V N Ostrovsky

Resonance and interference phenomena in the photoionisation of a hydrogen atom in a uniform electric field. II. Overlapping resonances and interference

For pt.I see ibid., vol.17, no.10, p.1981 (1984). The photoionisation cross section for a hydrogen atom placed in a uniform electric field is investigated as a function of the light frequency, Watson transformation allows one to represent the partial cross sections sum (i.e. the total cross section) as a sum of contributions of two series of complex cross section poles and the background term. Analytical formulae are obtained describing the cross section structure in various regions of photon energy and fields strength. The contribution of one of the series of poles is related qualitatively with the population of resonance states in the superposition of Coulomb and uniform fields (these states exist even for photon energies exceeding the zero-field atomic ionisation potential). The Fano parametrisation of resonance peaks is generalised for the overlapping resonance case. The second series of poles generates cross section oscillations corresponding to interference of photoelectrons ejected from the atom along the field axis with electrons moving in the same direction after reflection from the potential barrier bounding the classically accessible region. The interference structure proves to be suppressed compared with the short-range potential case where this mechanism of structure formation is unique. If the photon energy is less than 4 pi 2* (ionisation potential) then the resonance structure is significantly larger than the interference one in amplitude and differs in phase. When the photon energy is close to the ionisation potential the resonance peaks are strongly asymmetrical. A comparison is made with experiments where the structure is observed in the photoionisation of sodium and rubidium atoms.

Rydberg atom-ion collisions: classical overbarrier model for charge exchange

A novel classical overbarrier model for the charge exchange is formulated for low and medium collision velocities. The charge-exchange probability is expressed in analytical form. The results are compared with the classical Monte Carlo trajectory calculations for various partners (ground-state atom+multicharged ion, high Rydberg atom+ion with unit charge). The model reproduces well the experimental data for the collisions Na++Na(29s).

Doubly periodical in time and energy exactly soluble system with two interacting systems of states

The time-dependent matrix Schrodinger equation 1/ic( delta Psi / delta t)=H(t) Psi describing two bands of an infinite number of equidistant states with different energy spacings omega +or- in each band is studied. Both bands are linearly dependent on time t. The interaction upsilon =( square root ( omega - omega +)/ pi )tan pi s between the bands is considered to be equal for any pair of states from each band. Using the Fourier series transformation the instant eigenvalues E(t, s) are calculated which reveal the double periodicity in the energy-time plane. The corresponding eigenvalue surface in the (E, t, s)-space, apart from the triple periodicity, shows quite unexpected symmetry properties relative to the exchange of t and s, and relative to some inversions in the (E, t) plane. The latter one leads to a new equivalence between weak and strong coupling, a new kind of pseudocrossing and a new concept of antidiabatic states. The Fourier transformation reduces the problem to a 2*2 first-order differential operator. The diagonalization of H(r) for fixed t produces explicit expressions for the eigenvalues (adiabatic potential curves) and eigenstates (adiabatic basis). The time evolution operator is calculated both in the diabatic and adiabatic representations. The results are simplified for the special value of the interaction parameter.

Non-Franck-Condon transitions in the electron impact excitation of molecules. II. Semi-empirical approach: transitions in H2

For pt.I see ibid., vol.14, p.4389 (1981). The adiabatic theory developed in the first paper of this series is now applied to the d3 Pi u to X1 Sigma g+ electron impact excitation of the hydrogen molecule. It gives the opportunity to determine semi-empirically all vibro-rotational cross sections for the transitions occurring within the electronic transition studied. The theoretically well founded procedure of extracting information from the intensities of spectral lines excited with the gas-beam technique is proposed and put into practice. In particular, it is established that for the electronic transition in the H2 molecule considered there are substantial deviations from the Franck-Condon approximation. The principal and applied practical significances of this fact are discussed.

The symmetry of the electron-electron interaction operator in the dipole approximation

The operator for the interaction of a charged quantum particle with an excited hydrogen-like atom or ion is considered in the dipole approximation. A new additional integral of motion and related symmetry group are found. A broader approximate symmetry group and expressions for the eigenvalues and eigenfunctions are proposed in the semiclassical limit of large total orbital momentum. The qualitative peculiarities of the spectrum are discussed and limiting cases are considered. A comparison with the results of other authors and with analytical and numerical data is made. The results are applicable to the doubly excited states of two-electron atoms, scattering of charged particles on hydrogen-like atoms or ions, and spectral line broadening etc.

On the classification of the doubly excited states of the two-electron atom

Group-theoretical schemes of classification of the doubly excited states of the two-electron atom are based on the theory of addition of four angular momenta. A new scheme of classification of states with high total orbital momentum is proposed for the case when one electron is excited much more than another. The group-theoretical state vectors are compared with the results of the qualitative and numerical study of configuration interaction. Exceptions to the proposed classification scheme are discussed.

The exact solution of the multistate Landau-Zener type model: the generalized bow-tie model

The generalized bow-tie model (Yu?N?Demkov and V?N?Ostrovsky 2000 Phys. Rev. A 61 32705) is a particular generalization of the famous two-state Landau-Zener model widely used in atomic physics and beyond. It comprises an arbitrary number of states; the diabatic-potential curves are linear functions of time whereas the coupling matrix elements are constant. We derive a rigorous solution of the model by the contour integral method. The complete set of transition amplitudes is obtained by considering solution asymptotes for t???. It agrees with the transition probabilities evaluated earlier by heuristically appealing but non-rigorous reduction of the model to the sequence of two-state transitions. An unusual quasi-factorization property of the transition amplitude matrix is established. The entire matrix is expressed via a single complex-valued vector.

Effective ATI channels in high harmonic generation

Harmonic generation by an atom in a laser field is described by the three-step mechanism as proceeding via above-threshold ionization (ATI) followed by electron propagation in the laser-dressed continuum and subsequent laser-assisted recombination (LAR). The amplitude of the harmonic production is given by the coherent sum of contributions from different intermediate ATI channels labelled by the number, m, of absorbed laser photons. The range of m-values that give a substantial contribution is explored and found to be rather broad for high harmonic generation. The coherence effects are of crucial importance as they are responsible for the characteristic pattern of harmonic intensities with a plateau domain followed by a cut-off region. Due to the multiphoton nature of the process, an efficient summation of m-contributions can be carried out within the framework of the saddle-point method. The saddle points correspond to some complex-valued labels m = mc associated with the intermediate effective ATI channels in the three-step harmonic generation process. The advantage of this approach stems from the fact that summation over a large number of conventional ATI m-channels is replaced by summation over a small number of effective mc-channels. The equation governing mc has a transparent physical meaning: the electron ejected from the atom on the first (ATI) stage should return to the core to make LAR possible. The effective channel labels m move along characteristic trajectories in the complex plane as the system parameters vary. In the cut-off region of the harmonic spectrum a single effective channel contributes. For lower harmonics, in the plateau domain, two effective ATI channels become essential. The interference of their contributions leads to an oscillatory pattern in the harmonic generation rates. The calculated rates are in good agreement with the results obtained by other approaches.Harmonic generation by an atom in a laser field is described by the three-step mechanism as proceeding via above-threshold ionization (ATI) followed by the electron propagation in the laser-dressed continuum and the subsequent laser assisted recombination (LAR). An amplitude of harmonic production is given by the coherent sum of contributions from different intermediate ATI channels labeled by the number m of absorbed laser photons. The range of m-values that gives substantial contribution is explored and found to be rather broad for high harmonic generation. The coherence effects are of crucial importance being responsible for the characteristic pattern of harmonic intensities with a plateau domain followed by a cutoff region. Due to multiphoton nature of the process, an efficient summation of m-contributions can be carried out in the framework of the saddle point method. The saddle points correspond to some complex-valued labels m=m_c associated with the intermediate effective ATI channels in the three-step harmonic generation process. The advantage of this approach stems from the fact that summation over large number of conventional ATI m-channels is replaced by summation over small number of effective m_c-channels. The equation governing m_c has a transparent physical meaning: the electron ejected from the atom on the first (ATI) stage should return to the core to make LAR possible. The calculated rates are in good agreement with the results obtained by other approaches.

Planetary atom states: adiabatic invariant theory

In the asymmetric doubly excited states of the helium atom one electron is excited much more than the other. We consider the special type of such states with both electrons located on one side of the atomic nucleus. The new version of the classical adiabatic theory is developed using approximate separation of rapid and slow motions. It is based on the formalism of adiabatic invariants. The theory takes into account two important effects simultaneously: (i) exchange by the orbital momentum between the electrons; (ii) exchange by the energy. An effective Hamiltonian is constructed for the description of the slow motions. The semiclassical quantization is carried out. The energy spectrum is compared with the calculations by other methods. The present adiabatic scheme is shown to be superior to the previous version where the effective Hamiltonian for the slow motion is found as an average of the full Hamiltonian over the rapid phase. The relation between the two approaches is elucidated.

Wannier threshold law: rederivation and applicability range

The derivation of the threshold law for ionization of an atom by electron impact is reduced to calculation of the probability of the system survival in the vicinity of the Wannier ridge. The approach is applicable for a small but finite energy excess above the threshold. This reveals the energy range where the Wannier law applies as well as the nature and the character of the deviations outside this region.