Artigos de revistas: "Photonuclear reactions"

1

Schumacher, M. "Photonuclear reactions". Journal of Physics G: Nuclear Physics 14, S (dezembro de 1988): S235. http://dx.doi.org/10.1088/0305-4616/14/s/026.

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2

Bayram, Tuncay, Serkan Akkoyun, Serhat Uruk, Haris Dapo, Fatih Dulger e Ismail Boztosun. "Transition energy and half-life determinations of photonuclear reaction products of erbium nuclei". International Journal of Modern Physics E 25, n.º 12 (dezembro de 2016): 1650107. http://dx.doi.org/10.1142/s021830131650107x.

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Photon induced reactions are called as photonuclear reactions and used in many research fields of nuclear science and nuclear physics. The photonuclear data are used in many nuclear applications such as radiation shielding and protection, radiation transport analyses, reactor core design, activation analysis and nuclear waste transmutation. In the past, many studies had been devoted to extract photonuclear data covering the isotopic chart. However, there is still lack of existing data. In the present study, we have performed photonuclear reactions on erbium (Er) target by using clinical electron linear accelerators (cLINAC). By using measured residual activity of photonuclear reaction products of Er nuclei, we have determined the half-life of [Formula: see text]Er nucleus and transition energies of [Formula: see text]Ho nucleus. Also, new measurements on gamma-ray energies of the products have been determined accurately. Furthermore, this study shows that repurposed cLINAC with limited budget can contribute to the global nuclear science knowledge.

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3

Xu, Y., S. Goriely, D. L. Balabanski, S. Chesnevskaya, G. L. Guardo, M. La Cognata, H. Y. Lan, D. Lattuada, W. Luo e C. Matei. "Capture and photonuclear reaction rates involving charged-particles: Impacts of nuclear ingredients and future measurement on ELI-NP". EPJ Web of Conferences 178 (2018): 04007. http://dx.doi.org/10.1051/epjconf/201817804007.

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The astrophysical p-process is an important way of nucleosynthesis to produce the stable and proton-rich nuclei beyond Fe which can not be reached by the s- and r-processes. In the present study, the impact of nuclear ingredients, especially the nuclear potential, level density and strength function, to the astrophysical re-action rates of (p,γ), (α,γ), (γ,p), and (γ,α) reactions are systematically studied. The calculations are performed basad on the modern reaction code TALYS for about 3000 stable and proton-rich nuclei with 12≤Z≤110. In particular, both of the Wood-Saxon potential and the microscopic folding potential are taken into account. It is found that both the capture and photonuclear reaction rates are very sensitive to the nuclear potential, thus the better determination of nuclear potential would be important to reduce the uncertainties of reaction rates. Meanwhile, the Extreme Light Infrastructure-Nuclear Physics (ELI-NP) facility is being developed, which will provide the great opportunity to experimentally study the photonuclear reactions in p-process. Simulations of the experimental setup for the measurements of the photonuclear reactions 96Ru(γ,p) and 96Ru(γ,α) are performed. It is shown that the experiments of photonuclear reactions in p-process based on ELI-NP are quite promising.

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4

Ishkhanov, B. S. "Symmetries in photonuclear reactions". Moscow University Physics Bulletin 65, n.º 2 (abril de 2010): 69–80. http://dx.doi.org/10.3103/s0027134910020013.

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5

Rauscher, T. "Photonuclear Reactions in Astrophysics". Nuclear Physics News 28, n.º 3 (3 de julho de 2018): 12–15. http://dx.doi.org/10.1080/10619127.2018.1463016.

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6

Belli, P., R. Bernabei, S. d’Angelo, M. P. De Pascale, P. Picozza, M. Scafi, M. De Sanctis, A. Incicchitti e D. Prosperi. "Low-energy3He photonuclear reactions". Il Nuovo Cimento A 103, n.º 5 (maio de 1990): 721–29. http://dx.doi.org/10.1007/bf02789024.

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7

Findlay, D. J. S. "Applications of photonuclear reactions". Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 50, n.º 1-4 (abril de 1990): 314–20. http://dx.doi.org/10.1016/0168-583x(90)90374-4.

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8

Wang, X. L., Z. Y. Tan, W. Luo, Z. C. Zhu, X. D. Wang e Y. M. Song. "Photo-transmutation of long-lived radionuclide 135Cs by laser–plasma driven electron source". Laser and Particle Beams 34, n.º 3 (20 de junho de 2016): 433–39. http://dx.doi.org/10.1017/s0263034616000318.

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AbstractLaser-driven relativistic electrons can be focused onto a high-Z convertor for generating high-brightness γ-rays, which in turn can be used to induce photonuclear reactions. In this work, photo-transmutation of long-lived radionuclide 135Cs induced by laser–plasma–interaction-driven electron source is demonstrated using Geant4 simulation (Agostinelli et al., 2003 Nucl. Instrum. Meth. A506, 250). High-energy electron generation, bremsstrahlung, as well as photonuclear reaction are observed at four different laser intensities: 1020, 5 × 1020, 1021, and 5 × 1021 W/cm2. The transmutation efficiency depends on the laser intensity and target size. An optimum laser intensity, namely 1021 W/cm2, was found, with the corresponding photonuclear reaction yield reaching 108 J−1 of the laser energy. Laser-generated electrons can therefore be a promising tool for transmutation reactions. Potential application in nuclear waste management is suggested.

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9

Bakhshiyan, T. M., e G. H. Hovhannisyan. "Formation of medical radioisotope ¹¹¹In in photonuclear reactions". Journal of Instrumentation 19, n.º 07 (1 de julho de 2024): C07010. http://dx.doi.org/10.1088/1748-0221/19/07/c07010.

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Abstract The possibility of photonuclear production of 111In radioisotope has been investigated. The enriched target 112Sn was irradiated at the linear electron accelerator LUE-75 of A. Alikhanian National Science Laboratory (Yerevan, Armenia) at the bremsstrahlung endpoint energy Eγmax = 55 MeV. The cross section per equivalent quantum for reactions 112Sn(γ,x)111In, 112Sn(γ,n)111Sn, 112Sn(γ,2n)110Sn, 112Sn(γ,3n)109Sn,112 Sn(γ,pn)110mIn, 112Sn(γ,pn)110g110In, 112Sn(γ,p2n)109In have been measured via the method of activation and off-line γ-ray spectrometric technique. The cross section per equivalent quantum of the 111In in photonuclear reaction was compared with its cross section in proton induced reaction on cadmium targets and other possible 111In production routes. It is shown that the photonuclear method can be used for the production of 111In.

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10

Ishkhanov, B. S., I. M. Kapitonov, A. A. Kuznetsov, V. N. Orlin e Han Dong Yoon. "Photonuclear reactions on molybdenum isotopes". Physics of Atomic Nuclei 77, n.º 11 (novembro de 2014): 1362–70. http://dx.doi.org/10.1134/s106377881410007x.

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11

Belyshev, S. S., L. Z. Dzhilavyan, B. S. Ishkhanov, I. M. Kapitonov, A. A. Kuznetsov, V. N. Orlin e K. A. Stopani. "Photonuclear reactions on titanium isotopes". Physics of Atomic Nuclei 78, n.º 2 (março de 2015): 220–29. http://dx.doi.org/10.1134/s106377881502009x.

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12

Shibata, S., M. Imamura, T. Miyachi, M. Mutou, K. Sakamoto, Y. Hamajima, M. Soto, Y. Kubota, M. Yoshida e I. Fujiwara. "Photonuclear spallation reactions in Cu". Physical Review C 35, n.º 1 (1 de janeiro de 1987): 254–62. http://dx.doi.org/10.1103/physrevc.35.254.

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13

Rosa-Clot, M., e Magda Ericson. "Photonuclear reactions and dispersion relations". Zeitschrift f�r Physik A Atoms and Nuclei 320, n.º 4 (dezembro de 1985): 675–82. http://dx.doi.org/10.1007/bf01411870.

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14

Lotz, G. M., e H. S. Sherif. "Relativistic calculations for photonuclear reactions". Nuclear Physics A 537, n.º 3-4 (fevereiro de 1992): 285–302. http://dx.doi.org/10.1016/0375-9474(92)90357-p.

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15

Balabanski, Dimiter L. "What do we expect to learn from γ-beam experiments related to nuclear astrophysics at ELI-NP?" EPJ Web of Conferences 297 (2024): 01001. http://dx.doi.org/10.1051/epjconf/202429701001.

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This paper addresses some of the of open problems in photonuclear physics which await to be resolved using high-brilliance γ-ray beams, such as precise measurements of total or partial cross sections of photonuclear reactions related to astroparticle physics and nuclear astrophysics. The readiness for such measurements at ELI-NP, as well as the state-of-the-art instrumentation which is available are discussed. The possibility to utilize γ-beams with orbital angular momentum in photonuclear experiments is addressed, too.

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16

Asanov, Zh A., A. N. Ermakov, B. S. Ishkhanov, I. M. Kapitonov, Kyaw Kyaw Htun, I. V. Makarenko, D. R. Salakhutdinov e V. A. Chetvertkova. "Multiparticle photonuclear reactions in 203Tl nuclei". Bulletin of the Russian Academy of Sciences: Physics 71, n.º 3 (março de 2007): 332–35. http://dx.doi.org/10.3103/s1062873807030069.

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17

Enoto, Teruaki, Yuuki Wada, Yoshihiro Furuta, Kazuhiro Nakazawa, Takayuki Yuasa, Kazufumi Okuda, Kazuo Makishima et al. "Photonuclear reactions triggered by lightning discharge". Nature 551, n.º 7681 (novembro de 2017): 481–84. http://dx.doi.org/10.1038/nature24630.

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18

Holt, R. J. "Exclusive photonuclear reactions and asymptotic scaling". Physical Review C 41, n.º 5 (1 de maio de 1990): 2400–2402. http://dx.doi.org/10.1103/physrevc.41.2400.

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19

Ejiri, Hiroyasu, Tatsushi Shima, Shuji Miyamoto, Ken Horikawa, Yasuhisa Kitagawa, Yoshihiro Asano, Schin Daté e Yuji Ohashi. "Resonant Photonuclear Reactions for Isotope Transmutation". Journal of the Physical Society of Japan 80, n.º 9 (15 de setembro de 2011): 094202. http://dx.doi.org/10.1143/jpsj.80.094202.

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20

Hovhannisyan, G. H., T. M. Bakhshiyan e G. V. Martirosyan. "Photonuclear Reactions on Medium-Mass Nuclei". Journal of Contemporary Physics (Armenian Academy of Sciences) 57, n.º 4 (dezembro de 2022): 325–30. http://dx.doi.org/10.1134/s1068337222040119.

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21

He, Chuangye, Yongle Dang, Fulong Liu, Guangyong Fu, Di Wu, Yangping Shen, Zhiyu Han, Qiwen Fan, Bing Guo e Naiyan Wang. "Photonuclear reaction study with the (p, γ) resonance γ-source". EPJ Web of Conferences 239 (2020): 01014. http://dx.doi.org/10.1051/epjconf/202023901014.

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The (p, γ) resonance is a good way to produce monoenergetic γ rays. It becomes an important tool for studying photonuclear reactions. In this work, 13C(p, γ)14N resonance is studied to produce 9.17 MeV γ ray using the 2 × 1.7 MV tandem accelerator at CIAE. The flux of 9.17 MeV γ was determined to be 2.3 × 105/s. 197Au photoneutron cross section was measured to be 45.4 ± 6.9 mb under the irradiation of 13C(p, γ)14N resonance γ -source. The value is close to the previous results. It certificates that we have developed an experimental method for photonuclear reaction study.

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22

Kuzin, A., R. Rassool e MN Thompson. "De-excitation Gamma-ray Technique for Improved Resolution in Intermediate Energy Photonuclear Reactions". Australian Journal of Physics 49, n.º 6 (1996): 1075. http://dx.doi.org/10.1071/ph961075.

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Use of residual-state decay γ-rays could be a powerful tool in the study of photonuclear reactions. The practicality of this technique in a tagged-photon experiment is demonstrated for the first time with data on the 12C(γ,p) reaction.

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23

Bezshyyko, Oleg, Oleksandr Vodin, Larisa-Bezshyyko Golinka, Ihor Kadenko, Andrii Kotenko, Volodymyr Kushnir, Viktor Mitrochenko, Stanislav Olejnik, Sergey Perezhogin e Tetiana Povar. "Isomer ratios for products of photonuclear reactions on Rh". EPJ Web of Conferences 239 (2020): 01026. http://dx.doi.org/10.1051/epjconf/202023901026.

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Over the past several years various preequilibrium models for nuclear reaction mechanisms description were developed. Diversified detailed experimental data in the medium excitation energy region for nuclei are needed for reasonable selection among these theoretical models. Lack of experimental data in this energy region does essentially limit the possibilities for analysis and comparison of different preequilibrium theoretical models. For photonuclear reactions this energy range covers 30-100 MeV. Experimental measurements and estimations of isomer ratios for products of photonuclear reactions with multiple particle escape on antimony were performed using bremsstrahlung spectrum as projectile with end-point energies 74,9 and 85,7 MeV. Method of the induced activity measurement was applied. For acquisition of gamma spectra we used HPGe spectrometer with 20% relative efficiency. Linear accelerator of electrons LU-40 was a source of bremsstrahlung. Energy resolution of electron beam was about 1% and a mean electron current varied within (3.8 - 5.3)μA.

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24

Ermakov, A. N., B. S. Ishkhanov, I. M. Kapitonov, Kyaw Kyaw Htun e I. V. Makarenko. "Multineutron photonuclear reactions on the 197Au isotope". Moscow University Physics Bulletin 62, n.º 5 (outubro de 2007): 316–19. http://dx.doi.org/10.3103/s0027134907050104.

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25

Belyshev, S. S., L. Z. Dzhilavyan, B. S. Ishkhanov, I. M. Kapitonov, A. A. Kuznetsov, A. S. Kurilik e V. V. Khankin. "Photonuclear reactions on titanium isotopes 46-50Ti". Moscow University Physics Bulletin 69, n.º 5 (setembro de 2014): 363–73. http://dx.doi.org/10.3103/s0027134914050026.

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26

MENEZES, D. P., e A. F. R. DE TOLEDO PIZA. "COMMENTS ON PHOTONUCLEAR REACTIONS AT INTERMEDIATE ENERGIES". International Journal of Modern Physics E 01, n.º 02 (junho de 1992): 397–403. http://dx.doi.org/10.1142/s0218301392000217.

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Most of the recently published papers on photonuclear reactions at intermediate energies1 either adopt or criticize the theoretical description by Hebach et al.2 We implement here a simple and realistic calculation for the shell model knock-out contribution which considers a Woods-Saxon potential for the bound state and a shallower optical potential for the outgoing nucleon. Final states are explicitly orthogonalized to the initial state and the effects of the orthogonalization requirement are discussed.

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27

Belyshev, S. S., A. N. Ermakov, B. S. Ishkhanov, V. V. Khankin, A. S. Kurilik, A. A. Kuznetsov, V. I. Shvedunov e K. A. Stopani. "Studying photonuclear reactions using the activation technique". Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 745 (maio de 2014): 133–37. http://dx.doi.org/10.1016/j.nima.2014.01.057.

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28

Gonçalves, M., S. de Pina, D. A. Lima, W. Milomen, E. L. Medeiros e S. B. Duarte. "Many-body cascade calculation for photonuclear reactions". Physics Letters B 406, n.º 1-2 (julho de 1997): 1–6. http://dx.doi.org/10.1016/s0370-2693(97)00662-x.

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29

Bogdanov, O. V., S. B. Dabagov e Yu L. Pivovarov. "Photonuclear reactions by relativistic electron channeling radiation". Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 465 (fevereiro de 2020): 67–72. http://dx.doi.org/10.1016/j.nimb.2020.01.005.

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30

Zheltonozhskaya, M. V., V. A. Zheltonozhsky, E. N. Lykova, A. P. Chernyaev e V. N. Iatsenko. "Production of Zirconium-89 by photonuclear reactions". Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 470 (maio de 2020): 38–41. http://dx.doi.org/10.1016/j.nimb.2020.03.002.

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31

Malaney, Robert A., Grant J. Mathews e David S. P. Dearborn. "Stellar photonuclear reactions and the actinide cosmochronometers". Astrophysical Journal 345 (outubro de 1989): 169. http://dx.doi.org/10.1086/167892.

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32

Ishkhanov, B. S., e V. V. Varlamov. "Photonuclear reactions: Modern status of the data". Physics of Atomic Nuclei 67, n.º 9 (setembro de 2004): 1664–73. http://dx.doi.org/10.1134/1.1806905.

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33

Boztosun, I., H. Dapo, M. Karakoc, S. F. Ozmen, Y. Cecen, A. Coban, A. Cesur et al. "Photonuclear reactions induced by a clinical linac". Journal of Physics: Conference Series 590 (8 de abril de 2015): 012024. http://dx.doi.org/10.1088/1742-6596/590/1/012024.

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34

Rasulova, F. A., R. A. Aliev, S. S. Belyshev, A. A. Kuznetsov, V. V. Khankin, N. Yu Fursova e A. A. Shemukhin. "Photonuclear Reactions on Natural Mixture of Selenium". Physics of Atomic Nuclei 86, n.º 5 (outubro de 2023): 725–35. http://dx.doi.org/10.1134/s1063778823050356.

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35

Vagena, E., e S. Stoulos. "Average cross section measurement for 162Er(γ,n) reaction compared with theoretical calculations using TALYS". HNPS Proceedings 24 (1 de abril de 2019): 123. http://dx.doi.org/10.12681/hnps.1854.

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Bremsstrahlung photon beam delivered by a linear electron accelerator has been used to experimentally determine the near threshold photonuclear cross section data of nuclides. For the first time, (γ,n) cross section data was obtained for the astrophysical important nucleus 162Er. Moreover, theoretical calculations have been applied using the TALYS 1.6 code. The effect of the gamma ray strength function on the cross section calculations has been studied. A satisfactorily reproduction of the available experimental data of photonuclear cross section at the energy region below 20 MeV could be achieved. The photon flux was monitored by measuring the photons yield from seven well known (γ, n) reactions from the threshold energy of each reaction up to the end-point energy of the photon beam used. An integrated cross-section 87 ± 14 mb is calculated for the photonuclear reaction 162Er(γ,n) at the energy 9.2 - 14 MeV. The effective cross section estimated using the TALYS code range between 89 and 96 mb depending on the γ-strength function used. The result for 162Er(γ,n), is found to be in good agreement with the theoretical values obtained by TALYS 1.6. So, the present indirect process could be a valuable tool to estimate the effective cross section of (γ,n) reaction for various isotopes using bremsstrahlung beams.

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36

Gonçalves, M., E. C. de Oliveira, E. L. Medeiros, S. de Pina e S. B. Duarte. "Hot hypernucleus formation in high-energy photonuclear reactions". Brazilian Journal of Physics 34, n.º 3a (setembro de 2004): 919–23. http://dx.doi.org/10.1590/s0103-97332004000500057.

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37

Ermakov, A. N., I. V. Makarenko, V. N. Orlin, B. S. Ishkhanov e I. M. Kapitonov. "Multi-particle Photonuclear Reactions behind Giant Dipole Resonance". Journal of the Korean Physical Society 59, n.º 2(3) (12 de agosto de 2011): 1936–39. http://dx.doi.org/10.3938/jkps.59.1936.

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38

Haba, Hiromitsu. "Recoil Studies of Photonuclear Reactions at Intermediate Energies". Journal of Nuclear and Radiochemical Sciences 3, n.º 2 (2002): A11—A20. http://dx.doi.org/10.14494/jnrs2000.3.2_a11.

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39

Belyshev, S. S., B. S. Ishkhanov, V. V. Khankin, A. A. Kuznetsov, V. N. Orlin, M. M. Popova e K. A. Stopani. "Photonuclear Reactions on Bypassed Nuclei 84Sr and 92Mo". Bulletin of the Russian Academy of Sciences: Physics 82, n.º 6 (junho de 2018): 702–7. http://dx.doi.org/10.3103/s1062873818060060.

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40

Danagulyan, A. S., G. H. Hovhannisyan, T. M. Bakhshiyan, R. H. Avagyan, A. E. Avetisyan, I. A. Kerobyan e R. K. Dallakyan. "Photonuclear reactions on 112,118,124Sn, natTe, and natHf targets". Physics of Atomic Nuclei 77, n.º 11 (novembro de 2014): 1313–20. http://dx.doi.org/10.1134/s1063778814100056.

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41

Dietz, B., e H. A. Weidenmüller. "Photonuclear reactions induced by intense short laser pulses". Physics Letters B 693, n.º 3 (outubro de 2010): 316–22. http://dx.doi.org/10.1016/j.physletb.2010.07.061.

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42

Demekhina, N. A., e K. A. Amroyan. "Recoil studies of nuclei produced in photonuclear reactions". Zeitschrift f�r Physik A Hadrons and Nuclei 350, n.º 1 (março de 1994): 51–54. http://dx.doi.org/10.1007/bf01285051.

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43

Araki, M. "Nonmesonic photonuclear reactions in the three-nucleon system". Physical Review C 39, n.º 4 (1 de abril de 1989): 1251–60. http://dx.doi.org/10.1103/physrevc.39.1251.

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44

Lotz, G. M., e H. S. Sherif. "Relativistic DWBA calculations for medium energy photonuclear reactions". Physics Letters B 210, n.º 1-2 (agosto de 1988): 45–50. http://dx.doi.org/10.1016/0370-2693(88)90346-2.

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45

Das, Sruthy Jyothi. "Looking for QGP signatures in ultraperipheral PbPb collisions". EPJ Web of Conferences 296 (2024): 17005. http://dx.doi.org/10.1051/epjconf/202429617005.

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Ultraperipheral collisions of relativistic heavy ion beams lead to a diverse set of photon-nucleus (photonuclear) interactions. The measurements of particles and their interaction produced in photonuclear reactions can shed light on the QCD dynamics of these novel, extremely asymmetric colliding systems, with energies between those available at RHIC and the LHC. Previous studies by ATLAS indicate significant elliptic and triangular flow coefficients in these events [1]. Thus, it is imperative to check these events for other potential QGP signatures including radial flow, strangeness enhancement, and enhanced baryon/meson production. This proceeding presents the measurement of charged hadron yields in photonuclear collisions using 5.02 TeV Pb+Pb data collected in 2018 by ATLAS, with a dedicated photo-nuclear event trigger. The charged hadron yields are presented as a function of pseudorapidity and transverse momentum in different categories of event multiplicity. The results are compared with 5.02 TeV p+Pb data collected in 2016 by ATLAS, at the same event multiplicities. The results are also compared with calculations from DPMJET and hydrodynamic-based models. These comparisons enable detailed characterizations of photonuclear collision properties, including the photon energy distribution, and whether small QGP droplets may be formed.

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46

Khai, Nguyen Tuan, Tran Duc Thiep, Truong Thi An, Phan Viet Cuong e Nguyen The Vinh. "Neutron Yield from (γ, n) and (γ, 2n) Reactions following 100 MeV Bremsstrahlung in a Tungsten Target". Communications in Physics 19, n.º 1 (27 de maio de 2009): 53–58. http://dx.doi.org/10.15625/0868-3166/19/1/239.

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The photonuclear reactions of (γ, xn) or (γ, xnp) types can be used to produce high-intensity neutron sources for research and applied purposes. In this work a Monte-Carlo calculation has been used to evaluate the production yield of neutrons from the (γ, n) and (γ, 2n) reactions following the bremsstrahlung produced by a 100 MeV electron beam on a tungsten target.

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47

Bezshyyko, Oleg, Anatoliy Dovbnya, Larisa Golinka-Bezshyyko, Igor Kadenko, Oleksandr Vodin, Stanislav Olejnik, Gleb Tuller, Volodymyr Kushnir e Viktor Mitrochenko. "Isomer ratios for products of photonuclear reactions on 121Sb". EPJ Web of Conferences 146 (2017): 05016. http://dx.doi.org/10.1051/epjconf/201714605016.

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48

Belousov, A. S., e E. I. Malinovskii. "Relation of photonuclear reactions to π-meson photoproduction process". Bulletin of the Lebedev Physics Institute 39, n.º 8 (agosto de 2012): 234–38. http://dx.doi.org/10.3103/s1068335612080040.

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Nanova, Mariana. "In-medium Properties of theη′-Meson from Photonuclear Reactions". EPJ Web of Conferences 37 (2012): 03007. http://dx.doi.org/10.1051/epjconf/20123703007.

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Murgia, F., e P. Quarati. "Quasi-deuteron model and nucleon swelling in photonuclear reactions". Il Nuovo Cimento A 102, n.º 5 (novembro de 1989): 1337–45. http://dx.doi.org/10.1007/bf02800342.

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