Fitting continuum wavefunctions with complex Gaussians: Computation of ionization cross sections

Area of Science:

• Atomic and Molecular Physics
• Computational Quantum Chemistry
• Quantum Scattering Theory

Background:

• Accurate representation of continuum states is crucial for describing ionization processes.
• Traditional methods often face challenges with numerical stability and convergence.
• Gaussian basis sets are widely used but typically applied to bound states.

Purpose of the Study:

• To develop and validate a nonlinear optimization method for fitting continuum states using complex Gaussian functions.
• To assess the numerical feasibility and convergence of the complex Gaussian approach.
• To demonstrate the advantages of complex Gaussian expansions over real ones for scattering problems.

Main Methods:

• Implementation of a full nonlinear optimization technique.
• Fitting continuum states with complex Gaussian functions.
• Application to Coulomb functions, atomic hydrogen photoionization, and electron impact ionization (first Born approximation).

Main Results:

• Numerical feasibility and convergence range of the complex Gaussian method were established.
• Complex Gaussian expansions showed superiority over real Gaussian expansions for continuum states.
• An all-Gaussian approach (complex for continuum, real for bound states) yielded analytical matrix elements.
• Efficient performance was demonstrated for one-center target ionization processes.

Conclusions:

• The proposed nonlinear optimization method with complex Gaussians provides an efficient and accurate way to represent continuum states.
• This all-Gaussian approach simplifies calculations for ionization processes, offering a robust benchmark.
• The findings pave the way for broader applications in atomic and molecular quantum scattering problems.