Relativistic Many-body Perturbation Theory Method Research Articles

Excitation energies, radiative and autoionization rates, dielectronic satellite lines, and dielectronic recombination rates for excited states of Rb-like W from Kr-like W

Energy levels, radiative transition probabilities, and autoionization rates for [Ni], [Ni] ( = 4–7), [Ni], ( = 4–7), [Ni] (n = 5–7), and [Ni] (n = 6–7) states in Rb-like tungsten (W37+) are calculated using the relativistic many-body perturbation theory method (RMBPT code) and the Hartree–Fock-relativistic method (COWAN code). Autoionizing levels above the [Ni] threshold are considered. It is found that configuration mixing among [Ni] and [Ni] plays an important role for all atomic characteristics. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the [Ni] (n = 4–7) singly excited states, as well as the [Ni], [Ni], [Ni], [Ni], (n = 4–6), and [Ni] doubly excited nonautoionizing states in Rb-like W37+ ion. Contributions from the [Ni] (n = 6–7), [Ni] (n = 5–6), and [Ni] (n = 6–7) doubly excited autoionizing states are evaluated numerically. The high-n state (with n up to 500) contributions are very important for high temperatures. These contributions are determined by using a scaling procedure. Synthetic dielectronic satellite spectra from Rb-like W are simulated in a broad spectral range from 8 to 70 Å. These calculations provide highly accurate values for a number of W37+ properties useful for a variety of applications including for fusion applications.

Relativistic calculations of dielectronic recombination and satellite lines of an Ar-like Ni ion

Dielectronic recombination (DR) plays an important role in understanding atomic processes and identifying spectra, including astrophysical and tokamak plasmas in particular. Because this process involves numerous singly- and doubly-excited autoionizing states, which merge with continuum states, it is challenging to calculate, and relativistic data for a lot of ions do not exist. This paper focuses on relativistic calculations of dielectronic recombination in Ar-like Ni and dielectronic satellite lines in K-like Ni. Specifically, energy levels, radiative transition probabilities and autoionization rates for the [Ne]3s23p53dnl (n = 4–7), [Ne]3s23p54l′nl (n = 4–7), [Ne]3s3p63dnl (n = 4–7), [Ne]3s3p64l′nl (n = 4–7), [Ne]3s23p55l′5l and [Ne]3s3p65l′5l states in K-like nickel (Ni9 +) are calculated by the Hartree–Fock relativistic method (Cowan code) and the relativistic many-body perturbation theory method (RMBPT code). In addition, these results are compared with atomic data from two more codes, HULLAC and FAC, as well as with the NIST data. DR rate coefficients are determined for the singly-excited [Ne]3s23p6nl,(n = 4–7), as well as non-autoionizing doubly-excited [Ne]3s23p53d2, [Ne]3s23p53d4l, [Ne]3s3p63d4s and [Ne]3s3p63d4p states. Contributions from the autoionizing doubly-excited states [Ne]3s23p53dnl and [Ne]3s3p63dnl (with n up to 500), which are very important for calculating total DR rates, are estimated. Synthetic dielectronic satellite spectra from K-shell Ni are simulated in a broad spectral range from 45 to 600 Å.

Excitation energies, radiative and autoionization rates, dielectronic satellite lines and dielectronic recombination rates for excited states of Ag-like W from Pd-like W

Energy levels, radiative transition probabilities and autoionization rates for [Kr]4d94fnl (n = 4–9), [Kr]4d95l′nl (n = 5–9) and [Kr]4d96l′nl (n = 6–7) states in Ag-like tungsten (W27 +) are calculated using the relativistic many-body perturbation theory method, the multiconfiguration relativistic Hebrew University Lawrence Livermore Atomic Code and the Hartree–Fock-relativistic method. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the singly excited [Kr]4d10nl (n = 4–9) states. The total DR rate coefficient is derived as a function of electron temperature. These atomic data are important in the modelling of N-shell radiation spectra of heavy ions generated in various collision as well as plasma experiments. The tungsten data are particularly important for fusion application.

Excitation energies, radiative and autoionization rates, dielectronic satellite lines and dielectronic recombination rates for excited states of Mg-like W from Na-like W

Energy levels, radiative transition probabilities and autoionization rates for 1s22s22p63l′nl (n = 3–13, l ⩽ n − 1), 1s22s22p64l′nl (n = 4–7, l ⩽ n − 1) and 1s22s22p53l′3l″nl (n = 3–4, l ⩽ n − 1) states in Mg-like tungsten (W62+) are calculated using the Hartree–Fock-relativistic method (COWAN code), the multiconfiguration relativistic Hebrew University Lawrence Atomic Code (HULLAC code) and the relativistic many-body perturbation theory method (RMBPT code). Autoionizing levels above the thresholds 1s22s22p63l and 1s22s22p64l are considered. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the first excited odd- and even-parity states. It is shown that the contribution of the highly excited states is very important for the calculation of total DR rates. Contributions to DR rate coefficients from the excited 1s22s22p63l′nl states with n ⩾ 14 and 1s22s22p64l′nl states with n ⩾ 8 and additionally from core-excited 1s22s22p53l′3l″nl states with n ⩾ 5 are estimated by extrapolation of all atomic parameters. The orbital angular momentum quantum number l distribution of the rate coefficients shows two peaks at l = 2 and l = 5. The total DR rate coefficient is derived as a function of electron temperature. The dielectronic satellite spectra of W62+ are important for L-shell diagnostic of very high-temperature laboratory plasmas such as future ITER plasmas.

Excitation energies, radiative and autoionization rates, dielectronic satellite lines, and dielectronic recombination rates for excited states of Na-like W from Ne-like W

Energy levels, radiative transition probabilities, and autoionization rates for 1 s 2 2 s 2 2 p 5 3 l ′ nl , 1 s 2 2 s 2 p 6 3 l ′ nl ( n = 3 – 7 , l ⩽ n - 1 ) and 1 s 2 2 s 2 2 p 5 4 l ′ nl , 1 s 2 2 s 2 p 6 4 l ′ nl ( n = 4 – 6 , l ⩽ n - 1 ) states in Na-like tungsten ( W 63 + ) are calculated. Cowan’s relativistic Hartree–Fock method, the relativistic multiconfiguration method implemented in the Hebrew University Lawrence Livermore Atomic Code, and the relativistic many-body perturbation theory method, are used. Autoionizing levels above the threshold 1 s 2 2 s 2 2 p 6 are considered. It is found that configuration mixing [ 3 sns + 3 pnp + 3 dnd ] , [ 3 snp + 3 pns + 3 pnd + 3 dnp ] plays an important role for all atomic characteristics. Also strong mixing between states with 2 s and 2 p holes ( 1 s 2 2 s 2 2 p 5 3 l 1 nl 2 + 1 s 2 2 s 2 p 6 3 l 3 nl 4 ) occurs. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the excited 1 s 2 2 s 2 2 p 6 nl ( n = 3 – 7 , l ⩽ n - 1 ) states. It is shown that the contribution of the highly excited states is very important for calculation of total DR rates. Contributions from the autoionizing states 1 s 2 2 s 2 2 p 5 3 l ′ nl , 1 s 2 2 s 2 p 6 3 l ′ nl ( n ⩾ 8 ) and 1 s 2 2 s 2 2 p 5 4 l ′ nl , 1 s 2 2 s 2 p 6 4 l ′ nl ( n ⩾ 7 ) to the DR rate coefficients are estimated by extrapolation of all atomic parameters. The orbital angular momentum ( l) distribution of the rate coefficients shows a peak at l = 2 . The total DR rate coefficient is derived as a function of electron temperature. The dielectronic satellite spectra of W 63 + are important for L-shell diagnostics of very high-temperature laboratory plasmas such as future ITER fusion plasmas.

Atomic data for dielectronic satellite lines and dielectronic recombination into Ne 5+

Energy levels, radiative transition probabilities, and autoionization rates for B-like neon (Ne 5+) including 1s 22s 2 nl, 1s 22s2p nl, and 1s 22p 2 nl ( n = 2–11 and l = 0–7) states were calculated using a multiconfigurational Hartree–Fock method (Cowan code) and a relativistic many-body perturbation theory method (RMPT) code. Autoionizing levels above three thresholds (1s 22s 2 1S, 1s 22s2p 3P, 1s 22s2p 1P) were considered. We find that configuration mixing (2s 2 nl + 2p 2 nl) plays an important role for all atomic characteristics. Branching ratios relative to the first threshold and the intensity factor were calculated for satellite lines and dielectronic recombination rate coefficients for the 190 odd-parity and 198 even-parity excited states. The dielectronic recombination rate coefficients including 1s 22s 2 nl, 1s 22s2p nl, and 1s 22p 2 nl ( n = 2–11 and l = 0–7) states were calculated. The contributions from the excited states higher than n = 11 were estimated by extrapolation of all atomic characteristics to derive the total dielectronic recombination rate coefficient. It is found that the distribution of the rate coefficients as a function of the orbital angular momentum quantum number shows a peak at l = 5. The total dielectronic recombination rate coefficient was derived as a function of electron temperature. The dielectronic satellite lines were also obtained. The state selective dielectronic recombination rate coefficients to excited states of B-like neon were obtained, which are useful for modeling Ne VI spectral lines in a recombining plasma.

Large-scale calculation of dielectronic recombination parameters for Mg-like Fe

Energy levels, radiative transition probabilities and autoionization rates for 1s22s22p63l′nl (n = 3–12, l ⩽ n − 1) and 1s22s22p64l′nl (n = 4–7, l ⩽ n − 1) states in Mg-like iron (Fe14+) are calculated by the Hartree–Fock-relativistic method (Cowan code) and the relativistic many-body perturbation theory method (RMBPT code). Autoionizing levels above three thresholds 1s22s22p63s, 1s22s22p63p and 1s22s22p63d are considered. It is found that configuration mixings [3sns + 3pnp + 3dnd] and [3snp + 3pns + 3pnd + 3dnp] play an important role for all atomic characteristics. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the excited 444 odd-parity and 419 even-parity states. It is shown that the contribution of the highly-excited states is very important for calculation of total DR rates. Contributions from the excited 1s22s22p63l′nl states with n ⩾ 12 and 1s22s22p64l′nl states with n ⩾ 7 to DR rate coefficients are estimated by extrapolation of all atomic parameters. The total DR rate coefficient is derived as a function of electron temperature.

Excitation energies, radiative and autoionization rates, dielectronic satellite lines, and dielectronic recombination rates to excited states for B-like oxygen

Energy levels, radiative transition probabilities, and autoionization rates for B-like oxygen (O 3+) including 1s 22s 2 nl, 1s 22s2p nl, and 1s 22p 2 nl ( n = 2–8, l ⩽ n − 1) states are calculated using the multiconfiguration interaction Cowan code and a relativistic many-body perturbation theory method (RMBPT) code. Autoionizing levels above three thresholds (1s 22s 2 1S, 1s 22s2p 3P, and 1s 22s2p 1P) are considered. Configuration mixing (2s 2 nl + 2p 2 nl) plays an important part in all of the atomic properties considered. Branching ratios relative to the first threshold and the intensity factor are calculated for satellite lines and dielectronic recombination rate coefficients for the excited 105 odd-parity and 94 even-parity states. The dielectronic recombination rate coefficients are calculated including 1s 22s 2 nl, 1s 22s2p nl, and 1s 22p 2 nl ( n = 2–8, l ⩽ n − 1) states. The contribution from the excited states higher than n = 8 are estimated by extrapolation of all atomic properties to derive the total dielectronic recombination rate coefficient. The orbital angular momentum quantum number distribution of the rate coefficients shows a peak at l = 5. The total dielectronic recombination rate coefficient is derived as a function of electron temperature and the dielectronic satellite lines are also obtained. The state selective dielectronic recombination rate coefficients to excited states of B-like oxygen are obtained, which are useful for modeling O IV spectral lines in a recombining plasma.

Strengths and weaknesses of relativistic atomic structure calculations

Among the relativistic atomic structure theories developed in the last two decades, two methods - multiconfiguration Dirac-Fock (MCDF) and relativistic many-body perturbation theory (RMBPT) - have extensively been applied to calculate spectroscopic properties of neutral atoms as well as highly charged ions. The strengths and weaknesses of these methods are discussed with some examples. The MCDF method is based on the shell structure familiar to atomic physicists, and hence intuitively easier to understand. On the other hand, the RMBPT method is more systematic in introducing correlation and relativistic corrections and logically simpler to include quantum electrodynamic (QED) corrections and higher order relativistic effects than the MCDF method. A recent development in extensive relativistic configuration interaction is also described.

Formula omitted] type silicon Schottky barriers : A. Radziszewski and T. Skrabka. Solid-St. Electron.28 (7) 707 (1985)

Energy levels, radiative transition probabilities, and autoionization rates for B-like neon (Ne5+) including 1s22s2nl, 1s22s2pnl, and 1s22p2nl (n = 2–11 and l = 0–7) states were calculated using a multiconfigurational Hartree–Fock method (Cowan code) and a relativistic many-body perturbation theory method (RMPT) code. Autoionizing levels above three thresholds (1s22s2 1S, 1s22s2p 3P, 1s22s2p 1P) were considered. We find that configuration mixing (2s2nl + 2p2nl) plays an important role for all atomic characteristics. Branching ratios relative to the first threshold and the intensity factor were calculated for satellite lines and dielectronic recombination rate coefficients for the 190 odd-parity and 198 even-parity excited states. The dielectronic recombination rate coefficients including 1s22s2nl, 1s22s2pnl, and 1s22p2nl (n = 2–11 and l = 0–7) states were calculated. The contributions from the excited states higher than n = 11 were estimated by extrapolation of all atomic characteristics to derive the total dielectronic recombination rate coefficient. It is found that the distribution of the rate coefficients as a function of the orbital angular momentum quantum number shows a peak at l = 5. The total dielectronic recombination rate coefficient was derived as a function of electron temperature. The dielectronic satellite lines were also obtained. The state selective dielectronic recombination rate coefficients to excited states of B-like neon were obtained, which are useful for modeling Ne VI spectral lines in a recombining plasma.