### Article

## Structure factors for tunneling ionization rates of molecules: General grid-based methodology and convergence studies

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

We consider the one-dimensional stationary Schr¨odinger equation with a smooth double-well potential. We obtain a criterion for the double localization of wave functions, exponential splitting of energy levels, and the tunneling transport of a particle in an asymmetric potential and also obtain asymptotic formulas for the energy splitting that generalize the well-known formulas to the case of mirror-symmetric potential. We consider the case of higher energy levels and the case of energies close to the potential minimums. We present an example of tunneling transport in an asymmetric double well and also consider the problem of tunnel perturbation of the discrete spectrum of the Schr¨odinger operator with a single-well potential. Exponentially small perturbations of the energies occur in the case of local potential deformations concentrated only in the classically prohibited region. We also calculate the leading term of the asymptotic expansion of the tunnel perturbation of the spectrum.

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.

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.