Semiclassical Calculations of Recurrence Spectra for Lithium Atoms in Parallel Electric and Magnetic Fields

By using the region-splitting consistent and iterative method,we calculate the recurrence spectra of lithium atoms in parallel strong external electric and magnetic fields,and obtain the novel resonance structure in the photoabsorption spectrum above the ionization threshold with a constant scaled electric field at F=0.036,and a scaled energy at ε＝0.58 and ε=0.006,respectively.The results are compared with those of hydrogen obtained by using standard closed orbit theory.It is demonstrated that the core-scattered effects exhibited in combination recurrence play a great role.     

The quantum spectra analysis of the circular billiards in wells

We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier-transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classical method provides a bridge between quantum and classical mechanics.     

Quantum calculations for photodetachment cross sections of H-in an inhomogeneous electric field

We calculate the photodetachment cross sections of H in a gradient electric field based on traditional quantum approach. The system provides a rare example that the formulas for the cross sections can be explicitly derived by both the quantum approach and closed-orbit theory. The quantum results are compared with those of the closed-orbit theory. The correct phase values in the closed-orbit theory are essential and necessary to produce accurate cross sections. Our quantum results remove some previous ambiguities in assigning the phase values in the closed-orbit theory (G. C. Yang and M. L. Du 2007 Phys. Rev. A 75 029904E).     

Semiclassical Calculation of Recurrence Spectra of Li Rydberg Atom in Crossed Electric and Magnetic Field

Closed-orbit theory is a semiclassical technique for explaining the spectra of Rydberg atoms in external fields. Using the dosed-orblt theory and classical perturbation theory, we calculate the scaled recurrence spectra of Lithium atom in magnetic field plus a weak perpendicular electric field. The results show when the crossed electric field is added, the recurrence spectra are weakened greatly. As the scaled electric field f increases, the peaks of the recurrence spectra lose strength. Some recurrences are very sensitive and fall off rapidly as f increases, others persist till much higher f. As the electric field is stronger, some of the peaks revive. This phenomenon, caused by the interference among the electron waves that return to the nucleus, can be computed from the azimuthal dependence of the classical closed orbits.     

Semiclassical calculation of Rydberg He2^＋ molecular of recurrence spectra ion in a magnetic field

Making use of the molecular closed-orbit theory and a new model potential for the Rydberg molecule, we have calculated the recurrence spectra of He^2＋ molecular ion in a magnetic field for different quantum defects. The Fourier transform spectra of He^2＋ molecular ion may be used to perform a direct comparison between peaks in the spectra and the scaled action values of closed orbits of the excited electron in external fields. We find that the spectral modulations can be analysed in terms of the scattering of the excited electron on the molecular core. Unlike the case of the Rydberg atom where the elastic scattering is predominant, modulations produced by inelastic scattering are also vital to the photoabsorption spectrum of the Rydberg molecule. Our results are in good agreement with the quantum results, which suggests that our method is correct.     

Semiclassical calculation of the recurrence spectra of He Rydberg atom in perpendicular electric and magnetic fields

Closed orbit theory is a semiclassical technique for explaining the spectra of Rydberg atoms in external fields. By developing the closed orbit theory from two degrees of freedom to three non-separable degrees of freedom, we calculated the recurrence spectra of He Rydberg atom in perpendicular electric and magnetic fields. The closed orbits in the corresponding classical system have also been obtained. Fourier transformed spectra of He atoms have allowed direct comparison between the resonance peaks and the scaled action values of closed orbits, whereas the nonhydrogenic resonance can be explained in terms of the new orbits created by the core scattering. The semiclassical result is in good agreement with the quantum spectra, which suggests that our method is correct.     

Absorption and Recurrence Spectra of Sodium Rydberg Atom in a Strong External Magnetic Field

Using core-scattered closed-orbit theory, we calculate the photoabsorption and the scaled recurrence spectra of sodium Rydberg atom in strong magnetic fied below ionization threshoM. The non-Coulombic nature of the ionic core have been modified by a model potential, which includes an attractive Coulomb potential and a short-ranged core potential. A family of core-scattered nonhydrogenic closed orbits have also been discovered. The Fourier transformed spectra of sodium atom have allowed direct comparison between peaks in such plot and the scaled action values of closed orbits. The new peaks in the recurrence spectra of sodium atom have been considered as effects caused by the core scattering of returning waves at the ionic core. The results are compared with those of hydrogen case, which show that the core-scattered effects play an important role in alkali-metal atoms.     

Extracting Closed Classical Orbits from Quantum Recurrence Spectra of a Non-Hydrogenic Atom in Parallel Electric and Magnetic Fields

We show how to extract the closed orbits from the quantum spectra data. According to the closed orbit theory, each closed orbit produces a sharp peak in the recurrence spectra of a non-hydrogenic atom in parallel electric and magnetic fields. For a given initial state, closed-orbit theory gives the dependence of this recurrence amplitude on the initial angle of an orbit. By comparing the recurrence amplitude for different initial states, we can determine the initial angles of the closed classical orbits from the quantum recurrence spectra. Therefore, by integrating the Hamiltonian motion equations, we can obtain the closed orbits directly. This method can also be used to extract the closed orbits from the experimental data.     

A New Model Potential Acting on the Excited Electron Within Molecules： Application to Calculate the Recurrence Spectra of Excited H2 Molecules in Strong External Fields

By using the molecular orbit theory, we give a new model potential acting on the excited electron within a molecule. The potential is the total interaction energy of this electron with all the nuclei and other electrons.We find that the introduction of a new model potential results in an extreme increase of the number of closed orbits as compared to the hydrogen atom. Making use of the molecular closed-orbit theory (MCOT) and the new model potential, we calculate the recurrence spectra of H2 molecules in parallel electric and magnetic fields for different quantum defects. The modulations in the spectra can be analysed in terms of the scattering of the excited electron on the molecular core. Our results are in good agreement with the quantum results.     

能量ε<0时Li原子在平行电磁场中的光吸收谱研究

利用包括实散射的闭合轨道理论和分区自洽的迭代算法,计算了标度能量为ε =- 0 .0 3,标度电场F =0 .0 1时的平行电磁场中n≈ 4 0 ,m =0的Li原子闭合轨道以及光吸收谱.介绍了谱的标度特性 ,它对理解量子与经典之间的对应关系具有非常重要的意义.并与同样情况下的氢原子谱作了比较 .验证了离子实对光吸收过程的重要作用. By employing the semiclassical closed-orbit theory including core-scattering and region-splitting consistent iterative method, we calculate the closed-orbits and the recurrence spectra of n≈40, m=0 Li Rydbergatom in parallel electric and magnetic fields at scaled energy ε=-0.03. The constant scaled electric field is =0.01 . The novel spectral structures are compared with those of hydrogen obtaines by standard closed orbit theory. The effect of the core-scattering has been discussed.     

Semiclassical Calculation of Recurrence Spectra of Li Rydberg Atom in Crossed Electric and Magnetic Field

Closed-orbit theory is a semiclassical technique for explaining the spectra of Rydberg atoms in external fields. Using the closed-orbit theory and classical perturbation theory, we calculate the scaled recurrence spectra of Lithium atom in magnetic field plus a weak perpendicular electric field. The results show when the crossed electric field is added, the recurrence spectra are weakened greatly. As the scaled electric field f increases, the peaks of the recurrence spectra lose strength. Some recurrences are very sensitive and fall off rapidly as f increases; others persist till much higher f . As the electric field is stronger, some of the peaks revive. This phenomenon, caused by the interference among the electron waves that return to the nucleus, can be computed from the azimuthal dependence of the classical closed orbits.     

Semiclassical Calculation of Recurrence Spectra of He Rydberg Atom in Strong External Fields

Using core-scattered closed-orbit theory and region-splitting iterative method, we calculated the scaled recurrence spectra of helium atom in parallel electric and magnetic fields. Closed orbits in the corresponding classical system have also been obtained. When we search the closed orbits, in order to remove the Coulomb singularity of the classical Hamiltonian motion equations, we implement the Kustaanheimo-Stiefel transformation, which transforms the system from a three-dimensional to a four-dimensional one. The Fourier transformed spectrum of helium atom has allowed direct comparison between peaks in such plot and the scaled action values of closed orbits. The results are compared with those of the hydrogen case, which shows that the core-scattered effects play an important role in the recurrence spectra of the multi-electron Rydberg atom.     

Double-Pulse Spectra and Closed-Orbits: Photodetachment of H-in Parallel Electric and Magnetic Fields

We derive a formula for double-pulse spectra from closed-orbit theory. We then calculate the double-pulsephotodetachment spectra of H- in the presence of parallel electric and magnetic fields. We analyze the spectra in termsof closed-orbits of the system. We suggest a method for the measurement of a phase associated with each closed-orbit.     

外电场中Li原子回归谱的分岔效应

半经典闭合轨道在外场和激光参数的某些值附近发生分岔，导致波函数的发散，使原有的半经典闭合轨道理论失效-计算了高激发的Li原子在标度能量为ε=-2-94，标度电场在135 -86-1/4<160-11范围内光吸收谱的Fourier变换，分析了轨道分岔现 象及其影 响，并采用了一种适用于不同能域的统一近似方法修正了分岔点附近波函数-计算中考虑了 原子实多重散射组合回归效应，并把所得回归谱与用标准半经典闭合轨道理论对Li原子及H 原子的计算结果相比较，证明了轨道分岔效应的重要性- 关键词： 分岔 统一近似 半经典闭合轨道理论 回归谱     

Initial conditions of closed classical orbits from quantum spectra

A method is presented for determining the initial conditions of classical orbits from the quantum spectra of the diamagnetic hydrogen atom. Each classical trajectory which is closed at the nucleus produces a sinusoidal fluctuation in the photoabsorption spectrum. The amplitude of each orbit's contribution appears in the Fourier transform of a spectrum computed at constant scaled energy. For a given initial state, closed-orbit theory gives the dependence of this recurrence amplitude on the initial angle of an orbit. By comparing the recurrence amplitudes for different initial states, the initial conditions of closed classical orbits are determined from quantum spectra. (c) 1996 American Institute of Physics.     

Recurrence spectra of He atoms in strong external fields

1 Introduction The photo-absorption phenomenon of high Rydberg atoms in strong external fields has attracted much attention in recent years. The semiclassical closed-orbit theory[1,2] developed by Du and Delos has been extensively used to explain this phenomenon. This theory has successfully calculated and interpreted the photo-absorption spectra of H- in various external fields[3,4] and has been applied to describe the photo-excitation, wave packet dynamics of some atoms and molecules such…     

Absorption and Recurrence Spectra of Sodium Rydberg Atom in a Strong External Magnetic Field

Using core-scattered closed-orbit theory, we calculate the photoabsorption and the scaled recurrence spectra of sodium Rydberg atom in strong magnetic field below ionization threshold. The non-Coulombic nature of the ionic core have been modified by a model potential, which includes an attractive Coulomb potential and a short-ranged core potential. A family of core-scattered nonhydrogenic closed orbits have also been discovered. The Fourier transformed spectra of sodium atom have allowed direct comparison between peaks in such plot and the scaled action values of closed orbits. The new peaks in the recurrence spectra of sodium atom have been considered as effects caused by the core scattering of returning waves at the ionic core. The results are compared with those of hydrogen case, which show that the core-scattered effects play an important role in alkali-metal atoms.