Double atomic photoeffect in the relativistic domain: Angular and energy distributions of photoelectrons

We study the double ionization of the atomic K-shell by a single photon in the relativistic energy domain. The differential and total cross sections of the process are calculated. It is shown that the ratio of the cross sections of double and single ionization increases with the photon energy, tending to the limit 0.34/Z ², where Z is the atomic number or the nuclear charge. The formulas are found to be valid for Z≫1 and αZ≪1, where α=1/137 is the fine-structure constant. Zh. éksp. Teor. Fiz. 114, 1537–1554 (November 1998)     

K-shell ionization of atoms and ions by relativistic projectiles

We evaluate the total cross section for the single K-shell ionization of atoms and ions by the impact of relativistic electrons. The study is performed to leading orders of the QED perturbation theory with respect to the parameters αZ and 1/Z. The results obtained are in good agreement with experimental data for different atomic targets. In the case of moderate values of the nuclear charge Z, the total cross section is described by a simple analytic formula. The K-shell ionization by relativistic heavy particles is also considered.     

Cross sections for single and double ionization of atomic helium under impact by fast multiply charged ions

Expressions for the cross sections for single and double ionization of atomic helium in collisions with fast multiply charged ions are obtained in the collision parameter range υ ²≫Z≳υ, υ ₀<c, where Z and υ are, respectively, the ion charge and ion velocity, υ ₀ is the characteristic velocity of electrons in the atomic helium ground state, and c is the velocity of light. Zh. Tekh. Fiz. 68, 1–7 (March 1998)     

Annihilation of a relativistic positron and K-electron to yield a photon and second K-electron

We study the annihilation of a fast positron and a K-electron resulting in the emission of a photon and a second K-electron. It is assumed that all electrons and positrons move in the Coulomb field of the nucleus and that the Coulomb parameter αZ is much less than unity (α=1/137 is the fine-structure constant and Z is the atomic number). The electron-electron interaction, which is responsible for the ejection of the electron by the atom, is taken into account in the first order of perturbation theory. We calculate the differential and total cross sections of the process and construct the ratio of the cross sections of double and single ionization as a function of the energy of the incident positron. Finally, we establish the high-energy limit of this ratio, equal to 0.34/Z ². Zh. éksp. Teor. Fiz. 113, 786–804 (March 1998)     

Measurements of K-shell ionization cross sections of35Br,37Rb,39Y using low energy protons

K-shell ionization cross section measurements are reported for₃₅Br,₃₇Rb and₃₉Y targets caused by protons over 300–400 keV energy range in 20 keV increment. The K-shell ionization cross sections (σ _k ^l ) at different energies were deduced from the K_α and K_β X-ray production cross sections which were obtained from X-ray yields of the K_α and K_β transitions. The experimental values are compared with the calculated values of ECPSSR theory and empirical reference cross sections. The resultant K-shell ionization cross sections are found to be in reasonable agreement with the ECPSSR theory. The K_α/K_β intensity ratios are also presented and compared with other experimental values and also with the theoretical one-hole values given by Scofield.     

Ionization of hydrogen and helium atoms by highly charged fast ions in collisions with small momentum transfer

Ionization of hydrogen and helium atoms is studied for the case of “soft” collisions with highly charged fast ions with v≲Z≪v² and v≫v ₀, where Z is the ion charge, v is the collision velocity, and v ₀∼1 is the characteristic velocity of the electron in the ground state of the atom. Analytical expressions are derived for the singly and doubly differential cross section for ionization of a hydrogen atom accompanied by the ejection of a slow electron v _e≲v ₀, where v _e is the velocity of the ejected electron with respect to the recoil ion). The results are generalized to the case of single ionization of helium. It is shown that soft collisions provide the main contribution to the hydrogen ionization cross section and for all practical purposes determine the cross section for single ionization of helium. The asymmetry in the angular distribution of the ejected slow electrons and the properties of momentum exchange in such collisions are discussed. Finally, a formula for the cross section for single ionization of helium is proposed. Zh. éksp. Teor. Fiz. 112, 1966–1977 (December 1997)     

Contribution to the theory of Lorentzian ionization

The probability w _L of Lorentzian ionization, which arises when an atom or ion moves in a constant magnetic field, is calculated in the quasiclassical approximation. The nonrelativistic (v≲e ²/ℏ=1, v is the velocity of the atom) and ultrarelativistic (v→c=137) cases are examined and the stabilization factor S, which takes account of the effect of the magnetic field on tunneling of an electron, is found. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 391–396 (10 March 1997)     

Multiphoton ionization of molecules under the conditions of strong field-induced perturbation of Rydberg states

Multiphonon ionization of the H₂ molecule under the action of a weak (probe) field, which provides the initial population of the low-lying (working) level, and intense monochromatic linearly polarized radiation is studied. The multiphoton ionization process occurs under the conditions of strong field perturbation of two intermediate Rydberg series, np0(¹Σ _u ⁺ and np2(¹Π_u), of the optical R(0)branch which have different ionization potentials. The series are occupied simultaneously as a result of single-photon absorption by an excited H ₂ ^* molecule in the working state 4s σH′¹Σ _g ⁺ (v=0). As a result of the irregularity in the arrangement of the intermediate levels from a large group of states that are combined in the multiphoton ionization process a sharp and irregular change occurs in the dependence of the shifts and widths Γ_n of the levels on the intensity f of the strong field in a transition from one level to another. It is shown that for field intensities f such that the level widths remain much less than the splitting between the levels (Γ_n≪/n ³) the stabilizing effect (i.e., the field-induced narrowing of the levels as f→∞) in the form Γ_n ∝ 1/f ² (as happens in atoms with a structureless core) is not observed in molecular systems. Zh. éksp. Teor. Fiz. 115, 1987–2000 (June 1999)     

e + e − pair production in ultrarelativistic heavy-ion collisions at intermediate impact parameters

Using the semiclassical Green’s function in the Coulomb field, we analyze the probabilities of single and multiple e ⁺ e ⁻ pair production at a fixed impact parameter b between colliding ultrarelativistic heavy nuclei. We perform calculations in the Born approximation with respect to the parameter Z _Bα and exactly in Z _Aα, where Z _A and Z _B are the charge numbers of the corresponding nuclei. We also obtain the approximate formulas for the probabilities valid for Z _Aα, Z _Bα ≲ 1. The text was submitted by the authors in English.     

Deep impurity-center ionization by far-infrared radiation

An analysis is made of the ionization of deep impurity centers by high-intensity far-infrared and submillimeter-wavelength radiation, with photon energies tens of times lower than the impurity ionization energy. Within a broad range of intensities and wavelengths, terahertz electric fields of the exciting radiation act as a dc field. Under these conditions, deep-center ionization can be described as multiphonon-assisted tunneling, in which carrier emission is accompanied by defect tunneling in configuration space and electron tunneling in the electric field. The field dependence of the ionization probability permits one to determine the defect tunneling times and the character of the defect adiabatic potentials. The ionization probability deviates from the field dependence e(E) ∝ exp(E ²/E _c ² ) (where E is the wave field, and E _c is a characteristic field) corresponding to multiphonon-assisted tunneling ionization in relatively low fields, where the defects are ionized through the Poole-Frenkel effect, and in very strong fields, where the ionization is produced by direct tunneling without thermal activation. The effects resulting from the high radiation frequency are considered and it is shown that, at low temperatures, they become dominant. Fiz. Tverd. Tela (St. Petersburg) 39, 1905–1932 (November 1997)     

On the Hausdorff Dimension of Regular Points of Inviscid Burgers Equation with Stable Initial Data

Consider an inviscid Burgers equation whose initial data is a Lévy α-stable process Z with α>1. We show that when Z has positive jumps, the Hausdorff dimension of the set of Lagrangian regular points associated with the equation is strictly smaller than 1/α, as soon as α is close to 1. This gives a partially negative answer to a Conjecture of Janicki and Woyczynski (J. Stat. Phys. 86(1–2):277–299, 1997). Along the way, we contradict a recent Conjecture of Z. Shi () about the lower tails of integrated stable processes.     

Hot-electron-pumped K-shell X-ray laser

Amplified spontaneous inner-shell emission produced via an ultrafast burst of high-energy electrons from a femtosecond laser-produced plasma is proposed as a novel electron-pumped x-ray laser. In this scheme, a population inversion of the upper laser level is created via impact ionization of atomic inner shells by electron bombardment. Based on the requirement of a positive gain coefficient for amplifying spontaneous K _α line emission, a simple pumping threshold is found for the incident electron flux, and feasibility of the scheme is assessed for a range of low-Z elements. Published in English in the original Russian journal. Edited by Steve Torstveit. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 10, 771–776 (25 May 1998)     

Zero-Temperature Dynamics of ±J Spin Glasses¶and Related Models

We study zero-temperature, stochastic Ising models σ ^t on Z ^d with (disordered) nearest-neighbor couplings independently chosen from a distribution μ on R and an initial spin configuration chosen uniformly at random. Given d, call μ type ℐ (resp., type ℱ) if, for every x in Z ^d , σ _x ^t flips infinitely (resp., only finitely) many times as t→∞ (with probability one) – or else mixed type ℳ. Models of type ℒ and ℳ exhibit a zero-temperature version of “local non-equilibration”. For d=1, all types occur and the type of any μ is easy to determine. The main result of this paper is a proof that for d=2, ±J models (where μ=αδ _J +(1-α)δ_{- J} ) are type ℳ, unlike homogeneous models (type ℐ) or continuous (finite mean) μ's (type ℳ). We also prove that all other noncontinuous disordered systems are type ℳ for any d≥ 2. The ±J proof is noteworthy in that it is much less “local” than the other (simpler) proof. Homogeneous and ±J models for d≥ 3 remain an open problem. Received: 3 November 1999 / Accepted: 10 April 2000     

The generalized Bethe logarithm for tightly bound electrons

We derive a closed relativistic expression that makes it possible to calculate the self-energy of multiply charged ions in an external Coulomb field without resorting to a series expansion in powers of αZ. The expression contains the generalized Bethe logarithm for tightly bound electrons. We do numerical calculations of the self-energy for the 1s _1/2-electrons of multiply charged hydrogenlike ions. The proposed method allows for self-energy calculations for any values of the nuclear charge Z. Zh. éksp. Teor. Fiz. 112, 1197–1208 (October 1997)     

Scott Correction for Large Atoms and Molecules in a Self-Generated Magnetic Field

We consider a large neutral molecule with total nuclear charge Z in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that Z α ² ≤ κ ₀ for a sufficiently small κ ₀, where α denotes the fine structure constant. We show that, in the simultaneous limit Z → ∞, α → 0 such that κ = Z α ² is fixed, the ground state energy of the system is given by a two term expansion c ₁ Z ^7/3 + c ₂(κ) Z ² + o(Z ²). The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion.     

Experimental and theoretical analysis of bias ionization by?α-particles in a nitrogen laser

Nitrogen laser performance with TE configuration and wedge electrodes is analyzed with background ionization in the laser discharge channel by α particles at a low exposition rate. With the bias ionization, the laser power presents two peaks as a function of gas pressure, with one at the normal low pressure, without bias ionization, and the other at high pressure generated by bias ionization. A simple theoretical model has been developed in a trial to understand this behavior. This model was first tested in later results for a TE configuration nitrogen laser, with flat electrodes, without and with bias ionization. It has been observed that due to the competition between electrode shielding by positively charged α particles and bulk ionization by impact, the laser energy is suppressed with pressure below 50 Torr and enhanced above it.     

Mechanisms of resonant laser ionization

An experimental investigation and numerical simulation of resonant laser breakdown are performed. As a result, quantitative agreement between the experimental data on the parameters of a dense resonant plasma (the electron density and the electron temperature) and the results of calculations in the range of detunings of the laser radiation from resonance Δλ>2–2.5 nm, in which the spatial instability of the intense resonant laser beam and the absorption of radiation are minimal, is obtained for the first time. It is shown that the previously proposed mechanism of resonant breakdown associated with laser-induced associative ionization introduces only a small correction to the final extent of ionization of the resonant plasma and scarcely alters its temperature. The influence of quantum stimulated inverse bremsstrahlung processes, which are usually described as collisions of the second kind in the resonance case, on the energy gain by electrons is analyzed for the first time in reference to specific experimental findings. The numerical calculations show that at detunings of the order of the Rabi frequency, the mechanism by which electrons gain energy through the resonant system does not reduce to collisions of the second kind and can significantly increase the density of the resonant plasma. However, in this range of detunings the laser beam is still strongly perturbed by instability processes, precluding a proper comparison of the theory with experiment. At large Δλ the classical and quantum cases differ from one another only slightly, and the values of N _e calculated for both mechanisms lie within the measurement error. Zh. éksp. Teor. Fiz. 111, 1274–1296 (April 1997)     

Electron shake process following inner‐shell ionization

Electron shakeup and shakeoff probabilities accompanying inner‐shell ionization of atoms were calculated for K‐, L‐ and M‐shell electrons using hydrogenic wavefunctions. The dependence of shake probabilities on atomic number Z is estimated. It is found that both shakeoff and shakeup probabilities are proportional to 1/Z². Based on this Z‐dependence, the shakeup‐plus‐shakeoff probabilities are expressed in a simple analytical form with two parameters. Copyright © 2004 John Wiley & Sons, Ltd.     

Dynamics of α-clusters in N = Z nuclei

The systematics for binding energies per α-particle in N = Z nuclei, E _Bα/N _α, are studied up to ¹⁶⁴Pb. It is shown that, although a geometrical model can be used to explain the systematics for light nuclei, the binding energy per α-particle exhibits structures which are due to the well-known shells of the mean field of nucleons in nuclei. The overall dependence of E _Bα/N _α on N _α in N = Z nuclei (for the ground-state masses) can be described in a liquid-drop model of α-particles. Conditions for a phase change with the formation of an α-particle condensate, a dilute Bose gas in excited compound nuclei are discussed for E _Bα/N _α = 0, at the thresholds. This is achieved when the binding energy per nucleon in nuclei is equal to or smaller than in the α-cluster. At somewhat smaller excitation energies the appearance of a Bose gas with a closed-shell core (N = Z, e.g. of ⁴⁰Ca) is proposed within the same concept. The experimental observation of the decay of such condensed α-particle states is proposed with the coherent emission of several correlated α-particles not described by the Hauser-Feshbach approach for compound-nucleus decay. This decay will be observed by the emission of unbound resonances in the form of ⁸Be and ¹²C ^* (0⁺ ₂) clusters.     

Ground State Energy of Large Atoms in a Self-Generated Magnetic Field

We consider a large atom with nuclear charge Z described by non-relativistic quantum mechanics with classical or quantized electromagnetic field. We prove that the absolute ground state energy, allowing for minimizing over all possible self-generated electromagnetic fields, is given by the non-magnetic Thomas-Fermi theory to leading order in the simultaneous Z → ∞, α → 0 limit if Z α ² ≤ κ for some universal κ, where α is the fine structure constant.