Condensed Matter Physics Seminar

A semi-classical treatment invoking the electric-dipole approximation is a common starting point for a theoretical description of light–matter interactions. The latter approximation amounts to assuming that the wavelength of the electromagnetic field is long compared to the spatial extension of the molecular system such that the molecule effectively sees a uniform electric field. Formally it corresponds to retaining only the zeroth-order term of an expansion of the interaction operator in orders of the length of the wave vector. While this is often justifiable at low intensities in the optical range, the availability of high-energy X-ray photons and intense laser pulses motivates investigations into the effects of going beyond this simplification.In general, methods for going beyond the electric-dipole approximation have been based on multipole expansions of the minimal coupling light-matter interaction operator which, in truncated form, may introduce unphysical gauge-origin dependence into the molecular properties. This is particularly problematic for molecular systems where no natural choice of gauge origin exists. In a seminal paper, Bernadotte et al. presented an approach for the calculation of origin-independent intensities within the non-relativistic framework, beyond the electric dipole approximation, by truncating the oscillator strength, rather than the interaction operator, in orders of the wave vector. However, Lestrange et al. found that inclusion of the second-order oscillator strength of the electric-dipole allowed ligand K-edge transition of TiCl4 made the total oscillator strength negative.To avoid the above issues, we proposed using the full semi-classical light–matter interaction operator in the context of linear absorption spectroscopy in the non-relativistic regime. Our approach was next extended to the relativistic regime as well as to circularly polarized light. The relativistic extension not only has wider applicability, but is much simpler ! Our implementation in DIRAC features the full light-matter interaction, but also the multipole expansion to arbitrary order, including rotational averaging. This places us in the unique position of being able to investigate the convergence of the latter expansion.