Theoretical Transition Probabilities Research Articles

Atomic Transition Probabilities for Ultraviolet and Optical Lines of Tm ii * *Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS5-26555 (program GO-15657). This paper also includes data gathered with the 6.5 m Magellan Telescopes

We report new branching fraction measurements for 224 ultraviolet and optical transitions of Tm ii. These transitions range in wavelength (wavenumber) from 2350 to 6417 Å (42,532–15,579 cm−1) and originate in 13 odd-parity and 24 even-parity upper levels. Thirty-five of the 37 levels, accounting for 213 of the 224 transitions, are studied for the first time. Branching fractions are determined for two levels studied previously for comparison to earlier results. The levels studied for the first time are high lying, ranging in energy from 35,753 to 54,989 cm−1. The branching fractions are determined from emission spectra from two different high-resolution spectrometers. These are combined with radiative lifetimes reported in an earlier study to produce a set of transition probabilities and log(gf) values with accuracy ranging from 5% to 30%. Comparison is made to experimental and theoretical transition probabilities from the literature where such data exist. These new log(gf) values are used to derive an abundance from one previously unused Tm ii line in the UV spectrum of the r-process-enhanced metal-poor star HD 222925, and this abundance is consistent with previous determinations based on other Tm ii lines.

Evaluation of uncertainties in atomic data on spectral lines and transition probabilities

The present article discusses some recent advances in methods of critical evaluation of experimental data on wavelengths of spectral lines and theoretical data on transition probabilities and oscillator strengths for atoms and atomic ions. In particular, recently developed new statistical approaches to estimation of uncertainties of weighted means of multiple measurements are described, and a numerical toolbox implementing these new approaches is presented. There are also some new developments in estimation of uncertainties of theoretical transition probabilities. A short review of literature implementing these new procedures is provided, including a description of the methodology.Graphical abstract

Energy Levels and Transition Data of Cs VI

Previously reported atomic data (spectral lines, wavelengths, energy levels, and transition probabilities) were collected and systematically analyzed for Cs VI. The present theoretical analysis was supported by extensive calculations made for Cs VI with a pseudo-relativistic Hartree–Fock (HFR) method together with the superposition of configuration interactions implemented in Cowan’s codes. In this work, all previously reported energy levels and their (allowed) transition assignments were confirmed. A critically evaluated set of optimized energy levels with their uncertainties, observed and Ritz wavelengths along with their uncertainties, and theoretical transition probabilities with their estimated uncertainties were presented in the compilation. In addition to this, we determined the radiative transition parameters for several forbidden lines within the ground configuration 5s25p2 of Cs VI.

Transition Probabilities of Near-infrared Ce iii Lines from Stellar Spectra: Applications to Kilonovae

Kilonova spectra provide us with information of r-process nucleosynthesis in neutron star mergers. However, it is still challenging to identify individual elements in the spectra mainly due to the lack of experimentally accurate atomic data for heavy elements at near-infrared wavelengths. Recently, Domoto et al. proposed that the absorption features around 14500 Å in the observed spectra of GW170817/AT2017gfo are Ce iii lines. But they used theoretical transition probabilities (gf-values) whose accuracy is uncertain. In this paper, we derive the astrophysical gf-values of three Ce iii lines, aiming at verifying this identification. We model high-resolution H-band spectra of four F-type supergiants showing clear Ce iii absorption features by assuming stellar parameters derived from optical spectra in the literature. We also test the validity of the derived astrophysical gf-values by estimating the Ce iii abundances of Ap stars. We find that the derived astrophysical gf-values of the Ce iii lines are systematically lower by about 0.25 dex than those used in previous work of kilonovae, while they are still compatible within the uncertainty ranges. By performing radiative transfer simulations of kilonovae with the derived gf-values, we find that the identification of Ce iii as a source of absorption features in the observed kilonova spectra still stands, even considering the uncertainties in the astrophysical gf-values. This supports the identification of Ce in the spectra of GW170817/AT2017gfo.

Atomic Transition Probabilities of Neutral Calcium*

Abstract The goals of this study are (1) to test the best theoretical transition probabilities for Ca i (a relatively light alkaline earth spectrum) from a modern ab initio calculation using configuration interaction plus many-body perturbation theory against the best modern experimental transition probabilities and (2) to produce as accurate and comprehensive a line list of Ca i transition probabilities as is currently possible based on this comparison. We report new Ca i radiative lifetime measurements from a laser-induced fluorescence experiment and new emission branching fraction measurements from a 0.5 m focal length grating spectrometer with a detector array. We combine these data for upper levels that have both a new lifetime and new branching fractions to report log(gf) values for two multiplets consisting of nine transitions. Detailed comparisons are made between theory and experiment, including the measurements reported herein and a selected set of previously published experimental transition probabilities. We find that modern theory compares favorably to experimental measurements in most instances where such data exist. A final list of 202 recommended transition probabilities is presented, which covers lines of Ca i with wavelengths ranging from 2200 to 10000 Å. These are mostly selected from theory but are augmented with high-quality experimental measurements from this work and from the literature. The recommended transition probabilities are used in a redetermination of the Ca abundance in the Sun and in the metal-poor star HD 84937.

The branching ratio of intercombination [formula omitted]transitions in the RbCs molecule: Measurements and calculations

We observed the A1Σ+∼b3Π→a3Σ+/X1Σ+laser-induced fluorescence (LIF) of the RbCs molecule excited from the ground X1Σ+state by the Ti:Sapphire laser. The LIF spectra from the common perturbed levels of the singlet-triplet A ∼ b complex was recorded by the Fourier-transform (FT) spectrometer with the instrumental resolution of 0.03 cm−1. The relative intensity distribution in the rotationally resolved A∼b→a3Σ+(va)/X1Σ+(vX)progressions was measured, and their branching ratio was found to be about of 1÷5×10−4in the bound region of the a3Σ+and X1Σ+states. The experiment was complemented with the scalar- and full-relativistic calculations of the A/b−X/atransition dipole moments (TDMs) as functions of internuclear distance. The relative systematic error in the resulting ab initio TDM functions evaluated for the strong A−Xtransition was estimated as few percent in the energy region, where the experimental LIF intensities are relevant. The relative spectral sensitivity of the FT registration system, operated with the InGaAs diode detector and CaF beam-splitter, was calibrated in the range [6 500, 12 000] cm−1by a comparison of experimental intensities in the long A ∼ b → X(vX) LIF progressions of the K2 and KCs molecules with their theoretical counterparts evaluated using the ab initioA−XTDMs. Both experimental and theoretical transition probabilities can be employed to improve the stimulated Raman adiabatic passage process, a → A ∼ b → X, which is exploited for a laser assembling of ultracold RbCs molecules.

Measurements of experimental transition probabilities of 3p54p → 3p54s arrays in neutral argon.

We have determined the absolute transition probabilities of 27 emission lines of neutral argon originating from the 3p54p→3p54s transition array in the wavelength region from 650 to 1100 nm using an argon-filled hollow cathode discharge lamp. The absolute transition probabilities have been deduced using the lifetimes of the upper levels and the measured branching fractions. Atomic oscillator strengths and relative line strengths for all the transitions have been computed using calculated transition probabilities. The experimentally determined transition probabilities are found to be in good agreement with that calculated in the intermediate coupling (IC) scheme. The comparison of experimentally determined transition probabilities with reported theoretical transition probabilities confirms that the IC scheme for the lower as well as for the upper levels seems to be a useful scheme for the level designation for the 3p54p to 3p54s configuration-based levels in argon. Furthermore, the measured relative line strengths are used to validate the J-file sum rule for the 3p54p→3p54s transition array of argon. The reported transition probabilities, oscillator strengths, and relative line strengths are compared with the published data, showing good agreement.

Theoretical transition probabilities, radiative lifetimes and Stark broadening parameters of singly ionized magnesium

ABSTRACTThe presence of spectral lines of singly ionized magnesium (Mg ii) in stellar atmospheres has been reported in different stars. Recently, the low-resolution spectrum obtained from Supernova 2014 J in M82, in which Mg ii absorption lines centred on 4400 Å as well as 7600 Å stand out, has been analysed. This is the motive for the atomic data calculations in this work, which are of much interest in the astrophysical area. In this article, ab initio relativistic Hartree–Fock calculations in an intermediate coupling formalism using Cowan’s code allowed us to obtain the required transition probabilities to calculate the theoretical radiative lifetimes for excited nS−, nP−, nD− and nF− states of singly ionized magnesium. An asymptotic dependence of lifetime (τnl) on the effective principal quantum number (n*) has been determined. Also, the Griem semi-empirical approach was used to obtain the theoretical Stark parameters (width and shift) of spectral lines; these data are displayed for an electron density of 1017 cm−3 and temperatures T = 10–100 (×103 K). We have compared the results of lifetimes for 16 levels and Stark parameters for seven spectral lines with previously reported experiments available in the literature. Finally, we discuss the behaviour of the Stark parameters versus temperature for three relevant spectral lines (2802.70, 2797.99 and 7868.04 Å).

Experimental and theoretical lifetimes and transition probabilities for spectral lines in Nb II

Aims. We have measured and calculated lifetimes of high lying levels in Nb II, and derived absolute transition probabilities by combining the lifetimes with experimental branching fractions.Methods. The lifetimes were measured using time-resolved laser-induced fluorescence in a two-photon and two-step excitation scheme. The branching fractions were measured in intensity calibrated spectra from a hollow cathode discharge, recorded with a Fourier transform spectrometer. The calculations were performed with the relativistic Hartree–Fock method including core polarization.Results. We report experimental lifetimes of 13 levels in the 4d3(4F)5d and 4d3(4F)6s subconfigurations, at an energy around 70 000 cm−1. By combining the lifetimes with experimental branching fractions absolute transition probabilities of 59 lines are derived. The experimental results are compared with calculated values.

Experimental and Theoretical Radiative Lifetimes, Branching Fractions, Transition Probabilities, and Oscillator Strengths of Nb i Levels

Abstract Radiative lifetimes for 60 odd-parity levels of Nb i belonging to the 4d35s5p and 4d45p configurations, except for two levels with unknown configuration, which are in the energy range between 23,910.90 and 37,188.28 cm−1, are measured by the time-resolved laser-induced fluorescence technique. The lifetime values range from 7.1 to 118.7 ns with uncertainties less than 10%. To our knowledge, 45 lifetime values determined in this paper are reported for the first time. By combining the experimental lifetimes with measured or computed branching fractions, we obtain transition probabilities and oscillator strengths for the individual channels depopulating the investigated levels.

Theoretical wavelengths, energy levels, lifetimes, and transition probabilities for the silicon isoelectronic sequence Cd XXXV-Ba XLIII, W LXI

We have performed the theoretical calculations of wavelengths and excitation energies from ground state for 56 fine-structure levels as well as of oscillator strengths and radiative decay rates for all the electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels of the terms belonging to the $$3s^{2}3p^{2}$$ , $$3s^{2}3p3d$$ , $$3s3p^{3}$$ , $$3s3p^{2}3d$$ , $$3s^{2}3d^{2}$$ , and $$3p^{4}$$ configurations for the silicon isoelectronic sequence Cd XXXV-Ba XLIII, W LXI. The calculation is based on the multiconfiguration Dirac–Fock approach, and Breit interaction and quantum electrodynamic corrections are included. Electron correlation effects are taken into account by means of the expansions in terms of a basis of configuration state functions. To achieve the accuracy of the data, independent calculation is provided with similar data obtained from the flexible atomic code, taking W LXI as an example. Our results are compared with each other, and other available theories/experimental values and the energy levels/transition rates for a majority of strong transitions are found to be accurate to be better than 0.5%/10%. The present atomic data should be useful in controlled thermonuclear fusion research and technical plasma modeling.

Experimental and Theoretical Radiative Lifetimes, Branching Fractions, Transition Probabilities, and Oscillator Strengths of Some Highly Excited Odd-parity Levels in Ir i

Abstract Radiative lifetimes of 62 odd-parity levels of Ir i in the energy range between 32513.43 and 58625.10 cm−1 were measured using the time-resolved laser-induced fluorescence technique. The lifetime values obtained are in the range from 3.2 to 345 ns. To our best knowledge, 59 results are reported for the first time. These are compared to computed data deduced from a pseudo-relativistic Hartree–Fock model including core-polarization contributions. From the combination of the experimental lifetime measurements and branching fraction calculations, a new set of transition probabilities and oscillator strengths is derived for 134 Ir i spectral lines of astrophysical interest in the wavelength region from 205 to 418 nm.

E1 and E2 transitions for Fe XVI, Co XVII and Ni XVIII

Electric dipole and electric quadrupole transition data for sodium-like iron, cobalt and nickel have been calculated within the weakest bound electron potential model (WBEPM) theory using experimental energy levels and theoretical expectation values of orbital radii corresponding to those energy levels under the assumption of the $\mathit{LS}$ coupling scheme. The results obtained from this study provide theoretical transition probability and oscillator strength data requested in many fields of researches, especially astrophysics. The calculated transition data results have been compared with available data in the literature. The present results are consistent with earlier calculations. Some new electric quadrupole transition probability values not existing in the data bases, especially for iron have been obtained using this method.

Determination of the electric dipole (E1) gamma ray strength function of 56Mn from the Bn level to low levels by two-step gamma cascades

Investigation of gamma ray strength function is necessary to determine some nuclear characteristics, such as: spin, parity, electromagnetic transitions, cross section, … In this research, 55Mn target was activated on the neutron of 3rd horizontal channel of Dalat nuclear reactor. The experimental data was collected by event-event coincidence by gammagamma coincidence system. The 56Mn deexcitation afforded the collected of 49 gamma – gamma twostep cascades. This was applied on shell model to determine the spin, parity, electric dipole gamma strength function (E1) as well as comparing between the theoretical and experimental E1 transition probabilities

Mutual Information Analysis on Spatial Modulation Multiple Antenna System

Spatial modulation (SM) is a recently proposed multiple-input multiple-output (MIMO) architecture that exploits the space domain for information transmission. In this paper, SM systems with continuous amplitude-phase modulation (APM) and the corresponding maximum likelihood (ML) active transmit antenna detector are considered. We introduced a method to compute the theoretical transition probability matrix and the mutual information of the ML antenna detector. For SM multiple-input single-output (MISO) system, we derive the error probability and the mutual information of the antenna detector in closed-form. For multiple receive antenna SM system, the union bound of error probability and the lower bound of antenna detection mutual information are proposed. The analytical results are verified by numerical simulation over Rayleigh fading channels. We investigate systems with different number of antennas and APM symbol input distributions to evaluate the performance of SM. The joint APM and antenna detection mutual information of SM systems is compared to the capacity of vertical Bell Labs layered space-time (V-BLAST) spatial multiplexing MIMO scheme. Our research gives achievable transmission rates of SM-MISO/MIMO systems and can be a guideline for suitable application scenarios.

Assessing Uncertainties of Theoretical Atomic Transition Probabilities with Monte Carlo Random Trials.

This paper suggests a method of evaluation of uncertainties in calculated transition probabilities by randomly varying parameters of an atomic code and comparing the results. A control code has been written to randomly vary the input parameters with a normal statistical distribution around initial values with a certain standard deviation. For this particular implementation, Cowan’s suite of atomic codes (R.D. Cowan, The Theory of Atomic Structure and Spectra, Berkeley, CA: University of California Press, 1981) was used to calculate radiative rates of magnetic-dipole and electric-quadrupole transitions within the ground configuration of titanium-like iron, Fe V. The Slater parameters used in the calculations were adjusted to fit experimental energy levels with Cowan’s least-squares fitting program, RCE. The standard deviations of the fitted parameters were used as input of the control code providing the distribution widths of random trials for these parameters. Propagation of errors through the matrix diagonalization and summation of basis state expansions leads to significant variations in the resulting transition rates. These variations vastly differ in their magnitude for different transitions, depending on their sensitivity to errors in parameters. With this method, the rate uncertainty can be individually assessed for each calculated transition.

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.

HIGH-ACCURACY MR-MP PERTURBATION THEORY ENERGY AND RADIATIVE RATES CALCULATIONS FOR CORE-EXCITED TRANSITIONS IN Fe XVI

Accurate theoretical energy level, lifetime, and transition probability calculations of core-excited Fe XVI were performed employing the relativistic Multireference Moller-Plesset perturbation theory. In these computations the term energies of the highly excited n ≤ 5 states arising from the configuration 1s 22sk 2pm 3l p nl' q , where k + m + p + q = 9, l ≤ 3 and p + q ≤ 2 are considered, including those of the autoionizing levels with a hole-state in the L-shell. All even and odd parity states of sodium-like iron ion were included for a total of 1784 levels. Comparison of the calculated L-shell transition wavelengths with those from laboratory measurements shows excellent agreement. Therefore, our calculation may be used to predict the wavelengths of as of yet unobserved Fe XVI, such as the second strongest 2p-3d Fe XVI line, which has not been directly observed in the laboratory and which blends with one of the prominent Fe XVII lines.

SpMC: Modelling Spatial Random Fields with Continuous Lag Markov Chains

Currently, a part of the R statistical software is developed in order to deal with spatial models. More specifically, some available packages allow the user to analyse categorical spatial random patterns. However, only the spMC package considers a viewpoint based on transition probabilities between locations. Through the use of this package it is possible to analyse the spatial variability of data, make inference, predict and simulate the categorical classes in unobserved sites. An example is presented by analysing the well-known Swiss Jura data set. Introduction Originally, the spMC package (Sartore, 2013) was developed with the purpose of analysing categorical data observed in 3-D locations. It deals with stochastic models based on Markov chains, which may be used for the analysis of spatial random patterns in continuous multidimensional spaces (Carle and Fogg, 1997). Its results are easily interpretable and it is a good alternative to the T-PROGS software developed by Carle (1999), which is oriented towards modelling groundwater systems. The models considered in the spMC package are used to analyse any categorical random variable Z(s) at the d-dimensional position s 2 R d which satisfies the Markov property. Other R packages are also helpful for analysing categorical spatial data. For example, the gstat package (Pebesma, 2004) allows for analyses using traditional methods such as the parameter estimation of spatial models based on variograms and kriging techniques for predictions. All these methods and their variants are also available in other packages, e.g. geoRglm (Christensen and Ribeiro Jr, 2002) and RandomFields (Schlather, 2013). When Z(s) is assumed to be linked to a continuous hidden random process, these packages are useful for studying the covariance structure of the data. The spMC package extends the functionality of the T-PROGS software to R users. New useful functions are included for faster modelling of transition probability matrices, and efficient algorithms are implemented for improving predictions and simulations of categorical random fields. The main tasks and their functions are clearly summarised in Table 1. Three different fitting methods were implemented in the package. The first is based on the estimates of the main features that characterise the process, the second focuses on the minimisation of the discrepancies between the empirical and theoretical transition probabilities, and the third follows the maximum entropy approach. Once the model parameters are properly estimated, transition probabilities are calculated through the matrix- valued exponential function (see Higham, 2008, Algorithm 10.20 in Chapter 10). These transition probabilities are then combined to predict the category in an unsampled position. Three algorithms are used to simulate spatial random fields; those based on the kriging techniques (Carle and Fogg, 1996), those using fixed and random path methods (Li, 2007a; Li and Zhang, 2007), or those using multinomial categorical simulation proposed by Allard et al. (2011). In order to reduce computation time through OpenMP API (version 3.0; OpenMP Architecture Review Board, 2008), the setCores() function allows the user to change the number of CPU cores, so that one can mix shared memory parallel techniques with those based on the Message Passing Interface (The MPI Forum, 1993) as described in Smith (2000). Here, it will be shown how to perform a geostatistical analysis of the Jura data set (Goovaerts, 1997) using the spMC package (version 0.3.1). The data set consists of 359 sampled spatial coordinates and their respective observed realisations of two categorical variables (related to the rock-type and the land use) and some continuous variables (corresponding to the topsoil content).

K X-Ray Energies and Transition Probabilities for He-, Li- and Be-like Praseodymium ions

Theoretical transition energies and probabilities for He-, Li and Be-like Praseodymium ions are calculated in the framework of the multi-configuration Dirac-Fock method (MCDF), including QED corrections. These calculated values are compared to recent experimental data obtained in the Livermore SuperEBIT electron beam ion trap facility [1].