goncharov, S.A.; Trzaska, Wladyslaw Danilov, A.N., Demyanova, A.S., Ogloblin, A.A., Belyaeva, T.L., Goncharov, S.A., & Trzaska, W. (2016). Cluster rotational bands in 11B. In V. Greco, M. L. Cognata, S. Pirrone, F. Rizzo, & C. Spitaleri (Eds.), NN2015 : 12th International Conference on Nucleus-Nucleus Collisions 2015 (Article 04011). EDP Sciences. EPJ Web of Conferences, 117. https://doi.org/10.1051/epjconf/201611704011 2016 Cluster rotational bands in 11B A.N. Danilov1, A.S. Demyanova1,A.A.Ogloblin 1, T.L. Belyaeva2,S.A.Goncharov 3and W. Trzaska4 1National Research Center “Kurchatov Institute” Moscow, 123182, Russia 2Universidad Autonoma del Estado de Mexico, Toluca, 50000, Mexico 3Lomonosov Moscow State University, Moscow, 119991, Russia 4JYFL, Jyv¨askyl¨a, FIN-40500, Finland Abstract Differential cross-sections of 11B+αinelastic 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. 1 Introduction During long time 11B nucleus was considered as a good example of shell effects in light nuclei. Up to excitation energies ∼7MeV11B states were described by different variants of shell models. Recently, however, a number 201 ,0401 (2016) EPJ Web of Conferences DOI: 10.1051/ conf/201611 0401 epj 5 1177 NN 11  © The Authors, published by EDP Sciences SI . This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). F - of theoretical and experimental works appeared [3–5] with predictions about cluster configurations of various types co-existed in 11B. Particular attention was drawn to the idea that there may be states in 11B, which are analogs of the famous 0+ 2state in 12C nucleus (the socalled Hoyle state). The Hoyle state consists of three weakly interacting alpha - clusters and its properties were crucial for verification of the alpha - particle condensation theory [6]. One of the main suggestions of this theory is abnormally large radius of the Hoyle state. Accordingly, Hoyle state analogs in 11B must also have increased size. It was assumed [3] that the Hoyle state analog in 11B 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 11B (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 11B states remained open, we have undertaken a new study of inelastic 11B+αscattering 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. 2 Radii and moments of inertia of high-lying rotational bands in 11B The following rotational bands were predicted [3,5] in high excitation energy region in 11B. Most of these states were observed in our experiment: K= 3/2−: 8.56 (3/2−) - 10.34 (5/2−) - 11.60 - 13.14 (9/2−)MeV, K= 1/2+: 6.79 (1/2+) - 9.88 (3/2+) 11.60 (5/2+) 13.16 (7/2+)MeV, K= 3/2+: 7.98 (3/2+) - 9.27 (5/2+) - 10.60 (7/2+) - 12.63 (9/2+)MeV, K= 5/2+: 7.29 (5/2+) - 9.19 (7/2+) - 11.27 (9/2+)MeV. These rotational bands are shown in Fig. 1 together with the band in 12C, based on the Hoyle state. Data on angular momentum transfer with excitation states belonging to the specified bands, received from our experiment, are in agreement with known spin-parities of 11B states. However, for 6.79, 9.88, 10.34, 13.14 13.16 MeV states it could not determined unambiguously due to insufficient energy resolution. Several special features in J(J+ 1) dependence of excitation energies can be seen in Fig. 1. Firstly, moments of inertia of the band states are very high and comparable. The largest of them (2I/¯h2∼4.0, by the energy difference between the excitation 201 ,0401 (2016) EPJ Web of Conferences DOI: 10.1051/ conf/201611 0401 epj 5 1177 NN 11 2 Figure 1: Predicted [3,5] rotational bands in 11B at excitation energies E∗>7MeV. For comparison, rotational band [8], based on the Hoyle state (0+ 2,7.65MeV)of 12C, is shown. energies 11.60 and 10.34 MeV) are observed for higher members of the rotational band K= 3/2−, for which cluster structure 2α+tis predicted. It is interesting that it is much larger than the moment of inertia of its analog - the Hoyle state, for which 2I/¯h2= 2.7. Secondly, there is a clear correlation between the moments of inertia and the values of radii obtained from scattering data using MDM. Low-lying states of 11B have ”normal” radii and ”reduced” moments of inertia about 2I/¯h2∼1.1. These values are close to values for the first excited state of 12C, 4.44 MeV. ”Big” moments of inertia correspond to increased radii. Summary of the radii of the states measured using MDM is given in the Fig. 2. 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 11B. This leads to the conclusion that all states belonging to the bands under consideration, have abnormal size. Theoretical works [3–5] suggest a significant deformation of the rotational states of 11BwithE∗>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 12C nucleus and the rotational band based on it. These facts indicate probable cluster nature of the 11B 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]. 201 ,0401 (2016) EPJ Web of Conferences DOI: 10.1051/ conf/201611 0401 epj 5 1177 NN 11 3 Figure 2: Dependence of Rrms (root-mean-square radii, determined by MDM) on the excitation energy for states of 11B. The sizes of the plotted points are proportional to the moments of inertia of the states. Acknowledgements The work was supported in part by grants of Russian Science Foundation 14-12-00079, Russian Foundation for Basic Researches 14-02-00560 and 1502-01503 and the mobility grant from the Academy of Finland References [1] A.N. Danilov, A.S. Demyanova et al., Physics of Atomic Nuclei 78, No. 6, 777 (2015) [2] A.N. Danilov et al., Phys.Rev. C 80, 054603 (2009) [3] Y. Kanada-Enyo, Phys. Rev. C 75, 024302 (2007) [4] T. Yamada and Y. Funaki, Phys. Rev. C 82, 064315 (2010) [5] H. Yamaguchi et al., Phys. Rev. C83, 034306 (2011) [6] 6. A. Tohsaki, H. Horiuchi, P. Schuck, and G. Ropke, Phys. Rev. Lett. 87, 192501 (2001) [7] N. Burtebaev et al., Physics of Atomic Nuclei68, 1303 (2005) [8] A.A. Ogloblin et al., EPJ Web of Conferences, 66, 02074, (2014) 201 ,0401 (2016) EPJ Web of Conferences DOI: 10.1051/ conf/201611 0401 epj 5 1177 NN 11 4