Asymptotic normalization coefficients and halo radii of 12B in the excited states

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. Asymptotic normalization coefficients and halo radii of 12B in the excited states Belyaeva, T.L.; Goncharov, S.A.; Demyanova, A.S.; Ogloblin, A.A.; Danilov, A.N.; Maslov, V.A.; Sobolev, Yu.A.; Trzaska, Wladyslaw; Khlebnikov, S.V.; Tyurin, G.P.; Burtebaev, N.; Janseitov, D.; Mukhamejanov, E. Belyaeva, T.L., Goncharov, S.A., Demyanova, A.S., Ogloblin, A.A., Danilov, A.N., Maslov, V.A., Sobolev, Yu.A., Trzaska, W., Khlebnikov, S.V., Tyurin, G.P., Burtebaev, N., Janseitov, D., & Mukhamejanov, E. (2017). Asymptotic normalization coefficients and halo radii of 12B in the excited states. In M. L. Cognata, M. Lattuada, S. Palmerini, R. Pizzone, & C. Spitaleri (Eds.), Nuclear Physics in Astrophysics VIII (NPA8 2017) Catania, Italy, June 18-23, 2017 (Article 01004). EDP Sciences. EPJ Web of Conferences, 165. https://doi.org/10.1051/epjconf/201716501004 2017 Asymptotic normalization coefficients and halo radii of 12B in the excited states T.L. Belyaeva1,S.A. Goncharov2,A.S. Demyanova3,A.A. Ogloblin3,A.N. Danilov3,V.A. Maslov4, Yu.A. Sobolev4,W. Trzaska5,S.V. Khlebnikov6,G.P. Tyurin6,N. Burtebaev7,D. Janseitov7, and E. Mukhamejanov8 1Universidad Autónoma del Estado de México, C. P. 50000, Toluca, México 2Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow 119991, Russia 3NRC Kurchatov Institute, Moscow RU-123182, Russia 4Flerov Laboratory for Nuclear Research, JINR, 141980, Dubna, Moscow region, Russia 5Department of Physics, University of Jyväskylä, FIN-40014 Jyväskylä, P.O. Box 35, Finland 6V. G. Khlopin Radium Institute,194021, St. Petersburg, Russia 7Institute of Nuclear Physics, National Nuclear Center of Republic of Kazakhstan, Almaty, 050032, Republic of Kazakhstan 8al-Farabi Kazakh National university, Almaty, 050040, Republic of Kazakhstan Abstract. We present the results of measurements and analysis of the differential cross sections of the 11B(d,p)12B reaction leading to formation of the 1+ground state and the 0.953-MeV 2+, 1.674-MeV 2−, 2.621-MeV 1−, 2.723-MeV 0+, 3.389-MeV 3−excited states of 12B at Ed=21.5 MeV. The analysis of the data was carried out within the coupled-reaction-channels method for the direct neutron transfer and the HauserFeshbach formalism of the statistical compound-nucleus model. We deduced the spectroscopic factors, asymptotic normalization coefficients, and rms radii of the last neutron in all states studied. The existence of the neutron halos in the 1.674-MeV 2−and 2.621MeV 1−states was found in consistence with the earlier published data. New information about the enlarged rms radii (6.5 fm) of the last neutron in the unbound 3.389-MeV 3− states of 12B was obtained, which may indicate the evidence of the neutron halo with the orbital momentum of the last neutron equal to two. 1 Introduction The neutronand proton-transfer reactions with stable and radioactive beams in the traditional and inverse kinematics are justifiably regarded as an important source of spectroscopic and astrophysical information. An important application of the nucleon-transfer reactions is related to the determination of the last neutron and proton radii, including radii of nuclei in the short-lived excited states [1, 2]. The evidence of enlarged radii of nuclei in the excited states found by different methods [3–5] indicates the existence of neutron halos not only in the ground states of exotic nuclei, but also in the excites states of "normal" nuclei. © The Authors, published by EDP Sciences. 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/). EPJ Web of Conferences 165, 01004 (2017) DOI: 10.1051/epjconf/201716501004 NPA8 2017 2 Results The differential cross sections of d+11B elastic scattering and the 11B(d,p)12B (g.s., 0.95, 1.67, 2.62, 2.72, 3.39 MeV) reaction were measured at incident deuteron energy Elab =21.5 MeV in the angular range (∼5◦−85◦) at Jyvaskyla University cyclotron using the Large Scattering Chamber (LSC). The experimental elastic-scattering angular distribution was fitted with the optical potentials of the standard Woods-Saxon form, which included the real, spin-orbital, and imaginary (surface) components. The parameters were chosen on the base of the global parameterization. Calculations were carried out with code FRESCO [6]. The compound-nucleus (CN) analysis of the 11B(d,p)12B differential cross sections was carried out within the statistical Hauser-Feshbach formalism by using the computer code CNCOR [7]. It was found that the CN mechanism provides less than 0.1% of the cross sections at forward angles and about 1-3% at medium angles 60-80◦. The coupled-reaction-channels (CRC) analysis included the finite-range neutron transfer mechanism. The neutron single-particle (sp) overlap wave function in the deuteron with orbital angular momentum l=0 was chosen from Ref. [8]. The normalized sp overlap 11B+nwave functions were generated by the 11B+ninteraction potential for each state of 12B. Figure 1 shows the results of the CRC (dashed lines) and CN calculations (dotted lines) in comparison with the measured differential cross sections of the 11B(d,p)12B reaction populating the 2.723MeV 0+and 3.389-MeV 3−states. The solid curves represent the incoherent sum of the CN model and direct transfer calculations. 0 20 40 60 80 100 10-2 10-1 100 Θ c.m. (deg) 0 20 40 60 80 100 10-1 100 101 11 B(d,p 5 ) 12 B (3.39, 3 _ ) d σ /d Ω (mb/sr) Θ c.m. (deg) 11B(d,p4)12B (2.72, 0+) Figure 1. Differential cross sections of the 11B(d,p)12B reaction leading to the fourth excited 2.723-MeV 0+ state and the fifth excited 3.389-MeV 3−state of 12B measured in the present work (points) in comparison with the CRC (dashed line), CN (dotted line) calculations, and their sum (solid line). Table I shows the deduced spectroscopic factors (SFs), the neutron ANCs and the rms neutron radii in comparison with the results obtained by the DWBA analysis of this reaction in Refs. [1, 9, 10]. We found that the rms radii of the last neutron in all excited states studied are greater than that in the g.s. Thus for the 2−state, the excess is a factor of 1.55, and for the 1−state, it is a factor of 2.05, with respect to the rms radius of the g.s. The rms radius of the last neutron wave function of the fifth 3.389-MeV 3−excited state was found Rrms =6.5 fm. This value is a factor of 1.8 larger than that 2 EPJ Web of Conferences 165, 01004 (2017) DOI: 10.1051/epjconf/201716501004 NPA8 2017 2 Results The differential cross sections of d+11B elastic scattering and the 11B(d,p)12B (g.s., 0.95, 1.67, 2.62, 2.72, 3.39 MeV) reaction were measured at incident deuteron energy Elab =21.5 MeV in the angular range (∼5◦−85◦) at Jyvaskyla University cyclotron using the Large Scattering Chamber (LSC). The experimental elastic-scattering angular distribution was fitted with the optical potentials of the standard Woods-Saxon form, which included the real, spin-orbital, and imaginary (surface) components. The parameters were chosen on the base of the global parameterization. Calculations were carried out with code FRESCO [6]. The compound-nucleus (CN) analysis of the 11B(d,p)12B differential cross sections was carried out within the statistical Hauser-Feshbach formalism by using the computer code CNCOR [7]. It was found that the CN mechanism provides less than 0.1% of the cross sections at forward angles and about 1-3% at medium angles 60-80◦. The coupled-reaction-channels (CRC) analysis included the finite-range neutron transfer mechanism. The neutron single-particle (sp) overlap wave function in the deuteron with orbital angular momentum l=0 was chosen from Ref. [8]. The normalized sp overlap 11B+nwave functions were generated by the 11B+ninteraction potential for each state of 12B. Figure 1 shows the results of the CRC (dashed lines) and CN calculations (dotted lines) in comparison with the measured differential cross sections of the 11B(d,p)12B reaction populating the 2.723MeV 0+and 3.389-MeV 3−states. The solid curves represent the incoherent sum of the CN model and direct transfer calculations. 0 20 40 60 80 100 10-2 10-1 100 Θ c.m. (deg) 0 20 40 60 80 100 10-1 100 101 11 B(d,p 5 ) 12 B (3.39, 3 _ ) d σ /d Ω (mb/sr) Θ c.m. (deg) 11B(d,p4)12B (2.72, 0+) Figure 1. Differential cross sections of the 11B(d,p)12B reaction leading to the fourth excited 2.723-MeV 0+ state and the fifth excited 3.389-MeV 3−state of 12B measured in the present work (points) in comparison with the CRC (dashed line), CN (dotted line) calculations, and their sum (solid line). Table I shows the deduced spectroscopic factors (SFs), the neutron ANCs and the rms neutron radii in comparison with the results obtained by the DWBA analysis of this reaction in Refs. [1, 9, 10]. We found that the rms radii of the last neutron in all excited states studied are greater than that in the g.s. Thus for the 2−state, the excess is a factor of 1.55, and for the 1−state, it is a factor of 2.05, with respect to the rms radius of the g.s. The rms radius of the last neutron wave function of the fifth 3.389-MeV 3−excited state was found Rrms =6.5 fm. This value is a factor of 1.8 larger than that of the g.s. and exceeds considerably the rms radii of the neutron wave function in the 1.674-MeV 2− state of 12B. Table 1. Summary of the neutron spectroscopic factors, asymptotic normalization coefficients, rms radii, D1and D2coefficients for the states of 12B. Ex (MeV) ,Jπ fn2l2Sexp t n2l2 Cexp t 11Bn2 (fm−1) Rrms (fm) D1 % D2 %Ref. 0.0,1+11 1.35 ±0.23 3.16 ±0.32 19.9 70.2 [1] 0.69 [9, 10] 0.67 1.33 ±0.07 3.6±0.2 11 58 this work 1.674,2−20 1.80 ±0.43 4.01 ±0.61 53.6 91.9 [1] 0.57 [9, 10] 0.36 1.57 ±0.15 5.58 ±0.26 48.5 91 this work 2.621,1−20 0.88 ±0.15 5.64 ±0.90 66.8 96.3 [1] 0.75 [9, 10] 0.625 1.11 ±0.10 7.40 ±0.35 70 97 this work 3.389,3−22 0.5 [9, 10] 0.251 6.5±0.3 47 94 this work Coefficients D1(RN) determining the weight of the asymptotic part of the wave function and D2 estimating the contribution of the asymptotic part of the wave function to the rms radius define a probability of the halo-nucleon to be outside the range of the core potential, which is expected to be more than 50% for halo states. It is evident that the 2.621-MeV 1−state satisfies all criteria of the halo state with the enormous rms neutron radius, R(1−)=7.4±0.35 fm, and D1and D2coefficients equal to 70% and 97%, respectively. The 1.674-MeV 2−state apparently also can be considered as the halo state with the last neutron spending about 50% of its time outside the range of the core potential. The neutron rms radius in the 3.389-MeV 3−excited state was found equal to 6.5 fm that is 1.16 larger than that for the 1.674-MeV 2−state. The D1and D2are almost the same as for the 2−state. Thus, we can suggest that 12B in the 3.389-MeV 3−excited state also possesses the neutron halo. Note that this observation reveals the first halo excited state with a non-zero l2=2 orbital momentum of the last neutron. References [1] Z. H. Liu et al., Phis. Rev C 64, 034312 (2001). [2] T. L. Belyaeva et al., Phys. Rev. C 90, 064610 (2014). [3] T. Otsuka, N. Fukunishi, and H. Sagawa, Phys. Rev. Lett. 70, 1385 (1993). [4] A. A. Ogloblin et al., Phys. Rev. C 84, 054601 (2011). [5] A. A. Ogloblin et al., Nuclear size isomers: The excited states of light nuclei with cluster structure and nonstandard sizes, in Nuclear Particle Correlations and Cluster Physics. (World Scientific, Pekin, 2017) pp. 311-338. [6] I. J. Thompson, fresco user’s manual and code, available from the author. [7] T. L. Belyaeva, N. S. Zelenskaya, and N. V. Odintsov, Comput. Phys. Commun. 70, 161 (1992). [8] H. Esbensen, G. F. Bertsch, and K. A. Snover, Phys. Rev. Lett. 94, 042502 (2005). [9] J. E. Monhan, H. T. Fortune, C. M. Vincent, R. E. Segel, Phys. Rev. C 3, 2192 (1971). [10] H. Y. Lee et al., Phys. Rev. C 81,015802 (2010). 3 EPJ Web of Conferences 165, 01004 (2017) DOI: 10.1051/epjconf/201716501004 NPA8 2017