Representation of the three-body Coulomb Green's function in parabolic coordinates: paths of integration

The possibility is discussed of using straight-line paths of integration in computing the integral representation of the three-body Coulomb Green's function. In our numerical examples two different integration contours are considered. It is demonstrated that only one of these straight-line paths provides that the integral representation is valid

The JJ-matrix inverse scattering approach for coupled channels with different thresholds

The inverse scattering method within the $J$-matrix approach to the two coupled-channel problem is discussed. We propose a generalization of the procedure to the case with different thresholds.Comment: 20 pages, 3 figure

Relativistic mask method for electron momentum distributions after ionization of hydrogen-like ions in strong laser fields

Wavefunction-splitting or mask method, widely used in the non-relativistic calculations of the photoelectron angular distributions, is extended to the relativistic domain within the dipole approximation. Since the closed-form expressions for the relativistic Volkov states are not available within the dipole approximation, we build such states numerically solving a single second-order differential equation. We calculate the photoelectron energy spectra and angular distributions for highly charged ions under different ionization regimes with both the direct and the relativistic mask methods. We show that the relativistic mask method works very well and reproduces the electron energy and angular distributions calculated by the direct method in the energy range where both methods can be used. On the other hand, the relativistic mask method can be applied for longer laser pulses and/or higher photoelectron energies where the direct method may have difficulties

Parity nonconservation effect in the resonance elastic electron scattering on heavy He-like ions

We investigate the parity nonconservation effect in the elastic scattering of polarized electrons on heavy He-like ions, being initially in the ground state. The enhancement of the parity violation is achieved by tuning the energy of the incident electron in resonance with quasidegenerate doubly-excited states of the corresponding Li-like ion. We consider two possible scenarios. In the first one we assume that the polarization of the scattered electron is measured, while in the second one it is not detected.Comment: 13 pages, 3 figures, 2 table

Parity nonconservation effect in the dielectronic recombination of polarized electrons with heavy He-like ions

We investigate the parity nonconservation (PNC) effect in the dielectronic recombination (DR) of a polarized electron with a heavy He-like ion into doubly-excited $((1s 2p_{1/2})_{0} n{\kappa})_{1/2}$ and $\left(\left(1s 2s\right)_{0} n{\kappa}\right)_{1/2}$ states of Li-like ion. We determine the nuclear charge number $Z$ for which these opposite-parity levels are near to cross and, therefore, the PNC effect will be significantly enhanced. Calculations are performed for quantum numbers $n \geq 4$ and $\kappa = \pm 1$.Comment: 12 pages, 1 figur

Nucleon-nucleon interaction in the JJ-matrix inverse scattering approach and few-nucleon systems

The nucleon-nucleon interaction is constructed by means of the $J$-matrix version of inverse scattering theory. Ambiguities of the interaction are eliminated by postulating tridiagonal and quasi-tridiagonal forms of the potential matrix in the oscillator basis in uncoupled and coupled waves, respectively. The obtained interaction is very accurate in reproducing the $NN$ scattering data and deuteron properties. The interaction is used in the no-core shell model calculations of $^3$H and $^4$He nuclei. The resulting binding energies of $^3$H and $^4$He are very close to experimental values.Comment: Text is revised, new figures and references adde

The parabolic Sturmian-function basis representation of the six-dimensional Coulomb Green's function

The square integrable basis set representation of the resolvent of the asymptotic three-body Coulomb wave operator in parabolic coordinates is obtained. The resulting six-dimensional Green's function matrix is expressed as a convolution integral over separation constants.Comment: 14 pages, 2 figure

Complex-scaled ab initio QED approach to autoionizing states

Ab initio method based on a complex-scaling approach and aimed at a rigorous QED description of autoionizing states is worked out. The autoionizing-state binding energies are treated nonperturbatively in $\alpha Z$ and include all the many-electron QED contributions up to the second order. The higher-order electron correlation, nuclear recoil, and nuclear polarization effects are taken into account as well. The developed formalism is demonstrated on the $LL$ resonances in heliumlike argon and uranium. The most accurate theoretical predictions for the binding energies are obtained.Comment: 6 pages, 3 figure