Study On The Photoelectron Energy Spectra Of Hydrogen Atom By Intense Laser Field Using Strong Field Approximation Method

It is a great invention of human beings when the laser has been found in1960s.Hence, subjects are appearing what were associated with the laser. The physics ofintense field also has been appeared at that time. Owing to the rapid advancement oftechnology, more and more people pay attention to the phenomena about ionization ofatoms or molecules in the intense laser fields. People do resraech for theory andexperiment in order to know the strong field ionization processes of atoms withinteraction between the electromagnetic fields and material. The strong field physicshas basic theory until the Keldysh-Faisal-Reiss (KFR) theory appeared. The KFRtheory was creatived by Keldysh, Faisal, Reiss. Although Faisal theory and Reisstheory extended Keldysh theory, they also have something different, which caused thedifferent results. The discrepancy of the ionization rates for atoms between the lengthgauges (LG) and the velocity gauges (VG) is different. According to electromagneticinteraction is gauge invariant, one should produce the same results. But thediscrepancy between the KFR theories in the two gauges was indeed existing from alot of studies.This paper derived a general ionization rate of hydrogen atom in different boundstates using the velocity gauge by KFR theory. A detailed derivation for the hydrogenatom initial-state wavefunction in different states by Fourier transforms. We obtainthe ionization rates of H (2Px), H (2Py) and H (2Pz) from the so-called velocity gaugeforms of the Keldysh-Faisal-Reiss (KFR) theory for a linear polarized laser field. Adetailed derivation for the ionization rate of hydrogen atom in an intense laser fieldusing the length gauge is presented. Then the ionization rates of hydrogen atom usingthe length gauge and the velocity gauge were compared thoroughly. We alsonumerically compared ionization rates of hydrogen atom using the length gauge andthe velocity gauge, the numerical study clearly shows that the discrepancy betweenthe ionization rates of hydrogen atom in the length gauge and the velocity gauge wasindeed existing. In general, the discrepancy between the ionization rates in the velocity gauge and the length gauge is underestimated by a few orders.This part of paper listed only two general theoretical tools to solve the ionizationenergy spectra of atom. One is to numerically integrate the time-dependentSchr dinger equation (TDSE) and the other is based on the strong fieldapproximation (SFA). In this paper, we only used the SFA. A detailed derivation forthe ionization amplitude in the length gauge and the velocity gauge which was basedon the SFA. Then, we obtained the ionization energy spectra of hydrogen atom indifferent bound states in the length gauge and the velocity gauge. Certainly, wenumerically compared the ionization energy spectra of hydrogen atom in differentbound states in the length gauge and the velocity gauge. The numerical study clearlyshows that the curves were exactly similar in the length gauge and the velocity gaugeexcept the probability was underestimated by a few orders. Also, those pictures werecompared with the picture which using TDSE.At last, we summarize the whole study and expectative the next study in thefuture.