Free electron model

About: Free electron model is a research topic. Over the lifetime, 4678 publications have been published within this topic receiving 103535 citations.

Resonant phase-matching between a light wave and a free-electron wavefunction

Abstract: Quantum light–matter interactions of bound electron systems have been studied extensively. By contrast, quantum interactions of free electrons with light have only become accessible in recent years, following the discovery of photon-induced near-field electron microscopy (PINEM). So far, the fundamental free electron–light interaction in all PINEM experiments has remained weak due to its localized near-field nature, which imposes an energy–momentum mismatch between electrons and light. Here, we demonstrate a strong interaction between free-electron waves and light waves, resulting from precise energy–momentum phase-matching with the extended propagating light field. By exchanging hundreds of photons with the field, each electron simultaneously accelerates and decelerates in a coherent manner. Consequently, each electron’s quantum wavefunction evolves into a quantized energy comb, spanning a bandwidth of over 1,700 eV, requiring us to extend the PINEM theory. Our observation of coherent electron phase-matching with a propagating wave is a type of inverse-Cherenkov interaction that occurs with a quantum electron wavefunction, demonstrating how the extended nature of the electron wavefunction can alter stimulated electron–light interactions. Energy–momentum phase-matching enables strong interactions between free electrons and light waves. As a result, the wavefunction of the electron exhibits a comb structure, which was observed using photon-induced near-field electron microscopy.

Nonlinear terahertz response of n-type GaAs

Abstract: Excitation of an $n$-type GaAs layer by intense ultrashort terahertz pulses causes coherent emission at 2 THz. Phase-resolved nonlinear propagation experiments show a picosecond decay of the emitted field, despite the ultrafast carrier-carrier scattering at a sample temperature of 300 K. While the linear THz response is in agreement with the Drude response of free electrons, the nonlinear response is dominated by the super-radiant decay of optically inverted impurity transitions. A quantum mechanical discrete state model using the potential of the disordered impurities accounts for all experimental observations.

Images of photoelectrons formed in intense laser fields

Abstract: Spatial distributions of photoelectrons produced by multiphoton ionization of xenon atoms are recorded by projecting the expanding photoelectron cloud onto a two-dimensional position sensitive detector. The projected image provides a direct view of the squared angular wave functions of the free electrons as well as their energy distribution. The results confirm recent observations that intermediate state resonances with 5f and 4f character establish the dominant ionization paths at low intensity, for short pulse excitation at 640 and 620 nm. At higher intensity more complex superpositions occur with formation of electrons with continuous distributions at low energies.

The Hartree-Fock Equations for Continuous States with Applications to Electron Excitation of the Ground Configuration Terms of O $_{\text{I}}$

Abstract: Part I is concerned with the general theory of anti-symmetric wave functions for continuous states of atomic systems. For an (N+1)-electron system the complete wave function is expressed in terms of an expansion involving products of the N-electron core functions multiplied by free electron orbitals, the equations satisfied by the latter being obtained from the Schrodinger equation. It is shown that the only consistent means of obtaining anti-symmetric wave functions in approximate solutions is to make the expansion explicitly anti-symmetric. This procedure gives equations for the free-electron orbitals which are similar to bound-state Hartree-Fock equations. The further approximation of using Hartree-Fock wave functions for the core states is then discussed. Certain nl$^{q}$kl configurations are analyzed in detail using a total angular momentum representation. It is shown that the equations may be uncoupled if the energy differences between the nl$^{q}$ terms are neglected (exact resonance approximation), and that approximate solutions of the full coupled equations may be obtained in terms of the exact resonance solutions provided that a suitable normalization condition is used. Part II is concerned with applications to electron excitation of the ground configuration terms of O $\_{\text{I}}$. Distorted wave approximations show that other effects are insignificant compared to the contribution from the p angular momentum component of the free orbitals, but give for this results which are too large by several orders of magnitude. The coupled equations for the p-wave are solved in an exact resonance approximation, with neglect of 1s, 2s exchange interactions. At a check point an exact resonance solution including 1s, 2s exchange terms is obtained, and finally a complete solution of the coupled equations. Inelastic collision cross-sections calculated from the exact resonance solutions are found to be 72% (without 1s, 2s exchange) and 95% (with 1s, 2s exchange) of the result from the complete solution. Final curves for the collision parameters, which rise to within 70% of the limit set by charge conservation, are considered to be of an accuracy approaching that of the Hartree-Fock method for bound-state problems. A final section is concerned with the contributions of the p-wave to elastic scattering of slow electrons by O $\_{\text{I}}$.