Measurement of the Iron Spectrum in Cosmic Rays from 10 GeV/n to 2.0 TeV/n with the Calorimetric Electron Telescope on the International Space Station

被引:34
作者
Adriani, O. [1 ,2 ]
Akaike, Y. [3 ,4 ]
Asano, K. [5 ]
Asaoka, Y. [5 ]
Berti, E. [1 ,2 ]
Bigongiari, G. [6 ,7 ]
Binns, W. R. [8 ,9 ]
Bongi, M. [1 ,2 ]
Brogi, P. [6 ,7 ]
Bruno, A. [10 ]
Buckley, J. H. [8 ,9 ]
Cannady, N. [11 ,12 ,13 ]
Castellini, G. [14 ]
Checchia, C. [6 ]
Cherry, M. L. [15 ]
Collazuol, G. [16 ,17 ]
Ebisawa, K. [18 ]
Fuke, H. [18 ]
Gonzi, S. [1 ,2 ]
Guzik, T. G. [15 ]
Hams, T. [11 ]
Hibino, K. [19 ]
Ichimura, M. [20 ]
Ioka, K. [21 ]
Ishizaki, W. [5 ]
Israel, M. H. [8 ,9 ]
Kasahara, K. [22 ]
Kataoka, J. [23 ]
Kataoka, R. [24 ]
Katayose, Y. [25 ]
Kato, C. [26 ]
Kawanaka, N. [27 ,28 ]
Kawakubo, Y. [15 ]
Kobayashi, K. [3 ,4 ]
Kohri, K. [29 ]
Krawczynski, H. S. [8 ,9 ]
Krizmanic, J. F. [11 ,12 ,13 ]
Link, J. [11 ,12 ,13 ]
Maestro, P. [6 ,7 ]
Marrocchesi, P. S. [6 ,7 ]
Messineo, A. M. [7 ,30 ]
Mitchell, J. W. [12 ]
Miyake, S. [3 ,31 ]
Moiseev, A. A. [12 ,13 ,32 ]
Mori, M. [33 ]
Mori, N. [2 ]
Motz, H. M. [34 ]
Munakata, K. [26 ]
Nakahira, S. [18 ]
Nishimura, J. [18 ]
机构
[1] Univ Florence, Dept Phys, Via Sansone 1, I-50019 Sesto, Fiorentino, Italy
[2] Ist Nazl Fis Nucl, Sez Florence, Via Sansone 1, I-50019 Sesto, Fiorentino, Italy
[3] Waseda Univ, Waseda Res Inst Sci & Engn, Shinjuku Ku, 17 Kikuicho, Tokyo 1620044, Japan
[4] Japan Aerosp Explorat Agcy, JEM Utilizat Ctr, Human Spaceflight Technol Directorate, 2-1-1 Sengen, Tsukuba, Ibaraki 3058505, Japan
[5] Univ Tokyo, Inst Cosm Ray Res, 5-1-5 Kashiwa No Ha, Kashiwa, Chiba 2778582, Japan
[6] Univ Siena, Dept Phys Sci Earth & Environm, Via Roma 56, I-53100 Siena, Italy
[7] Ist Nazl Fis Nucl, Polo Fibonacci, Sez Pisa, Largo B Pontecorvo 3, I-56127 Pisa, Italy
[8] Washington Univ, Dept Phys, One Brookings Dr, St Louis, MO 63130 USA
[9] Washington Univ, McDonnell Ctr Space Sci, One Brookings Dr, St Louis, MO 63130 USA
[10] NASA GSFC, Heliospher Phys Lab, Greenbelt, MD 20771 USA
[11] Univ Maryland Baltimore Cty, Ctr Space Sci & Technol, 1000 Hilltop Circle, Baltimore, MD 21250 USA
[12] NASA GSFC, Astroparticle Phys Lab, Greenbelt, MD 20771 USA
[13] NASA GSFC, Ctr Res & Explorat Space Sci & Technol, Greenbelt, MD 20771 USA
[14] Natl Res Council CNR, Inst Appl Phys IFAC, Via Madonna del Piano 10, I-50019 Sesto, Fiorentino, Italy
[15] Louisiana State Univ, Dept Phys & Astron, 202 Nicholson Hall, Baton Rouge, LA 70803 USA
[16] Univ Padua, Dept Phys & Astron, Via Marzolo 8, I-35131 Padua, Italy
[17] Ist Nazl Fis Nucl, Sez Padova, Via Marzolo 8, I-35131 Padua, Italy
[18] Japan Aerosp Explorat Agcy, Inst Space & Astronaut Sci, Chuo Ku, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 2525210, Japan
[19] Kanagawa Univ, 3-27-1 Rokkakubashi, Yokohama, Kanagawa 2218686, Japan
[20] Hirosaki Univ, Fac Sci & Technol, Grad Sch Sci & Technol, Bunkyo Ku, Hirosaki, Aomori 0368561, Japan
[21] Kyoto Univ, Yukawa Inst Theoret Phys, Sakyo Ku, Kitashirakawa Oiwakecho, Kyoto 6068502, Japan
[22] Shibaura Inst Technol, Dept Elect Informat Syst, 307 Fukasaku, Saitama 3378570, Japan
[23] Waseda Univ, Waseda Res Inst Sci & Engn, Shinjuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan
[24] Natl Inst Polar Res, 10-3 Midori Cho, Tachikawa, Tokyo 1908518, Japan
[25] Yokohama Natl Univ, Fac Engn, Div Intelligent Syst Engn, 79-5 Tokiwadai, Yokohama, Kanagawa 2408501, Japan
[26] Shinshu Univ, Fac Sci, 3-1-1 Asahi, Matsumoto, Nagano 3908621, Japan
[27] Kyoto Univ, Hakubi Ctr, Sakyo Ku, Yoshida Honmachi, Kyoto 6068501, Japan
[28] Kyoto Univ, Grad Sch Sci, Dept Astron, Sakyo Ku, Kitashirakawa Oiwake Cho, Kyoto 6068502, Japan
[29] High Energy Accelerator Res Org, Inst Particle & Nucl Studies, 1-1 Oho, Tsukuba, Ibaraki 3050801, Japan
[30] Univ Pisa, Polo Fibonacci, Largo B Pontecorvo 3, I-56127 Pisa, Italy
[31] Natl Inst Technol, Ibaraki Coll, Dept Elect & Elect Syst Engn, 866 Nakane, Hitachinaka, Ibaraki 3128508, Japan
[32] Univ Maryland, Dept Astron, College Pk, MD 20742 USA
[33] Ritsumeikan Univ, Coll Sci & Engn, Dept Phys Sci, Kusatsu, Shiga 5258577, Japan
[34] Waseda Univ, Fac Sci & Engn, Global Ctr Sci & Engn, Shinjuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan
[35] Univ Denver, Dept Phys & Astron, Phys Bldg,Room 211,2112 East Wesley Ave, Denver, CO 80208 USA
[36] Natl Inst Informat & Commun Technol, Quantum ICT Adv Dev Ctr, 4-2-1 Nukui Kitamachi, Koganei, Tokyo 1848795, Japan
[37] Aoyama Gakuin Univ, Coll Sci & Engn, Dept Phys & Math, Chuo Ku, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 2525258, Japan
[38] Nihon Univ, Coll Ind Technol, 1-2-1 Izumi, Narashino, Chiba 2758575, Japan
[39] RIKEN, 2-1 Hirosawa, Wako, Saitama 3510198, Japan
[40] Osaka City Univ, Grad Sch Sci, Div Math & Phys, 3-3-138 Sugimoto, Sumiyoshi, Osaka 5588585, Japan
[41] Natl Inst Quantum & Radiat Sci & Technol, Inage Ku, 4-9-1 Anagawa, Chiba 2638555, Japan
[42] Nagoya Univ, Chikusa Ku, Nagoya, Aichi 4648601, Japan
[43] Ibaraki Univ, Coll Sci, 2-1-1 Bunkyo, Mito, Ibaraki 3108512, Japan
关键词
ENERGY-SPECTRA; HELIUM SPECTRA; NUCLEI; PROTON; ORIGIN; HEAVY; CALET;
D O I
10.1103/PhysRevLett.126.241101
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The Calorimetric Electron Telescope (CALET), in operation on the International Space Station since 2015, collected a large sample of cosmic-ray iron over a wide energy interval. In this Letter a measurement of the iron spectrum is presented in the range of kinetic energy per nucleon from 10 GeV/n to 2.0 TeV/n allowing the inclusion of iron in the list of elements studied with unprecedented precision by space-borne instruments. The measurement is based on observations carried out from January 2016 to May 2020. The CALET instrument can identify individual nuclear species via a measurement of their electric charge with a dynamic range extending far beyond iron (up to atomic number Z = 40). The energy is measured by a homogeneous calorimeter with a total equivalent thickness of 1.2 proton interaction lengths preceded by a thin (3 radiation lengths) imaging section providing tracking and energy sampling. The analysis of the data and the detailed assessment of systematic uncertainties are described and results are compared with the findings of previous experiments. The observed differential spectrum is consistent within the errors with previous experiments. In the region from 50 GeV/n to 2 TeV/n our present data are compatible with a single power law with spectral index -2.60 +/- 0.03.
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页数:7
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[1]   Direct Measurement of the Cosmic-Ray Carbon and Oxygen Spectra from 10 GeV/n to 2.2 TeV/n with the Calorimetric Electron Telescope on the International Space Station [J].
Adriani, O. ;
Akaike, Y. ;
Asano, K. ;
Asaoka, Y. ;
Bagliesi, M. G. ;
Berti, E. ;
Bigongiari, G. ;
Binns, W. R. ;
Bongi, M. ;
Brogi, P. ;
Bruno, A. ;
Buckley, J. H. ;
Cannady, N. ;
Castellini, G. ;
Checchia, C. ;
Cherry, M. L. ;
Collazuol, G. ;
Ebisawa, K. ;
Fuke, H. ;
Gonzi, S. ;
Guzik, T. G. ;
Hams, T. ;
Hibino, K. ;
Ichimura, M. ;
Ioka, K. ;
Ishizaki, W. ;
Israel, M. H. ;
Kasahara, K. ;
Kataoka, J. ;
Kataoka, R. ;
Katayose, Y. ;
Kato, C. ;
Kawanaka, N. ;
Kawakubo, Y. ;
Kobayashi, K. ;
Kohri, K. ;
Krawczynski, H. S. ;
Krizmanic, J. F. ;
Link, J. ;
Maestro, P. ;
Marrocchesi, P. S. ;
Messineo, A. M. ;
Mitchell, J. W. ;
Miyake, S. ;
Moiseev, A. A. ;
Mori, M. ;
Mori, N. ;
Motz, H. M. ;
Munakata, K. ;
Nakahira, S. .
PHYSICAL REVIEW LETTERS, 2020, 125 (25)
[2]   Direct Measurement of the Cosmic-Ray Proton Spectrum from 50 GeV to 10 TeV with the Calorimetric Electron Telescope on the International Space Station [J].
Adriani, O. ;
Akaike, Y. ;
Asano, K. ;
Asaoka, Y. ;
Bagliesi, M. G. ;
Berti, E. ;
Bigongiari, G. ;
Binns, W. R. ;
Bonechi, S. ;
Bongi, M. ;
Brogi, P. ;
Bruno, A. ;
Buckley, J. H. ;
Cannady, N. ;
Castellini, G. ;
Checchia, C. ;
Cherry, M. L. ;
Collazuol, G. ;
Di Felice, V ;
Ebisawa, K. ;
Fuke, H. ;
Guzik, T. G. ;
Hams, T. ;
Hasebe, N. ;
Hibino, K. ;
Ichimura, M. ;
Ioka, K. ;
Ishizaki, W. ;
Israel, M. H. ;
Kasahara, K. ;
Kataoka, J. ;
Kataoka, R. ;
Katayose, Y. ;
Kato, C. ;
Kawanaka, N. ;
Kawakubo, Y. ;
Kohri, K. ;
Krawczynski, H. S. ;
Krizmanic, J. F. ;
Lomtadze, T. ;
Maestro, P. ;
Marrocchesi, P. S. ;
Messineo, A. M. ;
Mitchell, J. W. ;
Miyake, S. ;
Moiseev, A. A. ;
Mori, K. ;
Mori, M. ;
Mori, N. ;
Motz, H. M. .
PHYSICAL REVIEW LETTERS, 2019, 122 (18)
[3]   Extended Measurement of the Cosmic-Ray Electron and Positron Spectrum from 11 GeV to 4.8 TeV with the Calorimetric Electron Telescope on the International Space Station [J].
Adriani, O. ;
Akaike, Y. ;
Asano, K. ;
Asaoka, Y. ;
Bagliesi, M. G. ;
Berti, E. ;
Bigongiari, G. ;
Binns, W. R. ;
Bonechi, S. ;
Bongi, M. ;
Brogi, P. ;
Buckley, J. H. ;
Cannady, N. ;
Castellini, G. ;
Checchia, C. ;
Cherry, M. L. ;
Collazuol, G. ;
Di Felice, V ;
Ebisawa, K. ;
Fuke, H. ;
Guzik, T. G. ;
Hams, T. ;
Hareyama, M. ;
Hasebe, N. ;
Hibino, K. ;
Ichimura, M. ;
Ioka, K. ;
Ishizaki, W. ;
Israel, M. H. ;
Kasahara, K. ;
Kataoka, J. ;
Kataoka, R. ;
Katayose, Y. ;
Kato, C. ;
Kawanaka, N. ;
Kawakubo, Y. ;
Kohri, K. ;
Krawczynski, H. S. ;
Krizmanic, J. F. ;
Lomtadze, T. ;
Maestro, P. ;
Marrocchesi, P. S. ;
Messineo, A. M. ;
Mitchell, J. W. ;
Miyake, S. ;
Moiseev, A. A. ;
Mori, K. ;
Mori, M. ;
Mori, N. ;
Motz, H. M. .
PHYSICAL REVIEW LETTERS, 2018, 120 (26)
[4]   Energy Spectrum of Cosmic-Ray Electron and Positron from 10 GeV to 3 TeV Observed with the Calorimetric Electron Telescope on the International Space Station [J].
Adriani, O. ;
Akaike, Y. ;
Asano, K. ;
Asaoka, Y. ;
Bagliesi, M. G. ;
Bigongiari, G. ;
Binns, W. R. ;
Bonechi, S. ;
Bongi, M. ;
Brogi, P. ;
Buckley, J. H. ;
Cannady, N. ;
Castellini, G. ;
Checchia, C. ;
Cherry, M. L. ;
Collazuol, G. ;
Di Felice, V. ;
Ebisawa, K. ;
Fuke, H. ;
Guzik, T. G. ;
Hams, T. ;
Hareyama, M. ;
Hasebe, N. ;
Hibino, K. ;
Ichimura, M. ;
Ioka, K. ;
Ishizaki, W. ;
Israel, M. H. ;
Javaid, A. ;
Kasahara, K. ;
Kataoka, J. ;
Kataoka, R. ;
Katayose, Y. ;
Kato, C. ;
Kawanaka, N. ;
Kawakubo, Y. ;
Krawczynski, H. S. ;
Krizmanic, J. F. ;
Kuramata, S. ;
Lomtadze, T. ;
Maestro, P. ;
Marrocchesi, P. S. ;
Messineo, A. M. ;
Mitchell, J. W. ;
Miyake, S. ;
Mizutani, K. ;
Moiseev, A. A. ;
Mori, K. ;
Mori, M. ;
Mori, N. .
PHYSICAL REVIEW LETTERS, 2017, 119 (18)
[5]   PAMELA Measurements of Cosmic-Ray Proton and Helium Spectra [J].
Adriani, O. ;
Barbarino, G. C. ;
Bazilevskaya, G. A. ;
Bellotti, R. ;
Boezio, M. ;
Bogomolov, E. A. ;
Bonechi, L. ;
Bongi, M. ;
Bonvicini, V. ;
Borisov, S. ;
Bottai, S. ;
Bruno, A. ;
Cafagna, F. ;
Campana, D. ;
Carbone, R. ;
Carlson, P. ;
Casolino, M. ;
Castellini, G. ;
Consiglio, L. ;
De Pascale, M. P. ;
De Santis, C. ;
De Simone, N. ;
Di Felice, V. ;
Galper, A. M. ;
Gillard, W. ;
Grishantseva, L. ;
Jerse, G. ;
Karelin, A. V. ;
Koldashov, S. V. ;
Krutkov, S. Y. ;
Kvashnin, A. N. ;
Leonov, A. ;
Malakhov, V. ;
Malvezzi, V. ;
Marcelli, L. ;
Mayorov, A. G. ;
Menn, W. ;
Mikhailov, V. V. ;
Mocchiutti, E. ;
Monaco, A. ;
Mori, N. ;
Nikonov, N. ;
Osteria, G. ;
Palma, F. ;
Papini, P. ;
Pearce, M. ;
Picozza, P. ;
Pizzolotto, C. ;
Ricci, M. ;
Ricciarini, S. B. .
SCIENCE, 2011, 332 (6025) :69-72
[6]   Properties of Iron Primary Cosmic Rays: Results from the Alpha Magnetic Spectrometer [J].
Aguilar, M. ;
Cavasonza, L. Ali ;
Allen, M. S. ;
Alpat, B. ;
Ambrosi, G. ;
Arruda, L. ;
Attig, N. ;
Barao, F. ;
Barrin, L. ;
Bartoloni, A. ;
Basegmez-du Pree, S. ;
Battiston, R. ;
Behlmann, M. ;
Beischer, B. ;
Berdugo, J. ;
Bertucci, B. ;
Bindi, V ;
de Boer, W. ;
Bollweg, K. ;
Borgia, B. ;
Boschini, M. J. ;
Bourquin, M. ;
Bueno, E. F. ;
Burger, J. ;
Burger, W. J. ;
Burmeister, S. ;
Cai, X. D. ;
Capell, M. ;
Casaus, J. ;
Castellini, G. ;
Cervelli, F. ;
Chang, Y. H. ;
Chen, G. M. ;
Chen, G. R. ;
Chen, H. S. ;
Chen, Y. ;
Cheng, L. ;
Chou, H. Y. ;
Chouridou, S. ;
Choutko, V ;
Chung, C. H. ;
Clark, C. ;
Coignet, G. ;
Consolandi, C. ;
Contin, A. ;
Corti, C. ;
Cui, Z. ;
Dadzie, K. ;
Delgado, C. ;
Della Torre, S. .
PHYSICAL REVIEW LETTERS, 2021, 126 (04)
[7]   Properties of Neon, Magnesium, and Silicon Primary Cosmic Rays Results from the Alpha Magnetic Spectrometer [J].
Aguilar, M. ;
Cavasonza, L. Ali ;
Ambrosi, G. ;
Arruda, L. ;
Attig, N. ;
Barao, F. ;
Barrin, L. ;
Bartoloni, A. ;
Basegmez-du Pree, S. ;
Battiston, R. ;
Becker, U. ;
Behlmann, M. ;
Beischer, B. ;
Berdugo, J. ;
Bertucci, B. ;
Bindi, V ;
de Boer, W. ;
Bollweg, K. ;
Borgia, B. ;
Boschini, M. J. ;
Bourquin, M. ;
Bueno, E. F. ;
Burger, J. ;
Burger, W. J. ;
Burmeister, S. ;
Cai, X. D. ;
Capell, M. ;
Casaus, J. ;
Castellini, G. ;
Cervelli, F. ;
Chang, Y. H. ;
Chen, G. M. ;
Chen, H. S. ;
Chen, Y. ;
Cheng, L. ;
Chou, H. Y. ;
Chouridou, S. ;
Choutko, V ;
Chung, C. H. ;
Clark, C. ;
Coignet, G. ;
Consolandi, C. ;
Contin, A. ;
Corti, C. ;
Cui, Z. ;
Dadzie, K. ;
Dai, Y. M. ;
Delgado, C. ;
Della Torre, S. ;
Demirkoz, M. B. .
PHYSICAL REVIEW LETTERS, 2020, 124 (21)
[8]   Observation of New Properties of Secondary Cosmic Rays Lithium, Beryllium, and Boron by the Alpha Magnetic Spectrometer on the International Space Station [J].
Aguilar, M. ;
Cavasonza, L. Ali ;
Ambrosi, G. ;
Arruda, L. ;
Attig, N. ;
Aupetit, S. ;
Azzarello, P. ;
Bachlechner, A. ;
Barao, F. ;
Barrau, A. ;
Barrin, L. ;
Bartoloni, A. ;
Basara, L. ;
Basegmez-du Pree, S. ;
Battarbee, M. ;
Battiston, R. ;
Becker, U. ;
Behlmann, M. ;
Beischer, B. ;
Berdugo, J. ;
Bertucci, B. ;
Bindel, K. F. ;
Bindi, V. ;
de Boer, W. ;
Bollweg, K. ;
Bonnivard, V. ;
Borgia, B. ;
Boschini, M. J. ;
Bourquin, M. ;
Bueno, E. F. ;
Burger, J. ;
Burger, W. J. ;
Cadoux, F. ;
Cai, X. D. ;
Capell, M. ;
Caroff, S. ;
Casaus, J. ;
Castellini, G. ;
Cervelli, F. ;
Chae, M. J. ;
Chang, Y. H. ;
Chen, A. I. ;
Chen, G. M. ;
Chen, H. S. ;
Cheng, L. ;
Chou, H. Y. ;
Choumilov, E. ;
Choutko, V. ;
Chung, C. H. ;
Clark, C. .
PHYSICAL REVIEW LETTERS, 2018, 120 (02)
[9]   Observation of the Identical Rigidity Dependence of He, C, and O Cosmic Rays at High Rigidities by the Alpha Magnetic Spectrometer on the International Space Station [J].
Aguilar, M. ;
Cavasonza, L. Ali ;
Alpat, B. ;
Ambrosi, G. ;
Arruda, L. ;
Attig, N. ;
Aupetit, S. ;
Azzarello, P. ;
Bachlechner, A. ;
Barao, F. ;
Barrau, A. ;
Barrin, L. ;
Bartoloni, A. ;
Basara, L. ;
Basegmez-du Pree, S. ;
Battarbee, M. ;
Battiston, R. ;
Becker, U. ;
Behlmann, M. ;
Beischer, B. ;
Berdugo, J. ;
Bertucci, B. ;
Bindel, K. F. ;
Bindi, V. ;
de Boer, W. ;
Bollweg, K. ;
Bonnivard, V. ;
Borgia, B. ;
Boschini, M. J. ;
Bourquin, M. ;
Bueno, E. F. ;
Burger, J. ;
Burger, W. J. ;
Cadoux, F. ;
Cai, X. D. ;
Capell, M. ;
Caroff, S. ;
Casaus, J. ;
Castellini, G. ;
Cervelli, F. ;
Chae, M. J. ;
Chang, Y. H. ;
Chen, A. I. ;
Chen, G. M. ;
Chen, H. S. ;
Cheng, L. ;
Chou, H. Y. ;
Choumilov, E. ;
Choutko, V. ;
Chung, C. H. .
PHYSICAL REVIEW LETTERS, 2017, 119 (25)
[10]   Precision Measurement of the Helium Flux in Primary Cosmic Rays of Rigidities 1.9 GV to 3 TV with the Alpha Magnetic Spectrometer on the International Space Station [J].
Aguilar, M. ;
Aisa, D. ;
Alpat, B. ;
Alvino, A. ;
Ambrosi, G. ;
Andeen, K. ;
Arruda, L. ;
Attig, N. ;
Azzarello, P. ;
Bachlechner, A. ;
Barao, F. ;
Barrau, A. ;
Barrin, L. ;
Bartoloni, A. ;
Basara, L. ;
Battarbee, M. ;
Battiston, R. ;
Bazo, J. ;
Becker, U. ;
Behlmann, M. ;
Beischer, B. ;
Berdugo, J. ;
Bertucci, B. ;
Bindi, V. ;
Bizzaglia, S. ;
Bizzarri, M. ;
Boella, G. ;
de Boer, W. ;
Bollweg, K. ;
Bonnivard, V. ;
Borgia, B. ;
Borsini, S. ;
Boschini, M. J. ;
Bourquin, M. ;
Burger, J. ;
Cadoux, F. ;
Cai, X. D. ;
Capell, M. ;
Caroff, S. ;
Casaus, J. ;
Castellini, G. ;
Cernuda, I. ;
Cerreta, D. ;
Cervelli, F. ;
Chae, M. J. ;
Chang, Y. H. ;
Chen, A. I. ;
Chen, G. M. ;
Chen, H. ;
Chen, H. S. .
PHYSICAL REVIEW LETTERS, 2015, 115 (21)