Rotational band in 12C based on the Hoyle state

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. Rotational band in 12C based on the Hoyle state Ogloblin, A.A.; Demyanova, A.S.; Danilov, A.N.; Dmitriev, S.V.; Belyaeva, T.L.; Goncharov, S.A.; Maslov, V.A.; Sobolev, Yu.G.; Trzaska, Wladyslaw; Khlebnikov, S.V. Ogloblin, A.A., Demyanova, A.S., Danilov, A.N., Dmitriev, S.V., Belyaeva, T.L., Goncharov, S.A., Maslov, V.A., Sobolev, Yu.G., Trzaska, W., & Khlebnikov, S.V. (2014). Rotational band in 12C based on the Hoyle state. 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 02074). EDP Sciences. EPJ Web of Conferences, 66. https://doi.org/10.1051/epjconf/20146602074 2014 Rotational band in 12C based on the Hoyle state A.A. Ogloblin1, A.S. Demyanova1, A.N. Danilov1, S.V. Dmitriev1, T.L. Belyaeva2, S.A. Goncharov3, V.A. Maslov4, Yu.G. Sobolev4, W. Trzaska5, and S.V. Khlebnikov6 1NRC “Kurchatov Institute”, Moscow, Russia 2Universidad Autonoma del Estado de Mexico, Mexico 3Lomonosov State university, Moscow Russia, 4JINR, Moscow region, Russia 5JYFL, Jyvaskyla, Finland 6Khlopin Radium Institute, St.-Petersburg, Russia Abstract. 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. 1 Introduction The structure of the 0+2, 7.65 MeV “Hoyle” state of 12C permanently attracts attention due to its importance for understanding many features of clustering phenomena in nuclei. During last decade there appeared several new theoretical approaches which predicted some unusual features of this state. The most ambitious among them was the model of alpha particle condensation (APC) [1] according to which the Hoyle state was expected to have enhanced dimensions resembling a gas of almost noninteracting alpha particles. Most of the other cluster models like the antisymmetrized molecular dynamics (AMD) also predicted the enhancement of the radius of the Hoyle state, though in a less extent. The experimental data on the inelastic scattering [2] supported these suggestions (the collection of the theoretical radii values together with the experimental one is given in Table.1). Table 1. RMS radii of the Hoyle state in 12C from different models and experiment. 1 2 3 4 5 6 7 8 9 10 EXP 3.83 3.27 4.31 3.47 3.38 3.22 3.53 2.90 2.4 2.89±0.04 1. Y. Funaki et al., Phys. Rev. C 80, 064326 (2009); 2. Y. Kanada-En'yo, Phys.Rev. C 75, 024302 (2007); 3. T. Yamada, P. Schuck, Eur. Phys. J. A 26, 185 (2005); 4. M. Kamimura, Nucl. Phys. A 351, 456 (1981); 5. M. Chernykh et al., Phys. Rev. Lett. 98, 032501 (2007); 6. M. Gai, EPJ Web of Conf. 38, 15001 (2012); 7. N. Furutachi, M. Kimura, Phys. Rev. C 83, 021303 (2011); 8. T.Suhara and Y.Kanada-En’yo, PTP, 123, 303 (2010); 9. E. Epelbaum, Phys. Rev. Lett. 106, 192501 (2011); 10. A.N. Danilov et al., Phys. Rev. C 80, 054603 (2009) a Corresponding author: [email protected] DOI: 10.1051/ C Owned by the authors, published by EDP Sciences, 2014 , / 02074 (2014) 201 66 epjconf EPJ Web of Conferences 46602074 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/20146602074 Moreover, another prediction of the APC that all three alpha particles in 12C should predominantly occupy the lowest s-orbit also was confirmed by experiment giving for the occupation probability Ws(α) = 0.6 [3] (to be compared with the theoretical value 0.7 - 0.8 [4]). Thus, the experiment definitely demonstrated the exotic features of the Hoyle state including those which could be interpreted as the manifestation of rudimentary APC (“ghost” of condensation). However, some new open questions appeared, and they were connected with possible existence in 12C of the excited states genetically connected with the Hoyle one. The idea that the Hoyle state might be the head of a rotational band became quite natural after appearance of the Morinaga’s model [5] describing this level as a chain-like configuration of three alpha particles. However, the extremely large moment of inertia required the location of the corresponding 2+ state at a too low excitation energy (no more than ~ 0.8 MeV). Recent experiments [6, 7] identified the 2+2 level in 12C at E* = 9.6 – 9.8 MeV. On the other hand, according to the APC model the 2+2 state is formed by lifting one of the α’s to the next d-orbit from the s one and has an extremely large RMS radius ~ 6 fm [8]. Consequently, in the frame of APC the 2+2 state should be almost spherical and cannot belong to a rotational band. Recently, the radius of the 2+2 state was determined [9] to be ~ 3.1 fm. i.e. practically the same as that of the Hoyle state. As the RMS rigid rotator radius estimated from the moment of inertia is quite close to this value (2.7 fm) these findings provide some arguments in favor of the suggestion that the states 0+2 - 2+2 really are the members of the second rotational band in 12C. Of course, the decisive conclusion could be done only after identification of the corresponding 4+ state. Some indication to existence of such a state was obtained in Ref. [10] claiming to the observation of a 4+ broad state at E* = 13.3 MeV. In any case this finding should be confirmed. 2 Results and discussion We measured the differential cross-sections of the inelastic α + 12C scattering at the alpha particles energy 65 MeV leading to the states of 12C at the excitation energies up to E* ≈ 20 MeV. The experiment was performed at the JYFL cyclotron at the alpha particles energy 65 MeV. The sets of ΔE – E telescopes installed in the scattering chamber LSC were used. The overall energy resolution was about 200 keV due to use of a beam monochromatization system. Besides, we reconstructed the cross-section of the inelastic scattering cross-section to the state 4+, 14.08 MeV from the data measured at 110 MeV previously [11] but unpublished at that time. Sample spectra at both energies are shown in Fig.1. They were decomposed into separate groups. 43 44 45 46 47 48 49 0 40 80 120 160 200 240 counts E(MeV) 12.71,1+ 13.35,213.75, 4+ 14.08,4+ 15.11,1+ 15.44,2+ 11.82,272 73 74 75 76 77 78 79 0 20 40 60 80 100 120 140 160 E(MeV) counts 10.84,112.71,1+ 13.35,213.75,4+ 14.08,4+ 15.11,1+ 15.44,2+ 11.82,2Figure 1. Sample α-particles spectra at E (α) = 65 MeV, Θ lab = 30.8o (left) and E (α) = 110 MeV, Θ lab = 43.6o (right). The results of the decomposition into the groups corresponding to the known levels of 12C and the new one at 13.75 MeV are shown. The decomposition procedure contained a few steps. First, the background approximated by the straight lines (Fig.1) was subtracted. Secondly, we chose several spectra at E (α) = 65 MeV measured at the backward angles where the background was practically negligible and tried to decompose them EPJ Web of Conferences 02074-p.2 into the groups corresponding to the known levels of 12C in the excitation energy region of interest: 15.44 (2+), 14.08 (4+), 15.11 (1+, T=1), 13.35 (2-), 12.71 (1+) and 11.83 (2-). In principle, the spectra could be reproduced, however, the χ2 value was significantly larger than in the other attempts and the intensity of the group corresponding to the state 2-, 13.35 MeV was several times larger than that related to the state 2-,11.83 MeV in all the spectra decomposed in this way. As the four last levels have abnormally parity (and one of them even T = 1) they could be excited only via some multi-step mechanisms. Consequently, we suggested that the cross-sections of the formation of both closely lying 2levels should be equal, and made the decomposition of the spectra under such condition. The result was that the inelastic scattering cross-section in the excitation energy region 13 – 14 MeV was not exhausted by the known 12C states. For this reason we have done two other types of decomposition assuming either the existence of a level with the parameters taken from Ref. [10] (E* = 13.3 MeV, Г = 1.7 MeV) or a new state whose excitation energy and width were adjusted. The second variant of decomposition led to a broad group corresponding to the new state E* = 13.75 ± 0.12 MeV, Г = 1.4 ± 0.15 MeV and gave better description of the data at both initial energies and practically at all the measured angles. The differential cross-sections of the inelastic scattering leading to the excitation 14.08 and 13.75 MeV states are shown in Fig.2 (Eα = 110 MeV) and Fig.3 (Eα = 65 MeV). 020 40 60 80 0,0 0,4 0,8 1,2 1,6 2,0 dd mb/sr) cm (deg) 020 40 60 80 0,0 0,4 0,8 1,2 1,6 2,0 d/d mb/sr) cm (deg) Figure 2. Differential cross-sections of the 12C + α inelastic scattering at E (α) = 110 MeV with excitation of the 14.08 MeV, 4+ (left) and 13.75 MeV (right) states. The red curves are calculated by DWBA with L = 4 and the similar parameters of OM potential and form factor obtained from the scattering data to the 2+1 (4.44 MeV) state (with necessary corrections to the difference of the initial energy). The blue curves are calculated using the diffraction scattering model with L = 4 and the diffraction radii R = 4.2 fm (left) and 5.0 fm (right). 020 40 60 80 0,0 0,4 0,8 1,2 d/d mb/sr) cm (deg) 020 40 60 80 0,0 0,4 0,8 1,2 ddmb/sr) cm (deg) Figure 3. The same as in Fig.2 at E (α) = 65 MeV One can see from Figs.2, 3 that the shapes of the angular distributions corresponding to the excitation of the 14.08 MeV, 4+ state and the 13.75 MeV one are quite similar in their main features (note two prominent maxima and minima at the angles larger than ~ 15o). The diffraction model calculations with the angular moment transfer L = 4 reproduce rather satisfactory their positions. In the case of the 14.08 MeV state the diffraction origin of these maxima and minima is well demonstrated by the observed shift of the main extremes with the energy to the smaller angles which INPC 2013INPC 2013 02074-p.3 is approximately proportional, as expected, to 1/E1/2. In the case of the 13.75 MeV state such shift manifests itself in much less extent and is observed only at the large angles. Probably, this is connected with some uncertainties in the spectra decomposition procedure. Nevertheless, it is reasonable to suggest the Iπ = 4+ value for the 13.75 MeV level. For preliminary DWBA analysis we deliberately used the parameters of the optical model (OM) potentials and the form factors which had been obtained by fitting the calculations to the inelastic scattering cross-sections to the 2+1 (4.44 MeV) state with necessary corrections to the differences in the energy. The agreement occurred to be rather poor even in the case of the 14.08 state where one might expect more similarity in the excitation the 2+ and 4+ states belonging to the same rotational band. It is interesting to note that the cross-section of the excitation of the 4+, 10.36 MeV state (being also a member of the rotational band) in the 16O (α, α’) reaction measured in Ref. [12] at the same center-of-mass energy (E lab = 104 MeV) practically coincides with our 12C + α data in the overlapping regions of the linear momentum transfers. The DWBA calculations [12] also did not reproduce the prominent maximum at ~ 25o. This result indicates the necessity of more detailed study of the dynamics of the reactions under discussion. The Modified diffraction model (MDM) [2] was used for estimating the radii of the 14.08 and 13.75 MeV states. The best fit was obtained with the diffraction radius of the transition to the 14.08 MeV state Rdif = 4.2 fm (left parts of Fig.2, 3), which is almost 1 fm less than that for the elastic scattering. A probable origin of this effect lies in large centrifugal barrier and will be discussed elsewhere. In spite of this the diffraction radius corresponding to the formation of the 13.75 0 5 10 15 20 -2 0 2 4 6 8 10 12 14 16 E*, MeV J(J+1) 0+ 2+ 4+ Figure 4. Rotational bands of 12C MeV state can be estimated relatively to that of the 14.08 MeV level. It occurred to be Rdif = 5.0 fm, i.e. 0.8 fm larger than that of the 14.08 state. This value agrees well with the differences between the ground and the excited 0+2 and 2+2 states (0.6 fm and 0.8 fm correspondingly according to [9]) providing another evidence of belonging of the 13.75 MeV level to the rotation band based on the Hoyle state (Fig.4). The work was supported by the RFBR grant No 12-02-000927-a. References 1. A. Tohsaki et al., Phys. Rev. Lett. 87, 192501 (2001) 2. A.N. Danilov et.al., Phys. Rev. C 80, 054603 (2009) 3. T.L. Belyaeva et al., Phys. Rev. C 82, 054618 (2010) 4. T. Yamada and P. Schuck, Phys. Rev. C 69, 024309 (2004) 5. H. Morinaga, Phys. Rev. 101, 254 (1956) 6. M. Freer et al., Phys. Rev. C 80, 041303 (2009) 7. M. Itoh, Phys. Rev. C 84, 054308 (2011) 8. T. Yamada and P. Schuck, Eur. Phys. J. A 26, 185 (2005) 9. A.A. Ogloblin, et al., Eur. Phys.J. A 41, 46 (2013) 10. M. Freer et al., Phys. Rev. C 83, 034314 (2011) 11. A.S. Demyanova et.al., Physics of Atomic Nuclei, v.72, No 10, 1611 (2009) 12. M. Harakeh et al., Nucl. Phys. A 265, 189 (1976) EPJ Web of Conferences 02074-p.4