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Rohilla A, Wang JG, Li GS, Ghorui SK, Zhou XH, Liu ML, Qiang YH, Guo S, Fang YD, Ding B, Zhang WQ, Huang S, Zheng Y, Li TX, Hua W, Cheng H. Occupancy of orbitals and the quadrupole collectivity in 45Sc nucleus. Appl Radiat Isot 2023; 199:110863. [PMID: 37276661 DOI: 10.1016/j.apradiso.2023.110863] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Revised: 05/18/2023] [Accepted: 05/18/2023] [Indexed: 06/07/2023]
Abstract
In the present work, the Doppler Shift Attenuation method (DSAM) was used to analyze the observed lineshapes of transitions from excited states in 45Sc, populated in the reaction 36Ar + 12C at a beam energy of 145 MeV. The interpretation and comparison of the experimental results have been performed with large-scale shell model calculations, involving different interactions like: GX1A, GX1J, FPD6, KB3 and ZBM2. KB3 and FPD6 (present work) interactions in the negative parity states, and in positive parity states ZBM2 are most pre-eminent in reproducing the results, due to the large configuration space describing strong collective effects. Furthermore, the present work also looks at the details of the shell model helping in improving the understanding for the occupancy of orbitals. The present investigation suggests the observation of stronger collectivity for positive parity states over negative parity states with predicted enhanced collectivity of states in 45Sc nucleus.
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Affiliation(s)
- A Rohilla
- CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China; School of Space Science and Physics, Institute of Space Sciences, Shandong University, Weihai 264209, People's Republic of China
| | - J G Wang
- CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China.
| | - G S Li
- CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China; School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China.
| | - S K Ghorui
- CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - X H Zhou
- CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - M L Liu
- CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - Y H Qiang
- CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - S Guo
- CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - Y D Fang
- CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - B Ding
- CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - W Q Zhang
- CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - S Huang
- CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - Y Zheng
- CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - T X Li
- China Institute of Atomic Energy, Beijing 102413, People's Republic of China
| | - W Hua
- Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, People's Republic of China
| | - H Cheng
- School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, People's Republic of China
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Guo S, Ding B, Zhou XH, Wu YB, Wang JG, Xu SW, Fang YD, Petrache CM, Lawrie EA, Qiang YH, Yang YY, Ong HJ, Ma JB, Chen JL, Fang F, Yu YH, Lv BF, Zeng FF, Zeng QB, Huang H, Jia ZH, Jia CX, Liang W, Li Y, Huang NW, Liu LJ, Zheng Y, Zhang WQ, Rohilla A, Bai Z, Jin SL, Wang K, Duan FF, Yang G, Li JH, Xu JH, Li GS, Liu ML, Liu Z, Gan ZG, Wang M, Zhang YH. Probing ^{93m}Mo Isomer Depletion with an Isomer Beam. Phys Rev Lett 2022; 128:242502. [PMID: 35776479 DOI: 10.1103/physrevlett.128.242502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Revised: 04/01/2022] [Accepted: 05/31/2022] [Indexed: 06/15/2023]
Abstract
The isomer depletion of ^{93m}Mo was recently reported [Chiara et al., Nature (London) 554, 216 (2018)NATUAS0028-083610.1038/nature25483] as the first direct observation of nuclear excitation by electron capture (NEEC). However, the measured excitation probability of 1.0(3)% is far beyond the theoretical expectation. In order to understand the inconsistency between theory and experiment, we produce the ^{93m}Mo nuclei using the ^{12}C(^{86}Kr,5n) reaction at a beam energy of 559 MeV and transport the reaction residues to a detection station far away from the target area employing a secondary beam line. The isomer depletion is expected to occur during the slowdown process of the ions in the stopping material. In such a low γ-ray background environment, the signature of isomer depletion is not observed, and an upper limit of 2×10^{-5} is estimated for the excitation probability. This is consistent with the theoretical expectation. Our findings shed doubt on the previously reported NEEC phenomenon and highlight the necessity and feasibility of further experimental investigations for reexamining the isomer depletion under low γ-ray background.
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Affiliation(s)
- S Guo
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - B Ding
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - X H Zhou
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - Y B Wu
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany
| | - J G Wang
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - S W Xu
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - Y D Fang
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - C M Petrache
- University Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
| | - E A Lawrie
- iThemba LABS, National Research Foundation, P.O. Box 722, 7131 Somerset West, South Africa
- Department of Physics and Astronomy, University of the Western Cape, P/B X17, Bellville ZA-7535, South Africa
| | - Y H Qiang
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - Y Y Yang
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - H J Ong
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
- Joint Department for Nuclear Physics, Lanzhou University and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
- Research Center for Nuclear Physics, Osaka University, Osaka 567-0047, Japan
| | - J B Ma
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - J L Chen
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - F Fang
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - Y H Yu
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - B F Lv
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - F F Zeng
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - Q B Zeng
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - H Huang
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - Z H Jia
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - C X Jia
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - W Liang
- Hebei University, Baoding 071001, People's Republic of China
| | - Y Li
- Hebei University, Baoding 071001, People's Republic of China
| | - N W Huang
- Department of Physics, Huzhou University, Huzhou 313000, China
| | - L J Liu
- Department of Physics, Huzhou University, Huzhou 313000, China
| | - Y Zheng
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - W Q Zhang
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - A Rohilla
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - Z Bai
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - S L Jin
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - K Wang
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - F F Duan
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - G Yang
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - J H Li
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - J H Xu
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
| | - G S Li
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - M L Liu
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - Z Liu
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - Z G Gan
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - M Wang
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
| | - Y H Zhang
- Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People's Republic of China
- School of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, People's Republic of China
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Cederwall B, Doncel M, Aktas Ö, Ertoprak A, Liotta R, Qi C, Grahn T, Cullen DM, Hodge D, Giles M, Stolze S, Badran H, Braunroth T, Calverley T, Cox DM, Fang YD, Greenlees PT, Hilton J, Ideguchi E, Julin R, Juutinen S, Raju MK, Li H, Liu H, Matta S, Modamio V, Pakarinen J, Papadakis P, Partanen J, Petrache CM, Rahkila P, Ruotsalainen P, Sandzelius M, Sarén J, Scholey C, Sorri J, Subramaniam P, Taylor MJ, Uusitalo J, Valiente-Dobón JJ. Lifetime Measurements of Excited States in ^{172}Pt and the Variation of Quadrupole Transition Strength with Angular Momentum. Phys Rev Lett 2018; 121:022502. [PMID: 30085703 DOI: 10.1103/physrevlett.121.022502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2018] [Revised: 04/19/2018] [Indexed: 06/08/2023]
Abstract
Lifetimes of the first excited 2^{+} and 4^{+} states in the extremely neutron-deficient nuclide ^{172}Pt have been measured for the first time using the recoil-distance Doppler shift and recoil-decay tagging techniques. An unusually low value of the ratio B(E2:4_{1}^{+}→2_{1}^{+})/B(E2:2_{1}^{+}→0_{gs}^{+})=0.55(19) was found, similar to a handful of other such anomalous cases observed in the entire Segré chart. The observation adds to a cluster of a few extremely neutron-deficient nuclides of the heavy transition metals with neutron numbers N≈90-94 featuring the effect. No theoretical model calculations reported to date have been able to explain the anomalously low B(E2:4_{1}^{+}→2_{1}^{+})/B(E2:2_{1}^{+}→0_{gs}^{+}) ratios observed in these cases. Such low values cannot, e.g., be explained within the framework of the geometrical collective model or by algebraic approaches within the interacting boson model framework. It is proposed that the group of B(E2:4_{1}^{+}→2_{1}^{+})/B(E2:2_{1}^{+}→0_{gs}^{+}) ratios in the extremely neutron-deficient even-even W, Os, and Pt nuclei around neutron numbers N≈90-94 reveal a quantum phase transition from a seniority-conserving structure to a collective regime as a function of neutron number. Although a system governed by seniority symmetry is the only theoretical framework for which such an effect may naturally occur, the phenomenon is highly unexpected for these nuclei that are not situated near closed shells.
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Affiliation(s)
- B Cederwall
- KTH Royal Institute of Technology, 10691 Stockholm, Sweden
| | - M Doncel
- Department of Physics, Oliver Lodge Laboratory, University of Liverpool, Liverpool L69 7ZE, United Kingdom
| | - Ö Aktas
- KTH Royal Institute of Technology, 10691 Stockholm, Sweden
| | - A Ertoprak
- KTH Royal Institute of Technology, 10691 Stockholm, Sweden
- Department of Physics, Faculty of Science, Istanbul University, Vezneciler/Fatih, 34134 Istanbul, Turkey
| | - R Liotta
- KTH Royal Institute of Technology, 10691 Stockholm, Sweden
| | - C Qi
- KTH Royal Institute of Technology, 10691 Stockholm, Sweden
| | - T Grahn
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - D M Cullen
- Schuster Building, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - D Hodge
- Schuster Building, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - M Giles
- Schuster Building, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - S Stolze
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - H Badran
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - T Braunroth
- Institut für Kernphysik, Universität zu Köln, 50937 Köln, Germany
| | - T Calverley
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - D M Cox
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - Y D Fang
- Research Center for Nuclear Physics, Osaka University, JP-567-0047 Osaka, Japan
| | - P T Greenlees
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - J Hilton
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - E Ideguchi
- Research Center for Nuclear Physics, Osaka University, JP-567-0047 Osaka, Japan
| | - R Julin
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - S Juutinen
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - M Kumar Raju
- Research Center for Nuclear Physics, Osaka University, JP-567-0047 Osaka, Japan
| | - H Li
- Grand Accélérateur National dâIons Lourds (GANIL), CEA/DSMâCNRS/IN2P3, F-14076 Caen Cedex 5, France
| | - H Liu
- KTH Royal Institute of Technology, 10691 Stockholm, Sweden
| | - S Matta
- KTH Royal Institute of Technology, 10691 Stockholm, Sweden
| | - V Modamio
- Department of Physics, University of Oslo, NO-0316 Oslo, Norway
| | - J Pakarinen
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - P Papadakis
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - J Partanen
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - C M Petrache
- Centre de Sciences Nucléaires et Sciences de la Matière, CNRS/IN2P3, Université Paris-Saclay, 91405 Orsay, France
| | - P Rahkila
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - P Ruotsalainen
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - M Sandzelius
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - J Sarén
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - C Scholey
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - J Sorri
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
- Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, I-35020 Legnaro, Italy
| | - P Subramaniam
- KTH Royal Institute of Technology, 10691 Stockholm, Sweden
| | - M J Taylor
- Division of Cancer Sciences, School of Medical Sciences, The University of Manchester, Manchester, M13 9PL, United Kingdom
| | - J Uusitalo
- epartment of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - J J Valiente-Dobón
- Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, I-35020 Legnaro, Italy
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