Hyperspherical Partial Wave Theory with Two-term Error Correction

TL;DR

This paper applies hyperspherical partial wave theory to electron-hydrogen ionization, introducing a two-term error correction method that improves the accuracy of SDCS calculations compared to benchmark results.

Contribution

The study develops a two-term error correction approach for hyperspherical partial wave calculations, enhancing the precision of T-matrix and SDCS results in electron-hydrogen ionization.

Findings

Two-term error correction significantly improves SDCS accuracy.

Fitted SDCS curves align well with benchmark data.

Error-corrected results outperform uncorrected calculations.

Abstract

Hyperspherical Partial Wave Theory has been applied to calculate T-matrix elements and Single Differential Cross-Section (SDCS) results for electron-hydrogen ionization process within Temkin-Poet model potential. We considered three different values of step length to compute the radial part of final state wave function. Numerical outcomes show that T-matrix elements and SDCS values depend on the step length h. Here, we have presented T-matrix elements and the corresponding SDCS results for 0.0075 a.u., 0.009 a.u. and 0.01 a.u. values of h and for 27.2eV, 40.8ev and 54.4eV impact energies. With the help of the calculated data for three different step lengths, we have been able to evaluate a two-term error function depending on the step length h. Finally, two-term error corrected T-matrix elements and the corresponding SDCS values have been computed. We fitted our two-term error corrected SDCS results by a suitable curve and compared with the benchmark results of Jones et al. [Phys. Rev. A, 66, 032717 (2002)]. Our fitted curves agree very well with the calculated results of Jones et al. and two-term error corrected SDCS results somewhere agree with the benchmark results. Two-term error corrected SDCS results are significantly better than the calculated SDCS results of different step lengths.