Relativistic Hartree Research Articles

Electric dipole transitions for 3d64s−3d64p in Mn I

We have calculated the logarithmic weighted oscillator strengths and transition probabilities (or rates) for 3d64s−3d64p electric dipole transitions in neutral manganese (Mn I, Z=25) by using two configuration interaction methods (the multiconfiguration Hartree–Fock (MCHF) method within the framework of Breit–Pauli relativistic corrections developed by Fischer and Cowan׳s relativistic Hartree–Fock (HFR) method). Results obtained have been compared with other calculations and experiments.

A comparative study between semi-empirical oscillator strength parametrization and relativistic Hartree–Fock methods for computing the radiative parameters in Zr II spectrum

In the present work, we compare the radiative transition rates computed by two different semi-empirical approaches, based on a parametrization of the oscillator strengths and on a pseudo-relativistic Hartree–Fock model including core-polarization effects, for spectral lines in singly ionized zirconium. A detailed comparison with available experimental results is also reported and an overall good agreement is observed between all sets of data allowing us to provide new reliable oscillator strengths for a large amount of Zr II lines in the wavelength region from 1616 to 14746Å. Moreover, we give radial integral values of the main atomic transitions deduced in this study: 〈4d25p|r1|4d25s〉=−3.1522 (0.0161), 〈4d25p|r1|4d3〉=1.7605 (0.0107), 〈4d25p|r1|4d26s〉=−1.481 (0.794) and〈4d25p|r1|4d25d〉=2.289 (0.014).

M1 and E2 transitions in the ground-state configuration of atomic manganese

Using the multiconfiguration Hartree–Fock approximation within the framework of the Breit–Pauli Hamiltonian (MCHF+BP) and the relativistic Hartree–Fock (HFR) approximation, we have calculated the forbidden transition (M1 and E2) parameters such as transition energies, logarithmic weighted oscillator strengths and transition probabilities between the fine-structure levels in the ground-state configuration of 3d54s2 for atomic manganese (Mn I, Z = 25). A discussion of these calculations for manganese using MCHF+BP and HFR methods is given here.

Probing the constituent structure of black holes

Based on recent ideas, we propose a framework for the description of black holes in terms of constituent graviton degrees of freedom. Within this formalism a large black hole can be understood as a bound state of N longitudinal gravitons. In this context black holes are similar to baryonic bound states in quantum chromodynamics which are described by fundamental quark degrees of freedom. As a quantitative tool we employ a quantum bound state description originally developed in QCD that allows to consider black holes in a relativistic Hartree like framework. As an application of our framework we calculate the cross section for scattering processes between graviton emitters outside of a Schwarzschild black hole and absorbers in its interior, that is gravitons. We show that these scatterings allow to directly extract structural observables such as the momentum distribution of black hole constituents.

Description of spin–orbit coupling in excited states with two-component methods based on approximate coupled-cluster theory

A generalization of the approximated coupled-cluster singles and doubles method and the algebraic diagrammatic construction scheme up to second order to two-component spinors obtained from a relativistic Hartree-Fock calculation is reported. Computational results for zero-field splittings of atoms and monoatomic cations, triplet lifetimes of two organic molecules, and the spin-forbidden part of the UV/Vis absorption spectrum of tris(ethylenediamine)cobalt(III) are presented.

New spectroscopic data for atomic tungsten XIV

The thirteen times ionized tungsten is isoelectronic with PmI. Wavelengths and transition probabilities for the 5s-5p and 5p-5d transitions of WXIV, identifying the ground state as 4f13 5s2 2F7/2 were calculated. Both, a relativistic Hartree Fock approach, including core-polarization effects, and a purely relativistic multiconfiguration Dirac-Fock method were used for the calculations. Particularly, 5s-5p transitions were compared with experimental results obtained with VUV electron beam ion trap (EBIT) spectroscopy.

Transition probabilities and radiative lifetimes of Mg III

There have been calculated transition probabilities for 365 lines arising from 2p5ns(n=3,4,5), 2p5np(n=3,4), 2p5nd(n=3,4), 2p5nf(n=4,5) and 2p5 5g configurations of Mg III and radiative lifetimes corresponding to 89 levels. These values were obtained in intermediate coupling (IC) by using ab initio relativistic Hartree–Fock (HFR) calculations. Later, we use the standard method of least square fitting of experimental energy levels for the IC calculations by means of Cowan’s computer codes. The vast majority of the calculated transition probabilities correspond to lines lying in the ultraviolet range (UV) which are of high interest in astrophysics. Our results are compared to those previously reported in the literature. Furthermore, the values of transition probabilities of configuration levels 2p5 4d, 2p5nf(n=4,5) and 2p5 5g are presented for the first time. In light of these findings, it is possible to extend the range of wavelengths which allows us to estimate the temperature in plasma diagnostic. In addition, our results for radiative lifetimes have been compared to the available experimental values.

Revised and extended analysis of the Zn-like Kr ion

The spectrum of the six times-ionized krypton (Kr VII) has been observed in the 300–4800Å wavelength range, resulting in 115 new classified lines. We revised the values for the previously known energy levels and extended the analysis to 38 new energy levels belonging to 4s5s, 4s6s, 4p4f, 4s6d and 4p4d, 4s5p, 4s4f, 4p5s, 4s5f, 4s6p, 4s6f even and odd configurations, respectively. For the prediction of the atomic parameters, energy levels and transition, regularities of atomic structure and relativistic Hartree–Fock calculations were used.

Extended analysis of fifth spectrum of bromine: Br V

The fifth spectrum of bromine (Br V) has been studied in the 200–2400Å wavelength region. The spectrum was photographed on a 3-m normal incidence vacuum spectrograph at the St. Francis Xavier University, Antigonish (Canada) and 6.65-m grazing incidence spectrograph at the Zeeman laboratory (Amsterdam). The light sources used were a triggered spark and sliding spark. The ground configuration of Br V is 4s24p. The excited configurations 4s4p2+4s2(4d+5d+5s+6s+7s+5g+6g)+4s4p(5p+4f)+4p24d in the even parity system and the 4p3+4s2(5p+6p+7p+4f)+4s4p4d+4s4p5s configurations in the odd parity system have been studied. Relativistic Hartree–Fock (HFR) and least squares fitted (LSF) parametric calculations have been used to interpret the observed spectrum. 99 levels of Br V have now been established, 43 being new. Among 394 classified spectral lines, 181 are newly classified. The level 4s27s 2S1/2 is revised. We estimate the accuracy of our measured wavelengths for sharp and unblended lines to be±0.005Å. The ionization limit is determined as 479,657±200cm−1 (59.470±0.025eV).

Treating Coulomb exchange contributions in relativistic mean field calculations: why and how

The energy density functional (EDF) method is very widely used in nuclear physics, and among the various existing functionals those based on the relativistic Hartree (RH) approximation are very popular because the exchange contributions (Fock terms) are numerically rather onerous to calculate. Although it is possible to somehow ‘mock up’ the effects of meson-induced exchange terms by adjusting the meson–nucleon couplings, the lack of Coulomb exchange contributions hampers the accuracy of predictions. In this work, we show that the Coulomb exchange effects can be easily included with good accuracy in a perturbative approach. Therefore, it would be desirable for future relativistic EDF models to incorporate Coulomb exchange effects, at least to some order of perturbation.

Superheavy magic structures in the relativistic Hartree–Fock–Bogoliubov approach

We have explored the occurrence of the spherical shell closures for superheavy nuclei in the framework of the relativistic Hartree–Fock–Bogoliubov (RHFB) theory. Shell effects are characterized in terms of two-nucleon gaps δ2n(p). Although the results depend slightly on the effective Lagrangians used, the general set of magic numbers beyond 208Pb are predicted to be Z=120, 138 for protons and N=172, 184, 228 and 258 for neutrons, respectively. Specifically the RHFB calculations favor the nuclide 120304 as the next spherical doubly magic one beyond 208Pb. Shell effects are sensitive to various terms of the mean-field, such as the spin-orbit coupling, the scalar and effective masses.

DIRHB—A relativistic self-consistent mean-field framework for atomic nuclei

The DIRHB package consists of three Fortran computer codes for the calculation of the ground-state properties of even–even atomic nuclei using the framework of relativistic self-consistent mean-field models. Each code corresponds to a particular choice of spatial symmetry: the DIRHBS, DIRHBZ and DIRHBT codes are used to calculate nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes, respectively. Reflection symmetry is assumed in all three cases. The latest relativistic nuclear energy density functionals are implemented in the codes, thus enabling efficient and accurate calculations over the entire nuclide chart. Program summaryProgram title: DIRHB package (codes DIRHBS, DIRHBZ and DIRHBT)Catalogue identifier: AESN_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AESN_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: noneNo. of lines in distributed program, including test data, etc.: 44516No. of bytes in distributed program, including test data, etc.: 317161Distribution format: tar.gzProgramming language: Fortran 77.Computer: All computers.Operating system: All operating systems. The Makefiles are specific for a Unix OS and have to be modified for Windows.RAM: Depends on the imposed symmetry and number of oscillator shells. For the triaxial test case it takes 300 MB.Classification: 17.22.Nature of problem:Ground-state properties of even–even open-shell nuclei can be calculated using the framework of self-consistent mean-field models based on relativistic energy density functionals. The structure of arbitrary heavy nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes, is modeled using the latest zero- and finite-range relativistic effective interactions. The particle–particle channel of the effective inter-nucleon interaction is described by a separable finite-range pairing force.Solution method:The current implementation of the model computes the mean-field solution of the nuclear many-body problem for even–even open-shell spherical and quadrupole deformed nuclei. The codes are used to solve the stationary relativistic Hartree–Bogoliubov equations in a self-consistent iteration scheme. At each iteration the matrix elements of the equations are updated using the modified Broyden method or the linear mixing method. The single-nucleon wave functions are expanded in a basis of spherical, axially symmetric or triaxial harmonic oscillator, depending on the assumed symmetry of the nuclear shape. For calculations that constrain the shape to specific values of the deformation parameters, the augmented Lagrangian method is used.Restrictions:Time-reversal and reflection symmetries are assumed. Open-shell even–even spherical and quadrupole deformed nuclei are considered.Running time:Depends on the imposed symmetry and number of oscillator shells. For the test cases it runs from few seconds (spherical) up to few hours (triaxial).

X-ray relative intensities at incident photon energies across the [formula omitted] ([formula omitted]) absorption edges of elements with [formula omitted

The intensity ratios, ILk/ILα1 (k=l,η,α2,β1,β2,15,β3,β4,β5,7,β6,β9,10,γ1,5,γ6,8,γ2,3,γ4) and ILj/ILα (j=β,γ), have been evaluated at incident photon energies across the Li (i=1–3) absorption edge energies of all the elements with 35≤Z≤92. Use is made of what are currently considered to be more reliable theoretical data sets of different physical parameters, namely, the Li (i=1–3) sub-shell photoionization cross sections based on the relativistic Hartree–Fock–Slater (RHFS) model, the X-ray emission rates based on the Dirac–Fock model, and the fluorescence and Coster–Kronig yields based on the Dirac–Hartree–Slater model. In addition, the Lα1 X-ray production cross sections for different elements at various incident photon energies have been tabulated so as to facilitate the evaluation of production cross sections for different resolved L X-ray components from the tabulated intensity ratios. Further, to assist evaluation of the prominent (Li−Sj) (Sj=Mj, Nj and i=1–3, j=1–7) resonant Raman scattered (RRS) peak energies for an element at a given incident photon energy (below the Li sub-shell absorption edge), the neutral-atom electron binding energies based on the relaxed orbital RHFS calculations are also listed so as to enable identification of the RRS peaks, which can overlap with the fluorescent X-ray lines.

Relativistic Hartree–Fock calculations of transition rates for allowed and forbidden lines in Nd IV

A pseudo-relativistic Hartree–Fock model including a large amount of configuration-interaction effects has been used to compute radiative decay rates for allowed and forbidden transitions in Nd IV. Detailed comparisons of transition probabilities, oscillator strengths and radiative lifetimes with data previously published are also reported and discussed in the present work.

Pion Tensor Force and Nuclear Binding Energy in the Relativistic Hartree–Fock Formalism

Pion Tensor Force and Nuclear Binding Energy in the Relativistic Hartree–Fock Formalism

M sub shell X-ray emission cross section measurements for Pt, Au, Hg, Pb, Th and U at 8 and 10 keV synchrotron photons

M sub shell X-ray emission cross sections of Pt, Au, Hg, Pb, Th and U at 8 and 10keV photon energies have been determined with linearly polarized photon beam from Indus-2 synchrotron source. The measured cross sections have been reported for the first time and were used to check the available theoretical Dirac–Hartree–Slater (DHS) and Dirac–Fock (DF) values reported in literature and also the presently derived Non Relativistic Hartree–Slater (NRHS), DF and DHS values for Mξ, Mδ, Mα, Mβ, Mγ, Mm1 and Mm2 group of X-rays.

Revised and extended analysis of Br IV

The spectrum of three-times ionized bromine Br IV has been studied in the 319–2350Å wavelength region. The spectrum was recorded on a 3-m normal incidence vacuum spectrograph at the St. Francis Xavier University, Antigonish (Canada) and 6.65-m grazing incidence spectrograph at the Zeeman laboratory (Amsterdam). The light sources used were a triggered spark and sliding spark, respectively. The ground configuration of Br IV 3d104s24p2, the excited configurations 3d104s4p3+3d104s24p (4d+5d+6d+5s+6s+7s) in the odd parity system and 3d104s24p (5p+4f+5f)+3d104s4p2 (4d+5s)+3d104p4 in the even parity system have been studied. Relativistic Hartree–Fock (HFR) and least squares fitted (LSF) parametric calculations were used to interpret the observed spectrum. 120 Levels of Br IV have now been established, 58 being new. Among 424 spectral lines, 277 are newly classified. The levels 4s4p35S2, 4s24p4d 3F4 and 4p5p (3P0, 1, 3D1, 2, 3S1) are revised. We estimate the accuracy of our measured wavelength for sharp and unblended lines to be ±0.005Å. The ionization limit is determined as 385,390±100cm−1 (47.782±0.012eV).

Theoretical oscillator strengths, transition probabilities, and radiative lifetimes of levels in Pb V

Theoretical values of oscillator strengths and transition probabilities for 306 spectral lines arising from the 5d9ns(n=7,8,9),5d9np(n=6,7),5d96d, and 5d9 5f configurations, and radiative lifetimes of 9 levels, of Pb V have been obtained. These values were obtained in intermediate coupling (IC) and using ab initio relativistic Hartree–Fock calculations including core-polarization effects. We use for the IC calculations the standard method of least squares fitting of experimental energy levels by means of computer codes from Cowan. We included in these calculations the 5d86s6p and 5d86s2 configurations. These calculations have facilitated the identification of the 214.25, 216.79, and 227.66 nm spectral lines of Pb V. In the absence of experimental results of oscillator strengths and transition probabilities, we could not make a direct comparison with our results. However, the Stark broadening parameters calculated from these values are in excellent agreement with experimental widening found in the literature.

Decay rates for radiative transitions in the Pr IV spectrum

Transition probabilities and oscillator strengths for electric dipole radiation in triply ionized praseodymium are reported for the first time in this paper. They were computed using a semi-empirical relativistic Hartree–Fock approach including core-polarization effects. Due to the lack of experimental data in the Pr IV spectrum, the accuracy of our results is estimated and discussed on the basis of comparisons between calculations performed with a similar physical model and laboratory measurements previously published for the isoelectronic ion Ce2+. In view of their great interest in optical materials and nanophotonics, radiative rates for forbidden lines within the 4f2 ground-state configuration of Pr3+ were also calculated in our work.

Neutron-skin thickness of 208Pb from the energy of the anti-analogue giant dipole resonance

The energy of the charge-exchange anti-analogue giant dipole resonance (AGDR) has been calculated for the 208Pb isotope using the state-of-the-art fully self-consistent relativistic proton–neutron quasiparticle random-phase approximation based on the relativistic Hartree–Bogoliubov model. It is shown that the AGDR centroid energy is very sensitively related to the corresponding neutron-skin thickness. The neutron-skin thickness of 208Pb has been determined very precisely by comparing the theoretical results with the available experimental data on E(AGDR). The result ΔRpn = 0.161 ± 0.042 agrees nicely with the previous experimental results.