Analytic presentation of a solution of the Schrödinger equation

High-precision approximate analytic expressions for energies and wave functions are found for arbitrary physical potentials. The Schrödinger equation is cast into the nonlinear Riccati equation, which is solved analytically in first iteration of the quasi-linearization method (QLM). The zeroth iteration is based on general features of the exact solution near the boundaries. The approach is illustrated on the Yukawa potential. The results enable accurate analytical estimates of effects of parameter variations on physical systems.     

Photoionization of the Bound Systems at High Energies

We consider photoionization of a system bound by the central potential V(r). We demonstrate that the high energy nonrelativistic asymptotics of the photoionization cross section can be obtained without solving the wave equation. The asymptotics can be expressed in terms of the Fourier transform of the potential by employing the Lippmann–Schwinger equation. We find the asymptotics for the screened Coulomb field. We demonstrate that the leading corrections to this asymptotics are described by the universal factor. The high energy nonrelativistic asymptotics is found to be determined by the analytic properties of the potential V(r). We show that the energy dependence of the asymptotics of photoionization cross sections of fullerenes is to large extent model-dependent. We demonstrate that if the fullerene field V(r) is approximated by the function with singularities in the complex plane, the power drop of the asymptotics is reached at the energies which are so high that the cross section becomes unobservably small. The preasymptotic behavior with a faster decrease of the cross sections becomes important in these cases.     

Dependence of nucleon parameters on condensates in QCD sum rules

The vacuum-condensate dependence of nucleon parameters is investigated within QCD sum rules. It is shown that, without allowance for radiative corrections, a solution to the sum-rule equations exists only under stringent constraints on condensate values. There is only an unphysical solution beyond the region specified by these constraints. It is found that the nucleon-mass value is stabilized upon taking into account radiative corrections.     

On the interactions of the high energy photoelectrons with the fullerene shell

The probability that photoionization of the caged atom in an endohedral system is accompanied by excitation of the fullerene shell is shown to be close to unity in broad intervals of the photoelectron energies. This is obtained by summation of the perturbative series for the interaction between the photoelectron and the fullerene shell. The result can be verified in experiments. As an outcome, interaction between the photoelectron ejected from the caged atom and the fullerene shell cannot be described by a static potential, since inelastic processes become decisively important.     

High-Energy Two-Electron Photoabsorption as a Three-Body Problem

We study the high-energy behaviour of double photoionization and of the ionization accompanied by excitation of the states n¹S and n³S of the H^– ion, helium atom, and light helium-like ions. We show that the high-energy nonrelativistic limit of the ionization+excitation to the single-ionization cross section ratio is still valid for the photon energies, corresponding to the relativistic energies of the outgoing electron. The same applies to the double photoionization of the triplet states. The situation for the double photoionization of singlet states differs due to the quasifree mechanism. All these ionization ratios are calculated by using the high-precision locally correct wave functions for the bound electrons. The importance of using locally correct functions is emphasized.     

Back-to-back emission of the electrons in double photoionization of helium

We calculate the double differential distributions and distributions in recoil momenta for the high energy non-relativistic double photoionization of helium atom. We show that the results of recent experiments provide the pioneering experimental manifestation of the quasifree mechanism for the double photoionization which was predicted long ago in our papers. This mechanism provides a surplus in distribution over the recoil momenta at small values of the latter, corresponding to nearly ??back-to-back?? emission of the photoelectrons. Also, in agreement with previous analysis we demonstrate that this surplus is due to the quadrupole terms of the photon-electron interaction. We present the characteristic angular distribution for the back-to-back electron emission. The confirmation of the quasifree mechanism existence opens a new area for exciting experiments, which are expected to increase our understanding of the electron dynamics and of the bound states structure.     

The final state interaction in the ionization following the internal nuclear conversion

With the final state interaction taken into account the spectrum of the secondary electrons and the integral characteristics of the ionization following the internal nuclear conversion are calculated. The general equations are obtained while the concrete data is presented for the conversion in₆₉Tm¹⁶⁹.     

Three-body nuclear interactions in the QCD sum rules

The QCD sum rules used to calculate the characteristics of single-particle nucleons are reviewed briefly. The contribution from three-body forces to the nucleon self-energies are calculated.