Photoionization Probability Research Articles

Relativistic effects in ionization of heavy hydrogen-like ions by short x-ray pulses

The probability of photoionization of a heavy hydrogen like ion is calculated within the relativistic perturbation theory. The Coulomb potential of a heavy nucleus is taken into account accurately by usage of the corresponding solutions of the Dirac equation. The obtained probability is compared with both nonrelativistic limit and with nonperturbative results based on the numerical solution of the time-dependent Dirac equation. Suppression of ionization is observed in the secondary ionization channel at photon frequency of about ℏ ω ≈ mc 2.

Внутридоплеровские резонансы, обусловленные фотоионизацией атомов в тонких газовых ячейках

By analogy with the well-tested method of high-resolution spectroscopy in thin gas cells for the processes of optical pumping of atoms, this work shows the possibility of detecting narrow sub-Doppler optical resonances caused directly by straight photoionization of atoms (or molecules) in such cells. The structure of the established nontrivial resonances substantially depends on the probability of photoionization of atoms and dimensions of such a cell, the internal thickness of which is many times smaller than its diameter. Of particular interest is the broadening of the considered sub-Doppler resonances, which is determined directly by the photoionization cross section of atoms and the intensity of radiation causing ionization. Under certain conditions, such photoionization broadening can be measured experimentally with high accuracy, as a result of which it is possible to obtain new important information about ionization processes in atoms and molecules.

Sub-Doppler resonances caused by photoionization of atoms in thin gas cells

By analogy with the well-tested method of high-resolution spectroscopy in thin gas cells for the processes of optical pumping of atoms, this work shows the possibility of detecting narrow sub-Doppler optical resonances caused directly by straight photoionization of atoms (or molecules) in such cells. The structure of the established nontrivial resonances substantially depends on the probability of photoionization of atoms and dimensions of such a cell, the internal thickness of which is many times smaller than its diameter. Of particular interest is the broadening of the considered sub-Doppler resonances, which is determined directly by the photoionization cross section of atoms and the intensity of radiation causing ionization. Under certain conditions, such photoionization broadening can be measured experimentally with high accuracy, as a result of which it is possible to obtain new important information about ionization processes in atoms and molecules. Keywords: sub-Doppler resonances, photoionization of atoms, thin gas cell, transit-time relaxation of atoms.

Circular Dichroism in the Photoionization of Unpolarized Atoms by Two Crossing Photon Beams

The polarization dependence of the photoionization probability was analyzed in the case when a randomly oriented atom is irradiated by two crossing polarized monochromatic photon beams with the same frequency. It was found that the angular distributions of photoelectrons exhibit the effect of circular dichroism (CD), which consists of the dependence of the photoionization probability on the sign of the circular polarization degree of each beam. We demonstrate that the CD effect exists only for coherent crossing photon beams. It was shown that CD effects are strongly dependent on the phase difference between the electric field vectors of the photon beams and have a quite large magnitude. The possibilities of the experimental observation of CD effects are discussed.

Switching the relaxation pathway by steric effects in conjugated dienes

Modification of a molecular structure at the minimum-energy conical intersection (MECI) on the relaxation pathway of the smallest conjugated polyene, trans-1,3-butadiene (BD), was achieved by substituting the hydrogen atoms at the end of the molecular chain with methyl groups. At the MECI between S1 and S0, BD is known to have a pyramidalized structure; therefore, the substituted methyl groups are expected to hinder this pyramidalization and change the relaxation pathway. Here, the relaxation dynamics of three conjugated dienes: BD, trans-1,3-pentadiene (PD), and 2,5-dimethyl-2,4-hexadiene (HD), were investigated by time-resolved photoelectron spectroscopy (TRPES) using single-order high harmonic pulses. Ultrafast relaxation to the ground state with decay times of less than 100 fs was observed in all three molecules. The potential energy curves from the theoretical calculation show the common features among these dienes, which explains the similar relaxation dynamics. However, HD was found theoretically to have a transoid structure at MECI between S1 and S0, while BD and PD both had pyramidalized structures. The relaxation pathway switching was corroborated experimentally by analysis of the photoelectron spectra specifically appearing in HD after a few hundred femtoseconds upon photoexcitation. The larger twist in the transoid structure stimulates molecular vibrations that modulated the photoionization probabilities.

XFEL and HHG interaction with matter: Effects of ultrashort pulses and random spikes

The theory of photoionization describing the interaction of x-ray free-electron laser (XFEL) pulses and high-harmonic-generated (HHG) radiation is generalized to ultrashort laser pulses, where the concept of the standard ionization probability per unit time in Fermi’s golden rule and in Einstein’s theory breaks down. Numerical calculations carried out in terms of a generalized photoionization probability for the total duration of pulses in the near-threshold regime demonstrate essentially nonlinear behavior, while absolute values may change by orders of magnitude for typical XFEL and HHG pulses. XFEL self-amplified spontaneous emission pulses are analyzed to reveal general features of photoionization for random and regular spikes: the dependences of the nonlinear photoionization probability on carrier frequency and spike duration are very similar, allowing an analytical expectation value approach that is valid even when there is only limited knowledge of random and regular parameters. Numerical simulations carried out for typical parameters demonstrate excellent agreement.

Fano resonance model for the processes of photoionization of two-well heterostructures in a transverse electric field

A theoretical model is proposed for observing Fano resonances in a two-well structure in an electric field directed along the growth axis of the structure. Theoretical considerations make it possible to estimate the probability of photoionization of the structure depending on the values of the varied structural parameters. Comparison of the curves of the dependences of resonant photoionization on energy, constructed for different values of the electric field strength, allows us to judge the nature and degree of the field effect on the formation of Fano resonances. In addition, it becomes possible, based on the experimental values of the photoionization probabilities of the double-well structure, to solve the inverse problem: to estimate the possible structural parameters from the fixed shapes of the Fano resonance line. In the proposed scheme for the formation of Fano resonances, transitions to quasi-discrete levels against the background of a continuum of states above the QW are also considered, which make a corresponding contribution to the destructive interference of the photoionization paths of the two-well structure and lead to certain transformations of the asymmetric curves of Fano resonances depending on the strength of the external electric field.

Studies of H2 photoionization by a strong ultrashort x-ray pulse on base of a trajectory method

Photoionization of the hydrogen molecule was studied using our previously developed semiclassical trajectory method. The focus was on the parameters of the field for which there are no other results, namely a short photo-pulse with photon energies from soft to hard x-rays and with intensities including superatomic values. We calculated photoionization probabilities for the single and double ionization of H2. In the superatomic field we observed the transient from single-photon to multiphoton double photoionization, the inversion of single and double ionization probabilities, and distinct stabilization effect for the single photoionization. We also observed a specific behavior in the single photoionization probability dynamics with a dip in the middle of the pulse, which becomes extremely deep for a field approaching relativistic intensity. The agreement of our previous results with independent data on the helium atom in superatomic field is an important argument in favor of the efficiency of the used method. This allows us to hope that the probabilities of photoionization of a hydrogen molecule in an atomic and superatomic x-ray field obtained in this work are not only the first, but also quite reasonable results on the indicated process.

A general framework for photoionization calculations applied to nonthermal gas discharges in air

A general framework for photoionization rate calculations in a constant pressure gaseous medium is introduced. The formulation includes the number of photons emitted per unit volume per unit time per unit wavelength due to a radiating source, photobasorption cross sections and density of species comprising the medium, and the photoionization probability (i.e. photoionization yield) of the species being photoionized. We derive a standard integral representation of the photoionization problem that may be readily converted to a set of Helmholtz differential equations for efficient calculation of the photoionization rate. The model is applied to the photoionization problem in air in which , , , , singlet states of N2 are excited due to collisions with electrons generated as a result of nonthermal discharges. Radiative decay from these states gives rise to respective band systems Birge-Hopfield I, Birge-Hopfield II, Worley-Jenkins, Worley, and Carroll-Yoshino, and to photons which are generally energetic enough to ionize O2. The excitation rates and contribution of each band system to photoionization of O2 in air are calculated for the first time. Using recently measured electron impact excitation cross sections of these states, and the recently measured extreme ultraviolet (XUV) spectra of N2, we quantify the emission from each singlet state. Absorption of emission is modeled using measured photoabsorption cross sections of N2 and O2. The photoionization rate of O2 upon absorption of a photon with a certain energy is calculated using experimental values for the photoionization yield of O2. Finally, we introduce a set of coefficients which define the differential representation of the problem of photoionization in air. The developed modeling framework allows accurate solution of photoionization problems in air for the broad range Torr cm, where is the partial pressure of O2 in air in units of Torr ( Torr at atmospheric pressure) and R in cm is a characteristic spatial dimension of the system of interest. The model performance is demonstrated using a set of artificial sources leading to photoionization over a representative range of values and a realistic problem of dynamics of a double-headed streamer in air that was used in previous photoionization literature. The validity of the modeling framework is demonstrated by comparisons with the photo-ion yield function in air, , derived from the classic photoionization model of Zheleznyak et al () and more recent experimental data on photoionization in air.

Uncertainties in Secondary Fluorescence Correction in EPMA

Secondary fluorescence is an inevitable effect that has to be taken into account in any algorithm for quantitative electron probe microanalysis (EPMA) as an additional correction. Moreover, secondary fluorescence worsens spatial resolution of EPMA, as discussed once more in two recent papers. Secondary fluorescence is excited both by characteristic radiation and by the X-ray continuum. In most cases the correction is small. There are, however, cases, e.g. the determination of low heavy metal concentration in a light matrix, where the contribution of secondary fluorescence exceeds 10% of the measured X-ray line intensity. For secondary fluorescence correction the measured X-ray line intensity has to be divided by the correction factor (1+I_flchar/I_p +I_flcont/I_p )≈(1+I_flchar/I_p )(1+I_flcont/I_p ) in order to get those intensity I_p, which is excited only by the primary electrons and enables the determination of specimen composition. I_flchar and I_flcont mean the calculated characteristic and continuums fluorescence intensities. In order to get the intensity of fluorescence radiation, the absorption of the exciting radiation in the specimen, the photoionization probability and the self-absorption of the emitted line must be calculated. This can be performed in a straightforward way. The critical quantity is the X-ray yield of the exciting atoms in case of fluorescence by characteristic radiation and the bremsstrahlung yield of the specimen in case of continuum fluorescence. In the former case it is reasonable to apply the same physical model to calculate I_flchar and I_p.

Communication: Multi-mass velocity map imaging study of the ultraviolet photodissociation of dimethyl sulfide using single photon ionization and a PImMS2 sensor.

This study of the photodissociation of dimethyl sulfide at λ = 227.5 nm demonstrates the opportunities (and some of the challenges) of product detection using vacuum ultraviolet photoionization combined with recently developed multi-mass imaging methods. The capability of imaging different charged products simultaneously allows determination of the primary fragmentation dynamics through, for example, product fragment momentum and angular distribution matching and reveals potential complications from dissociative ionization, product alignment-dependent photoionization probabilities, and the effects of space charging.

Evaluation of the photoionization probability of H2+ by the trajectory semiclassical method

The trajectory-based method for calculating the probabilities of transitions in the quantum system developed in our previous works and tested for atoms is applied to calculating the photoionization probability for the simplest molecule – hydrogen molecular ion. In a weak field it is established a good agreement between our photoionization cross section and the data obtained by other theoretical methods for photon energy in the range from one-photon ionization threshold up to 25 a.u. Photoionization cross section in the range 25<ω≤100 a.u. was calculated for the first time judging by the literature known to us. It is also confirmed that the trajectory method works in a wide range of the field magnitudes including superatomic values up to relativistic intensity.

Photoionization of hydrogen molecular ion by ultrashort photo-pulse in a wide range of field magnitudes

The probabilities of photoionization of hydrogen molecular ion by ultrashort laser field were evaluated on base of earlier developed trajectory method. The results are obtained in a wide range of field magnitudes up to superatomic fields approaching relativistic intensities. In a weak field gained results are in good agreement with the data obtained by other methods. In a strong field the photoionization probability behaviour resembles some features of the so called stabilization effect in atoms.

Photoionization of a Statistic Atom by Ultrashort Wavelet Pulses

Photoionization of atoms by ultrashort electromagnetic wavelet pulses is investigated within the framework of a statistical model. Integral representations of the total probability of atom ionization are obtained within the time over which the pulse acts. It is shown that the dependence of this probability on the pulse duration in the considered case is bell-shaped. The wavelet pulse duration at which the maximum photoionization probability is reached is determined for different charges of atomic nuclii.

The dynamics of lithium atom photoionization by ultrashort-pulse x-rays

The beam intensity has to approach relativistic values in order to achieve atomic resolution in diffraction studies of molecule’s structure using x-ray free electron lasers. The existing methods for evaluating the sample damage in such conditions have a number of limitations. The damaging dynamics can be studied by the trajectory method developed in our previous studies. It enables one to calculate the probability of photoionization of atoms in a wide range of x-ray field parameters, including those for strong ultrashort x-ray pulses approaching relativistic intensity. The method also enables one to bypass many limitations of other methods in the analysis of the dynamics of sample damaging process. In this paper we use this method to evaluate the probability of lithium atom photoionization by ultrashort-pulse x-rays.

A modified trajectory method of evaluation of multiphoton ionization probability

Trajectory methods are successfully applied for description of the photoionization process in a strong laser field and, in particular, for multiphoton ionization. A trajectory method that we developed before is one of them. Testing using the method on such objects as hydrogen, helium, and lithium showed that it allows calculating of photoionization probabilities with separation of contributions of different multiplicities for multielectron systems in a very wide range of photopulse parameters. However, for a weak field, the method does not reproduce a correct dependence of multiphoton ionization probability on field intensity if the photon energy is below the ionization threshold. We present a procedure that makes it possible to overcome this drawback. The modified method works in a wide range of field intensities, including superatomic fields. We calculated the photoionization probability of a hydrogen atom as a simple example of its application.

Effects of ultrashort laser pulses on angular distributions of photoionization spectra

We study the photoelectron spectra by intense laser pulses with arbitrary time dependence and phase within the Keldysh framework. An efficient semianalytical approach using analytical transition matrix elements for hydrogenic atoms in any initial state enables efficient and accurate computation of the photoionization probability at any observation point without saddle point approximation, providing comprehensive three dimensional photoelectron angular distribution for linear and elliptical polarizations, that reveal the intricate features and provide insights on the photoionization characteristics such as angular dispersions, shift and splitting of photoelectron peaks from the tunneling or above threshold ionization(ATI) regime to non-adiabatic(intermediate) and multiphoton ionization(MPI) regimes. This facilitates the study of the effects of various laser pulse parameters on the photoelectron spectra and their angular distributions. The photoelectron peaks occur at multiples of 2ħω for linear polarization while odd-ordered peaks are suppressed in the direction perpendicular to the electric field. Short pulses create splitting and angular dispersion where the peaks are strongly correlated to the angles. For MPI and elliptical polarization with shorter pulses the peaks split into doublets and the first peak vanishes. The carrier envelope phase(CEP) significantly affects the ATI spectra while the Stark effect shifts the spectra of intermediate regime to higher energies due to interference.

Ionization without interference

Ionization of hydrogen-like ions by intense, circularly polarized laser pulses is analyzed under the scope of the relativistic strong-field approximation. We show that, for specific parameters of the laser field, the energy spectra of photoelectrons present a broad region without interference (supercontinuum) which can be controlled by modifying the laser field intensity. The physical interpretation of the process is developed according to the Keldysh theory, emphasizing the importance of the complex-time saddle point contributions to the total probability of photoionization. The corresponding polar-angle distributions present an asymmetry attributed to radiation pressure effects.

Evaluation of the probability of hydrogen atoms photoionization in a strong ultrashort laser field using the trajectory method

A method for calculating transition probabilities based on an earlier developed trajectory approach is tested by the example of evaluating the probability of photoionization of the hydrogen atom exposed an ultrashort optical pulse.

Simulation of crystal and electronic structures of octahedral molybdenum cluster complex compound Cs&lt;sub&gt;2&lt;/sub&gt;[Mo&lt;sub&gt;6&lt;/sub&gt;Cl&lt;sub&gt;14&lt;/sub&gt;] using various DFT functionals

The electronic and structural characteristics of the octahedral molybdenum cluster-based ternary compound, Cs2[Mo6Cl14], were investigated based on density functional theory (DFT) and subsequent comparisons with experimentally observed results. The geometry optimization and band structure calculations of Cs-2[Mo6Cl14] were performed using three standard functionals: local density approximation, Perdew-Burke-Ernzerhof (PBE) as a generalized gradient approximation, and PBE revised for solid compounds (PBEsol). The validity of the calculated results was experimentally examined via X-ray powder diffraction, ultravioletvisible (UV-vis) diffuse reflection, and X-ray photoemission spectra (XPS) measurements. PBEsol was found to show the best performance in terms of reproducing the experimentally refined lattice structure of the compound. The calculated band gap energy (E-g) was consistent with the value evaluated from the UV-vis measurement. Furthermore, the XPS valence spectrum of the compound was well reproduced by the calculated projected density of state weighted with the photoionization probabilities of Al K-alpha. Although the spectral shapes simulated using the three functionals were similar, PBEsol reproduced the energy levels of the electronic states of both [Mo6Cl14](2-) and Cs+ ion with greater consistency. Therefore, it was concluded that PBEsol is the most appropriate functional for DFT calculations of the metal cluster-based lattice system. (C) 2017 The Ceramic Society of Japan. All rights reserved.