Novel method for directnumerical solution of scattering equations

• Project/Area Number: 21540406
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Atomic/Molecular/Quantum electronics
• Research Institution: University of Tsukuba
• Principal Investigator: TOSHIMA Nobuyuki 筑波大学, 数理物質系, 教授 (10134488)
• Co-Investigator(Kenkyū-buntansha): TONG Xiao-min 筑波大学, 数理物質系, 准教授 (80422210)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2012: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000); Fiscal Year 2011: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000); Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2009: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
• Keywords: 原子・分子 / 散乱理論 / 反陽子捕獲 / 再散乱過程 / 短パルス強レーザー / 多価イオン / 高次高調波 / 干渉 / 因果律 / CEP / オージェ効果 / 赤外レーザー / 超短パルスレーザー / 相対論的補正 / 共鳴状態

Research Abstract

Novel method was developed for solving scattering equations of the processes in which hundreds of thousand channels are coupled. Those processes can never be solved by the traditional method in which scattering differential equations are solved as a boundary-condition problem. In our method the Schroedinger equations is converted to a time-dependent integral equation and it is solved as an initial-condition problem corresponding to the causality using the direct integration method on the grid representation. On the way of the research, the procedure turned out to be applicable to wide physical processes other than the scatterings and it was successfully applied to the dynamics of atoms and molecules in short-pulse strong laser fields.

Research Products

• [Journal Article] Photoionization dynamics in the presence of attosecond pulse trains and strong fields (2013)
  • Author(s): N.Shivaram, H.Timmers, X.M.Tong,and A.Sandhu
  • Journal Title: Chemical Physics Volume: 414 Pages: 139-148
  • DOI: 10.1016/j.chemphys.2012.05.006
  • NAID: 120007137028
  • Peer Reviewed
• [Journal Article] Classical-quantum correspondence in atomic ionization by midinfrared pulses: Multiple peak and interference structures (2013)
  • Author(s): C. Lemmel, J. Burgdorfer,…, X.M. Tong
  • Journal Title: Physical Review A Volume: 87 Issue: 1
  • DOI: 10.1103/physreva.87.013421
  • NAID: 120007137079
  • Peer Reviewed
• [Journal Article] Classical-quantum correspondence in atomic ionization by midinfrared pulses: Multiple peak and interference structures (2013)
  • Author(s): C. Lemell, J. Burgdorfer, S. Grafe, K. Dimitriou, D. Arbo, and X.M. Tong
  • Journal Title: Physical Review A Volume: 87
  • NAID: 120007137079
  • Peer Reviewed
• [Journal Article] Directvisualization of laser-driven electronmultiple-scattering and tunneling distance in strong-field ionization (2012)
  • Author(s): D.D.Hickstein,…,X.M.Tong,..,N.Toshima,…H.C.Kapteyn
  • Journal Title: Physical Review Letters Volume: 109 Issue: 7
  • DOI: 10.1103/physrevlett.109.073004
  • Peer Reviewed
• [Journal Article] Attosecond-Resolved Evolution of a Laser-Dressed Helium Atom: Interfering ExcitationPaths and Quantum Phases (2012)
  • Author(s): N.Shivaram, H.Timmers, X.M.Tong, and A.Sandhu
  • Journal Title: Physical Review Letters Volume: 108 Issue: 19
  • DOI: 10.1103/physrevlett.108.193002
  • Peer Reviewed
• [Journal Article] Experimental Demonstration of the Breit Interaction which Dominates the Angular Distribution of X-ray Emission in Dielectronic Recombination (2012)
  • Author(s): Zhimin Hu; Xiaoying Han; Yueming Li; Kato, D.; Xiaomin Tong; Nakamura, N
  • Journal Title: Phys. Rev. Lett Volume: 108 Issue: 7 Pages: 73002-73002
  • DOI: 10.1103/physrevlett.108.073002
  • NAID: 120007130729
  • Peer Reviewed
• [Journal Article] Anomalous alignment dependence of the third-order harmonic of H2+ions in intense laser fields (2012)
  • Author(s): Y.J.Jin, X.M.Tong, and N. Toshima
  • Journal Title: Physical Review A Volume: 86 Issue: 5
  • DOI: 10.1103/physreva.86.053418
  • NAID: 120007137144
  • Peer Reviewed
• [Journal Article] Measurement of the absolute timing of attosecond XUV bursts with respect to the driving field (2012)
  • Author(s): N.Shivaram, H.Timmers, X.M.Tong, and A.Sandhu
  • Journal Title: Physical Review A Volume: 85 Issue: 5
  • DOI: 10.1103/physreva.85.051802
  • NAID: 120007130605
  • Peer Reviewed
• [Journal Article] Low-energy peak structure in strong-field ionization by mid-infrared laser-pulses: two-dimensional focusing by the atomic potential (2012)
  • Author(s): C.Lemell,,…,X.M.Tong,…and .Graeffe
  • Journal Title: Physical Review A Volume: 85 Issue: 1
  • DOI: 10.1103/physreva.85.011403
  • NAID: 120007130784
  • Peer Reviewed
• [Journal Article] Mass polarization effect on the resonant energy of p-He^+ ions and the protonium formation in low-energy antiproton-hydrogen-atom collisions (2012)
  • Author(s): X.M.Tong, et al.
  • Journal Title: Physical Review A Volume: 85 Issue: 3
  • DOI: 10.1103/physreva.85.032709
  • Peer Reviewed
• [Journal Article] Mass polarization effect on the resonant energies of pbar-He+ ions and the protonium formation in low-energy antiproton-hydrogen-atom collisions (2012)
  • Author(s): X.M.Tong, N.Toshima
  • Journal Title: Physical Review A Volume: 85
  • Peer Reviewed
• [Journal Article] Attosecond streaking in the low-energy region as a probe of rescattering (2011)
  • Author(s): X. H. Xu, L. Y. Peng, Z, Zhang, Q. H. Gong, X. M. Tong, E. A. Pronin, and A. F. Starace
  • Journal Title: Physical Review Letters Volume: 107 Issue: 18
  • DOI: 10.1103/physrevlett.107.183001
  • NAID: 120007137368
  • Peer Reviewed
• [Journal Article] Laser information encoded in atomic asymmetrical ionization in few-cycle laser fields (2011)
  • Author(s): T. Tabe, N. Ono, X. M. Tong, and N. Toshima
  • Journal Title: Physical Review A Volume: 84 Issue: 2
  • DOI: 10.1103/physreva.84.023409
  • Peer Reviewed
• [Journal Article] Theory and experiment on laser enabled inner-valence Auger decay of rare gas atoms (2011)
  • Author(s): X. M. Tong, P. Ranitovic, C. W. Hogle, M. M. Murnane, H. C. Kapteyn, and N. Toshima
  • Journal Title: Physical Review A Volume: 84 Issue: 1
  • DOI: 10.1103/physreva.84.013405
  • Peer Reviewed
• [Journal Article] Alignment dependent ionization of hydrogen molecules in intense laser fields (2011)
  • Author(s): Y. J. Jin, X. M. Tong, and N. Toshima
  • Journal Title: Physical Review A Volume: 83 Issue: 6
  • DOI: 10.1103/physreva.83.063409
  • NAID: 120007130862
  • Peer Reviewed
• [Journal Article] Controlling the xuv transparency of helium using two-pathway quantum interference (2011)
  • Author(s): R. Ranitovic, X. M. Tong, C. W. Hogle, X. Zhou, Y. Liu, N. Toshima, M. M. Murnane, and H. C. Kapteyn
  • Journal Title: Physical Review Letters Volume: 106 Issue: 19
  • DOI: 10.1103/physrevlett.106.193008
  • Peer Reviewed
• [Journal Article] Laser enabled Auger decay in rare-gasatoms (2011)
  • Author(s): R. Ranitovic, X. M. Tong, C. W. Hogle, X. Zhou, Y. Liu, N. Toshima, M. M. Murnane, and H. C. Kapteyn
  • Journal Title: Physical Review Letters Volume: 106 Issue: 5
  • DOI: 10.1103/physrevlett.106.053002
  • Peer Reviewed
• [Journal Article] Controlling the XUV transparency of Helium using two-pathway quantum interference (2011)
  • Author(s): P.Ranitovic, X.M.Tong,, …, N.Toshima,…, H.C. Kapteyn
  • Journal Title: Physical Review Letters Volume: 106
  • NAID: 120007130894
  • Peer Reviewed
• [Journal Article] Alignment-dependent ionization of hydrogen molecules in intense laser fields (2011)
  • Author(s): Y.J.Jin, X.M.Tong, N.Toshima
  • Journal Title: Physical Review A Volume: 83
  • NAID: 120007130862
  • Peer Reviewed
• [Journal Article] Theory and experiment on laser-induced inner-valence Auger decay of rare-gas atoms (2011)
  • Author(s): X.M.Tong, P.Ranitovic,…N.Toshima
  • Journal Title: Physical Review A Volume: 84
  • Peer Reviewed
• [Journal Article] Laser-information encoded in atomic asymmetric ionization in few-cyclelaser fields (2011)
  • Author(s): T.Tabe, N.Ono, X.M.Tong, N.Toshima
  • Journal Title: Physical Review A Volume: 84
  • Peer Reviewed
• [Journal Article] Laser-enhanced Auger Decay in rare-gas atoms (2011)
  • Author(s): P.Ranitovic, X.M.Tong,,…, N.To shima,…, H.C.Kapteyn
  • Journal Title: Physical Review Letters Volume: 106
  • Peer Reviewed
• [Journal Article] Double ionization of He in an intense laser field via rescattering process (2010)
  • Author(s): T. Ishikawa, X. M. Tong, and N. Toshima
  • Journal Title: Physical Review A Volume: 82 Issue: 3
  • DOI: 10.1103/physreva.82.033411
  • Peer Reviewed
• [Journal Article] Controlling atomic structures and photo-absorption processes by an infrared laser (2010)
  • Author(s): X. M. Tong and N. Toshima
  • Journal Title: Physical Review A Volume: 81 Issue: 6
  • DOI: 10.1103/physreva.81.063403
  • Peer Reviewed
• [Journal Article] Infrared-laser-assisted photoionization of helium by coherent extreme ultraviolet light (2010)
  • Author(s): X. M. Tong and N. Toshima
  • Journal Title: Physical Review A Volume: 81 Issue: 4
  • DOI: 10.1103/physreva.81.043429
  • NAID: 120007138155
  • Peer Reviewed
• [Journal Article] Mechanisms of infrared-laser-assisted atomic ionization by attosecond pulses (2010)
  • Author(s): X. M. Tong, P. Ranitovic, C. L. Cocke, and N. Toshima
  • Journal Title: Physical Review A Volume: 81 Issue: 2
  • DOI: 10.1103/physreva.81.021404
  • Peer Reviewed
• [Journal Article] Enhanced ionization of hydrogen molecularions in an intense laser field via amultiphoton resonance (2010)
  • Author(s): Y.J. Jin, X.M. Tong, and N. Toshima
  • Journal Title: Physical Review A Volume: 81 Issue: 1
  • DOI: 10.1103/physreva.81.013408
  • Peer Reviewed
• [Journal Article] Infrared-laser assisted photoionization of helium by coherent extreme ul traviolet light (2010)
  • Author(s): X.M. Tong, N.Toshima
  • Journal Title: Physical Review A Volume: 81
  • NAID: 120007138155
  • Peer Reviewed
• [Journal Article] Controlling atomic structures and photoabsorption processes by an infrared laser (2010)
  • Author(s): X.M. Tong, N.Toshima
  • Journal Title: Physical Review A Volume: 81
  • NAID: 120007138089
  • Peer Reviewed
• [Journal Article] Double ionization of He in an intense laser field via a rescattering process (2010)
  • Author(s): T.Ishikawa, X.M.Tong, N.Toshima
  • Journal Title: Physical Review A Volume: 82
  • NAID: 120007137915
  • Peer Reviewed
• [Journal Article] Enhanced ionization of hydrogen molecular ions in an intense laser field via a multiphoton resonance (2010)
  • Author(s): Y.J.Jin, X.M.Tong, N.Toshima
  • Journal Title: Phys.Rev.A 81
  • NAID: 120007138234
  • Peer Reviewed
• [Journal Article] Mechanisms of infrared-laser-assisted atomic ionization by attsecond pulses (2010)
  • Author(s): X.M.Tong, P.Ranitovic, C.L.Cocke, N.Toshima
  • Journal Title: Phys.Rev.A 81
  • Peer Reviewed
• [Journal Article] Atomic photoabsorption process controlled by static and oscillating magnetic fields (2009)
  • Author(s): T. Shirahama, X. M. Tong, K. Hino, and N. Toshima
  • Journal Title: Physical Review A Volume: 80 Issue: 4
  • DOI: 10.1103/physreva.80.043414
  • NAID: 120007131377
  • Peer Reviewed
• [Journal Article] 2009 Green's function for multielectron ions and its application to radiative recombination involving dielectronic recombinations (2009)
  • Author(s): Tong X M, Nakamura N, Ohtani S, Watanabe T and Toshima N
  • Journal Title: Physical Review Volume: A80 Issue: 4 Pages: 42502-42502
  • DOI: 10.1103/physreva.80.042502
  • Peer Reviewed
• [Journal Article] Coulomb focusing effect on the space distribution of the rescattering electronwavepacket in the laser-atom interaction (2009)
  • Author(s): K. Sasaki, X. M. Tong, and N. Toshima
  • Journal Title: Journal of Physics B Volume: 42 Issue: 16 Pages: 165603-165603
  • DOI: 10.1088/0953-4075/42/16/165603
  • Peer Reviewed
• [Journal Article] Coulomb focusing effect on the space distribution of the rescattering electron wave packet in the laser-atom interaction (2009)
  • Author(s): K.Sasaki, X.M.Tong, N.Toshima
  • Journal Title: J.Phys.B 42
  • NAID: 120007131523
  • Peer Reviewed
• [Journal Article] Green's function for multielectron ions and its application to radiative recombination involving dielectronic recombination (2009)
  • Author(s): X.M.Tong, N.Nakamura, S.Ohtani, T.Watanabe, N.Toshima
  • Journal Title: Phys.Rev.A 80
  • NAID: 120007131379
  • Peer Reviewed
• [Journal Article] Atomic photoabsorption process controlled by static and oscillating magnetic fields (2009)
  • Author(s): T.Shirahama, X.M.Tong, K.Hino, N.Toshima
  • Journal Title: Phys.Rev.A 80
  • NAID: 120007131377
  • Peer Reviewed
• [Presentation] Controlling atomic photoabsorption processes by mid-infrared lasers (2012)
  • Author(s): X.M.Tong and N.Toshima
  • Organizer: 10^<th> Asian Int. Seminar on Atomic and Molecular Physics
  • Place of Presentation: 台湾国立大学、台北、台湾
  • Year and Date: 2012-10-25
• [Presentation] Anomalous alignment dependence of the third order harmonics from H_2^+ ions in intense laser fields (2012)
  • Author(s): Y.J.Jin, X.M.Tong and N.Toshima
  • Place of Presentation: Berlin, ドイツ
  • Year and Date: 2012-08-30
• [Presentation] Protonium formation in low-energy antiproton-hydrogen-atom collisions A case study of the V-coordinates with the mass polarization tem (2012)
  • Author(s): X.M.Tong and N.Toshima
  • Organizer: Int. Conf. Many Particle Spectroscopy of Atoms,Molecules, Clusters and Surfaces
  • Place of Presentation: Berlin, ドイツ
  • Year and Date: 2012-08-30
• [Presentation] 水素原子による反陽子捕獲のヤコビ座標を用いた精密計算 (2012)
  • Author(s): 仝暁民、戸嶋信幸
  • Organizer: 日本物理学会2012年年次大会
  • Place of Presentation: 関西学院大学
  • Year and Date: 2012-03-24
• [Presentation] 水素原子による反陽子捕獲のヤコビ座標を用いた精密計算 (2012)
  • Author(s): 仝暁民、戸嶋信幸
  • Organizer: 日本物理学会年次大会
  • Place of Presentation: 関西学院大学(西宮市)
  • Year and Date: 2012-03-24
• [Presentation] Protonium formation in low-energy antiproton-hydrogen-atom collisions (2012)
  • Author(s): X.M.Tong and N.Toshima
  • Organizer: Int. Conf. Many Particle Spectroscopy of Atoms, Moleculesm Clusters and Surfaces
  • Place of Presentation: Lakeside Convention Center, Berlin
• [Presentation] Anomalous alignment dependence of the third order harmonics from H2+ ions in intense laser fields (2012)
  • Author(s): Y.J.Jin, X.M.Tong and N.Toshima
  • Organizer: Int. Conf. Many Particle Spectroscopy of Atoms, Moleculesm Clusters and Surfaces
  • Place of Presentation: Lakeside Convention Center, Berlin
• [Presentation] Controling atomic photoabsooption processes by mid-infrared lasers (2012)
  • Author(s): X.M.Tong and N.Toshima
  • Organizer: 10th Asian Int. Seminar on Atomic and Molecular Physics
  • Place of Presentation: National Taiwan University, Taipei
• [Presentation] Controlling the XUV transparency using two-pathway quantum interference (2011)
  • Author(s): P. Ranitovic, X.M. Tong,,……,N. Toshima,…,H.C. Kapteyn
  • Organizer: 27^<th> International Conference on Photonic, Electronic and Atomic Collisions
  • Place of Presentation: Queen's University (Belfast, 英国)
  • Year and Date: 2011-08-02
• [Presentation] Controlling the XUV transparency using two-pathway quantum interferenee (2011)
  • Author(s): P.Ranitovic, X.M.Tong,, …, N.Toshima,…, H.C.Kapteyn
  • Organizer: 27^<th> International Conference on Photonic, Electronic and Atomic Collisions
  • Place of Presentation: Queen's University (Belfast, England)
  • Year and Date: 2011-08-02
• [Presentation] Alignment dependent ionization of H2 molecules in intense laser field (2011)
  • Author(s): Y.J. Jin, X.M. Tongand N. Toshima
  • Organizer: 27^<th> International Conference on Photonic, Electronic and Atomic Collisions
  • Place of Presentation: Queen's University (Belfast, 英国)
  • Year and Date: 2011-08-01
• [Presentation] Alignment dependent ionization of H2 molecules in intense laser field (2011)
  • Author(s): Y.J.Jin, X.M.Tong, N.Toshima
  • Organizer: 27^<th> International Conference on Photonic, Electronic and Atomic Collisions
  • Place of Presentation: Queen's University (Belfast, England)
  • Year and Date: 2011-08-01
• [Presentation] Infrared laser enabled sub-shell Auger decay of Ar atoms (2011)
  • Author(s): X.M. Tong, P. Ranitoic, ……,and N. Toshima
  • Organizer: 3^<rd> international Conference of Attosecond Physics
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-07-08
• [Presentation] Infrared laser enabled sub-shell Auger decay of Ar atoms (2011)
  • Author(s): X.M.Tong, P.Ranitoic, …, N.Toshima
  • Organizer: 3^<rd> international Conference of Attosecond Physics
  • Place of Presentation: 北海道大学(札幌)
  • Year and Date: 2011-07-08
• [Presentation] Alignment dependent ionization of H2 molecules in intense laser field (2011)
  • Author(s): Y.J. Jin, X.M. Tong and N. Toshima
  • Organizer: 12^<th> International Conference on Multiphoton Processes
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-07-05
• [Presentation] Information encoded in carry-envelope-phase dependent ionization (2011)
  • Author(s): T.Tabe, N.Ono, X.M. Tong, and N. Toshima
  • Organizer: 12^<th> International Conference on Multiphoton Processes
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-07-05
• [Presentation] Information encoded in carry-envelope-phase depdendent ionization (2011)
  • Author(s): T.Tabe, N.Ono, X.M.Tong, N.Toshima
  • Organizer: 12^<th> International Conference on Multiphoton Processes
  • Place of Presentation: 北海道大学(札幌)
  • Year and Date: 2011-07-05
• [Presentation] Alignment dependent ionization of H2 molecules in intense laser field (2011)
  • Author(s): Y.J.Jin, X.M.Tong, N.Toshima
  • Organizer: 12^<th> International Conference on Multiphoton Processes
  • Place of Presentation: 北海道大学(札幌)
  • Year and Date: 2011-07-05
• [Presentation] パルスレーザーによる水素分子電離確率の偏光軸方向依存性 (2011)
  • Author(s): 金英俊、仝暁民、戸嶋信幸
  • Organizer: 日本物理学会2011年年次大会
  • Place of Presentation: 新潟大学
  • Year and Date: 2011-03-25
• [Presentation] パルスレーザーによる水素分子電離確率の偏光軸方向依存性 (2011)
  • Author(s): 金英俊、仝暁民、戸嶋信幸
  • Organizer: 日本物理学会年次大会
  • Place of Presentation: 新潟大学
  • Year and Date: 2011-03-25
• [Presentation] Ionization of hydrogen molecular ion in an intense laser field (2010)
  • Author(s): Y.J. Jin, X.M. Tongand N. Toshima
  • Organizer: Conference on computational physics 2009
  • Place of Presentation: 高雄、台湾
  • Year and Date: 2010-12-17
• [Presentation] Controlling the atomic photo-excitation by a periodic magnetic field (2010)
  • Author(s): T. Shirahama, X.M. Tong, K. Hino and N. Toshima
  • Organizer: Conference on computational physics 2009
  • Place of Presentation: 高雄、台湾
  • Year and Date: 2010-12-17
• [Presentation] Time-dependent method in the laser-atom interactions (2010)
  • Author(s): X.M. Tong and N. Toshima
  • Organizer: Conference on computational physics 2009
  • Place of Presentation: 高雄、台湾
  • Year and Date: 2010-12-17
• [Presentation] Controling the atomic photo-exciation by a periodic magnetic field (2010)
  • Author(s): T.Shirahama, 仝暁民, K.Hino, 戸嶋信幸
  • Organizer: Conference on computational physics 2009
  • Place of Presentation: 高雄、台湾
  • Year and Date: 2010-12-17
• [Presentation] 再散乱過程によるヘリウム原子2重電離の理論研究 (2010)
  • Author(s): 石川倫大、仝暁民、戸嶋信幸
  • Organizer: 日本物理学会2010年秋季大会
  • Place of Presentation: 大阪府立大学
  • Year and Date: 2010-09-25
• [Presentation] 再散乱過程によるヘリウム原子2重電離の理論研究 (2010)
  • Author(s): 石川倫大、仝暁民、戸嶋信幸
  • Organizer: 日本物理学会秋季大会
  • Place of Presentation: 大阪府立大学
  • Year and Date: 2010-09-25
• [Presentation] 強レーザー場中における再散乱電子の空間分布 (2009)
  • Author(s): 佐々木康祐、仝暁民、戸嶋信幸
  • Organizer: 日本物理学会2009年秋季大会
  • Place of Presentation: 熊本大学
  • Year and Date: 2009-09-27
• [Presentation] 強レーザー場中における水素分子イオンのクーロン爆発 (2009)
  • Author(s): 金英俊、仝暁民、戸嶋信幸
  • Organizer: 日本物理学会2009年秋季大会
  • Place of Presentation: 熊本大学
  • Year and Date: 2009-09-27
• [Presentation] Fano共鳴理論の新展開 (2009)
  • Author(s): 仝暁民
  • Organizer: 日本物理学会2009年秋季大会
  • Place of Presentation: 熊本大学
  • Year and Date: 2009-09-26
• [Book] 量子力学 (2011)
  • Author(s): 戸嶋信幸
  • Total Pages: 344
  • Publisher: 理工図書
• [Remarks] (1) PosterAward. Toshiyuki Terunuma. Concept of gated fluoroscopic imaging and dose decrease effect for tracking respiratory moving tumor. 11^<th> Japan-Korea Medical Physics. 2011.9.29-10.1,福岡 (2) Outstanding Poster Award. Toshiyuki Terunuma.
  • URL: http://vivaldi.bk.tsukuba.ac.jp/index.htm
• [Remarks]
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