Comparative Research On Different Analytical Methods For Strong Field Approximation Theory With Two Gauges

The Keldysh-Faisal-Reiss(KFR)theory on the ionization of atoms and molecules in a strong laser field,also known as the strong field approximation theory(SFA),is widely used to understand the experimental phenomena of laser interaction with atoms and molecules.There are three different forms of KFR theory.The difference mainly comes from three aspects.First of all,the applied Hamiltonian of the interaction between the electron and the laser has different forms,which is usually referred to as the application of different gauges.Keldysh applies the length gauge,while Faisal and Reiss apply the velocity gauge.Faisal and Reiss use the same gauge.Different from the method used by Faisal,Reiss uses the inverse time Green function,and the results are consistent.The method of Reiss is widely used in concrete calculation.Due to the gauge invariance of the interaction of electromagnetic field,the results of the ionization rate with different gauges should be the same.However,the actual calculations show that for the same atom and the same laser parameters,the results of the ionization rate calculated by different gauges are different,even several orders of magnitude in some conditions.Secondly,the analytical methods used are different.Keldysh uses the saddle-point method(SPM),Reiss uses the generalized Bessel functions(GBF),and the ionization rate formula derived is also completely different.Thirdly,Keldysh applied two simplifications:one is??/E_B(27)(27)1,which is necessary to perform the contour integral with the SPM;another is the small final kinetic momentum approximation,to obtain a simple formula of ionization rate.Keldysh theory uses the length gauge(LG)and saddle point approximation(SPM)analytical methods,namely(LG+SPM).Reiss theory adopts the velocity gauge(VG)and analytical method of the generalized Bessel function(GBF)expansion(VG+GBF).Starting from Keldysh theory,Bauer applied a generalized Bessel function expansion similar to that used in Reiss theory,and obtained a so-called"exact Keldysh theory"ionization rate formula,namely(LG+GBF).So,if we derive the ionization rate formula based on the Keldysh-Faisal-Reiss strong field approximation theory,applying velocity gauge(VG)and saddle point approximation(SPM)analytical method,what will happen?This thesis is devoted to the study of this problem.Based on the Reiss theory,the formulas for the ionization rate of atoms and photoelectron energy spectrum are derived by using the velocity gauge and the saddle point approximation method(VG+SPM).It fills the gap of combination of gauge and analytical method.Next,taking the ionization of the ground hydrogen atoms in the linearly polarized laser field as an example,numerical calculations are made and compared with the calculation results of Keldysh theory,Reiss theory,and Bauer theory.It is found that the different calculation results for the same process not only comes from the different gauges,but also from the application of different analytical methods.In the past,many authors used the Keldysh theory and the Reiss theory to study the ionization process of the same atom in the laser field.The results were different,and some even had several orders of magnitude differences.They attributed the differences to the so-called"gauge dependence"problem caused by the two theories.Our research shows that this conclusion is biased,at least not comprehensive.The inconsistency between the results of the ionization rate for the same atom in the laser field by Keldysh theory and Reiss theory is not only due to different gauges,but also due to the application of different analytical methods in the two theories.This is one of the important conclusions of this thesis.This thesis also studies the influence of Coulomb interaction between the ionized outgoing electron and the remaining positively charged ion in the photoionization process.In our theoretical model(VG+SPM),Coulomb correction is introduced in two different ways to calculate the ionization rate.The calculation results are compared with those of Keldysh theory and Reiss theory.The results show that,firstly,for different theoretical models,the Coulomb correction has increased the ionization rate.Secondly,Coulomb correction reduces gap between the theoretical calculations of different gauges.Thirdly,the Coulomb correction narrows the gap for different analytical methods.In a word,the Coulomb correction makes the theories of different gauges and different analytical methods for the same ionization process tend to be consistent.This thesis further considers the effects of non-dipole effects based on strong field approximation.The photoelectron energy spectrum of hydrogen atoms in the laser field is calculated under the velocity gauge,especially the low energy part of the energy spectrum.In addition,the Coulomb correction is introduced.The formula of photoelectron energy distribution including Coulomb correction is derived,and the photoelectron spectrum of photoionization of hydrogen atom is calculated.From the calculation results,it can be found that the photoelectron spectrum has a very obvious low energy structure.Although the non-dipole correction has an effect on the low energy region of photoelectron energy distribution,the effect is little.The Coulomb correction has great influence on the energy distribution of photoelectron,and the low energy structure has obvious change.