Multiphoton atomic ionization in the field of a very short laser pulse

Closed analytic expressions are derived for the probability of multiphoton atomic and ionic ionization in a variable electric field ?(t), which are applicable for arbitrary Keldysh parameters γ. Dependencies of the ionization probability and photoelectron pulse spectrum on the shape of a very short laser pulse are analyzed. Examples of pulse fields of various forms, including a modulated light pulse with a Gaussian or Lorentz envelope, are considered in detail. The interference effect in the photoelectron energy spectrum during atomic ionization by a periodic field of a general form is examined. The range of applicability of the adiabatic approximation in the multiphoton ionization theory is discussed. The imaginary time method is used in the calculations, which allows the probability of particle tunneling through oscillating barriers to be effectively calculated.     

An approach for unipolar corona discharge in N2/O2 gas mixture by considering townsend conditions

In this study (α/p) = f(E/p) functional relation is derived for the gas mixture of N₂/O₂ by considering Townsend approach, and formation mechanism of corona discharge is investigated for the coaxial electrode system located in this gas medium. The electron energy distribution function (EEDF) which is required for estimation of ionization coefficient, is determined by considering probability distribution function of inelastic electron collisions versus energy. An algorithm for determining ionization coefficient for binary gas mixture is presented. The development and motion of the electron avalanche in inter-electrode gap are studied by considering the effect of positive space charges. It is determined by considering the derived mathematical expressions that the formation of corona discharge is related with the variation of the current characteristics in inter-electrode gaps depending on the change of potential of central electrode.     

Energy dependence of the ionization probability of sputtered Cu and Ni

Despite its great sensitivity, the usefulness of secondary ion mass spectrometry (SIMS) for many applications has been limited by an inadequate understanding of the probability of sputtering an atom in an ionized state. To determine this ionization probability for clean Cu and Ni surfaces, I have measured the energy distribution of sputtered neutrals and ions by quadrupole mass filtering and retarding potential analysis using potential modulation differentiation. Analysis of sputtered neutrals was accomplished by electron impact ionization. Because the neutrals outnumber the ions by at least two orders of magnitude, the ratio of sputtered ions to neutrals is an accurate measure of the ionization probability. For energies below 20 eV the dependence of the ionization probability on energy goes as P(E) α Eⁿ, where n = 0.65 for clean Cu. The absorption of oxygen on the Cu surface increases the total ion yield while causing a reduction in the value of the exponent n. Similar results are found for nickel, where n = 0.54 for the clean surface.     

Ionization probability of the bound impurity states of two-dimensional electrons under strong magnetic and finite electric fields

The ionization probability of the bound impurity states in a semiconductor inversion layer under strong magnetic fields H is calculated as a function of temperature and electric field value E. The conditions for relatively large ionization probability are determined. The possibility of the bound state ionization must be taken into account for the interpretation of the inversion layer properties at the Shubnikov-De Haas conductivity minima.     

Comparison of four methods for processing data on exponential decay

Multiphoton resonant ionization in the case of a doubly degenerate intermediate bound state is studied. In the Keldysh-Feisal-Reiss approach, expressions for the energy and angular photoelectron distributions and the quasi-classical formula for the total rate of resonant ionization are obtained. It is shown that the ionization rate may be both higher and lower than the ionization rate in the usual case depending on the relationship between parameters. A situation with a strongly suppressed probability of resonant ionization is possible. In the near-threshold region, the angular dependence of the probability of photoelectron escape is shown to be weaker in comparison with the case of ionization via a nondegenerate level.     

Impact parameter dependence of the probability for K-shell ionization by nuclei

The probability W for the atomic ionization by nuclei as a function of the impact parameter x is expressed through the ionization matrix element M_if. Values of W(x) for K-shell ionization calculated with the first Born M_if are compared with the experimental data and other calculations.     

Determination of energy dependent ionization probabilities of sputtered particles

We present a novel method to determine the spectral ionization probability of sputtered species as a function of their emission velocity or energy. The technique is based on detection of neutral and ionic species in a reflectron time-of-flight mass spectrometer under otherwise identical experimental conditions. Using a pulsed ion extraction scheme in combination with sufficiently short primary ion pulses, the spectral ionization probability α⁺(v) can be determined without knowledge of possible energy discrimination effects in instrument transmission. Comparing the measured ionization probability with theoretical predictions, we find that none of the prevailing ionization models is capable of describing the experimental data over the whole velocity range studied.     

δ-Electrons fromK- andL-shell ionization in relativistic systems

Inner-shell ionization in adiabatic heavy-ion collisions is calculated within the monopole approximation by using the relativistic united-atom representation for the wave functions. As an example, ionization probability and energy distribution of theδ-electrons is given for the (Pb, Pb) system and compared with experiment.     

Probability of ionization of sputtered particles as a function of their energy: Part I: Negative Si ions

In this study we have investigated how the probability of ionization of sputtered Si atoms to form negative ions depends on the energy of the atoms. We have determined the ionization probability from experimental SIMS energy distributions using a special experimental technique, which included de-convolution of the energy distribution with an instrumental transmission function, found by separate measurements.We found that the ionization probability increases as a power law ∼E^0.677 for particles sputtered with energies of 0-10 eV, then becomes a constant value (within the limits of experimental error) for particles sputtered with energies of 30-100 eV. The energy distributions of Si⁻ ions, measured under argon and cesium ion sputtering, confirmed this radical difference between the yields from low and high-energy ions.To explain these results we have considered ionization mechanisms that are different for the low energy atoms (<10 eV) and for the atoms emitted with higher energy (>30 eV).     

Impact parameter dependence of the probability for removal of the 2s and 2p atomic electrons by nuclei

The probability W(x) of inner shell ionization by nuclei as a function of the impact parameter x is expressed through the ionization matrix element M_if. Values of W(x) for removal of the 2s and 2p electrons are calculated with the first Born M_if and compared with the SCA result.     

Calculation of cross sections of simultaneous ionization in ion-atom collisions by the generalized geometrical model

The geometrical model (GM) of ionization in ion—atom collisions [8, 9] was generalized to describe ionization of both colliding particles (simultaneous ionization) due to electron—electron interaction. The generalized GM (GGM) allows calculation of the cross sections for electron loss by an incident particle with simultaneous target ionization at collision velocities higher than characteristic electron velocities, accurate within a factor of two with respect to the Born or impulse approximation. An advantage of the GGM, except for its simplicity, is easy calculation of p(b) (p is the ionization probability and b is the impact parameter), which makes it possible to include the contribution of simultaneous ionization into more general approximate schemes for calculating cross sections of multielectron ionization of atoms or ions.     

Single attosecond burst generation during ionization of excited atoms by intense ultrashort laser pulses

We develop an analytical approach to describing the generation of a single attosecond burst during barrier-suppression ionization of a hydrogen atom by an intense laser pulse. We derive analytical expressions that describe the evolution of the electron wave packet in the time interval between the detachment from the atom and the collision with the parent ion for an arbitrary initial atomic state by assuming the atom to be fully ionized in one laser-field half-period. For various s-states, we derive expressions for the profile of the attosecond burst generated when the electron packet collides with the ion and analyze the dependence of its generation efficiency on the principal quantum number n of the initial atomic state. The results obtained are compared with the results of three-dimensional numerical calculations. We show that the attosecond pulse generation efficiency can be several orders of magnitude higher than that in the case of ionization from the ground state when pre-excited atomic states are used.     

Effect of light polarization on multi-photon ionization of the one-electron atom

On the basis of the one-electron model of an atom or ion (nuclear charge Z « 137) the complete ratio of probabilities for multi-photon ionization by circularly and linearly polarized light is derived (in contrast to previous expressions giving its maximal value only).     

Ionization of a two-dimensional quantum dot by the field of an electromagnetic wave

The process of ionization of a two-dimensional quantum dot by the field of a linearly polarized electromagnetic wave is studied. For the first time, analytic expressions for the ionization rate and partial probabilities of the process per unit time are obtained. The dependence of the probability of the process on the parameters of the confining potential and the Keldysh parameter are studied. The results of the work are compared with the earlier results on one- and three-dimensional nanostructures with a short-range potential.     

An absolute measurement of the probability for 1s σ and 2p σ excitation of the leadK shell

Using particle x-ray coincidence techniques, the probability forK shell ionization has been measured absolutely at two impact parameters for collisions of 5.8 MeV/amu²⁰⁸Pb on Ag and Au. In the asymmetric collision system Pb-Ag, the 1sσ excitation probability of the PbK shell is 2.2% at 25 fm impact parameter, and an exponential probability distribution falls off too quickly to account for the measured total cross section. For the symmetric system Pb-Au, the latter conclusion is also made for the 2pσ excitation probability although in this case, the probability is much larger being 29% at 42 fm.     

Pure multi-photon ionization of the ground 1S and metastable 2S state of the hydrogen atom with plane-polarized light of threshold frequency

Formulas for N-photon ionization of the hydrogen atom states 1S and 2S with plane-polarized light at the threshold frequency $\text{ω=}\text{I}\text{N}\text{h}\text{?}$ (I ionization energy) are proposed and shown to reduce in the one-photon case to the well-known Stobbe expressions.     

Ionization of Rydberg atoms by the kicks of half-cycle pulses

We present a quantum mechanical model to study the ionization of quasione-dimensional Rydberg atoms interacting with half-cycle pulses (HCPs) and use it to demonstrate the inadequacy of semiclassical approaches to calculate ionization probabilities of such atoms subject to the impact of more than one HCP. For a single-kicked atom both models correctly reproduce the experimentally observed ‘s-curve’ as can be seen by plotting the ionization probability P as a function of momentum transfer q₁. We demonstrate that for a twice-kicked atom, the semiclassical model yields numbers for P which are not physically realizable. For fixed values of momentum transfers q₁ and q₂, in a twice-kicked atom, the ionization probability as a function of time delay between the kicks exhibits periodic decay and revival. The results of the semiclassical approach appear to agree with the quantum mechanical values at the times of revival of P, else these show considerable deviation. We attempt to provide a physical explanation for the limitation of the semiclassical approach.     

A fluctuation problem in particle transport theory I

The fluctuation in the number of collision suffered by particles as they slow down in a moderating medium is studied via a probability balance equation. The equation describes the collision history of foreign particles slowing down in a host medium and also accounts for the recoil particles produced in the collision. The equations are solved by the introduction of a generating function from which the space and time dependent probability distributions are obtained. That is, the probability that a particle will suffer just N collisions to reach energy E at a time t after injection. In the space dependent case it is the probability that a particle suffers just N collisions to travel a given path length before coming to rest.Explicit expressions for the means and variances are obtained by solving a difference equation. From this solution it has been possible to obtain exact expressions for hard spheres and for a variety of models based on the inverse power law approximation. A number of new results are presented and some old ones rederived in a more efficient and general manner. The results are of value in the understanding of radiation damage cascades and in neutron slowing down in moderating materials.     

Random walks with ‘spontaneous emission’ on lattices with periodically distributed imperfect traps

We study random walks on d-dimensional lattices with periodically distributed traps in which the walker has a finite probability per step of disappearing from the lattice and a finite probability of escaping from a trap. General expressions are derived for the total probability that the walk ends in a trap and for the moments of the number of steps made before this happens if it does happen. The analysis is extended to lattices with more types of traps and to a model where the trapping occurs during special steps. Finally, the Green's function at the origin G(0; z) for a finite lattice with periodic boundary conditions, which enters into the main expressions, is studied more closely. A generalization of an expression for G(0; 1) for the square lattice given by Montroll to values of z different from, but close to, 1 is derived.     

Correlation of momenta of electrons and the nucleus in atoms

The process of resonant multiphoton ionization of a hydrogen atom in the ground 1s state is studied by direct numerical integration of the nonstationary Schrödinger equation for a quantum system in an electromagnetic field. The dependence of photoionization probability on the radiation intensity is found to be nonmonotonic. It is established that the minima of ionization correspond to multiphoton resonances between the ground state and one of the excited (Rydberg) atomic states perturbed by the laser field. It is shown that ionization is suppressed due to rearrangement of Rydberg states in a strong electromagnetic field and is accompanied by efficient Raman Λ transitions, which connect a set of closely lying Rydberg states via the continuum.