E. G. Drukarev

Two-electron photoionization of helium

Cross sections of such processes as double photoionization and photoionization accompanied by excitation of He-like atomic systems are investigated in the limit of high, but still not relativistic, photon energies. In addition to total cross sections electron energy and angular distributions are also obtained. Coulomb wave and Green functions were employed in the momentum representation. Results for the total double ionization cross section as a function of photon energy are close to those obtained by predecessors with much more complicated ground state wavefunctions. The cross section of ionization with simultaneous excitation differs considerably from those obtained before. Angular and energy distributions of ionized electrons, are, to this extent, investigated for the first time.

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.

Wavefunctions of Helium-Like Systems in Limiting Regions ¶

We find an approximate analytic form for the solution ψ(r1, r2, r12) of the Schrödinger equation for a system of two electrons bound to a nucleus in the spatial regions r1 = r2 = 0 and r12 = 0, which are of great importance for a number of physical processes. The forms are based on the well-known behavior of ψ(r1, r2, r12) near the singular triple coalescence point. The approximate functions are compared to the locally exact ones obtained earlier by the correlation function hyperspherical harmonic (CFHH) method for the helium atom, light helium-like ions, and the negative ion of hydrogen H−. The functions are shown to determine a natural basis for the expansion of CFHH functions in the considered spatial region. We demonstrate how these approximate functions simplify calculations of high-energy ionization processes.

Quasifree mechanism in ionization processes

We discuss a specific quasifree mechanism (QFM) of the ionization processes, which requires only small momentum transfer to the nucleus. The QFM mechanism is important in the kinematical regions where the two-electron system can absorb a photon without participation of the nucleus. The QFM leads to the complicated shape of the double photoionization spectrum curve, providing the breakdown of the nonrelativistic high energy asymptotic of the double-to single photoionization ratio. Calculation of the QFM contribution requires a consistent theoretical approach. Use of oversimplified approximations leads to misleading results. In certain kinematical regions the QFM provides the leading contribution, and thus the results obtained without inclusion of QFM are erroneous. Experimental detection of QFM is a complicated, but interesting problem.

Asymptotic behavior of photoionization cross section in a central field

Abstract We demonstrate that the high energy nonrelativistic asymptotics for the photoionization cross section in a central field V(r) can be obtained without solving of the wave equations for the bound and outgoing electrons. The asymptotics is expressed in terms of the asymptotics of the Fourier transform V(p) of the field. We show that the cross sections drop in the same way for the fields with the Coulomb short distance behavior. The character of the cross sections energy behavior is related to the analytical properties of the function V(r). The cross sections exhibit power drop for the potentials which have singularities on the real axis. They experience the exponential drop if V(r) has singularities in the complex plane. Graphical abstract

Role of the atomic electron shell in the double β decay

We demonstrate that the limiting energy available for ejected electrons in double beta decay is diminished by about 400 eV due to inelastic processes in the atomic electronic shell.

On the distribution of electrons in the double ionization of helium-like ions by Compton scattering

The Compton scattering of a high energy photon by a helium-like ion, followed by the ionization of two electrons, is considered outside of the Bethe surface of Compton scattering with the knock-out of a single electron. The role of shake-off (SO), of final state interactions (FSI) and of the quasi-free mechanism (QFM) is analysed. The triple and double differential distributions are calculated. It is demonstrated for the first time that in certain kinematical regions the process is dominated by the FSI and by the QFM, while the SO contribution is much smaller.

Interelectron correlations in photoionization of outer shells near inner shell thresholds

We have studied the role of virtual excitations of inner shells upon outer shell photoionization. The calculations were performed in the frames of the Random Phase Approximation with Exchange (RPAE) and its generalized version GRPAE that take into account variation of the atomic field due to electron elimination and the inner vacancies decay. We apply both analytic approximation and numeric computations. The results are presented for 3p electrons in Ar and for 4d-electrons in Pd near inner shells thresholds. The effect considered proved to be quite noticeable.

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.

Two‐electron processes in atom‐photon interactions

Two‐electron processes in atom‐photon interactions have been studied. Various mechanisms of double photoionization, angular correlations, total cross sections, energy distributions and results for non‐Helium like systems are discussed.