A new set of relativistic screening constants for the screened hydrogenic model

Abstract

Keywords:Screening constants Screened hydrogenic model A new Relativistic Screened Hydrogenic Model has been developed to calculate atomic data needed to compute the optical and thermodynamic properties of high energy density plasmas. The model is based on a new set of universal screening constants, including nij-splitting that has been obtained by fitting to a large database of ionization potentials and excitation energies. This database was built with energies compiled from the National Institute of Standards and Technology (NIST) database of experimental atomic energy levels, and energies calculated with the Flexible Atomic Code (FAC). The screening constants have been computed up to the 5p¡/2 subshell using a Genetic Algorithm technique with an objective function designed to minimize both the relative error and the maximum error. To select the best set of screening constants some additional physical criteria has been applied, which are based on the reproduction of the filling order of the shells and on obtaining the best ground state configuration. A statistical error analysis has been performed to test the model, which indicated that approximately 88% of the data lie within a ±10% error interval. We validate the model by comparing the results with ionization energies, transition energies, and wave functions computed using sophisticated self-consistent codes and experimental data.

Relativistic screened hydrogenic radial integrals

“…Using this method and analytical screened hydrogenic wave functions, they proposed a SHM model with nlj splitting which was strictly valid for the ground states of He-like to U-like ions. Recently, we have developed a New Relativistic Screened Hydrogenic Model (NRSHM) based on a new set of universal screening constants [22], obtained by fitting to a database containing 61,356 high quality atomic data. It was conceived to deal with ground and excited configurations of medium and highly ionized atoms and in this paper we will make use of it to compute the screened charges Q^ and Q¡¿.…”

“…This model calculates the energy levels of the multielectron atom by using the analytical expressions of the hydrogenic atom computed with appropriate screened nuclear charges [19][20][21][22][23][24][25]. The SHM used in the average ion model context provides electronic populations with good accuracy and it also allows computing the opacity, the emissivity and the equation of state of plasma easily.…”

Modelling of spectral properties and population kinetics studies of inertial fusion and laboratory-astrophysical plasmas

“…The code was developed within the framework of an average atom model. The needed atomic data are computed using a relativistic screened hydrogenic model based on a new set of universal screening constants including j-splitting [5]. These screening constants were obtained from the fit to a wide database of high-quality atomic energies, ionization potentials and transition energies taken from [6,7].…”

The combined use of screening and quantum defect parameters in the study of ionized atoms

“…In particular, in the last years, several works have appeared in this Journal, both for non-relativistic and relativistic configurations ([3e6]). In this work, we do not repeat the advantages of the SHM but we treat a matter explicitly mentioned only by Mendoza et al [6] although well known for many practitioners of this approximation: for neutrals and low-ionization degrees, the radial hydrogenic wavefunctions of the valence electrons are very different from HartreeeFock (HF) calculations. 1 Although the author and the readers of this journal are not, in general, interested in low ionization degrees, the failure of the SHM in this range leaves a bitter taste to the atomic physicists.…”

“…All our data about energy values were computed with the published constants from Mendoza et al [6] with no use of empirical data.…”