Cluster states 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 states in 11B Danilov, A.N.; Demyanova, A.S.; Ogloblin, A.A.; Dmitriev, S.V.; Belyaeva, T.L.; Goncharov, S.A.; Gurov, Yu.B.; Maslov, V.A.; Sobolev, Yu.G.; Trzaska, Wladyslaw; Khlebnikov, S.V.; Burtebaev, N.; Zholdybayev, T.; Saduyev, N.; Heikkinen, Pauli; Julin, Rauno; Tyurin, Grigory Danilov, A.N., Demyanova, A.S., Ogloblin, A.A., Dmitriev, S.V., Belyaeva, T.L., Goncharov, S.A., Gurov, Yu.B., Maslov, V.A., Sobolev, Yu.G., Trzaska, W., Khlebnikov, S.V., Burtebaev, N., Zholdybayev, T., Saduyev, N., Heikkinen, P., Julin, R., & Tyurin, G. (2014). Cluster states in 11B. In S. Lunardi, P. Bizzeti, S. Kabana, C. Bucci, M. Chiari, A. Dainese, P. D. Nezza, R. Menegazzo, A. Nannini, & C. S. A. J. Valiente-Dobon (Eds.), INPC 2013 – International Nuclear Physics Conference Firenze, Italy, June 2-7, 2013 (Article 03007). EDP Sciences. EPJ Web of Conferences, 66. https://doi.org/10.1051/epjconf/20146603007 2014 Cluster states in 11B A.N. Danilov1a, A.S. Demyanova1, A.A. Ogloblin1, S.V. Dmitriev1, T.L.Belyaeva2, S.A.Goncharov3, Yu.B. Gurov4, V.A. Maslov5, Yu.G. Sobolev5, W. Trzaska6, S.V. Khlebnikov7, N. Burtebaev8, T. Zholdybayev8, N. Saduyev9, P. Heikkinen6, R. Julin6, G.P. Tyurin6 1 NRC Kurchatov Institute, Moscow 123182, Russia 2 Universidad Autonoma del Estado de Mexico, Codigo Postal 50000, Toluca, Mexico 3 Lomonosov Moscow State University, Moscow, Russia 4 MEPhi, Moscow, Russia 5 JINR, Moscow region, Russia 6 JYFL, Jyvaskyla, Finland 7 Khlopin Radium Institute, St.-Petersburg, Russia 8 Nuclear Physics Institute, Almaty, Kazakhstan 9 Al-Farabi Kazakh National University, Kazakhstan Abstract. 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. 1 Introduction Progress in the theory of cluster physics, in particular, the hypothesis about possible existence of the alpha-particle condensate in nuclei initiated work to find nuclear states with extremely large size. It was predicted that two levels in 11B: ½-, E * = 8.56 MeV and ½+ (possibly at 12.56 MeV) have the root mean square radii Rrms = 3.1 fm [1] and ~ 6 fm [2] correspondingly, while the ground state has Rrms = 2.29 fm. For checking these predictions differential cross sections of the inelastic scattering α + 11B at E(α) = 65 MeV were measured and analyzed together with the data obtained at different energies. The analysis was done by the Modified Diffraction Model (MDM) [3]. This method allows determining the radii R*rms of the excited states via the difference of the diffraction radii of the excited and the ground states using the expression: R*= R0 + [R* dif− Rdif (0)] (1) Here R0 is the RMS of the ground state of the nucleus under discussion, R* dif and Rdif (0) are the diffraction radii determined from the positions of the minima and maxima of the experimental angular distributions of the inelastic and elastic scattering correspondingly. Such approach allowed finding the a Corresponding author: [email protected] DOI: 10.1051/ C Owned by the authors, published by EDP Sciences, 2014 , / 03007 (2014) 201 66 epjconf EPJ Web of Conferences 46603007 This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20146603007 consistent values of the RMS radius of the Hoyle state from 2H, 3He, 4He, 6Li, 12C inelastic scattering measured on the 12C target in a wide energy range [4]. The goal of the experiment was to determine the radii values of the exciting states in 11B using MDM. 2 Experimental data We measured the differential cross-sections of the inelastic α + 11B scattering with excitation the states of 11B up to E* ~ 14 MeV. The experiment was done at the JYFL cyclotron K130, Jyvaskyla University, Finland using LSC (Large Scattering Chamber) with ΔE-E telescopes of semiconductor counters. The target was an 11B self-supported film of 0.275 mb/cm2 thickness. The only significant impurity was 12C. The beam monochromatization system was used allowing providing the total energy resolution of the experiment to be 150 keV. A sample spectrum is shown on Fig. 1. 40 45 50 0 80 160 240 11.6 counts E (MeV) g.s.12C 4.4412C 2.12 4.44 5.02 6.74 7.29 7.98 8.56 9.27 10,34 10.6 11.27 12.6 12.92 13.1 g.s. Figure 1. A sample α-particles spectrum at E (α) =65 MeV, Θ=53.5 deg. 3 Results and discussions 3.1 8.56 MeV state The value of the 8.56MeV state radius was determined to be Rrms = 2.87 ± 0.12 fm, which is 0.6 fm larger than the radius of the ground state being in agreement with the previous data (Rrms = 2.99 ± 0.18 fm from Ref. [5]). The obtained radius is practically equal to the radius of the second excited state of 12C, the Hoyle state. The radius of the Hoyle state was determined to be Rrms = 2.89 ± 0.04fm [3]. So the obtained result together with the similarity of the shapes of the angular distributions (Fig. 2) and the similarity of the energy dependence of diffraction radii (Fig. 3) clearly indicates to the similarity of the structures of the 8.56 MeV state of 11B and the Hoyle state of 12C. The 8.56 MeV state can be considered as an analogue of the Hoyle state in neighboring nuclei. EPJ Web of Conferences 03007-p.2 0 10 20 30 40 50 60 70 80 90 0,01 0,1 1 10 d/dΩ (mb/sr) CM Figure 2. Differential cross-sections of inelastic scattering α + 11B at Eα=65 MeV leading to 8.56 MeV state (red points) and inelastic scattering α + 12C at Eα=65 MeV leading to 7.65 MeV state (black points) 0 100 200 300 4,0 4,5 5,0 5,5 6,0 6,5 Rdif (fm) Ec.m.(MeV) Figure 3. Energy dependence of diffraction radii: black dashed line – diffraction radii for elastic scattering α + 12C, red dashed line – for 7.65 Hoyle state, black points – for elastic α + 11B, black solid line – linear fit for black points, red points – for 8.56 MeV state, red solid line – linear fit for red points 3.2 Rotational band based on 8.56 MeV state We got preliminary results for the differential cross-section of the inelastic scattering leading to 10.34 MeV (5/2-) and 13.1 MeV (9/2-) states. These states are predicted [6,7] as the second and the fourth members of the rotational band based on the 8.56 MeV state. The behavior of the angular distribution of the inelastic scattering with the excitation of the 13.1 MeV state is the same as for the inelastic scattering of α + 12C with the excitation of the 14.08 MeV (Fig. 4). The last is well known to be excited by transition L=4. The MDM was used for estimating the radius of the 13.1 MeV state. The best fit was obtained with the diffraction radius Rdif =4.5 fm, the value which coincides with that of the L = 4 transition in the 12C (α, α’) reaction to a new state of 12C at E* = 13.75 MeV [8] belonging to the rotational band based on the Hoyle state. In some articles [6] there are assumptions that the 13.1 MeV state is the member of the hypothetical rotational band based on the ground state. Within these assumptions the previous member of this band is the 6.74 MeV state with abnormally large inertia momentum. We have got the angular distribution with the excitation of this state and didn’t observe any RMS radius enlargement, what is naturally can be expected in accordance with sharp increase of inertia momentum. It is quite possible that abovementioned rotational band doesn’t exist and lowlying states of 11B have normal shell-model structure. So the 13.1 MeV is more probable to be the member of the band based on the 8.56 MeV state. INPC 2013 03007-p.3 0 20 40 60 80 0,01 0,1 1 10 d  /dΩ (mb/sr) CM Figure 4. Differential cross-sections of inelastic scattering α + 11B at Eα = 65 MeV leading to 13.1 MeV state (red points) and inelastic scattering α + 12C at Eα = 65 MeV leading to 14.08 MeV state (black points) 3.3 12.56 MeV state For the 12.56 MeV (½+, T=3/2) state [9] of 11B there exists contradictory information concerning its isospin. The model [2] suggest that Jπ=½+, T = ½. In our experiment we observed a group of states, among them is the state with excitation energy 12.6 MeV. Also such state was detected in the resonance reaction 7Li + α [6]. A T = 3/2 state is unexpected to be observed in the inelastic alpha particle scattering, so isospin of this state is T = ½. Preliminary analysis of angular distribution indicates to angular transferred momentum L=1, so spin of this state is 3/2+, in agreement with [6]. Thus, we can conclude that the predictions [2] were not confirmed. Theoretical calculations are in a progress. The work was supported by the Grant of RFBR, No 12-02-000927-a. References 1. Y. Kanada-En’yo, Phys. Rev. C 75, 024302 (2007) 2. T. Yamada and Y. Funaki, Phys. Rev. C 82, 064315 (2010) 3. A.N. Danilov et al., Phys.Rev. C 80, 054603 (2009) 4. A.S. Demyanova et al., Nucl. Phys. A 805, 489 (2008) (Proceedings of the 23rd Intern. Nuclear Physics Conference (INPC2007), Tokyo, Japan, 3-8 June, 2007 5. A.S.Demyanova et al., Int. J. of Modern Physics E 20, 915 (2011) 6. H. Yamaguchi et al., Phys. Rev. C 83, 034306 (2011) 7. T. Sahara and Y. Kanada-En’yo, Phys. Rev. C 85, 054320, (2012) 8. A.A. Ogloblin et al., Proceeding of this conf. INPC2013, poster number - NS 160 9. F. Ajzenberg-Selove, Nucl. Phys. A 506, 1 (1990) EPJ Web of Conferences 03007-p.4