Time-Dependent Treatment of Electron-Hydrogen Scattering for Higher Angular Momenta (l>0)


The time-dependent approach to electron-atom scattering is emerging as an alternative to more conventional methods of treating atomic collisions. Solving the time-dependent Schrödinger equation directly has several very attractive features including a completely nonperturbative solution, dense representation of the nonphysical positive energy states, circumvention of the need to explicitly impose boundary conditions for ionization, and the convenience of being able to “watch” the electronic probability density evolve though the collision. Two principal approaches have so far been applied to treat electron-atom scattering, namely, the time-dependent close couping (TDCC) method and what we refer to as the time-dependent Hylleraas (TDH) method. The TDCC method solves coupled equations with two variables within a truncated infinite sum over individual angular momenta for each total angular momentum L of the system. In contrast, the TDH method avoids an infinite summation over the angular momenta of the individual electrons at the expense of solving a coupled equation with three variables for each L. The TDH method has previously been used for L=0 only. An important question, therefore, concerns whether the TDH method would represent a numerical advantage over the TDCC method for higher L values. This issue is investigated in this paper.



Keywords and Phrases

Approximation theory; Eigenvalues and eigenfunctions; Electron energy levels; Electron transitions; Hydrogen; Impact ionization; Integration; Polynomials; Probability density function; Quantum theory; Wave equations; Angular momentums; Quantum collision processes; Wave functions; Wave packets; Electron scattering

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