Intermediate Coupling Calculations Research Articles

Effective collision strengths for excitation and de-excitation of nebular [O iii] optical and infrared lines with κ distributed electron energies

We present effective collision strengths for electron excitation and de-excitation of the ten forbidden transitions between the five lowest energy levels of the astronomically abundant doubly-ionised oxygen ion, O^{2+}. The raw collision strength data were obtained from an R-matrix intermediate coupling calculation using the Breit-Pauli relativistic approximation published previously by the authors. The effective collision strengths were calculated with kappa-distributed electron energies and are tabulated as a function of the electron temperature and kappa.

Theoretical Stark widths and shifts of spectral lines of 2p5nf and 2p55g configurations of Mg III

In this paper, we report theoretical Stark widths and shifts calculated using the Griem semi-empirical approach, which corresponds to 111 spectral lines of Mg III. The values of these Stark broadening parameters of spectral lines that arise from levels of 2p5nf and 2p55g configurations of Mg III are presented in the literature for the first time. The aim of this work is to provide values to estimate the electron density of plasma Mg III in astrophysics and industrial applications. The data are presented for the temperatures T = 0.5–10.0 (104 K) and for an electron density of 1017 cm−3. The matrix of elements used in these calculations has been determined from 23 configurations of Mg III: 2s22p6, 2s22p53p, 2s22p54p, 2s22p54f and 2s22p55f for the even parity and 2s22p5ns (n = 3–6), 2s22p5nd (n = 3–9), 2s22p55g and 2s2p6np (n = 3–8) for the odd parity. For the intermediate coupling calculations, we use the standard method of least square fitting from experimental energy levels by means of Cowan’s computer code. Lines with wavelengths of 134.6460, 135.2800, 189.0380, 190.0043, 192.8424, 408.2939 and 409.4375 nm have high probabilities and also have high values of broadening. Therefore, these lines can be used in some applications. A common regularity for the Stark width of the 189.038 nm spectral line of Mg III is discussed.

Theoretical Stark broadening parameters for spectral lines arising from the 2p5ns, 2p5np and 2p5nd electronic configurations of Mg iii

In the present work we report theoretical Stark widths and shifts calculated using the Griem semi-empirical approach, corresponding to 237 spectral lines of Mg iii. Data are presented for an electron density of 1017 cm−3 and temperatures T = 0.5–10.0 (104K). The matrix elements used in these calculations have been determined from 23 configurations of Mg iii: 2s22p6, 2s22p53p, 2s22p54p, 2s22p54f and 2s22p55f for even parity and 2s22p5ns (n = 3–6), 2s22p5nd (n = 3–9), 2s22p55g and 2s2p6np (n = 3–8) for odd parity. For the intermediate coupling (IC) calculations, we use the standard method of least-squares fitting from experimental energy levels by means of the Cowan computer code. Also, in order to test the matrix elements used in our calculations, we present calculated values of 70 transition probabilities of Mg iii spectral lines and 14 calculated values of radiative lifetimes of Mg iii levels. There is good agreement between our calculations and experimental radiative lifetimes. Spectral lines of Mg iii are relevant in astrophysics and also play an important role in the spectral analysis of laboratory plasma. Theoretical trends of the Stark broadening parameter versus the temperature for relevant lines are presented. No values of Stark parameters can be found in the bibliography.

Magnetic dipole and electric quadrupole transitions in the trivalent lanthanide series: Calculated emission rates and oscillator strengths

Given growing interest in optical-frequency magnetic dipole transitions, we use intermediate coupling calculations to identify strong magnetic dipole emission lines that are well suited for experimental study. The energy levels for all trivalent lanthanide ions in the 4fn configuration are calculated using a detailed free ion Hamiltonian, including electrostatic and spin-orbit terms as well as two-body, three-body, spin-spin, spin-other-orbit, and electrostatically correlated spin-orbit interactions. These free ion energy levels and eigenstates are then used to calculate the oscillator strengths for all ground-state magnetic dipole absorption lines and the spontaneous emission rates for all magnetic dipole emission lines including transitions between excited states. A large number of strong magnetic dipole transitions are predicted throughout the visible and near-infrared spectrum, including many at longer wavelengths that would be ideal for experimental investigation of magnetic light-matter interactions with optical metamaterials and plasmonic antennas.

Magnetic and electrical properties of(Pu,Lu)Pd3

We present measurements of the magnetic susceptibility, heat capacity and electrical resistivity of Pu$_{1-x}$Lu$_x$Pd$_3$, with $x$=0, 0.1, 0.2, 0.5, 0.8 and 1. PuPd$_3$ is an antiferromagnetic heavy fermion compound with $T_N=24$~K. With increasing Lu doping, both the Kondo and RKKY interaction strengths fall, as judged by the Sommerfeld coefficient $\gamma$ and N\'eel temperature $T_N$. Fits to a crystal field model of the resistivity also support these conclusions. The paramagnetic effective moment $\mu_{\mathrm{eff}}$ increases with Lu dilution, indicating a decrease in the Kondo screening. In the highly dilute limit, $\mu_{\mathrm{eff}}$ approaches the value predicted by intermediate coupling calculations. In conjunction with an observed Schottky peak at $\sim$60~K in the magnetic heat capacity, corresponding to a crystal field splitting of $\sim$12~meV, a mean-field intermediate coupling model with nearest neighbour interactions has been developed.

Dielectronic recombination data for dynamic finite-density plasmas

We have calculated total and final-state resolved partial dielectronic recombination (DR) rate coefficients for 32 H-like ions: He+ through Zn29+ plus Kr35+, Mo41+ and Xe53+. Breit–Pauli intermediate coupling calculations have been carried-out which allow for l-mixing within the He-like autoionizing complex. We discuss the comparison of these results with those of other workers, and with experiment. Fitting coefficients which describe the total DR rate coefficients are presented in this paper. A full set of partial results can be accessed from the Atomic Data and Analysis Structure (ADAS) database or from the Oak Ridge Controlled Fusion Atomic Data Center under http://www-cfadc.phy.ornl.gov/data_and_codes.

Electron-impact excitation of neon: a pseudo-state convergence study

A number of convergent close-coupling and R-matrix with pseudo-state (RMPS) calculations for H-like, He-like, Li-like and Be-like ions have demonstrated that coupling to the target continuum can have large effects on the electron-impact excitation cross sections of neutral and low-charge species. However, no one has yet attempted such advanced calculations on a system as complex as neutral neon. We report on a series of RMPS calculations of electron-impact excitation of Ne using recently developed parallel Breit–Pauli R-matrix programs. Our largest calculation included 235 spectroscopic and pseudo-state levels in the close-coupling expansion of the target. Although the results clearly reveal the importance of coupling to the target continuum in this atom, the pseudo-state expansion is not yet sufficiently complete to provide reliable cross sections for energies above the ionization limit. However, this is the largest intermediate-coupling calculation that can be performed with present computer resources. Thus, we have also carried out a series of RMPS calculations in LS coupling with different pseudo-state expansions. Comparisons of these results have allowed us to determine the approximate size of the pseudo-state expansion required to achieve convergence in future intermediate-coupling calculations for neon.

Determination of the $\ion{Ni}{xviii}$ plasma recombination rate coefficient

The electron-ion recombination and electron-impact ionization of several astrophysically abundant C, N, O, and Ni ions have been investigated using the synchrotron storage ring CRYRING. The recombination rate coefficients predominanty used in the analyses of emission line spectra and for ionization balance calculations are determined from isoelectronic fits and extrapolations of theoretical and limited experimental results available from the literature. The rate coefficients reported by various authors differ by an order of magnitude for various ion species. For low temperature plasmas(<104 K), the available information on resonant recombination rate coefficients is even more limitied and, unfortunately, most available data has been determined from LS coupling calculations, which can have adverse effects on recombination rates due to the mistreatment of autoionizing states. For ions of C, N, and O, the production of metastable states complicates the experimental rate coefficient determinations. Some attempts have been made in this work to utilize both recombination and electron-impact ionization in estimating the metastable ion beam fractions present. Other metastable fractions have been determined by comparing the experimental recombination spectra to intermediate coupling calculations. Some of the absolute recombination rate coefficients reported in this work are given for the first time while many others vastly improve the spectral resolution of previous experiments, allowing for a more detailed study of the low energy resonances which contribute to the resonant recombination rate coefficient at low plasma electron temperatures. This increased resolution has also lead to the observation of trielectronic recombination resonances which greatly influence low temperature recombinaion rates in some ions.

First experimental investigation of the KLL Auger spectrum of Ge ( Z=32)

The KLL Auger spectrum of 73Ge from the electron capture decay of 73As was measured with 7 eV instrumental resolution using a combined electrostatic spectrometer and a source prepared by a gas-chemical method. The energies and relative intensities of all the nine resolved KLL lines were precisely determined. A rather poor agreement was found between the measured KLL transition energies and predictions of the widely used semiempirical calculations. Our relative KLL transition intensities agree only with results of the relativistic calculations in intermediate coupling with configuration interaction. The predicted influence of the relativistic effects on the KL 1L 2( 3P 0) transition rate was also proven.

Core-level magnetic circular dichroism as a probe for electron-correlation effects

Abstract We show how the spectral structure of the magnetic circular dichroism (MCD) in core-level spectroscopy can be analysed using angular momentum algebra. The results are supported by full-multiplet calculations in intermediate coupling, which for localized materials are in very good agreement with the experimental results. To demonstrate the general applicability we analyse a wide variety of systems. For didactical reasons we start off with the photoemission from an l shell and the spin–orbit split core j levels using a one-particle model, followed by the more realistic examples of rare earths 4f photoemission from an incompletely filled shell and N 4,5 X-ray absorption as the intermediate state in resonant photoemission. This gives a clear indication of the restrictions imposed by the one-particle model. We show that even for itinerant metals, such as nickel and iron, the 2p photoemission spectra cannot be explained using a one-particle model. Recent experimental results for the Ni 2p photoemission of nickel metal show that inter-configurational mixing has to be taken into account in order to understand the detailed structure of the MCD. Apart from its invaluable use to quantify the ground-state spin and orbital magnetic moments, MCD therefore also provides a powerful tool to study—in an element-specific way—the electron-correlation effects arising in a large variety of materials.

Measurements of Spectral Line Strengths Within some CI Multiplets Belonging to the 3p–3d and 3p–4s Transition Arrays

With a high-current wall-stabilized arc, operated in helium with small admixtures of CO2, relative line strengths for some prominent infrared multiplets of neutral carbon have been measured. The results are analyzed in conjunction with previously obtained experimental data in the visible and near infrared region of the spectrum. Our experimental results are compared with those resulting from the Russell-Saunders coupling scheme and with recent sophisticated intermediate coupling calculations. The results of this paper may be helpful for the improvement of atomic structure codes used for line strength calculations. The determined relative line strengths may also be useful in astrophysical applications.

An experimental investigation of some KLL and L3MM Auger transitions for Z=58, 59, and 61:

Abstract The KL1L2 Auger doublet of 14059Pr and the KLL Auger spectrum of 14561Pm from the electron capture decay of 140Nd and 145Sm, respectively, have been measured with high instrumental resolutions using a combined electrostatic spectrometer and sources prepared by a modified Langmuir–Blodgett method. An exceptional agreement of the determined KL1L2(3P0)/(1P1) intensity ratios of 0.42(2) and 0.45(1) for 140Pr and 145Pm, respectively, with the respective calculated values of 0.419 and 0.450 has proved the predicted strong influence of the relativistic effects on the KL1L2(3P0) transition intensity. While the measured relative intensities of the KLL transitions in 145Pm were found to agree well with the relativistic intermediate coupling calculations, the measured relative energies deviate from results of the widely used semi-empirical calculations. A doublet structure of the KL2L3(1D2) line of 145Pm with a splitting of 18.3(6) eV has been observed. We made an assumption that this structure originates in two different K shell excitation processes. The measured absolute energies of 28 397(3), 29 423.1(26), and 31 542.9(15) eV for the KL2L3 transition in 140Ce, 140Pr, and 145Pm, respectively, were found to be higher by about 20 eV than the semi-empirical values. The most intense L3MM line groups of 145Pm have also been measured but not evaluated. The absolute energy of the L3M4M5(1G4) transition has been determined to be 4342.6(16) eV. The energy of the M1 61.2 keV nuclear transition in 145Pm has been improved to be 61 226.5(17) eV using the measured energy of 16 042.5(15) eV of the K-61.2 conversion line. Values of 19.2(5) and 25.3(9) eV were determined for natural widths of the K shell and KL2L3 transition of 145Pm, respectively.

Large-scale Breit-Pauli R-matrix Calculations for Transition Probabilities of Fe V

Ab initio theoretical calculations are reported for the electric (E1) dipole allowed and intercombination fine structure transitions in Fe V using the Breit–Pauli R-matrix (BPRM) method. We obtain 3865 bound fine structure levels of Fe V and 1.46 × 106 oscillator strengths, Einstein A-coefficients and line strengths. In addition to the relativistic effects, the intermediate coupling calculations include extensive electron correlation effects that represent the complex configuration interaction (CI). For bound-bound transitions the BPRM method, based on atomic collision theory, entails the computation of the CI wavefunctions of the atomic system as an (electron+target ion) complex. The target ion Fe VI is represented by an eigenfunction expansion of 19 fine structure levels dominated by the spectroscopic configuration 3d3, and a number of correlation configurations. Fe V bound levels are obtained with angular and spin symmetries SLπ and Jπ of the (e + Fe VI) system such that 2S + 1 = 5,3,1, L ≤ 10, J ≤ 8. The bound levels are obtained as solutions of the Breit-Pauli (e + ion) Hamiltonian for each Jπ, and are designated according to the ‘collision’ channel quantum numbers. A major task has been the identification of these large number of bound fine structure levels in terms of standard spectroscopic designations. A new scheme, based on the analysis of quantum defects and channel wavefunctions, has been developed. The identification scheme aims particularly to determine the completeness of the results in terms of all possible bound levels with n ≤ 10, l ≤ n - 1, for applications to analysis of experimental measurements and plasma modeling. Sample results are presented and the accuracy of the results is discussed. A comparison of the dipole length and velocity oscillator strengths is presented, indicating an uncertainty of 10–20% for most transitions.

Calculation of dielectronic recombination rate coefficients for hydrogen-like titanium, chromium, and nickel

Dielectronic recombination (DR) rate coefficients are calculated for hydrogen-like Ti, Cr, and Ni at plasma temperatures 0.1–10 keV. The DR processes considered here are of the type 1 s+ εl→(2 ln 1 l 1)→1 sn 2 l 2+ γ. Explicit intermediate coupling calculations with configuration interactions have been performed for all intermediate resonance states with n=2–8. The 1/ n 3 scaling was employed to estimate the DR rate coefficients for n>8. The total DR rate coefficients have been obtained by summing over all partial DR rates. We find that the 1/ n 3 scaling law underestimates the DR rates summed over all states of each n. The present calculation yields significantly larger total DR rates for hydrogen-like ions compared to previous calculations reported in the literature.

Precise measurement of the KLL and KLX Auger spectra of cadmium from the EC-decay of 111In

Abstract The KLL and KLX Auger spectra of Cd from the EC-decay of 111 In have been analyzed with the 7 eV instrumental resolution using a combined electrostatic spectrometer and a source prepared by a modified Langmuir–Blodgett method. Energies and relative intensities of all the nine well resolved KLL lines have been precisely determined. While the latter quantities were found to be in very good agreement with the relativistic intermediate coupling calculations, the former ones deviate from results of the widely used semi-empirical calculations especially in the case of the absolute energies. The predicted strong influence of the relativistic effects on the KL 1 L 2 ( 3 P 0 ) transition intensity has been proved. Most of the main KLX Auger lines have been well separated and their complex structures have been observed. Accurate energies and intensities obtained for these lines have been compared with results of calculations. The intermediate coupling splitting of the KL 2 L 2 and KL 3 L 3 lines have been revealed. The KLX/KLL, KLN(O)/KLM, and KXY/KLL group intensity ratios have also been determined. A conclusion is made that further finer theoretical investigation on the complex interaction mechanism for two inner-shell vacancies is still very much needed.

Magnetic circular dichroism inTb 3d→4fresonant photoemission

We present an elegant method to calculate the magnetic circular dichroism in the resonant photoemission decay of lanthanides. By recoupling the angular momenta we obtain fundamental spectra which require only the reduced matrix elements. The full multiplet calculations in intermediate coupling using the t-matrix approach are compared to new experimental results for the Tb $3\stackrel{\ensuremath{\rightarrow}}{d}4f$ resonant photoemission taken at high-energy resolution. The agreement for the ${M}_{4,5}$ absorption structures as well as for the $4f$ photoemission is remarkably good. Angular momentum coupling plays an important role in the magnetic circular dichroism (MCD). As a rule we find that a strong negative ${}^{8}S$ peak in the resonant photoemission MCD is indicative for a dominantly ${J}^{\ensuremath{'}}=7$ character in the intermediate x-ray absorption state while a strong positive ${}^{6}I$ peak indicates a dominantly ${J}^{\ensuremath{'}}=5$ character. The photoemission signal observed for the ${}^{6}H$ and ${}^{6}G$ final states is reduced compared to the calculation, which might be due to configuration interaction with other shells, such as the $5p$ and $5d.$ At higher photon energies within the ${M}_{4,5}$ absorption, an enhanced photoemission is found at binding energies above 12 eV, which can be ascribed to ``spin-flip'' transitions.

Intermediate-coupling calculations of the effects of interacting resonances on dielectronic recombination in a static electric field

Recently, we demonstrated that the enhancement of dielectronic recombination by an electric field, or crossed electric and magnetic fields, may be reduced by the interaction between resonances through a common continuum @Phys. Rev. Lett. 80, 1402 ~1998!#. However, these calculations were carried out in a configurationaverage ~CA! approximation and the question then remained as to how these predicted reductions might be affected when one removes the degeneracy inherent in the CA approximation and includes the interactions between the resonant states associated with individual intermediate-coupled levels. In the present paper we address that issue for the case of dielectronic recombination in the presence of an electric field. Indeed we have found that these more detailed calculations support the general conclusions of our earlier work and provide additional insight into the effects of interacting resonances on dielectronic recombination in the presence of fields. Results for the Li-like ions C, Ne, and Si are presented. @S1050-2947~98!02712-7#

Theoretical calculations of dielectronic recombination in crossed electric and magnetic fields

Recently, Robicheaux and Pindzola [Phys. Rev. Lett. 79, 2237 (1997)] reported on model calculations of dielectronic recombination (DR) in the presence of crossed electric and magnetic fields. They showed that the enhancement of the DR by an electric field may be increased further when a magnetic field perpendicular to the electric field is present in the collision region. In this paper, we describe the results of distorted-wave calculations of dielectronic recombination in the presence of crossed electric and magnetic fields for Li-like C${}^{3+}$ and Si${}^{11+}$. Two sets of calculations are performed and compared. The first is based on a full intermediate-coupling (IC) calculation, while the second is based on a much simpler configuration-average (CA) approximation. Both sets of calculations predict substantial added enhancement of DR due to the magnetic field. However, the CA approximation overestimates the field-enhanced DR as compared to both the IC calculations and previous measurements of total recombination. Comparisons of our IC results with total recombination measurements are not possible because the IC Hamiltonian matrices are too large for the high values of $n$ included in these experiments; however, in anticipation of possible high-resolution experimental studies of partial DR in fields, we report on an IC calculation of the crossed-fields enhancement of DR as a function of electric-field strength for $n$=24 in Si${}^{11+}$.

Spin-polarized photoemission from shallow core levels in localized materials

We present spin-resolved photoemission measurements from the 5p core levels of Gd and Tb metal. In contrast to the 3d transition-metal 3p spectra, the rare-earth 5p spin-resolved spectra show a detailed fine structure that cannot be explained within a one-electron model. The spin-orbit, Coulomb, and exchange interactions have to be treated on an equal footing. For the case of Gd, a remarkable agreement is obtained between experiment and theory when the spin polarization of the 5p emission is analyzed on the basis of atomic-multiplet calculations in intermediate coupling. For Tb, however, small discrepancies remain that cannot be analyzed in the absence of a more detailed magnetic characterization. The results emphasize strongly the potential of spin analysis in core-level studies. {copyright} {ital 1997} {ital The American Physical Society}

Effects of relativity on the KL1L2(3P0) Auger transition rate of 65159Tb

Abstract The KLL Auger spectrum of 65 159 Tb from the 66 159 Dy decay and, separately, its KL 1 L 2 doublet have been measured at an instrumental resolution of 33 and 20 eV, respectively, using a combined electrostatic spectrometer. Energies and relative intensities of the nine individual KLL transitions have been determined and compared with the theoretical results. The accurate value of 0.53(2) obtained for the KL 1 L 2 ( 3 P 0 ) ( 1 P 1 ) intensity ratio proved the strong influence of the effects of relativity on the KL 1 L 2 ( 3 P 0 ) transition predicted by the relativistic calculations in intermediate coupling with configuration interaction. In addition, an energy of 57995(3) eV has been determined for the nuclear transition in 159 Tb by means of our measured energy of 5999.0(25) eV for the K-58 conversion line.