Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Validity and meaning of the momentum-translation approximation for bound states in a radiation field

Alain Decoster

Published Mar 1, 1974• 17 citations
Publisher

Abstract

The conditions of validity for the momentum-translation approximation of Reiss are found much more stringent than was thought before: multiphotonic transitions induced by one strong field cannot be described by this method. First-order transitions between bound states dressed by a strong low-frequency field can be calculated, but the method gives nothing but a trivial result; only for the ionization of a dressed atom is the approximation found useful.

DOI
10.1103/physreva.9.1446

Related papers

Momentum-Translation Approximation outside Its Domain of Applicability

John E. Rogerson, Robert N. De Witt, Howard R. Reiss

The momentum-translation approximation is valid for electromagnetic transitions in bound systems caused by external radiation of photon energy much less than the transition energy. Its utility is explored here for two types of problems that violate that restriction. One application is to resonant bound-bound multiphoton transitions of low multiphoton order, and results are compared to recent perturbative calculations. The other application is to both the transition rate and the spectrum of two-photon spontaneous emission from the metastable $2S$ state in hydrogen. Predicted transition rates are too low, but the spectrum agrees well with the known results. All momentum-translation results follow from simple closed-form analytical expressions.

Physical Review A•Jan 1, 1973•12 citations

Reiss Approximation at Moderate Intensities

S. N. Haque

In this paper we show that for an intensity parameter much less than unity, the Reiss approximation for the multiphoton ionization of atoms is equivalent to the neglect of the mean-frequency term in the treatment of Bebb and Gold. We have also improved upon the result of Reiss by including a first-order term. As an example of the above result, numerical values for many-photon $1s\ensuremath{\rightarrow}2s$ transitions in hydrogen atoms are presented and are compared with the exact values of Gontier and Trahin.

Physical Review A•Aug 1, 1973•1 citation

Strong-field high-frequency approximation to the multiphoton ionization of hydrogen

Fabio Trombetta, S. Basile, G. Ferrante

The strong-field multiphoton ionization of atoms is considered and a theoretical approach dealing nonperturbatively with the radiation field formulated. The general computational scheme is the conventional perturbation theory, but the intermediate states are dressed by the field. We present in detail a method to dress the continuum states and to study the dipole transitions within the continuum. In the high-frequency domain, the proposed procedure rapidly converges over a wide range of field intensity and offers an interesting framework for calculating ionization rates for arbitrary numbers of absorbed (above-threshold) photons and field polarization.

Journal of the Optical Society of America B•Apr 1, 1990•6 citations

Multiphoton Ionization of Hydrogen Atoms in the Semiclassical Treatment of an Intense Radiation Field

Surya P. Tewari

The transition probability for the multiphoton ionization of the ground-state hydrogen atom by an intense electromagnetic field has been calculated following a nonperturbative method developed by Reiss. One distinctive feature of the calculation is a minor reduction in the power-law dependence of the interaction parameter in the transition probability.

Physical Review A•Nov 1, 1972•3 citations

Dressed-state perturbation theory for multiphoton ionization of atoms

Liwen Pan, Bala Sundaram, Lloyd Armstrong

We introduce a perturbation theory using dressed bound states to include higher-order transition processes in the calculation of atomic multiphoton ionization. We calculate the ionization probability of hydrogen atoms using this theory and compare the results with the lowest-order perturbation result. We also calculate the shift of the hydrogen atom’s ground state that is due to the external field.

Journal of the Optical Society of America B•May 1, 1987•23 citations

Bound-free transitions in electromagnetic field of arbitrary intensity

N. K. Rahman, Farhad H. M. Faisal

A useful new method of calculation for bound-free transitions under the momentum translation approximation for multiphonon processes is outlined.

Journal of Physics B Atomic and Molecular Physics•Mar 1, 1973•10 citations
The conditions of validity for the momentum-translation approximation of Reiss are found much more stringent than was thought before: multiphotonic transitions induced by one strong field cannot be described by this method. First-order transitions between bound states dressed by a strong low-frequency field can be calculated, but the method gives nothing but a trivial result; only for the ionization of a dressed atom is the approximation found useful.
The momentum-translation approximation is valid for electromagnetic transitions in bound systems caused by external radiation of photon energy much less than the transition energy. Its utility is explored here for two types of problems that violate that restriction. One application is to resonant bound-bound multiphoton transitions of low multiphoton order, and results are compared to recent perturbative calculations. The other application is to both the transition rate and the spectrum of two-photon spontaneous emission from the metastable 2S2S2S state in hydrogen. Predicted transition rates are too low, but the spectrum agrees well with the known results. All momentum-translation results follow from simple closed-form analytical expressions.
In this paper we show that for an intensity parameter much less than unity, the Reiss approximation for the multiphoton ionization of atoms is equivalent to the neglect of the mean-frequency term in the treatment of Bebb and Gold. We have also improved upon the result of Reiss by including a first-order term. As an example of the above result, numerical values for many-photon $1s\ensuremath{\rightarrow}2s$ transitions in hydrogen atoms are presented and are compared with the exact values of Gontier and Trahin.
The strong-field multiphoton ionization of atoms is considered and a theoretical approach dealing nonperturbatively with the radiation field formulated. The general computational scheme is the conventional perturbation theory, but the intermediate states are dressed by the field. We present in detail a method to dress the continuum states and to study the dipole transitions within the continuum. In the high-frequency domain, the proposed procedure rapidly converges over a wide range of field intensity and offers an interesting framework for calculating ionization rates for arbitrary numbers of absorbed (above-threshold) photons and field polarization.