Plasma Confined Ground and Excited State Helium Atom: A Comparison Theorem Study Using Variational Monte Carlo and Lagrange Mesh Method

The energy eigenvalues of the ground state helium atom and lowest two excited states corresponding to the configurations 1s2s embedded in the plasma environment using Hulthén, Debye–Hückel and exponential cosine screened Coulomb model potentials are investigated within the variational Monte Carlo method, starting with the ultracompact trial wave functions in the form of generalized Hylleraas–Kinoshita functions and Guevara–Harris–Turbiner functions. The Lagrange mesh method calculations of energy are reported for the He atom in the ground and excited 1S and 3S states, which are in excellent agreement with the variational Monte Carlo results. Interesting relative ordering of eigenvalues are reported corresponding to the different screened Coulomb potentials in the He ground and excited electronic states, which are rationalized in terms of the comparison theorem of quantum mechanics.

A treecode based on barycentric Hermite interpolation for electrostatic particle interactions

A particle-cluster treecode based on barycentric Hermite interpolation is presented for fast summation of electrostatic particle interactions in 3D. The interpolation nodes are Chebyshev points of the 2nd kind in each cluster. It is noted that barycentric Hermite interpolation is scale-invariant in a certain sense that promotes the treecode’s efficiency. Numerical results for the Coulomb and screened Coulomb potentials show that the treecode run time scales like O(N log N), where N is the number of particles in the system. The advantage of the barycentric Hermite treecode is demonstrated in comparison with treecodes based on Taylor approximation and barycentric Lagrange interpolation.

Doubly-Excited States of Beryllium-Like Ions with Screened Coulomb Potentials

The screening effects of the interaction potentials on the lowest 1S doubly-excited states of beryllium-like ions were investigated by calculating the density of resonance states within the framework of the stabilization method. Two types of screened interaction potentials, namely static screened Coulomb potential and exponential cosine screened Coulomb potential, were taken into consideration. A model potential was used to describe the interaction between the core and outer electrons, and the Be-like ions were treated as being effectively three-body systems. Calculations were performed for Be and B+. It was possible to calculate the energy and width of one doubly-excited state of Be and four doubly-excited states of B+ lying above the 1s22p threshold. Significant changes were found to exist in the behaviour of the width with varying screening parameters. To the best of our knowledge, such an investigation on the doubly-excited states of Be-like ions under screened environments is the first reported calculation of this type in the literature.