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Chin. Phys. B, 2020, Vol. 29(4): 043205    DOI: 10.1088/1674-1056/ab75ce

Filling gap of combination of gauge and analytical method in KFR-like theory

Jian Li(李健)1,2, Feng-Cai Ma(马凤才)3
1 School of Physical Science and Technology, Inner Mongolia University, Hohhot 010021, China;
2 Department of Science, Shenyang Aerospace University, Shenyang 110036, China;
3 Department of Physics, Liaoning University, Shenyang 110036, China
Abstract  Bauer recently presented a formula for the ionization rate of a hydrogen atom in a strong linearly polarized laser field [J. Phys. B 49 145601 (2016)]. He started from the Keldysh probability amplitude in the length gauge and utilized Reiss's method in the velocity gauge. Instead, according to the Reiss probability amplitude in the velocity gauge and Keldysh's derivation for the length gauge, we derive a formula for the ionization rate of a ground-state hydrogen atom or a hydrogen-like atom in a strong linearly polarized laser field. We compare the numerical results of the total ionization rate and the photoelectron energy distribution calculated from our formula with the results from Keldysh, Reiss, and Bauer. We find that the apparent discrepancies in the ionization rate are caused not only by different gauges, but also by different analytical methods used to derive the ionization rate.
Keywords:  velocity gauge      ionization rate      energy spectra  
Received:  25 November 2019      Revised:  06 February 2020      Published:  05 April 2020
PACS:  32.80.Rm (Multiphoton ionization and excitation to highly excited states)  
  33.80.Rv (Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states))  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11274149 and 11304185) and the Program of Shenyang Key Laboratory of Optoelectronic Materials and Technology, China (Grant No. F12-254-1-00).
Corresponding Authors:  Jian Li, Feng-Cai Ma     E-mail:;

Cite this article: 

Jian Li(李健), Feng-Cai Ma(马凤才) Filling gap of combination of gauge and analytical method in KFR-like theory 2020 Chin. Phys. B 29 043205

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