Exact Keldysh theory of strongfield ionization: Residue method versus saddlepoint approximation
Abstract
In recent articles [K. Mishima , Phys. Rev. A, 66, 033401 (2002); S. D. Chao, Phys. Rev. A, 72, 053414 (2005)] it was proposed to use the residue theorem for the exact calculation of the transition amplitude describing strongfield ionization of atomic systems within Keldysh theory. This should avoid the necessity of applying the method of steepest descent (saddlepoint approximation). Comparing the results of both approaches for atomic hydrogen a difference by a factor of 2 was found for the 1s and an even more drastic deviation for the 2s state. Thus it was concluded that the use of the saddlepoint approximation is problematic. In this work the deviations are explained and it is shown that the previous conclusion is based on an unjustified neglect of an important contribution occurring in the application of the residue theorem. Furthermore, the applicability of the method of steepest descent for the ionization of Rydberg states is discussed and an improvement of the standard result is suggested that successfully removes the otherwise drastic failure for large principal quantum numbers.
 Publication:

Physical Review A
 Pub Date:
 March 2007
 DOI:
 10.1103/PhysRevA.75.033403
 arXiv:
 arXiv:physics/0610032
 Bibcode:
 2007PhRvA..75c3403V
 Keywords:

 32.80.Rm;
 33.80.Rv;
 Multiphoton ionization and excitation to highly excited states;
 Physics  Atomic Physics;
 Physics  Computational Physics
 EPrint:
 7 pages, 3 figures, 1 table