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Electron-electron correlation forms the basis of difficulties encountered in many-body physics. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in the correlation. In an effort to tackle the many-body problem, an empirically determined symmetry-dependent partition fraction for the electron-electron interaction energy between two interacting states of helium atom is suggested in this study. Using the partition fraction and the lowest-order approximation of the multipole series expansion of the electron-electron interaction, a simple parameter-free pseudopotential for a two-electron system is derived. The groundstate, singly and doubly excited state non-relativistic energies generated by the pseudopotential are in reasonable agreement with literature values., Comment: arXiv admin note: text overlap with arXiv:1708.04061

Electron-electron interactions and correlations form the basis of difficulties encountered in the theoretical solution of problems dealing with multi-electron systems. Accurate treatment of the electron-electron problem is likely to unravel some nice physical properties of matter embedded in the interaction. In an effort to tackle this many-body problem, a symmetry-dependent all electron potential generalised for an n-electron atom is suggested in this study. The symmetry dependence in the proposed potential hinges on an empirically determined angular momentum dependent partitioning fraction for the electron-electron interaction. With the potential, all atoms are treated in the same way regardless of whether they are open- or closed-shell using their system specific information. The non-relativistic groundstate ionisation potentials for atoms with up to 103 electrons generated using the all-electron potential are in reasonable agreement with the existing experimental and theoretical data. The effects of higher-order non-relativistic interactions as well as the finite nuclear mass of the atoms are also analysed., Comment: arXiv admin note: substantial text overlap with arXiv:1711.07645

As experimentalists explore new opportunities in strong field radiation offered by current generation light sources, new theoretical tools become inevitable in dealing with the challenging non-linear dynamics that come into play as a result of the increasing laser intensities and the shorter wavelengths. While many theoretical studies employ the electric dipole approximation for convenience reasons, in the strong-field regime the validity of this approximation is questionable. We have made a detailed comparison of the expansion of the retardation term, $e^{i\mathbf{k} \cdot \mathbf{r}}$ in both Taylor and Rayleigh series multipole approximations with the angle between the radial vector and the direction of propagation chosen arbitrarily to be $45^{\circ}$. It is verified in this paper that the Rayleigh plane-wave expansion provides a larger validity range in comparison to the widely used Taylor expansion. We also take note that the Taylor approximated spherical Bessel functions reproduce the lower limits of the regular spherical Bessel functions but deviates strongly in the asymptotic region. We conclude that the use of the Rayleigh plane-wave expansion provides the most accurate contribution of any given order of the multipole expansion. The discrepancy in the dipole and non-dipole photoelectron energy spectra as predicted by these approximations using short-wavelength intense laser pulses interacting with hydrogen atom in its ground state show the importance of the higher-order terms absent in the Taylor expansion.