Atomic Transition Probabilities Research Articles

Physics package based on intracavity laser cooling 87Rb atoms for space cold atom microwave clock

Abstract This article proposes a new physics package to enhance the frequency stability of the space cold atom clock with the advantages of a microgravity environment. Clock working processes, including atom cooling, atomic state preparation, microwave interrogation, and transition probability detection, are integrated into the cylindrical microwave cavity to achieve a high-performance and compact physics package for the space cold atom clock. We present the detailed design and ground-test results of the cold atom clock physics package in this article, which demonstrates a frequency stability of 1.2 × 10-12 τ-1/2 with a Ramsey linewidth of 12.5 Hz, and a better performance is predicted with a 1 Hz or a narrower Ramsey linewidth in microgravity environment. The miniaturized cold atom clock based on intracavity cooling has great potential for achieving space high-precision time-frequency reference in the future.

Correction for the calculated XANES spectra of 1,4,7,10-alkyltetracenes considering the total electron yield (TEY) efficiency of sp2- and sp3-carbon atoms.

The calculated X-ray-absorption-near-edge-structure (XANES) spectra in the CK region of 1,4,7,10-alkyltetracenes, which are composed of both sp2-C atoms in the tetracene ring and sp3-C atoms in the alkyl-chains, can be corrected by considering the total electron yield (TEY) efficiency of sp3-C relative to sp2-C. In the correction, the previously measured TEY efficiency of k = 0.51 is applied to the calculated transition probabilities for sp3-C atoms. Then the calculated CK-XANES obtained from density functional theory (DFT) calculations can well reproduce the measured TEY-CK-XANES. Especially, the calculated π*/σ* peak intensity ratios are in good agreement with the measured ones. This suggests that a similar correction for the calculated XANES is necessary for compounds composed of multi-components with different TEY efficiencies.

Experimental and Semiclassical Stark Widths and Shifts for Spectral Lines of Neutral and Ionized Atoms (A Critical Review of Experimental and Semiclassical Data for the Period 2008 Through 2020)

This Review Article compares new experimental and corresponding semiclassical Stark broadened data for non-hydrogenic spectral lines of neutral atoms and positive ions. This Review covers the period 2008 until the end of 2020 and presents the continuation of previous critical reviews from 1976 (two), 1984 (two), 1990, 2002, and one from 2009. This Review reports the Stark broadening parameters of 1665 spectral lines belonging to 35 elements with 61 different atomic and ion species. The data are taken from 60 papers. Experimental data are arranged by elements and spectra, and these are reported in tables in alphabetical and numerical order, respectively. Each experimental Stark broadening parameter is followed with estimated accuracy. The experimental Stark broadening and shift data presented in the tables are compared with the corresponding semiclassical results available in the literature. In addition, for comparison experiments versus semiclassical theoretical Stark broadening parameters, a numerically improved theoretical approach developed based on Griem and co-workers’ theory is used to evaluate Stark widths and shifts of all studied lines whenever required atomic energy levels data and transition probabilities are available. At the end of the text report, for each analyzed neutral or ion species, the information about the location of the same species data in preceding reviews is given.

Atomic Transition Probabilities for Transitions of Si i and Si ii and the Silicon Abundances of Several Very Metal-poor Stars ∗ ∗ Based on observations made with the NASA/ESA Hubble Space Telescope (HST), obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. Other data

We report new measurements of branching fractions for 20 UV and blue lines in the spectrum of neutral silicon (Si i) originating in the 3s 23p4s 3Po 1,2,1Po 1, and 3s3p 3 1Do 1,2 upper levels. Transitions studied include both strong, nearly pure LS multiplets as well as very weak spin-forbidden transitions connected to these upper levels. We also report a new branching fraction measurement of the 4P1/2–2Po 1/2,3/2 intercombination lines in the spectrum of singly ionized silicon (Si ii). The weak spin-forbidden lines of Si i and Si ii provide a stringent test on recent theoretical calculations, to which we make comparison. The branching fractions from this study are combined with previously reported radiative lifetimes to yield transition probabilities and log(gf) values for these lines. We apply these new measurements to abundance determinations in five metal-poor stars.

FitAik: A package to calculate least-square fitted atomic transitions probabilities

We present a new method implemented in our new package FitAik, to perform least-squares fitting of calculated and experimental atomic transition probabilities, by using the mono-electronic transition integrals 〈nℓ|r|n′ℓ′〉 (with r the electronic radial coordinate) as adjustable quantities. FitAik is interfaced to the Cowan suite of codes, for which it automatically writes input files and reads output files. We illustrate our procedure with the example of Er+ ion, for which the agreement between calculated and experimental Einstein coefficients is found to be very good. The source code of FitAik can be found on GitLab, and the calculated Einstein coefficients are stored in our new database CaDDiAcS. They are also used to calculate the dynamic dipole polarizability of Er+.

Improvement of the short- and long-term stability of high performance portable optically pumped cesium beam atomic clock

The research of optically pumped cesium beam atomic clock (OPCB) at Peking University has lasted for decades. At present, the short-term frequency stability is 3×10−12/τ and the long-term (5-day) frequency stability can reach 7 × 10−15. The optimization methods of the short-term frequency stability are using laser induced beam spectrum to stabilize the laser frequency, using cyclic transition to detect the atomic state and using a cesium oven with a collimator to generate the cesium atomic beam. The methods of obtaining the good long-term frequency stability are controlling the microwave power based on the atomic transition probability, controlling the C-field intensity based on Zeeman frequency and controlling the laser power using fluorescence. The compact optically pumped cesium beam atomic clock of Peking University is expected to contribute to the field of timing, positioning, navigation and high speed digital communication.

OPTIMIZED RELATIVISTIC MANY-BODY PERTURBATION THEORY IN CALCULATIONS OF ATOMIC SPECTRAL AND RADIATION CHARACTERISTICS: Eu ATOM

The new formalism of the relativistic gauge-invariant perturbation theory (RMBPT-ODF) with the optimized Dirac-Fock approximation and a generalized energy approach is applied to the study of energy, radiation, and spectroscopic characteristics of a group of heavy atomic systems, in particular, energy levels and transition probabilities and oscillator strengths of the transitions 4f7(8S)6s2 8S7/2 4f7(8S)6s6p 8P5/2,7.2,9.2, 4f7(8S)6s7p 8P5/2,7\2, 4f7(8S)6s8p 8P9/2,7\2 in spectrum of the europium atom Eu I. It is shown that the required formalism, in comparison with the standard non-optimized relativistic Hartree-Fock and Dirac-Fock methods, allows obtaining more accurate data both on energies and amplitudes and probabilities of radiative transitions, which is due to the use of the optimized zero ODF approximation, a fairly complete and effective account of complex many-body exchange-correlation effects. The contribution due to the polarization of the core reaches 30% of the value of the oscillator strength; the value of the calibration-invariant contribution to the radiation width is fractions of a percent, in contrast to all existing methods of modern atomic spectroscopy, for which the contribution reaches 5-50%.

Fermi two-atom problem: Nonperturbative approach via relativistic quantum information and algebraic quantum field theory

In this work we revisit the famous Fermi two-atom problem, which concerns how relativistic causality impacts atomic transition probabilities, using the tools from relativistic quantum information and algebraic quantum field theory. The problem has sparked different analyses from many directions and angles since the proposed solution by Buchholz and Yngvason [Phys. Rev. Lett. 73, 613 (1994)]. Some of these analyses employ various approximations, heuristics, and perturbative methods, which tends to render some of the otherwise useful insights somewhat obscured. It is also noted that they are all studied in flat spacetime. We show that current tools in relativistic quantum information, combined with an algebraic approach to quantum field theory, are now powerful enough to provide fuller and cleaner analysis of the Fermi two-atom problem for arbitrary curved spacetimes in a completely nonperturbative manner. Our result gives the original solution of Buchholz and Yngvason a very operational reinterpretation in terms of qubits interacting with a quantum field and allows for various natural generalizations and inclusion of detector-based local measurement for the quantum field [Phys. Rev. D 105, 065003 (2022)].

Improved Atomic Transition Probabilities for UV and Optical Lines of Hf II and Determination of the Hf Abundance in Two Metal-poor Stars*

Abstract We report new branching fraction measurements for 199 UV and optical transitions of Hf ii. These transitions range in wavelength (wavenumber) from 2068 to 6584 Å (48,322–15,183 cm−1) and originate in 17 odd-parity upper levels ranging in energy from 38,578 to 53,227 cm−1. The branching fractions 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 25%. Comparison is made to transition probabilities from the literature where such data exist. We use these new transition probabilities to derive improved Hf abundances in two metal-poor stars. HD 196944 is enhanced in s-process elements, and we derive log ε (Hf) = −0.72 ± 0.03 (σ = 0.09) from 12 Hf ii lines. HD 222925 is enhanced in r-process elements, and we derive log ε (Hf) = 0.32 ± 0.03 (σ = 0.11) from 20 Hf ii lines. These measurements greatly expand the number of potentially useful Hf ii lines for analysis in UV and optical spectra.

Calculation of Transition Probabilities in Quantum Mechanics with a Nonnegative Distribution Function in the Maple Computer Algebra System

In the Maple computer algebra system, an algorithm is implemented for symbolic and numerical computations for finding the transition probabilities for hydrogen-like atoms in quantum mechanics with a nonnegative quantum distribution function (QDF). Quantum mechanics with a nonnegative QDF is equivalent to the standard theory of quantum measurements. However, the presence in it of a probabilistic quantum theory in the phase space gives additional possibilities for calculating and interpreting the results of quantum measurements. The methods of computer algebra seem to be necessary for the relevant calculations. The calculation of the matrix elements of operators is necessary for determining the energy levels, oscillator strengths, and radiation transition parameters for atoms and ions with an open shell. Transition probabilities are calculated and compared with experimental data. They are calculated using the Galerkin method with the Sturm functions of the hydrogen atom as coordinate functions. The verification of the model showed good agreement between the calculated and experimentally measured transition probabilities.

Ground state excitation of an atom strongly coupled to a free quantum field

This paper presents a nonperturbative treatment of strong-coupling induced effects in atom-field systems which cannot be seen in traditional perturbative treatments invoking compromising assumptions such as the Born-Markov, rotating wave or Fermi Golden rule. We consider an atom whose internal degrees of freedom are modeled by a harmonic oscillator, bilinearly coupled to a scalar quantum field, representing one of the two polarizations of an electromagnetic field. Because the whole system is Gaussian we can solve this problem exactly. Using the open quantum system conceptual framework and the influence functional formalism we derive the dynamics of the reduced density matrix for the atom which enables the calculation of atomic transition probability and other relevant physical quantities. Finding an exact solution to this problem has the distinct advantage of enabling one to capture fully the strong coupling regime and discover interesting effects such as spontaneous ground state excitation which is unfathomable in perturbative treatments. The conventional description of atomic-optical activities is predicated on the assumption that the state of the total atom-field system is a product state of the atomic excitations and the photon number states, an assumption which is valid only for vanishingly weak coupling. The correct energy eigenfunctions to use should be that of the Hamiltonian of the combined atom-field system. Other features associated with finite to strong coupling effects such as resonance peak broadening and transition from a gapped to a gapless spectrum can all be understood from this perspective. Finally, to put the issues in a proper perspective we take the perturbative limit of the exact results and compare them with those from conventional TDPT. This enables one to pin-point where the deficiencies of TDPT lie as one removes the ultra-weak coupling assumption.

Approach to quantitative spectroscopy of atomic vapor in optical nanocells.

We present a method for recovery of narrow homogeneous spectral features out of a broad inhomogeneous overlapped profile based on second-derivative processing of the absorption spectra of alkali metal atomic vapor nanocells. The method is shown to preserve the frequency positions and amplitudes of spectral transitions, thus being applicable for quantitative spectroscopy. The proposed technique was successfully applied and tested for measurements of hyperfine splitting and atomic transition probabilities, development of an atomic frequency reference, determination of isotopic abundance, study of atom-surface interaction, and determination of magnetic-field-induced modification of atomic transition frequency and probability. The obtained experimental results are fully consistent with theoretical modeling.

Atomic Transition Probabilities for UV and Blue Lines of Fe ii and Abundance Determinations in the Photospheres of the Sun and Metal-poor Star HD 84937

Abstract We report new branching fractions (BFs) for 121 UV lines from the low-lying odd-parity levels of Fe ii belonging to the z6Do, z6Fo, z6Po, z4Fo, z4Do, and z4Po terms of the 3d6(5D)4p configuration. These lines range in wavelength from 2250 to 3280 Å and originate in levels ranging in energy from 38,459 to 47,626 cm−1. In addition, we report BFs for 10 weak blue lines connecting to the z4Do term that range in wavelength from 4173 to 4584 Å. The BFs are combined with radiative lifetimes from the literature to determine transition probabilities and log(gf) values. Comparison is made to selected experimental and theoretical data from the literature. Our new data are applied to iron abundance determinations in the Sun and in metal-poor star HD 84937. For the Sun, eight blue lines yield log ε(Fe) = 7.46 ± 0.03, in agreement with standard solar abundance estimates. For HD 84937 the observable wavelength range extends to the vacuum UV (λ ≥ 2327 Å), and from 75 lines we derive log ε(Fe) = 5.26 ± 0.01 (σ = 0.07), near to the metallicity estimates of past HD 84937 studies.

Quantitative atomic spectroscopy, a review of progress in the optical-UV region and future opportunities

The development of tunable dye lasers and a simple atomic and ionic beam source for all elements were critical in establishing a reliable absolute scale for atomic transition probabilities in the optical to near UV regions. The laboratory astrophysics program at the University of Wisconsin - Madison (UW) concentrates on neutral and singly-ionized species transitions that are observable in astronomical spectra of cool stars, emphasizing the rare earth n(eutron)-capture elements and the Fe-group elements that are important inputs to early Galactic nucleosynthesis studies. The UW program is one of several productive efforts on atomic transition probabilities. These programs generally use time-resolved laser-induced-fluorescence (TR-LIF) to accurately measure total decay rates and data from high resolution Fourier transform spectrometers (FTSs) to determine emission branching fractions (BFs). The UW laboratory results almost always are directly linked to astronomical chemical composition efforts. There are good opportunities to extend similar research to other wavelength regions.

Transition Probabilities of Sc i and Sc ii and Scandium Abundances in the Sun, Arcturus, and HD 84937

Abstract New branching fraction (BF) measurements for lines of Sc i and Sc ii from 24 Fourier transform spectra calibrated using standard lamps and the Ar branching ratio method are reported. The BFs for 259 lines are converted to absolute atomic transition probabilities using published radiative lifetimes from laser-induced fluorescence measurements. Detailed comparison to earlier published BF measurements corroborates most of the earlier results, with the exception of the yellow-line multiplet of Sc ii near 17,500 cm−1 or ≈5700 Å. The BFs of lines in this multiplet are found to be systematically too small by several error bars in earlier research. These new lab data on Sc, as well as recent hyperfine-structure studies, are applied to determine the abundance of scandium in the Sun, Arcturus, and HD 84937. General agreement is found with previous scandium abundance determinations in these stars. New consideration of scandium in metal-poor stars confirms that Sc abundances are correlated with Ti and V abundances.

Measurement of atomic transition probabilities with laser-induced breakdown spectroscopy using the 3D Boltzmann plot method

This work presents a method for the determination of atomic transition probability of the emission lines of a given element using the 3D Boltzmann plot method. The method exploits the third (temporal) dimension of a classical 2D Boltzmann plot for the determination of the plasma parameters. As an example and test of the proposed method, we acquired several time-resolved spectra during laser ablation of pure tungsten sample at different energies. The time interval in which the conditions of Local Thermal Equilibrium can be guaranteed was estimated. The results lead to a criterion for the selection of preferred atomic spectral for the measurements of plasma parameters. The effect of self-absorption on the measured transition probabilities is also evaluated and discussed.

Rydberg Energy Levels and Quantum Defects of some Semiconductor Elements

Weakest bound Electron Potential Model Theory has turned out to be a successful theory in explaining many atomic properties, namely, energy levels, transition probabilities and oscillator strengths. The theory has also been used to calculate Rydberg energy levels and quantum defects. In this paper we studied semiconductor elements Boron and Silicon. We calculated energy levels of Rydberg atoms of Boron and Silicon up to n = 50 levels using WBEPMT. We also calculated quantum defects in principle quantum number for various configurations of these elements.

Transition Probabilities of Co ii Weak Lines to the Ground and Low Metastable Levels.

New branching fraction (BF) measurements based primarily on data from a cross-dispersed echelle spectrometer are reported for 84 lines of Co ii. The BFs for 82 lines are converted to absolute atomic transition probabilities using radiative lifetimes from laser-induced fluorescence (LIF) measurements on 19 upper levels of the lines. A lifetime of 3.3(2) ns for the z5D0 level is used based on LIF measurements for lifetimes of the four other levels in the z5D term. Twelve of the eighty-four lines are weak transitions connecting to the ground and low metastable levels of Co+. Another 46 lines are strong transitions connecting to the ground and low metastable levels of Co+. For these lines, log(gf) values were measured in earlier studies and, with a few exceptions, are confirmed in this study. Such lines, if unblended in stellar spectra, have the potential to yield Co abundance values unaffected by any breakdown of the local thermodynamic equilibrium approximation in stellar photospheres because the ground and low metastable levels of Co+ are the primary population reservoirs of Co in the photospheres of interest. Weak lines, if unblended, are useful in photospheres with high Co abundance, and strong lines are useful in metal-poor photospheres. New hyperfine structure A constants for 28 levels of ionized Co from least-squares fits to Fourier transform spectra line profiles are reported. These laboratory data are applied to re-determine the Co abundance in the metal-poor halo star HD 84937. BFs and transition probabilities for 19 lines are reported for the first time.

Improving the Ar i and ii branching ratio calibration method: Monte Carlo simulations of effects from photon scattering/reflecting in hollow cathodes

The Ar i and ii branching ratio calibration method is discussed with the goal of improving the technique. This method of establishing a relative radiometric calibration is important in ongoing research to improve atomic transition probabilities for quantitative spectroscopy in astrophysics and other fields. Specific suggestions are presented along with Monte Carlo simulations of wavelength dependent effects from scattering/reflecting of photons in a hollow cathode.

Hysteresis Effects on a Non-uniform Transmission Line with Induced Quantum Mechanical Atomic Transitions

This study describes the effect of hysteresis on the generation of the higher harmonics in the line voltage and current in a non-uniform transmission line when we include a quadratic non-linear term having memory to account for the hysteresis effect in the inductance part of line. The simulational analysis using MATLAB is presented which works with a non-uniform line having hysteresis. These simulations are based on a theoretical spatial Fourier analysis combined with perturbation theory which is used without bothering about source and load. The line differential equations are solved approximately in the space- time-frequency domain using perturbation theory and the numerical computations have been carried out for the voltage and current amplitude characteristics. In Appendix 1, some theoretical explanations that support our non-linear memory-based hysteresis model based on Landau’s equation of precession of a magnetic moment in a magnetic field are included. This paper also includes a brief derivation of atomic transition probability produced by e-m radiation from the transmission line falling on an atom in the far field zone. This calculation enables us to derive maximum likelihood estimation(MLE) of the hysteresis parameters by measuring which atomic transitions have occurred.