Complete numerical solution of electron-hydrogen model collision problem above the ionization threshold

Area of Science:

• Atomic and Molecular Physics
• Quantum Mechanics
• Computational Chemistry

Background:

• The S-wave (Temkin-Poet) model simplifies electron-hydrogen collisions by neglecting angular momentum.
• Accurate calculation of scattering amplitudes, especially ionization, is crucial for understanding atomic collisions.
• Previous methods struggled with convergence for Coulomb three-body problems.

Purpose of the Study:

• To present benchmark results for electron-hydrogen collisions in the S-wave model.
• To demonstrate a novel method for achieving convergent ionization amplitudes.
• To provide accurate scattering data for comparison with other theoretical approaches.

Main Methods:

• Numerical integration of Schrodinger's equation.
• Application of correct asymptotic boundary conditions.
• Focus on the S-wave approximation, neglecting angular momentum.

Main Results:

• Complete scattering results (elastic, inelastic, ionization) obtained with 1% accuracy.
• Demonstrated convergence of ionization amplitudes using direct matching to asymptotic boundary conditions.
• Presented results for impact energies of 54.4 eV and 40.8 eV.

Conclusions:

• Direct matching to asymptotic boundary conditions successfully yields convergent ionization amplitudes for a Coulomb three-body problem.
• The S-wave model with accurate boundary conditions provides reliable benchmark data for electron-hydrogen scattering.
• The findings offer a validated computational approach for atomic collision studies.