Charlotte Froese Fischer and Ian Philip Grant were both eminent in the numerical treatment of atomic structure theory. How do they still guide future work in “my” research sector, experimental atomic spectroscopy and lifetime measurements, which uses fast ion beams and ion traps?
The field of matter wave interferometry is rapidly advancing on multiple frontiers [...]
A collection of short stories about Barry Irwin Schneider (1940–2024), to whom this Special Issue of Atoms is dedicated.
In scattering and tunnelling-to-continuum problems, the regular and irregular solution pairs to the one-particle radial Schrödinger equation follow various amplitude and phase difference conventions at infinity. The Milne transformation of the Schrödinger equation (a.k.a. the Phase-Amplitude Method) leads to a solution pair whose form inherently complies with scattering theory’s requirements of common amplitude and phase difference of π/2 at the r→∞ limit. On occasion, applications favoured the adoption of the reverse phase convention. In this work we present a formal framework that permits switching of the regular/irregular solution pairs between representations. To showcase the formalism, two exemplar potential curves are investigated: a repulsive Coulomb barrier and the Coulomb-Stark potential, the latter corresponding to the hydrogen atom in the presence of a static homogeneous electric field. Analysis of the results, assessment of the methodology and a discussion of possible extensions are also included. Ultimately, this work shows that it is the regular solution that acts as the thread that binds together the different representations.
An algorithm for large-scale correlated calculations on atoms is presented that significantly reduces the scaling of these calculations with the number of single-particle functions used to construct the N-particle states. The reduction is provided in the stage in which the Hamiltonian matrix is contracted with the coefficients or amplitudes of the basis states in an iterative procedure such as the Davidson method. The algorithm relies on the representation of the radial one-particle functions on a grid, and it makes use of the multipole expansion of the electron–electron interaction in a sequence of transformations on the spinors, coefficients, and potentials. It also uses prototyping for the angular integrals and evaluation of recoupling coefficients for the configuration state functions (CSFs) separately rather than for pairs of CSFs. The scaling is verified with calculations on two-electron atoms and analyzed in terms of the number of operations required for each stage of both the proposed algorithm and the conventional methods.
