Multichannel continuum states by a least-squares approach in a spline basis: application to He and H^-photoionization

Abstract

A recently proposed algorithm for the determination of the continuum wavefunction employing a 8-spline basis set expansion and a least-squares approach is extended to a full multichannel formulation employing a general close coupling expansion of the continuum wavefunction. Photoionization of the He atom up to the n = 4 threshold and Uup to the n = 3 threshold are described with a pure close coupling wavefunction (16 and 9 channels respectively), and an accurate full CI expansion for the ground state. Excellent agreement with previous accurate calculations is obtained for total and partial cross sections, resonance parameters and angular distributions. For He a nine-channel wavefunction allows photoionization to be described up to 2 keV. Modification of the boundary conditions to describe long Rydberg series is successfully tested, The proposed algorithm appears to be a general and flexible approach for the description of multichannel continuum wave. functions by basis set expansion.

R-matrix approach with proper boundary conditions for dissipative and nondissipative collision processes

“…This value of Z eff is somewhat smaller than the value 27/16 ≈ 1.69 which minimizes the ground-state energy of He in a crude independent-particle model; the smaller value is plausible because when the active electron is close to the nucleus the spectator electron is more fully screened from the nucleus. With the optical potential included, we estimate the ratio σ 2p+2s /σ 1s to be 0.578 at 250 eV compared to the values 0.509 and 0.566, respectively, predicted by Decleva et al [13] and measured by Wehlitz et al [14] Cross sections for photoionization to the 1s and to the n = 2 states of He + are shown in Figs. 1 and 2 for photon energies from 80 to 250 eV.…”

“…The probability that the spectator electron relaxes into the 1s, rather than the 2s, state of He + is approximately | 1s,Z|1s,Z eff | 2 = 2 6 (ZZ eff ) 3 (Z + Z eff ) 6 . [13]; circles, experimental data from Bizau and Wuilleumier [15].…”

Integration by Cell Algorithm for Slater Integrals in a Spline Basis

“…A different type of grid can easily be used in different regions. In atomic physics calculation, a general grid for both bound and continuum states for arbitrary nuclear charges was introduced by Fischer [7,20] and subsequently applied successfully in the calculation of photoionization [12,21]. In the grid definition, four different parameters are introduced.…”

“…Because of the apparently large number of numerical operations needed to evaluate this integral accurately, they finally concluded that B-splines were not suitable for atomic structure calculations. However, there has recently been a renewed interest in the use of B-splines in complex atomic systems: Bottcher and Strayer [2] applied the B-splines to time-dependent problems, Johnson and co-workers to many-body perturbation theory [3][4][5], Fischer and co-workers [6][7][8][9] to Hartree-Fock calculations and continuum problems, Hansen and co-workers to orthogonal operators and Rydbergy series [10,11], Decleva and co-workers [12][13][14] to multichannel continuum problems, and van der Hart to R-matrix theory [15]. More detailed discussions can be found in a recent review by Sapirstein and Johnson [16].…”

Multiple excitation in photoionization using B-splines

“…Froese Fischer and her co-workers (Froese Fischer and Idrees, 1990;Brage et al, 1992;) had independently applied the B-splines to the continuum with success. Other earlier works employing nonrelativistic B-spline-based orbitals include calculations by Chang (1990Chang ( , 1993a, Tang et al (1990), Wang (1991a, 1991b), Tang (1991, 1992), Chen and Hsue (1992), Chen (1993), van der Hart and Hansen (1992a, 1992b, Chang and Zhen (1993), Chang and Zhu (1993), Tang and Bachau (1993), Cormier et al (1993), Xi et al (1993), and Decleva et al (1994). Extension to the relativistic conÞguration-interaction procedure was also carried out by Chen et al (1993).…”