Helium atom in a box: Doubly excited levels within theS-wave model

Abstract

A complete nonperturbative close-coupling solution of the helium atom in a box problem is presented by developing two numerical techniques. The first technique is the direct solution by diagonalization of the Hamiltonian, and the second is based on a constrained relaxation of the wave functions. A Feshbach projection operator of the direct solutions to the bound-continuum subspaces allows a comparison of the low-lying autoionization levels obtained in both methods. Time-dependent propagation of these doubly excited wave functions is analyzed, allowing the calculation and the visualization of the autoionization process. In this work, results are presented for the S-wave model in which the electrons are restricted to spherical states and all angular correlations have been eliminated.

Time-resolved resonant photoionization of He using a time-dependent Feshbach method with ultrashort laser pulses

“…For instance, it is interesting to study the coherent excitation and decay of metastable superexcited states using pump-probe laser pulses with time delays comparable in magnitude to autoionization lifetimes in order to trace the fast dynamics involved. The decay dynamics of doubly excited states in the helium atom has already been addressed using time-dependent close-coupling methods implemented in a numerical lattice [3][4][5]. Also, attosecond pump-probe laser schemes have been proposed to probe ultrafast electron motion in singly excited [6] and doubly excited states in helium [7].…”

A study of two-electron quantum dot spectrum using discrete variable representation method

“…Maybe the most common quantum dot with two interacting electrons is the two-dimensional isotropic harmonic potential. [38][39][40][41] However, many other models have been used, such as the spherical box with finite 42 and infinite [43][44][45][46] walls, the two-dimensional harmonic potential with anharmonic correction, 47 the one-dimensional, 48 square 49,50 and cubic 51,52 boxes with infinite walls, the ellipsoidal quantum dot, 53 the Gaussian confining potential, 54 the two-dimensional anisotropic harmonic potential, 55 and the three-dimensional isotropic [56][57][58][59][60] and anisotropic 61,62 potentials.…”

Spin and spatial dynamics in electron-impact scattering offS-wave He usingR-matrix-with-time-dependence theory

“…We estimate that this lack of access to an immediate 2s2s yield introduces an uncertainty of approximately 10% to the RMT 2s2s cross section. Previous studies have shown the theoretical timedependent description of autoionisation to be an interesting challenge [21][22][23]. We can identify such autoionisation dynamics within the RMT model of the scattering process.…”