### Article

## Integral-equation approach to the weak-field asymptotic theory of tunneling ionization

An integral equation approach to the weak-field asymptotic theory (WFAT) of tunneling ionization is developed. An integral representation for the exact partial amplitudes of ionization into parabolic channels is derived. The WFAT expansion for the ionization rate follows immediately from this relation. Integral representations for the coefficients in the expansion are obtained. The integrals accumulate where the ionizing orbital has large amplitude and are not sensitive to its behavior in the asymptotic region. Hence, these formulas enable one to reliably calculate the WFAT coefficients even if the orbital is represented by an expansion in Gaussian basis, as is usually the case in standard software packages for electronic structure calculations. This development is expected to greatly simplify the implementation of the WFAT for polyatomic molecules, and thus facilitate its growing applications in strong-field physics.

We present a general methodology for evaluating structure factors defining the orientation dependence of tunneling ionization rates of molecules, which is a key process in strong-field physics. The method is implemented at the Hartree-Fock level of electronic structure theory and is based on an integralequation approach to the weak-field asymptotic theory of tunneling ionization, which expresses the structure factor in terms of an integral involving the ionizing orbital and a known analytical function. The evaluation of the required integrals is done by three-dimensional quadrature which allows calculations using conventional quantum chemistry software packages. This extends the applications of the weak-field asymptotic theory to polyatomic molecules of almost arbitrary size. The method is tested by comparison with previous results and illustrated by calculating structure factors for the two degenerate highest occupied molecular orbitals (HOMOs) of benzene and for the HOMO and HOMO-1 of naphthalene

Ionization processes for a two dimensional quantum dot subjected to combined electrostatic and alternating electric fields of the same direction are studied using quantum mechanical methods.We derive analytical equations for the ionization probability in dependence on characteristic parameters of the system for both extreme cases of a constan telectric field and of a linearly polarized electromagnetic wave.The ionization probabilities for a superposition of dc and low frequency ac electric fields of the same direction are calculated.The impulse distribution of ionization probability for a system bound by short range forces is found for a superposition of constant and alternating fields. The total probability for this process per unit of timeis derived within exponential accuracy.Forthe first time the influence of alternating electric field on electron tunneling probability induced by an electrostatic field is studied taking into account the pre-exponential term.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

By using superconducting quantum interference device (SQUID) magnetometry, we investigated anisotropic high-field (H less than or similar to 7T) low-temperature (10 K) magnetization response of inhomogeneous nanoisland FeNi films grown by rf sputtering deposition on Sitall (TiO2) glass substrates. In the grown FeNi films, the FeNi layer nominal thickness varied from 0.6 to 2.5 nm, across the percolation transition at the d(c) similar or equal to 1.8 nm. We discovered that, beyond conventional spin-magnetism of Fe21Ni79 permalloy, the extracted out-of-plane magnetization response of the nanoisland FeNi films is not saturated in the range of investigated magnetic fields and exhibits paramagnetic-like behavior. We found that the anomalous out-of-plane magnetization response exhibits an escalating slope with increase in the nominal film thickness from 0.6 to 1.1 nm, however, it decreases with further increase in the film thickness, and then practically vanishes on approaching the FeNi film percolation threshold. At the same time, the in-plane response demonstrates saturation behavior above 1.5-2T, competing with anomalously large diamagnetic-like response, which becomes pronounced at high magnetic fields. It is possible that the supported-metal interaction leads to the creation of a thin charge-transfer (CT) layer and a Schottky barrier at the FeNi film/Sitall (TiO2) interface. Then, in the system with nanoscale circular domains, the observed anomalous paramagnetic-like magnetization response can be associated with a large orbital moment of the localized electrons. In addition, the inhomogeneous nanoisland FeNi films can possess spontaneous ordering of toroidal moments, which can be either of orbital or spin origin. The system with toroidal inhomogeneity can lead to anomalously strong diamagnetic-like response. The observed magnetization response is determined by the interplay between the paramagnetic-and diamagnetic-like contributions.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.