We report calculations of Delbrück scattering that include all-order Coulomb corrections for photon energies above the threshold of electron-positron pair creation. Our approach is based on the application of the Dirac-Coulomb Green function and accounts for the interaction between the virtual electron-positron pair and the nucleus to all orders in the nuclear binding strength parameter $αZ$. Practical calculations are performed for the scattering of 2.754 MeV photons off plutonium atoms. We find that including the Coulomb corrections enhances the scattering cross section by up to 50% in this case. The obtained results resolve the long-standing discrepancy between experimental data and theoretical predictions and demonstrate that an accurate treatment of the Coulomb corrections is crucial for the interpretation of existing and guidance of future Delbrück scattering experiments on heavy atoms.
We study Delbrück scattering in a Coulomb field in the presence of a laser field. The amplitudes are calculated in the Born approximation with respect to the Coulomb field and exactly in the parameters of the laser field having arbitrary strength, spectral content and polarization. The case of high energy initial photon energy is investigated in detail for a monochromatic circularly polarized laser field. It is shown that the angular distribution of the process substantially differs from that for Delbrück scattering in a pure Coulomb field. The value of the cross section under discussion may e…
The scattering of photons of x-ray energy off a Coulomb field in very forward scattering region may be thought as the refraction effect due to the Coulomb field. The cross section of the scattering can be computed from the photon bending angle obtained in geometrical optics. Its dependence on the fine structure constant is nonanalytic and softer than would the box diagrams of Delbruck scattering suggest. The refractive scattering is a nonlocal effect occurring over the distance scale of the impact parameter, and therefore may not be described by the single-box diagrams. We suggest that the sca…
We perform a detailed analysis of how the interplay between the residual binding potential and a strong laser field influences above-threshold ionization (ATI), employing a semi-analytical, Coulomb-corrected strong-field approximation (SFA) in which the Coulomb potential is incorporated in the electron propagation in the continuum. We find that the Coulomb interaction lifts the degeneracy of some SFA trajectories, and we identify a set of orbits which, for high enough photoelectron energies, may be associated with rescattering. Furthermore, by performing a direct comparison with the standard S…
We calculate resonances in three-body systems with attractive Coulomb potentials by solving the homogeneous Faddeev-Merkuriev integral equations for complex energies. The equations are solved by using the Coulomb-Sturmian separable expansion approach. This approach provides an exact treatment of the threshold behavior of the three-body Coulombic systems. We considered the negative positronium ion and, besides locating all the previously know $S$-wave resonances, we found a whole bunch of new resonances accumulated just slightly above the two-body thresholds. The way they accumulate indicates t…
We present an ab initio analytic theory to account for both the very low energy structure (VLES) [C. Y. Wu et al., Phys. Rev. Lett. 109, 043001 (2012); W. Quan et al., Phys. Rev. Lett. 103, 093001 (2009)], and the low energy structure (LES) [W. Quan et al. Phys. Rev. Lett. 103, 093001 (2009); C.I. Blaga et al., Nat. Phys. 5, 335 2009)] of above threshold ionization. The origin of both VLES and LES lies in a forward scattering mechanism by the Coulomb potential. We parameterize the S matrix in terms of ?, which is the displacement of the the classical motion of an electron in the laser field. W…
A theory describing above-threshold ionization of atoms and ions in a strong electromagnetic field is presented. It is based on the widely known strong field approximation and incorporates the Coulomb interaction between the photoelectron and the nucleus using the method of complex classical trajectories. A central result of the theory is the Coulomb-corrected ionization amplitude whose evaluation requires little extra numerical effort. By comparing our predictions with the results of ab initio numerical solutions for two examples we show that the new theory provides a significant improvement …
We consider the electron-positron pair production by a photon in Coulomb field near threshold. We obtain the analytical results for the particle energy spectrum and angular distribution exactly in the parameter $Ze^2/\hbar v$. We show that Furry-Sommerfeld-Maue approximation for the wave functions used by Nishina, Tomonaga and Sakata is not sufficient and leads to wrong results.
The role of Coulomb focusing in above-threshold ionization in an elliptically polarized mid-infrared strong laser field is investigated within a semiclassical model incorporating tunneling and Coulomb field effects. It is shown that Coulomb focusing up to moderate ellipticity values is dominated by multiple forward scattering of the ionized electron by the atomic core that creates a characteristic low-energy structure in the photoelectron spectrum and is responsible for the peculiar energy scaling of the ionization normalized yield along the major polarization axis. At higher ellipticities, th…
Aiming at the investigation of above-threshold ionization in super-strong laser fields with highly charged ions, we develop a Coulomb-corrected strong field approximation (SFA). The influence of the Coulomb potential of the atomic core on the ionized electron dynamics in the continuum is taken into account via the eikonal approximation, treating the Coulomb potential perturbatively in the phase of the quasi-classical wave function of the continuum electron. In this paper the formalism of the Coulomb-corrected SFA for the nonrelativistic regime is discussed employing velocity and length gauge. …
Using the recently developed Coulomb Quantum Orbit Strong-Field Approximation (CQSFA), we perform a systematic analysis of several features encountered in above-threshold ionization (ATI) photoelectron angle-resolved distributions (PADs), such as side lobes, and intra- and intercycle interference patterns. The latter include not only the well-known intra-cycle rings and the near-threshold fan-shaped structure, but also previously overlooked patterns. We provide a direct account of how the Coulomb potential distorts different types of interfering trajectories and changes the corresponding phase…
We study photoelectron angular distributions (PADs) near the ionization threshold with a newly developed Coulomb quantum-orbit strong-field approximation (CQSFA) theory. The CQSFA simulations present an excellent agreement with the result from time-dependent Schrödinger equation method. We show that the low-energy fan-shaped structure in the PADs corresponds to a subcycle time-resolved holographic structure and stems from the significant influence of the Coulomb potential on the phase of the forward-scattering electron trajectories, which affects different momenta and scattering angles unequal…
We develop a relativistic Coulomb-corrected strong field approximation (SFA) for the investigation of spin effects at above-threshold ionization in relativistically strong laser fields with highly charged hydrogen-like ions. The Coulomb-corrected SFA is based on the relativistic eikonal-Volkov wave function describing the ionized electron laser-driven continuum dynamics disturbed by the Coulomb field of the ionic core. The SFA in different partitions of the total Hamiltonian is considered. The formalism is applied for direct ionization of a hydrogen-like system in a strong linearly polarized l…
Formulating a quasiclassical approach we determine the cross section for the complete four-body break-up of the lithium ground state following single photon absorption from threshold up to 220 eV excess energy. In addition, we develop a new classification scheme for three-electron ionizing trajectories in terms of electron-electron collisions, thereby identifying two main ionization paths which the three electrons in the ground state of lithium follow to escape to the continuum. The dominant escape paths manifest themselves in a characteristic ``T-shape'' break-up pattern of the three electron…
The nonperturbative role of multiple forward scattering for Coulomb focusing in mid-infrared laser fields and its dependence on a laser intensity and wavelength are investigated for low-energy photoelectrons at above-threshold ionization. We show that high-order rescattering events can have comparable contributions to the Coulomb focusing and the effective number of rescattering depends weakly on laser parameters in the classical regime. However, the relative contribution of the forward scattering to the Coulomb focusing and the Coulomb focusing in total decrease with the rise of the laser int…
We provide approximate analytic expressions for above-threshold ionization (ATI) transition probabilities and photoelectron angular distributions (PADs). These analytic expressions are more general than those existing in the literature and include the residual binding potential in the electron continuum propagation. They successfully reproduce the ATI side lobes and specific holographic structures such as the near-threshold fan-shaped pattern and the spider-like structure that extends up to relatively high photoelectron energies. We compare such expressions with the Coulomb quantum orbit stron…
After electrons tunnel out of a laser-Coulomb-formed barrier, %formed by the strong laser field and the atomic Coulomb potential, the movement of the tunneling electron can be affected by the Coulomb tail. We show that this Coulomb effect induces a large time difference (longer than a hundred attoseconds) between the exiting time at which the electron exits the barrier and the ionization time at which the electron is free. This large time difference has important influences on strong-field processes such as above-threshold ionization and high-harmonic generation, with remarkably changing time-…
The description of threshold fragmentation under long range repulsive forces is presented. The dominant energy dependence near threshold is isolated by decomposing the cross section into a product of a back ground part and a barrier penetration probability resulting from the repulsive Coulomb interaction. This tunneling probability contains the dominant energy variation and it can be calculated analytically based on the same principles as Wannier's description for threshold ionization under attractive forces. Good agreement is found with the available experimental cross sections on detachment …
The threshold law for N-body fragmentation under dipole forces is formulated. It emerges from the energy dependence of the normalization of the correlated continuum wave function for N fragments. It is shown that the dipole threshold law plays a key role in understanding all threshold fragmentation phenomena since it links the classical threshold law for long-range Coulomb interactions to the statistical law for short-range interactions. Furthermore, a tunnelling mechanism is identified as the common feature which occurs for all three classes of interactions, short-range, dipole and Coulomb.
We consider an analytic approach to the elucidation of the role played by Coulomb interaction in the formation of the spectrum and angular distributions of the electrons produced by above threshold ionization of the atoms. Our approach is based on allowance for the multiple scattering of a photoelectron by the Coulomb potential of the residual ion, with pickup of a field photon in each scattering act. The amplitude of a process with direct ionization of the atom and subsequent scattering of the photoelectron in the continuum by the Coulomb potential of the residual ion are found.
We study mutual ionization in collisions between atomic hydrogen and helium at impact velocities near the electronic threshold for this process (determined by the condition that kinetic energy of an equivelocity free electron is approximately equal to the sum of binding energies of active electrons in the projectile and target). We show that this process is substantially influenced by the Coulomb repulsion between the emitted electrons and that the atomic nuclei are very strongly involved in the momentum balance along the collision velocity.
The optical theorem is applied to the process of electron-positron pair creation in the superposition of a nuclear Coulomb and a strong laser field. We derive new representations for the total production rate as two-fold integrals, both for circular laser polarization and for the general case of elliptic polarization, which has not been treated before. Our approach allows us to obtain by analytical means the asymptotic behaviour of the pair creation rate for various limits of interest. In particular, we consider pair production by two-photon absorption and show that, close to the energetic thr…
Electron-positron pair creation due to combined nuclear Coulomb and strong laser fields is investigated for the tunneling regime. The energy spectra and angular distributions of the pair are found analytically for the first time. The energy spectrum for each lepton exhibits a sharp maximum located well above the threshold for any polarization of the laser field. The angular distributions of leptons depend on the polarization: for the linear polarization both leptons move predominantly along the laser beam direction; for the circular polarization leptons are emitted in a thin-walled cone center…
A three-body scattering process in the presence of Coulomb interaction can be decomposed formally into a two-body single channel, a two-body multichannel and a genuine three-body scattering. The corresponding integral equations are coupled Lippmann-Schwinger and Faddeev-Merkuriev integral equations. We solve them by applying the Coulomb-Sturmian separable expansion method. We present elastic scattering and reaction cross sections of the $e^++H$ system both below and above the $H(n=2)$ threshold. We found excellent agreements with previous calculations in most cases.
Intermediate-state Coulomb-corrected strong-field approximation for rescattering processes
Shanxi University（山西大学）；Shenzhen Technology University（深圳技术大学）；University of Science and Technology of China（中国科学技术大学）；Hefei National Laboratory（合肥国家实验室）
We study high-order harmonic generation in aligned molecules close to the ionization threshold. Two distinct contributions to the harmonic signal are observed, which show very different responses to molecular alignment and ellipticity of the driving field. We perform a classical electron trajectory analysis, taking into account the significant influence of the Coulomb potential on the strong-field-driven electron dynamics. The two contributions are related to primary ionization and excitation processes, offering a deeper understanding of the origin of high harmonics near the ionization thresho…
Within a semiclassical description of above-threshold ionization (ATI) we identify the interplay between intracycle and intercycle interferences. The former is imprinted as a modulation envelope on the discrete multiphoton peaks formed by the latter. This allows to unravel the complex interference pattern observed for the full solution of the time-dependent Schrödinger equation (TDSE) in terms of diffraction at a grating in the time domain. These modulations can be clearly seen in the dependence of the ATI spectra on the laser wavelength. Shifts in energy modulation result from the effect of t…
We have investigated the energy correlation of the two electrons from nonsequential double ionization of helium atom in 800 nm laser fields at intensities below the recollision threshold by quantum calculations. The circular arcs structure of the correlated electron momentum spectra reveals a resonant double ionization process in which the two electrons transit from doubly excited states into continuum states by simultaneously absorbing and sharing excess energy in integer units of the photon energy. Coulomb repulsion between the two electrons in continuum states is responsible for the dominan…
