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AIP conference proceedings

Time dependent approach to photodetachment in E, B and parallel E and B fields

William P. Reinhardt

Published Jan 1, 1987• 0 citations
Publisher

Abstract

Photodetachment leading to outgoing s‐wave and pz‐wave electrons in dc electric and magnetic fields along the z‐axis, alone and in combination, is treated using a zero order model which neglects the (weak) interaction between the atom and detached electron. Threshold laws and interferences arising in the mixed field case are illustrated, and qualitatively discussed using a time dependent fomulation which gives the total detachment cross section as the fourier transform of the dipole auto‐correlation function. First order time dependent perturbation theory is then used to indicate the insensitivity of the results to inclusion of an atomic final state interaction.

DOI
10.1063/1.36900

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Physical Review A•Jul 1, 1998•11 citations
Photodetachment leading to outgoing s‐wave and pz‐wave electrons in dc electric and magnetic fields along the z‐axis, alone and in combination, is treated using a zero order model which neglects the (weak) interaction between the atom and detached electron. Threshold laws and interferences arising in the mixed field case are illustrated, and qualitatively discussed using a time dependent fomulation which gives the total detachment cross section as the fourier transform of the dipole auto‐correlation function. First order time dependent perturbation theory is then used to indicate the insensitivity of the results to inclusion of an atomic final state interaction.
The behavior of the photodetachment cross section of the ${S}^{\ensuremath{-}}$ ion near thresholds in a magnetic field is derived. This cross section is shown to have an oscillatory dependence on photon energy. The calculation is based on first-order time-dependent perturbation theory, and final-state interactions are ignored. The weights of individual transitions between the various Zeeman sublevels for different light polarizations are given in terms of the appropriate angular momentum coupling coefficients. Broadening of the features of the cross section due to the motion of the ions is included in the calculation. The Wigner-law behavior known to be valid for zero magnetic field is shown to result from the magnetic field dependent cross section in the limit of low magnetic field. The theory is shown to be in good agreement with experimental results. The extension of the theory to other atomic negative ions is discussed.
The effect of final-state interactions on the photodetachment cross section of negative ions in a magnetic field is discussed. Experiments on the location of the 2P32^{2}P_{\frac{3}{2}}2P23​​ threshold in ${\mathbf{S}}^{\ensuremath{-}}$ as a function of magnetic field show clearly the effect of the zero-point energy of an electron in a magnetic field. The experiments also give a precise value for the electron affinity and provide information about the interaction between the atom and the detached electron.
An analytic momentum-space wave function for an electron in both laser and static uniform electric fields is presented. It is used to obtain analytic multiphoton detachment cross sections in a static, uniform electric field which include effects of static-field-induced electron-photon interactions. These general results are not restricted to weak laser intensities or to weak static-field strengths and depend only on (a) the electric dipole approximation and (b) the approximation that final-state electron-atom interactions are ignored. Four specific predictions of our general formulas for the most interesting case of linearly polarized light polarized along the static-field direction are presented for weakly bound electrons initially in an s state. First, the effects of a weak static electric field on N-photon detachment cross sections near threshold are shown to be described by two modulation factors, one for odd N and one for even N, which depend only on a scaled energy. Second, for photodetachment in a static electric field, effects of static-field-induced electron-photon interactions are demonstrated. Third, the lifetime against field ionization is presented. Fourth, the cross section for electric-field-induced stimulated emission is presented. Numerical results for the latter three effects are presented for the ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ ion. The simpler case of circularly polarized light directed along the static-electric-field direction is treated briefly. In particular, we show for this case that the static- and laser-field effects are uncoupled and that the near-threshold, weak static-electric-field modulation factors for the N-photon detachment cross sections are dependent on N.
We examine the dynamics of electrons photodetached from the H– ion in time-dependent electric and magnetic fields for the first time. The photodetachment microscopy patterns caused by a time-dependent gradient electric field and magnetic field have been analyzed in great detail based on the semiclassical theory. The interplay of the gradient electric field and magnetic field forces causes an intricate shape of the electron wave and multiple electron trajectories generated by a fixed energy point source can arrive at a given point on the microchannel-plate detector. The interference effects between these electron trajectories cause the oscillatory structures of the electron probability density and electron current distribution, and a set of concentric interference fringes are found at the detector. Our calculation results suggest that the photodetachment microscopy interference pattern on the detector can be adjusted by the electron energy, magnetic field strength, and position of the detector plane. Under certain conditions, the interference pattern in the electron current distribution might be seen on the detector plane localized at a macroscopic distance from the photodetachment source, which can be observed in an actual photodetachment microscopy experiment. Therefore, we make predictions that our work should serve as a guide for future photodetachment microscopy experiments in time-dependent electric and magnetic fields.
A multichannel study of the photodetachment of a negative ion such as ${\mathrm{S}}^{\mathrm{\ensuremath{-}}}$ in the presence of a constant electric field is presented. The analysis is carried out as a series of frame transformations for the outgoing photoelectron. An earlier analysis in the absence of the external field is now augmented by the further transformations from spherical to cylindrical symmetry that are required. The interplay between the various thresholds due to fine structure in the negative ion and residual atom and the effects of the external field are analytically treated. The net effect is to eliminate the thresholds, to induce modulations in the detachment cross section, and to introduce field-assisted-tunneling contributions to the photodetachment. Numerical illustrations are provided. Our treatment closely parallels similar treatments of photoionization of neutral atoms in an electric field and of photodetachment in a magnetic field.
We present a detailed theoretical formulation of the problem of an electron moving in a static electric field, a laser field, and an atomic potential. Our formulation treats the electron-atom interaction in the zero-range potential approximation and employs both the quasienergy approach and an analytic expression for the Green's function describing electron propagation in a combination of static and laser electric fields. Our formulation is applied to one- and two-photon detachment of ${\mathrm{H}}^{\ensuremath{-}}$ in a strong static electric field and takes into account all final-state interactions of the detached electron with the static and laser fields and with the atomic core. Our results show that rescattering effects are small in the case of one-photon detachment, where our results are close to those obtained previously by Gao and Starace [Phys. Rev. A 42, 5580 (1990)], who ignored rescattering effects but who found a strong-field treatment of the laser field to be important, even in the limit of weak laser fields, owing to interference terms involving both the laser and static electric fields. Our results for two-photon detachment of ${\mathrm{H}}^{\ensuremath{-}}$, on the other hand, show that rescattering effects are very significant. In the presence of a strong static electric field, moreover, the two-photon detachment cross section is found to be very sensitive to the magnitude of the static field.