A screened hydrogenic model with fine structure splitting

Smith, C.

doi:10.1016/j.hedp.2010.11.001

Cited by 9 publications

(12 citation statements)

References 15 publications

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“…1. Nevertheless, in order to compare them with other model different to FAC, in Table 9 we show the transition energies for the ground state of Ni-like Xe compared with experimental data measured by Badnell et al [47] obtained from the paper of Smith [22]. The NRSHM shows good agreement with experimental data and with those obtained from Smith's model, having errors lower than 2.2%.…”

Section: Transition Energiesmentioning

confidence: 54%

“…expressions (see appendices). We compare our results with the those obtained from FAC [30], GRASP [41], DFT DAVID code [38], and Smith's SHM model [22], As can be seen, theXa type values are closer to the calculations of DAVID code, while the HF type values agree better with GRASP. Thus, we can see that the differences among the numerical models is similar to that found between the NRSHM and any of them.…”

Section: Electron Binding Energiesmentioning

confidence: 61%

“…In fact, Perrot when reviewing the theoretical basis of the SHM [17], concludes that an empirical adjustment of the screening constants is always necessary to obtain good results, because of the crude approximation of using universal screening constants underlying the SHM model basis in which screening parameters do not depend on each atomic configuration. In spite of this, some authors have developed algorithms for ab initio determination of the screening constants, in both a non-relativistic [21] and in a relativistic framework [22].…”

Section: Introductionmentioning

confidence: 99%

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

Mendoza¹,

Rubiano²,

Gil³

et al. 2011

High Energy Density Physics

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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.

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Section: Transition Energiesmentioning

confidence: 54%

Section: Electron Binding Energiesmentioning

confidence: 61%

Section: Introductionmentioning

confidence: 99%

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

Mendoza¹,

Rubiano²,

Gil³

et al. 2011

High Energy Density Physics

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“…The numerical values of the parameters determined by least-squares analysis are shown in Equations (12) through (17). The G 1 and F 2 values have units of a.u.…”

Section: Resultsmentioning

confidence: 99%

Application of the Screened Hydrogenic Model to Light Atoms

Smithwick¹

2021

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The purpose of this work was to develop a Screened Hydrogenic Model (SHM) to accurately calculate the electron energies for light atoms and ions with up to ten electrons for atomic numbers up to 18. The total energy of an atom or ion was calculated with effective nuclear charges and screening parameters for each electron type (1s, 2s and 2p) within a specific electron configuration. Multiple energy states, centered at the total energy, were calculated for electron configurations that have Russell-Saunders coupling. The energy of each electron included its relativistic energy, E REL , but close overall agreement between the calculated and experimental energies of multi-electron configurations required that the one-electron expression for E REL be modified in a simple manner. In the present work, 98% of the 587 calculated energies for light atoms/ions have a relative error within ±0.1% of the corresponding experimental energies. The effective nuclear charges described in this work allow hydrogen-like wave functions to be defined for the electrons within a multi-electron configuration. The SHM, described in this work, is available for future calculations involving light atoms and ions.

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“…Since it is not simple to determine unambiguously which set of screening constants is the best, we have investigated the impact of different sets (see Refs. [45][46][47]). The two latter depend on principal n and orbital ℓ quantum numbers.…”

Section: Introductionmentioning

confidence: 99%

Simple electron-impact excitation cross-sections including plasma density effects

Pain,

Benredjem

2021

Preprint

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The modeling of non-local-thermodynamic-equilibrium plasmas is crucial for many aspects of high-energy-density physics. It often requires collisional-radiative models coupled with radiativehydrodynamics simulations. Therefore, there is a strong need for fast and as accurate as possible calculations of the cross-sections and rates of the different collisional and radiative processes. We present an analytical approach for the computation of the electron-impact excitation (EIE) cross-sections in the Plane Wave Born (PWB) approximation. The formalism relies on the screened hydrogenic model. The EIE cross-section is expressed in terms of integrals, involving spherical Bessel functions, which can be calculated analytically. In order to remedy the fact that the PWB approximation is not correct at low energy (near threshold), we consider different correcting factors (Elwert-Sommerfeld, Cowan-Robb, Kilcrease-Brookes). We also investigate the role of plasma density effects such as Coulomb screening and quantum degeneracy on the EIE rate. This requires to integrate the collision strength multiplied by the Fermi-Dirac Distribution and the Pauli blocking factor. We show that, using an analytical fit often used in collisional-radiative models, the EIE rate can be calculated accurately without any numerical integration, and compare our expression with a correction factor presented in a recent work.

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A screened hydrogenic model with fine structure splitting

Cited by 9 publications

References 15 publications

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

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

Application of the Screened Hydrogenic Model to Light Atoms

Simple electron-impact excitation cross-sections including plasma density effects

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