Abstract
Over recent years in Belfast we have developed numerical grid methods for solving the two-electron time-dependent Schrödinger equation (TDSE) in its full-dimensionality 1–4]. We have specifically had in mind during these developments the TDSE for laser-driven helium and, more recently, that for the laser-driven hydrogen molecule. Our developments were initially prompted, and continue to be stimulated, by the experimental interest [5–8] in these few-electron strongly time-dependent systems. As reported elsewhere in this volume, advances in laser technology and in detection techniques [9] steadily increase the possibilities and refinement of experimental measurement. For instance, angular information regarding the ionization of both electrons can now be gained and the upcoming free-electron lasers will soon make available unprecedented high radiation intensities in the UV to soft X-ray regimes. If theory is to play a meaningful role, and especially a predictive one in such circumstances, sophisticated calculational methods, typified by those we set out to summarize below, are required.
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References
E.S. Smyth, J.S. Parker, K.T. Taylor: Comput. Phys. Commun. 114, 1 (1998)
J.S. Parker, L.R. Moore, E.S. Smyth, K.T. Taylor: J. Phys. B: At. Mol. Opt. Phys. 33, 1057 (2000)
D. Dundas, J.F. McCann, J.S. Parker, K.T. Taylor: J. Phys. B: At. Mol. Opt. Phys. 33, 3261 (2000)
D. Dundas: Phys. Rev. A 65, 023408 (2002)
B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, K.C. Kulander: Phys. Rev. Lett. 73, 1227 (1994)
T.H. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, R. Dörner: Nature 405, 658 (2000)
M.R. Thompson, M.K. Thomas, P.F. Taday, J.H. Posthumus, A.J. Langley, L.J. Frasinski, K Codling: J. Phys. B: Mol. Opt. Phys. 30, 5755 (1997)
R. Lafon, J.L. Chaloupka, B. Sheehy, P.M. Paul, P. Agostini, K.C. Kulander, L.F. DiMauro: Phys. Rev. Lett. 86, 2762 (2001)
B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C.D. Schroter, J. Deipenwisch, J.R.O. Lopez-Urrutia, C. Hohr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, W. Sandner: Phys. Rev. Lett. 87, 043003 (2001)
W.E. Arnoldi: Quart. Appl. Math. 9, 17 (1951)
H. Tal-Ezer, R. Kosloff: J. Chem. Phys. 81, 3967 (1984)
T.J. Park, J.C. Light: J. Chem. Phys. 85, 5870 (1986)
H. van der Vorst: J. Comput. Appl. Math. 18, 249 (1987)
E. Gallopoulos, Y. Saad: SIAM J. Sci. Stat. Comput. 13, 1236 (1992)
A. Nauts, R.E. Wyatt: Phys. Rev. Lett. 51, 2238 (1983)
J.C. Light, I.P. Hamilton, J.V. Lill: J. Chem. Phys. 82, 1400 (1985)
M. Hesse, D. Baye: J. Phys. B: At. Mol. Opt. Phys. 32, 5605 (1999)
D. Baye, M. Hesse, J.M. Sparenberg, M. Vincke: J. Phys. B. At. Mol. Opt. Phys. 31, 3439 (1998) .
J.T. Muckerman, R.V. Weaver, T.A.B. Kennedy, T. Uzer. In: Numerical Grid Methods and Their Applications to Schrödinger’s Equation, ed. by C. Cerjan (Kluwer Academic Publishers, The Netherlands 1993) pp. 89–119
V.S. Melezhik, D. Baye: Phys. Rev. C 59, 3232 (1999)
K. Sakimoto: J. Phys. B: At. Mol. Opt. Phys. 33, 5165 (2000)
D. Baye, P-H. Heenen: J. Phys. A: Math. Gen. 19, 2041 (1986)
B. Sheehy, R. Lafon, M. Widmer, B. Walker, L.F. DiMauro, P.A. Agostini, K.C. Kulander: Phys. Rev. A 58, 3942 (1998)
J.S. Parker, L.R. Moore, D. Dundas, K.T. Taylor: J. Phys. B: Mol. Opt. Phys. 33, L691 (2000)
K.T. Taylor, J.S. Parker, D. Dundas, E.S. Smyth, S. Vivirito: Laser Phys. 9, 98 (1999)
J.S. Parker, L.R. Moore, K.J. Meharg, D. Dundas, K.T. Taylor: J. Phys. B: At. Mol. Opt. Phys. 34, L69 (2001)
H. Karabulut, E.L. Sibert III: J. Phys. B: At. Mol. Opt. Phys. 30, L513 (1997)
D. Dundas, K.J. Meharg, J.F. McCann and K.T. Taylor: J. Phys. B. At. Mol. Opt. Phys. to be published 2002
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Taylor, K.T. et al. (2003). Numerical Grid Methods. In: Ullrich, J., Shevelko, V. (eds) Many-Particle Quantum Dynamics in Atomic and Molecular Fragmentation. Springer Series on Atomic, Optical, and Plasma Physics, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-08492-2_9
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