Spectroscopy of exotic states of 13C

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. Spectroscopy of exotic states of 13C Demyanova, A.S.; Danilov, A.N.; Dmitriev, S.V.; Ogloblin, A.A.; Belyaeva, T.L.; Burtebaev, N.; Drobyshev, P.; Goncharov, S.A.; Gurov, Yu. B.; Heikkinen, Pauli; Julin, Rauno; Khlebnikov, S.V.; Maslov, V.A.; Nassurlla, N.; Penionzhkevich, Yu.E.; Sobolev, Yu.G.; Trzaska, Wladyslaw; Tyurin, Grigory; Zherebchevskii, V.I. Demyanova, A.S., Danilov, A.N., Dmitriev, S.V., Ogloblin, A.A., Belyaeva, T.L., Burtebaev, N., Drobyshev, P., Goncharov, S.A., Gurov, Y. B., Heikkinen, P., Julin, R., Khlebnikov, S.V., Maslov, V.A., Nassurlla, N., Penionzhkevich, Yu.E., Sobolev, Yu.G., Trzaska, W., Tyurin, G., & Zherebchevskii, V.I. (2014). Spectroscopy of exotic states of 13C. 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 02027). EDP Sciences. EPJ Web of Conferences, 66. https://doi.org/10.1051/epjconf/20146602027 2014 Spectroscopy of exotic states of 13C A.S. Demyanova1a, A.N. Danilov1, S.V. Dmitriev1, A.A. Ogloblin1, T.L. Belyaeva2, N. Burtebaev3, P. Drobyshev3, S.A. Goncharov4, Yu.B. Gurov5, P. Heikkinen6, R. Julin6, S.V. Khlebnikov7, V.A. Maslov8, N. Nassurlla3, Yu.E. Penionzhkevich8, Yu.G. Sobolev8, W. Trzaska6, G.P. Tyurin6, V.I. Zherebchevskii9 1NRC Kurchatov Institute, Moscow, Russia, 2Universidad Autonoma del Estado de Mexico, Mexico 3Nuclear Physics Institute, Almaty, Kazakhstan 4Lomonosov Moscow State University, Moscow, Russia 5MEPhi, Moscow, Russia 6 JYFL, Jyvaskyla University, Jyvaskyla, Finland 7Khlopin Radium Institute, St.-Petersburg, Russia 8 JINR, Dubna, Moscow Region, Russia 9St.-Petersburg State University, St.-Petersburg, Russia Abstract. 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. 1 Introduction 13C is a good example of a “normal” nucleus well described by the shell model. Its level scheme is reliably determined up to the excitation energies ~ 10 MeV (see e.g. [1]). However, some new approaches such as the hypothesis [2] of the α-particle condensation suggests that cluster states with an enhanced radius can appear. The famous Hoyle state (0+2, E* = 7.65 MeV) in 12C was considered as the most probable candidate for having such structure. It was also expected [3] that the analogues of the Hoyle state would reveal themselves in some neighboring nuclei, e.g., the 1/2¯ (E* = 8.86MeV) state in 13C. Our analysis [4] of the 13C + α scattering data measured at E (α) = 388 MeV [5] really demonstrated a considerable enhancement of the radius of this particular state. However, the method of extracting the radii used in Ref. [4] (the Modified diffraction model, MDM [6]) may not quite adequate at high energies (≥ 100 MeV) when nuclei are too transparent. Besides, the existence in 13C of some states with enhanced dimensions but of different structure was discussed as well. Thus, a neutron halo was identified in the first excited state 3.09 MeV (1/2+) by two independent and complementary methods [7, 8]. There are predictions [9] that the 3/2¯2, 9.90 MeV state and the a Corresponding author: [email protected] DOI: 10.1051/ C Owned by the authors, published by EDP Sciences, 2014 , / 02027 (2014) 201 66 epjconf EPJ Web of Conferences 46602027 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/20146602027 members of the rotational band based on it also are diluted. Consequently, new measurements especially at lower energies are highly desirable. In this paper we studied the inelastic and elastic 13C + α scattering at E (α) = 65 MeV with the aim of measuring the radii of 13C excited states. In addition to our standard approach using MDM we also analyzed the shifts of the rainbow (Airy) minima in the angular distribution according to the idea proposed in Ref. 10. The main attention was devoted to three 13C levels: 8.86 MeV (1/2¯), 3.09 MeV (1/2+) and 9.90 MeV (3/2¯) state. 2 Results and discussion The experiment was done at the JYFL cyclotron, Finland. A set of the ΔE – E telescopes was used for detection of the alpha-particles. A self-supporting 13C target (0.3 mg/cm2) with the 98% enrichment was used. It contained some impurities of 12C and 16O. A system of reducing the energy spread of the cyclotron beam down to 0.3 % was used. A sample spectrum is shown in Fig. 1(left). The differential cross-sections of 13С + α elastic scattering are presented in Fig.1 (right) with the results of optical model calculations. 44 46 48 50 52 54 56 58 0 40 80 120 160 200 10.46 9.9 counts Eα, MeV 12Cg.s 8.86 Θ=38.5 11.8 9.64 11.01 9.5 7.5 6.86 16O6.92 3.68 12C4.44 g.s. 3.09 Figure 1. Left: A sample spectrum (θ =38.5o) for the 13C + α scattering at E (α) = 65 MeV. Right: Differential cross-sections of the 13С + α elastic scattering in ratio to the Rutherford one at 65 MeV together with the results of optical model (OM) calculations (solid curve). The dashed curve corresponds to the far component of the cross-section at zero absorption (W = 0). The position of the rainbow minimum is denoted by an arrow. 0 20406080100120 10-3 10-2 10-1 100 101 102 dσ/dΩ (mb/sr) ΘCM (deg) 0 102030405060708090100 0,01 0,1 1 10 dσ/dΩ (mb/sr) Θcm (deg) Rainbow min Diffraction 12C: 7.65 13C: 8.86 Figure 2. Left: Differential cross-sections of the inelastic 13С + α scattering leading to the 8.86 MeV state in 13C. The results of DWBA calculations (L = 0) are shown by the solid curve. Right: Comparison of the inelastic cross-sections with the excitation of the 8.86 MeV (1/2¯) state in 13C (red points) and 0+2, 7.65 MeV (Hoyle) state in 12C (black points). The positions of the rainbow minima are denoted by the arrows. The measured differential scattering cross-section leading to the excitation of the 1/2¯, 8.86 МeV state is presented together with the DWBA calculations in Fig. 2(the left part). The abovementioned EPJ Web of Conferences 02027-p.2 angular distribution is presented in comparison with that for the Hoyle state at the same energy in Fig.2 (the right part). Similar diffraction patterns corresponding to the angular momentum transfer L = 0 were observed. The rainbow (Airy) minima were also identified. For the 8.86 MeV state the minimum is located at the angle larger than that in the case of the elastic scattering and smaller than for the Hoyle state. According to Ref. [10] the observed shifts of the Airy minima positions to the larger angles in the inelastic differential cross-sections relative to that of the elastic one indicate an enhancement in the radius of the excited state. The measured differential cross-sections of the inelastic 13C + α (65 MeV) scattering leading to the 9.90 MeV and 3.09 MeV states are presented in Fig.3 in the left and right parts correspondingly. 0 102030405060708090 0,01 0,1 1 Θ CM(deg) dσ/d Ω (mb/sr) 020406080100120 10-3 10-2 10-1 100 101 102 103 dσ/d Ω (mb/sr) ΘCM(deg) Figure 3. Left: Differential cross-sections of the inelastic 13С + α (65 MeV) scattering to the 9.90 MeV (3/2¯) state. The results of DWBA calculations are shown by a solid curve for angular momentum transfer L = 2. The position of the Airy minimum is denoted by an arrow. Right: The same for the 3.09 MeV (1/2+) state with L = 1. The diffraction structure of the measured cross-sections was analysed by MDM, and the radii of all three 13C excited states were determined (Table1). The RMS radius of the 8.86 MeV state (2.68±0.10 fm) is a little smaller than the radius of the Hoyle state (Rrms = 2.89 ± 0.04 fm [6]). This result is in agreement with previous estimates [4] obtained from the analysis of the literature data. The observed Table 1. Diffraction and RMS radii of 13C states obtained by MDM E*, MeV, IπRdif, fm Rrms, fm 0.00, 1/2¯ (5.31±0.07) 2.31 3.09, 1/2+(5.96±0.06) 2.92±0.07 8.86, 1/2¯ (5.66±0.10) 2.68±0.10 9.90, 3/2¯ (5.00± 0.12) 2.00±0.14 shift of the positions of the Airy minima in 12C and 13C confirms the conclusion reached by the MDM analysis. Thus, the obtained results clearly indicate that the 1/2¯, 8.86 MeV state and the Hoyle state (Fig.2, right) have much in common and probably could be named analogues. On the other hand, the Hoyle state is the head of a rotational band [11] but there is no indication of the existence of the analogue band based on the 8.86 MeV state. This difference may reflect important difference in the structure of the both states. The radius of the 3.09 MeV state was determined to be Rrms = 2.92 ± 0.07 fm. Our previous result obtained from the analysis of some published data at lower energies gave Rrms = 2.74 ± 0.06 fm [8]. The position of the Airy minimum was not determined in the present work. However in any case it is located in the range (~ 55o – 70o) sufficiently larger than the corresponding minimum in the elastic scattering to indicate the radius enhancement. A neutron halo radius Rh of the 3.09 MeV state can be determined [12] from the asymptotic normalization coefficients (ANC) extracted by the analysis of the 12C (d, p) 13C*(3.09 MeV) reaction. Then Rh can be transformed to the corresponding RMS radius of the state. The details of the method are given in our paper [13]. The RMS radius obtained there INPC 2013 02027-p.3 from the analysis of the (d, p)-reactions at different energies is Rrms = 2.68 ± 0.26 fm. Thus, all the used methods, MDM, ANC and nuclear rainbow gave (qualitatively) similar results. This finding increases the reliability both of the halo observation in the 3.09 MeV state and the application of the MDM and ANC models for radii determination. The MDM analysis of the differential cross-section corresponding to the formation of the 9.90 MeV state showed that the predicted radius enhancement for the 9.90 MeV state in 13C [9] does not take place. As one can see from Fig. 3 (left) the position of the Airy minimum observed in the inelastic cross-section coincides with that in the elastic scattering angular distribution (Fig.1, right) confirming the result obtained by MDM. It is interesting to note that the 9.90 MeV state and the other members of its rotational band are strongly excited in the α-cluster transfer reactions (6L,d) and (7Li, t) on 9Be [14] while the 8.86 MeV state is not. This means that the α-cluster structures of the 8.86 and 9.90 MeV states are different: the latter one has a strong 9Be + α component which is absent in the 8.86 MeV state. If the 8.86 MeV state really does not form a rotational band this fact would provide evidence enabling its structure to be compared to that of the Hoyle state. The obtained results demonstrate a co-existence of different structures in 13C. A more elaborate theoretical study of structure of the states under discussion is required. The work was partly supported by RFBR grant 12-02-00927. References [1] W. von Oertzen, M. Freer, Y. Kanada-En’yo, Phys. Rep. 432, 43 (2006) [2] A. Tohsaki, H. Horiuchi, P. Schuck and G. Röpke, Phys. Rev. Lett. 87, 192501 (2001); P. Schuck et al., Nucl.Phys. А 738, 94 (2004) [3] M. Milin and W. von Oertzen, Eur. Phys. J. A 14, 295 (2002) [4] A.S. Demyanova et al., Int. J. Modern. Phys. E 20, No 4, 915 (2011) [5] T. Kawabata et al., Journal of Physics: Conference Series, 111, 012013 (2008); Journal of Modern Physics E 17, 2071 (2008) [6] A.N. Danilov et al., Phys. Rev. C 80, 054603 (2009) [7] Z.H. Liu et al., Phys. Rev. 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