Higher order expansion of Keldysh integral for hydrogen atom and molecular ion

Abstract

In this paper we provide a systematic method of finding the higher order asymptotic expansion of the Keldysh integral using the hydrogen atom as an example. Comparisons with exact numerical integration shows that the second-order correction improves the the first-order results significantly. We extend this method to molecular ionisation in H and calculate the total ionisation rate. The results are in good agreement with the exact solution of the time-dependent Schrödinger equation.

Keywords:

• strong field ionisation
• asymptotic expansion
• molecular ion
• residue theorem
• LCAO
• saddle point
• method of steepest descent

Acknowledgements

The authors thank NSERC for providing financial support and SHARCNET for providing computational time.