Solving close-coupling equations in momentum space without singularities for charged targets

The analytical treatment of the Green’s function in the convergent close-coupling method (Bray et al., 2016) has been extended to charged targets. Furthermore, we show that this approach allows for calculation of cross sections at zero channel energy. For neutral targets this means the electron scattering length may be obtained from a single calculation with zero incident energy. For charged targets the non-zero excitation cross sections at thresholds can also be calculated by simply setting the incident energy to the exact threshold value. These features are demonstrated by considering electron scattering on H and He+This work was supported by resources provided by the Pawsey Supercomputing Centre with funding from the Australian Research Council, Grant DP160102106. ASK acknowledges partial support from the US National Science Foundation under Award No. PHY1415656

Strong field sub-femtosecond electronic processes

This thesis is comprised of theoretical investigations on several different strong field and/or sub-femtosecond processes resulting from the interaction between atoms and short laser pulses. Said theory is based on the numeric solution of the time-dependent Schro\"odinger equation (TDSE) by high performance computing methods. Specifically, Chapter 2 examines the Attoclock, a strong field problem designed to clock the escape of an electron as it tunnel ionises. In which, we present both the result of a collaboration yielding the first agreement between ab initio theory and experiment [Sainadh et al., Nature 568, 75 (2019)], and a straightforward model based on classical scattering for an idealised version of the problem [Bray et al., Phys. Rev. Lett. 121, 123201 (2018)]. Chapter 3 considers reconstruction of attosecond beating by interference of two-colour transitions (RABBITT) in which an attosecond pulse train 'pump' and infrared pulse 'probe' simultaneously impinge on a target with a precisely controlled delay between them. The oscillating phase of the ionisation probability as a function of this delay yields the angular anisotropy parameter and Wigner time delay for its corresponding energy. We calculate and present these quantities for the valence p-shell of various noble gas atoms [Bray et al., Phys. Rev. A 97, 063404 (2018)] and additionally examine the effect of an encapsulating C60 fullerene cage on the 4d shell of Xe [Bray et al., Phys. Rev. A 98, 043427 (2018)]. In Chapter 4 we look at the effect of electron correlation on high harmonic generation (HHG), the process by which attosecond pulses are produced, from one and two colour fields. We perform single active electron calculations for the 5p shell of Xe and model the correlation as an enhancement factor taken as the ratio between photoionisation cross-sections computed with and without said correlations. Doing so we report solid agreement with experimentally observed spectra for both field setups [Bray et al., Phys. Rev. A 100, 013404 (2019)]. Finally, Chapter 5 investigates the non-dipole problem of the state resolved strong field acceleration of neutral species. This requires the solution of the coupled two-body TDSE of the centre of mass and reduced mass electron, each with three degrees of freedom, in a non-spatially uniform field. Accordingly it necessitates its own dedicated solution method. Developing and applying said method to atomic hydrogen we compute an acceleration for each state consistent with experimental observation [Bray et al., Phys. Rev. Lett., Submitted]. Additionally our method allows us, via comparison with classical expressions, to derive the time at which each excited state was produced and, by similar means, an effective polarisibility for the ground state. Most interestingly this latter value is of opposite sign to the typical +9/2, providing an unambiguous signature of having entered the Kramers-Henneberger regime

Solving close-coupling equations in momentum space without singularities

Solving the close-coupling equations for electron–atom scattering in momentum space involves the solution of coupled integral equations, which contain principal value singularities. These can be accurately treated numerically using an on-shell subtraction technique. Here we show how the singularities may be taken into account analytically, leading to an alternative approach to the solution of the integral equations. The robustness of the method is demonstrated by considering the S-wave model of e-H scattering across eight orders of magnitude of incident energies

Solving close-coupling equations in momentum space without singularities II

The implementation of the convergent close-coupling method, whereby the principal-value singularity is treated analytically (Bray et al., 2015), has been extended to non-zero angular momenta. Its utility is demonstrated through application to proton scattering on excited states of positronium at incident energies spanning six orders of magnitude. It is shown that the analytic treatment is necessary in the case of highly excited positronium states

Solving close-coupling equations in momentum space without singularities for charged targets

The analytical treatment of the Green's function in the convergent close-coupling method (Bray et al., 2016) has been extended to charged targets. Furthermore, we show that this approach allows for calculation of cross sections at zero channel energy. For neutral targets this means the electron scattering length may be obtained from a single calculation with zero incident energy. For charged targets the non-zero excitation cross sections at thresholds can also be calculated by simply setting the incident energy to the exact threshold value. These features are demonstrated by considering electron scattering on H and He+