Intermediate Coupling Effects Research Articles

Observation of 5f intermediate coupling in uranium x-ray emission spectroscopy

The first observation of Intermediate Coupling effects in the occupied 5f states has been made using x-ray Emission Spectroscopy (XES). In the past, the impact of Intermediate Coupling of the 5f states in actinides has long been observed and quantified, using x-ray Absorption Spectroscopy (XAS) to probe the unoccupied 5f states, providing great insight into the enigma of 5f electronic structure. However, no measure of its effects in the occupied states had been reported before this. Moreover, because the 5f occupied states in UF4 are almost completely of 5f5/2 character, the observed effect in XES is twice that in XAS for UF4.

A Schematic Two Overlapping-Band Model for Superconducting Sulfur Hydrides: The Isotope Mass Exponent

The high value of the isotope shift in sulfur hydrides supports a phonon-mediated pairing scenario of superconductivity for these high-temperature superconductors which are consistent with the Bardeen–Cooper–Schrieffer (BCS) framework. Knowing that a large electronic density of states enhances the critical temperature (Tc), generalized Fermi surface topologies are used to increase it. A multicomponent model within the BCS framework is proposed in this work for sulfur hydride superconductors. This model is used to evaluate some properties of the H3S superconductor. Strong and intermediate coupling effects are taken into account with the effective McMillan approximation, and the isotope coefficient is evaluated as a function of the coupling parameter as well as other relevant parameters of the model.

X‐ray emission via Kα resonance complexes in gold ions

The excitation energies from ground state for 63 fine structure levels of the terms belonging to 1 s2, 1snl, 2lnl′ (n = 2,3), 3l3l′ (l ≠ ≠l′) configurations of Au77+, as well as oscillator strengths for electric‐dipole‐allowed and intercombination transitions among the fine‐structure levels were theoretically evaluated. The important relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian. Extensive comparisons are performed with several approximations and previous data sets in order to size up contributing effects and to estimate accuracy ratings. The atomic excitation is obtained by electron impact in close coupling approach. For optically allowed transitions, the electron‐impact collision strengths at collision energy up to 80 keV are reported. The results are relevant to the laboratory and astrophysical plasmas.

Oscillator strengths for spin-changing P–D transitions in He I including the effect of a finite nuclear mass and intermediate coupling

We have calculated the electric dipole (E1) oscillator strengths and spontaneous decay rates for 12 spin-changing P–D transitions of atomic helium. We included the effects of the finite nuclear mass and the anomalous magnetic moment of the electron. The specific transitions for 4He are [Formula: see text] and [Formula: see text] with n = 2, 3, 4 and n′ = 3, 4. To include the effects of intermediate coupling between pure LS and jj, we used the Breit formulation for the spin–orbit and spin–other-orbit operators and combined the results of the exact diagonalization of the 2 × 2 energy matrix with pseudostate expansions to perform the perturbation sums over intermediate states. We calculated both the length and velocity gauges as a check on numerical accuracy and the validity of the transition operators.

Partially resolved super transition array method

The partially resolved transition array model for radiative transitions between ordinary electronic configurations is extended to the super configuration approach. The specific application incorporates intermediate coupling effects into transition arrays to describe the transition from LS to JJ coupling without the ad hoc approximations introduced in past formulations. More generally, the extended concept permits stepwise refinement of the super transition array method towards the line-by-line limit in ordinary configurations. Thus, the formalism forms a framework for a hybrid scheme to combine detailed line accounting and statistical methods.

Fine-structure energy levels, oscillator strengths and lifetimes in Al-like chromium

We have performed large scale calculations of excitation energies from ground state for 97 fine-structure levels as well as of oscillator strengths and radiative rates for all electric-dipole-allowed and intercombination transitions among the fine-structure levels of the terms belonging to the (1s22s22p6)3s23p, 3s3p2, 3s23d, 3p3, 3s3p3d, 3p23d, 3s3d2, 3s24s, 3s24p, 3s24d, 3s24f and 3s3p4s configurations of Al-like chromium. These states are represented by very extensive configuration-interaction wave functions obtained with the configuration-interaction version 3 computer code of Hibbert. The important relativistic effects in intermediate coupling are included through the Breit-Pauli approximation. Small adjustments to the diagonal elements of Hamiltonian matrices have been made so that energy splittings are as close as possible to the energy values of the National Institute of Standards and Technology. From the radiative rates, we have also calculated radiative lifetimes of fine-structure levels. Generally, the calculated excitation energies, oscillator strengths and the radiative rates are found to be in good agreement with those obtained from other sophisticated calculations. However, significant differences between present calculated lifetimes and those from the calculation of Fischer and co-workers for a few fine-structure levels are noted and discussed. Also the present calculated lifetime for level 3s24s(2S0.5) is found to be in excellent agreement with the experimental value given by Thornbury and co-workers. With this calculation, we also predict new data for several fine-structure levels, where no other theoretical and/or experimental results are available.

Excitation energies, oscillator strengths and lifetimes in Mg-like vanadium**Our calculated data (wavelengths λ (in Å), oscillator strengths in both the length fL and velocity fV forms and the transition probabilities in the length form AL) for all 1108 transitions in V XII are available with the first author ().

Excitation energies from the ground state for 86 fine-structure levels as well as oscillator strengths and radiative decay rates for all fine-structure transitions among the levels of the terms (1s22s22p6)3s2(1S), 3s3p(1,3Po), 3s3d(1,3D), 3s4s(1,3S), 3s4p(1,3Po), 3s4d(1,3D), 3s4f(1,3Fo), 3p2(1S, 3P, 1D), 3p3d(1,3Po, 1,3Do, 1,3Fo), 3p4s(1,3Po), 3p4p(1,3S, 1,3P, 1,3D), 3p4d(1,3Po, 1,3Do, 1,3Fo), 3p4f(1,3D, 1,3F, 1,3G) and 3d2(1S, 3P, 1D,3F,1G) of V XII are calculated using extensive configuration-interaction wave functions obtained with the configuration-interaction version 3 computer code of Hibbert. The important relativistic effects in intermediate coupling are included through the Breit–Pauli approximation. In order to keep our calculated energy splittings as close as possible to the corresponding experimental values, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. The mixing among several fine-structure levels is found to be very strong. Our fine-tuned excitation energies, including their ordering, are in excellent agreement (better than 0.25%) with the available experimental results. From our calculated radiative decay rates, we have also calculated the radiative lifetimes of fine-structure levels. Generally, our calculated data for the excitation energies and radiative decay rates are found to agree reasonably well with other available calculations. However, significant differences between our calculated lifetimes and those from the calculation of Froese Fischer et al (2006 At. Data Nucl. Data Tables 92 607) for a few fine-structure levels, mainly those belonging to the 3p4d configuration, are noted and discussed. Also, our calculated lifetime for the longer-lived level 3s3p(3P1) is found to be in excellent agreement with the corresponding value of Curtis (1991 Phys. Scr. 43 137).

Fine-structure energy levels, radiative rates and lifetimes in Si-like nickel

Large scale CIV3 calculations of excitation energies from ground state as well as of oscillator strengths and radiative decay rates for all electric–dipole-allowed and intercombination transitions among the fine-structure levels of the terms belonging to the (1s22s22p6)3s23p2, 3s3p3, 3p4, 3s23p3d, 3s23p4s, 3s23p4p, 3s23p4d and 3s23p4f configurations of Ni XV, are performed using very extensive configuration-interaction wave functions. The relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian. In order to keep our calculated energy splittings as close as possible to the National Institute of Standard and Technology (NIST) values, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. Our calculated excitation energies, including their ordering, are in excellent agreement with the available NIST results. From our radiative decay rates we have also calculated radiative lifetimes of the fine-structure levels. It is noted that our calculated radiative rates show significant disagreement (23–30%) with those calculated by Ishikawa and Vilkas (2002 Phys. Scr.65 219) for the transitions involving the 3s3p3(5S2) level. For this high spin level 3s3p3(5S2) our calculated lifetime is found to be in excellent agreement with the experimental value of Träbert et al (1989 Z. Phys. D 11 207). In this calculation, we also predict many additional new and accurate data for various optically allowed and intercombination transitions to complete the void in the existing data.

Fine-structure energy levels and radiative rates in Si-like chlorine

Excitation energies and radiative rates for electric dipole (E1) transitions among the 86 fine-structure levels belonging to the configurations (1s22s22p6)3s23p2, 3s3p3, 3s23p3d, 3p4, 3s23p4s, 3s23p4p, 3s3p2(2S)4s, 3s3p2(2P)4s, 3s3p2(4P)4s, 3s3p2(2D)4s, 3s23p4d and 3s23p4f of Cl IV are calculated using extensive configuration-interaction (CI) wave functions obtained with the CIV3 computer code of Hibbert. The relativistic effects in intermediate coupling are incorporated by means of the Breit-Pauli Hamiltonian. In order to keep the calculated energy splittings close to the energy values of the National Institute for Standards and Technology, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. Our calculated energy levels, including their orderings, are in excellent agreement with the available NIST values. The mixing among several fine-structure levels is found to be very strong. From our radiative rates we have also calculated radiative lifetimes of the fine-structure levels. Significant differences between our calculated lifetimes and those from a sophisticated calculation for a few low lying levels are noted and discussed. In this calculation, we also predict new data for several fine-structure levels where no other theoretical and/or experimental results are available.

Fine-structure energy levels, oscillator strengths and lifetimes in Cu XVI**Table 6 with all the calculated lines is available from the first author (e-mail: g_p_gupta1@yahoo.co.in).

We have performed large-scale CIV3 calculations of excitation energies from ground state for 69 fine-structure levels as well as of oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the fine-structure levels of the terms belonging to the (1s22s22p6)3s23p2, 3s3p3, 3p4, 3s23p3d, 3s23p4s, 3s23p4p, 3s23p4d, and 3s23p4f configurations of Cu XVI. These states are represented by very extensive configuration-interaction (CI) wave functions obtained with the computer code CIV3 of Hibbert. The important relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made so that the energy splittings are as close as possible to the energy values of those from the National Institute for Standards and Technology. The mixing among several fine-structure levels is found to be very strong. From our radiative decay rates we have also calculated radiative lifetimes of the fine-structure levels. Our calculated lifetime for the high spin level 3s3p3(5S2) is found to be in excellent agreement with the experimental value of Trabert et al (1988 J. Opt. Soc. Am. B 5 2173). In this calculation, we also predict new data for several fine-structure levels where no other theoretical and/or experimental results are available.

Fine-structure energy levels and radiative decay rates in Al-like vanadium

Large-scale calculations of excitation energies from ground state for 97 fine-structure levels as well as of oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the (1s22s22p6)3s23p(2P0), 3s3p2(2S,2P,2D,4P), 3s23d(2D), 3p3(4S0,2P0,2D0), 3s3p(3P0)3d(2P0,2D0,2F0,4P0,4D0,4F0), 3s3p(1P0)3d(2P0,2D0,2F0), 3p2(1S)3d(2D), 3p2(1D)3d(2S,2P,2D,2F,2G), 3p2(3P)3d(2P,2D,2F,4P,4D,4F), 3s3d2(2S,2P,2D,2F,2G,4P,4F), 3s24s(2S), 3s24p(2P0), 3s24d(2D), 3s24f(2F0), 3s3p(3P0)4s(2P0,4P0) and 3s3p(1P0)4s(2P0) states of V XI are performed using extensive configuration-interaction (CI) wavefunctions. The calculations used the CIV3 computer code of Hibbert. The important relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian. In order to keep our calculated energy splittings as close as possible to the National Institute of Standard and Technology (NIST) values, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. Our calculated excitation energies, including their ordering, are in excellent agreement with the available NIST results. From our radiative decay rates, we have also calculated radiative lifetimes of some fine-structure levels. Generally, very good agreement between our calculated lifetimes and those from sophisticated calculation is realized for many fine-structure levels. However, a few significant differences are noted and discussed.

Correlation effects on fine-structure energy levels, oscillator strengths and lifetimes in Ca VII

Energy levels, oscillator strengths, and transition probabilities for transitions among the fine-structure levels of the terms belonging to the 3s23p2, 3s3p3, 3s23p3d, 3p4, 3s23p4s, 3s23p4p, 3s23p4d, and 3s23p4f configurations of Si-like Calcium are calculated using extensive configuration-interaction (CI) wave functions obtained with the CIV3 computer code of Hibbert. The relativistic effects in intermediate coupling are incorporated by means of the Breit-Pauli Hamiltonian. The energy splitting of 70 fine-structure levels, oscillator strengths and transition probabilities for electric-dipole-allowed and intercombination transitions and, also the lifetimes of fine-structure levels are presented and compared with available experimental and other theoretical results.

Large-scale CIV3 calculations of fine-structure energy levels and radiative rates in Al-like copper

We have performed large-scale CIV3 calculations of excitation energies from the ground state for 97 fine-structure levels as well as of oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the fine-structure levels of the terms belonging to the (1s22s22p6)3s23p, 3s3p2, 3s23d, 3p3, 3s3p3d, 3p23d, 3s3d2, 3s24s, 3s24p, 3s24d, 3s24f, and 3s3p4s configurations of Cu XVII. These states are represented by very extensive configuration-interaction (CI) wave functions obtained with the CIV3 (Configuration-Interaction Version 3) computer code of Hibbert. The important relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian, which consists of the nonrelativistic term plus the one-body mass correction, Darwin term, and spin–orbit, spin–other-orbit, and spin–spin operators. To keep our calculated energy splittings as close as possible to the experimental values (wherever available), we have made small adjustments to the diagonal elements of the Hamiltonian matrices. Our calculated excitation energies, including their ordering, are in excellent agreement with the available experimental results. From our radiative decay rates we have also calculated radiative lifetimes of some fine-structure levels. The mixing among several fine-structure levels is found to be so strong that the correct identification of these levels becomes very difficult. We believe that our extensive calculations will be useful to experimentalists in identifying the fine-structure levels in their future work. In this calculation we also predict new data for several fine-structure levels where no other theoretical and (or) experimental results are available.

Fine-structure energy levels, oscillator strengths and lifetimes in Co XV

Excitation energies from ground state for 97 fine-structure levels as well as oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the fine-structure levels of the terms belonging to the (1s 22s 22p 6)3s 23p, 3s 3 p 2, 3s 23d, 3p 3, 3s3p3d, 3p 23d, 3s3d 2, 3s 24s, 3s 24p, 3s 24d, 3s 24f, and 3s3p4s configurations of Co XV are calculated, using extensive configuration-interaction (CI) wave functions, obtained with the CIV3 computer code of Hibbert. The important relativistic effects in intermediate coupling are included through the Breit-Pauli approximation via spin-orbit, spin-other-orbit, spin-spin, Darwin and mass correction terms. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made. Our calculated excitation energies, including their ordering, are in excellent agreement with the experimental results and the experimentally compiled energy values of the National Institute for Standards and Technology (NIST) wherever available. The mixing among several fine-structure levels is found to be very strong, with most of the strongly mixed levels belonging to the (1s 22s 22p 6)3p 23d and 3s3d 2 configurations. The strong mixing among several fine-structure levels makes it very difficult to identify them uniquely. Perhaps, that may be the reason for the lack of both experimental and theoretical results for these levels. We believe that our extensive calculated values can guide experimentalists in identifying the fine-structure levels in their future work. From our radiative decay rates we have also calculated radiative lifetimes of some fine-structure levels. In this calculation we also predict new data for several fine-structure levels where no other theoretical and/or experimental results are available.

Oscillator strengths and lifetimes in Ge XXI

We have calculated energy splittings of 53 fine-structure levels as well as oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the (1s22s22p6)3s2(1S), 3s3p(1,3Po), 3s3d(1,3D), 3s4s(1,3S), 3s4p(1,3Po), 3s4d(1,3D), 3s4f(1,3Fo), 3p2(1S,3P,1D), 3p3d(1,3Po,1,3Do,1,3Fo), 3p4s(1,3Po) and 3d2(1S,3P,1D,3F,1G) states of Ge XXI, using extensive configuration–interaction (CI) wavefunctions, obtained with the CIV3 computer code of Hibbert. The important relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian. In order to keep our calculated energy splittings as close as possible to the experimental values, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. Our excitation energies, including their ordering, are in excellent agreement with the available experimental results. The enormous mixing among several fine-structure levels makes it very difficult to identify them correctly with the result that their positions in the calculation of Ivanova et al are interchanged compared to our results and the experimental values. From our transition probabilities, we have also calculated radiative lifetimes of some fine-structure levels. Our calculated oscillator strengths and the lifetimes are found to be in good agreement with the other available theoretical results. In this calculation, we also predict new data for several fine-structure levels where no other theoretical and/or experimental results are available.

Magnetic measurements and crystal field investigation on single crystals of Er(CF 3SO 3) 3·9H 2O

Single crystals of erbium tri-fluoromethanesulfonate (ErTFMS) were prepared from the slow evaporation of the aqueous solution. The principal magnetic susceptibilities perpendicular to the c-axis of the hexagonal crystal was measured down to 13 K. Principal magnetic anisotropy was also measured from 300 K down to 80 K which provides principal susceptibility parallel to the c-axis down to 80 K. A very good theoretical simulation of the thermal variation of principal magnetic susceptibilities of ErTFMS has been obtained with a crystal field (CF) of C 3h site symmetry, in which J-mixed eigenvectors and intermediate coupling effects have been used. No ordering effects were noticed down to the lowest temperature (13 K) attained, indicating the inter-ionic interaction to be of predominantly dipolar type. The g-values are found to be g ∣∣=8.86 and g ⊥=1.62, respectively. The Schottky anomaly in the electronic heat capacity at about 80 K has been computed from the Stark pattern. The thermal behavior of quadrupole splitting and hyperfine heat capacity were calculated from the CF analysis.

Fine-structure energy levels, oscillator strengths and lifetimes in Mn XIII

We have performed large scale CIV3 calculations of excitation energies from ground state for 98 fine-structure levels as well as of oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the fine-structure levels of the terms belonging to the (1s22s2 2p6)3s2 3p, 3s3p2, 3s23d, 3p3, 3s3p3d, 3p2 3d, 3s3d2, 3s2 4s, 3s2 4p, 3s24d, 3s2 4f and 3s3p4s configurations of Al-like manganese. These states are represented by very extensive configuration-interaction (CI) wavefunctions obtained with the CIV3 computer code of Hibbert. The important relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian. In order to keep our calculated energy splittings as close as possible to the experimental values, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. Our calculated excitation energies, including their ordering, are in excellent agreement with the available experimental results. From our radiative decay rates, we have also calculated radiative lifetimes of some fine-structure levels. Differences between our calculated lifetimes and those of Froese Fisher et al (2006 At. Data Nucl. Data Tables 92 607) for several fine-structure levels are discussed.

Fine-structure energy levels, oscillator strengths and lifetimes in Mg-like chromium

Excitation energies from ground state for 86 fine-structure levels as well as oscillator strengths and radiative decay rates for all fine-structure transitions among the levels of the terms (1s22s22p6)3s2(1S), 3s3p(1,3Po), 3s3d(1,3D), 3s4s(1,3S), 3s4p(1,3Po), 3s4d(1,3D), 3s4f(1,3Fo), 3p2(1S, 3P, 1D), 3p3d(1,3Po, 1,3Do, 1,3Fo), 3p4s(1,3Po), 3p4p(1,3S, 1,3P, 1,3D), 3p4d(1,3Po, 1,3Do, 1,3Fo), 3p4f(1,3D, 1,3F, 1,3G) and 3d2(1S, 3P, 1D, 3F,1G) of Cr XIII are calculated using extensive configuration-interaction (CI) wave functions obtained with the CIV3 computer code of Hibbert. The important relativistic effects in intermediate coupling are included through the Breit-Pauli approximation via spin-orbit, spin-other-orbit, spin-spin, Darwin and mass correction terms. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made. The mixing among several fine-structure levels is found to be very strong. Our excitation energies, including their ordering, are in excellent agreement (better than 0.5%) with the available experimental results. From our transition probabilities, we have also calculated radiative lifetimes of some fine-structure levels. Our calculated lifetime for the longer-lived level 3s3p(3P1) is found to be in excellent agreement with the experimental result of Curtis compared to other theoretical calculations.

Energy levels, oscillator strengths and lifetimes in Si-like Ca VII

Energy levels, oscillator strengths and transition probabilities for transitions among the fine-structure levels of the terms belonging to the 3s23p2, 3s3p3, 3s23p3d, 3p4, 3s23p4s, 3s23p4p, 3s23p4d and 3s23p4f configurations of Ca VII are calculated using extensive configuration-interaction (CI) wavefunctions obtained with the CIV3 (configuration interaction version 3) computer code of Hibbert. The relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian which consists of the non-relativistic term plus the one-body mass correction, Darwin term, and spin–orbit, spin–other–orbit, and spin–spin operators. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made, so that the energy splittings are as close as possible to the experimental values. The energy splitting of 70 fine-structure levels, oscillator strengths and transition probabilities for electric-dipole-allowed and intercombination transitions and, also the lifetimes of fine-structure levels are presented and compared with available experimental and other theoretical results. Our calculated fine-structure energies, including their ordering, show excellent agreement (better than 0.5%) with the available experimental results. In this calculation, we also predict new data for several levels where no other theoretical and experimental results are available.

Calculated energy levels and lifetimes in Ca X

Excitation energies of the lowest 30 fine-structure levels as well as of oscillator strengths and radiative decay rates for transitions among the terms belonging to configurations within the principal quantum number n = 6 of Na-like calcium, are calculated using configuration-interaction (CI) wavefunctions. These wavefunctions are obtained using the CIV3 computer code of Hibbert. The important relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian. In order to keep our calculated energy splittings as close as possible to the experimental values, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. Our excitation energies, including their ordering, are in excellent agreement with the available experimental results. From our transition probabilities, we have also calculated radiative lifetimes of all fine-structure levels. The significant difference between the experimental results of Trabert et al (1996 J. Phys. B: At. Mol. Opt. Phys. 29 2647) and the existing theoretical values for the lifetimes of several levels is discussed and explained.