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Atoms, Volume 7, Issue 2 (June 2019)

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Cover Story (view full-size image) The measurements of electron and positron magnetic moments underway should improve 10-fold upon a 3 [...] Read more.
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Open AccessArticle
Stochastic Electrodynamics: Lessons from Regularizing the Harmonic Oscillator
Received: 29 April 2019 / Revised: 30 May 2019 / Accepted: 9 June 2019 / Published: 10 June 2019
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Abstract
In this paper, the harmonic oscillator problem in Stochastic Electrodynamics is revisited. Using the exact shape of the Lorentz damping term prevents run-away effects. After introducing a cut-off in the stochastic power spectrum and regularizing the stochastic force, all relevant integrals are dominated [...] Read more.
In this paper, the harmonic oscillator problem in Stochastic Electrodynamics is revisited. Using the exact shape of the Lorentz damping term prevents run-away effects. After introducing a cut-off in the stochastic power spectrum and regularizing the stochastic force, all relevant integrals are dominated by resonance effects only and results are derived that stem from those in the quantum ground state. For an orbit with specific position and momentum at an initial time, the average energy and the average rate of energy change are evaluated, which stem with each other. Resonance effects are highlighted along the way. An outlook on the hydrogen ground state problem is provided. Full article
(This article belongs to the Special Issue Stochastic Electrodynamics)
Open AccessArticle
The Role of Relativistic Many-Body Theory in Electron Electric Dipole Moment Searches Using Cold Molecules
Received: 30 April 2019 / Revised: 25 May 2019 / Accepted: 28 May 2019 / Published: 10 June 2019
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Abstract
In this review article, we survey some of our results pertaining to the search for the electric dipole moment of the electron (eEDM), using heavy polar molecules. In particular, we focus on the relativistic coupled cluster method (RCCM) and its applications to eEDM [...] Read more.
In this review article, we survey some of our results pertaining to the search for the electric dipole moment of the electron (eEDM), using heavy polar molecules. In particular, we focus on the relativistic coupled cluster method (RCCM) and its applications to eEDM searches in YbF, HgX (X = F, Cl, Br, and I), BaF, HgA (A = Li, Na, and K), and YbOH. Our results are presented in a systematic manner, by first introducing the eEDM and its measurement using molecules, the importance of relativistic many-body theory, and finally our results, followed by future prospects. Full article
(This article belongs to the Special Issue Search for New Physics with Cold and Controlled Molecules)
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Open AccessReview
Shock Waves in Laser-Induced Plasmas
Received: 7 May 2019 / Revised: 3 June 2019 / Accepted: 5 June 2019 / Published: 7 June 2019
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Abstract
The production of a plasma by a pulsed laser beam in solids, liquids or gas is often associated with the generation of a strong shock wave, which can be studied and interpreted in the framework of the theory of strong explosion. In this [...] Read more.
The production of a plasma by a pulsed laser beam in solids, liquids or gas is often associated with the generation of a strong shock wave, which can be studied and interpreted in the framework of the theory of strong explosion. In this review, we will briefly present a theoretical interpretation of the physical mechanisms of laser-generated shock waves. After that, we will discuss how the study of the dynamics of the laser-induced shock wave can be used for obtaining useful information about the laser–target interaction (for example, the energy delivered by the laser on the target material) or on the physical properties of the target itself (hardness). Finally, we will focus the discussion on how the laser-induced shock wave can be exploited in analytical applications of Laser-Induced Plasmas as, for example, in Double-Pulse Laser-Induced Breakdown Spectroscopy experiments. Full article
(This article belongs to the Special Issue Laser Plasma Spectroscopy Applications)
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Open AccessArticle
Optical Rotation Approach to Search for the Electric Dipole Moment of the Electron
Received: 30 April 2019 / Revised: 2 June 2019 / Accepted: 5 June 2019 / Published: 7 June 2019
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Abstract
The P,T-odd Faraday effect (i.e., rotation of the polarization plane of light propagating through a medium in presence of the external electric field due to P, T symmetry violating interactions) is considered for several atomic species: Ra, Pb, Tl, [...] Read more.
The P , T -odd Faraday effect (i.e., rotation of the polarization plane of light propagating through a medium in presence of the external electric field due to P , T symmetry violating interactions) is considered for several atomic species: Ra, Pb, Tl, Hg, Cs, and Xe. Corresponding theoretical simulation of P , T -odd Faraday experiment, with already achieved intracavity absorption spectroscopy characteristics and parameters, is performed. The results show that the magnetic dipole transitions in the Tl and Pb atoms as well as the electric dipole transitions in the Ra, Hg and Cs atoms are favorable for the observation of the P , T -odd Faraday optical rotation. The estimation of the rotation angle of the light polarization plane demonstrates that recently existing boundaries for the electron electric dipole moment can be improved by one-two orders of magnitude. Full article
(This article belongs to the Special Issue Search for New Physics with Cold and Controlled Molecules)
Open AccessArticle
Analytical Solution of the Hanle Effect in View of CLASP and Future Polarimetric Solar Studies
Received: 5 March 2019 / Revised: 28 May 2019 / Accepted: 29 May 2019 / Published: 4 June 2019
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Abstract
We have solved a problem of the Hanle effect for the hydrogen Lyman-α line in an intuitive and straightforward way. The Stokes parameters amid an anisotropic radiation field and a magnetic field are derived as an analytical formula which enables us to [...] Read more.
We have solved a problem of the Hanle effect for the hydrogen Lyman- α line in an intuitive and straightforward way. The Stokes parameters amid an anisotropic radiation field and a magnetic field are derived as an analytical formula which enables us to conduct immediate analyses of observation data taken by spectro-polarimetry. The derived formula is, in particular, supposed to be used for the analysis of the data taken by CLASP (Chromospheric Lyman-Alpha Spectro-Polarimeter), which has aimed at measuring the linear polarization in the hydrogen Lyman- α line (121.6 nm) and then evaluating the magnetic field in the upper chromosphere and the transition region. The dependence of the Stokes parameters on the strength and direction of the magnetic field and on the observation angle is derived with our analytical model. The results show a satisfactory agreement with those of a more rigorous numerical calculation where the radiative transfer is taken into account and the consistency is assured between the anisotropic randiation field and the polarized atomic state. Full article
(This article belongs to the Special Issue Plasma Spectroscopy in the Presence of Magnetic Fields)
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Open AccessArticle
Transition Rates for 3s3p2 4P–3s3p4s 4Po Transitions in Al i
Received: 1 May 2019 / Revised: 23 May 2019 / Accepted: 26 May 2019 / Published: 4 June 2019
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Abstract
Fully relativistic calculations have been performed for two multiplets, 3s3p24P and 3s3p4s4Po, in Al i. Wave functions were obtained for all levels of these multiplets using the [...] Read more.
Fully relativistic calculations have been performed for two multiplets, 3 s 3 p 2 4 P and 3 s 3 p 4 s 4 P o , in Al i. Wave functions were obtained for all levels of these multiplets using the grasp programs. Reported are the E1 transitions rates for all transitions between levels of these multiplets. Transition energies and transition rates are compared with observed values and other theory. Our calculated transition rates are smaller by about 10% than observed rates, reducing a large discrepancy between earlier calculations and experiments. Full article
(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)
Open AccessArticle
Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying Z
Received: 29 April 2019 / Revised: 16 May 2019 / Accepted: 29 May 2019 / Published: 3 June 2019
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Abstract
The question of stability of a given quantum system made up of charged particles is of fundamental interest in atomic, molecular, and nuclear physics. In this work, the stability for the negatively charged positronium (Ps)-like ions or the three-body system (Ze [...] Read more.
The question of stability of a given quantum system made up of charged particles is of fundamental interest in atomic, molecular, and nuclear physics. In this work, the stability for the negatively charged positronium (Ps)-like ions or the three-body system ( Z e + , e , e ) with Yukawa potentials is studied using correlated exponential wavefunctions based on the Ritz variational method. We obtained the critical screening parameter μ C as a function of the continuously varied nuclear charge Z , the critical nuclear charge Z C as a function of the screening parameter μ , and the ionization energies in terms of the screening parameter μ and Z . The critical nuclear charge for the bare Coulomb system ( Z e + , e , e ) obtained using 700-term correlated exponential wavefunctions is in accord with the reported results. The ionization energy, μ C , and Z C for the Yukawa system ( Z e + , e , e ) exhibit interesting behaviors. The present study describes the possible nonexistence of Borromean binding as well as Efimov states. The possible existence of quasi-bound resonances states for the negatively charged screened Ps-like ions is briefly discussed. Full article
(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)
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Open AccessArticle
Line Shapes in a Magnetic Field: Trajectory Modifications I: Electrons
Received: 15 February 2019 / Revised: 21 May 2019 / Accepted: 22 May 2019 / Published: 27 May 2019
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Abstract
In recent work, the effect of a magnetic field on the line shapes via the modification of electron perturber trajectories was considered. In the present paper we revisit this idea using a variation of the Collision-time Statistics method, in order to account for [...] Read more.
In recent work, the effect of a magnetic field on the line shapes via the modification of electron perturber trajectories was considered. In the present paper we revisit this idea using a variation of the Collision-time Statistics method, in order to account for a l l relevant perturbers. We also obtain line profiles for the hydrogen L α line for conditions of astrophysical interest. Although the Collision-time statistics method works for both electrons and ions, we apply a simplification here that results in an excessive number of ions having to be simulated. As a result, the present, simplified version, is typically only appropriate for electrons. Full article
(This article belongs to the Special Issue Plasma Spectroscopy in the Presence of Magnetic Fields)
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Open AccessArticle
Extraction of Zero-Point Energy from the Vacuum: Assessment of Stochastic Electrodynamics-Based Approach as Compared to Other Methods
Received: 16 February 2019 / Revised: 12 May 2019 / Accepted: 17 May 2019 / Published: 23 May 2019
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Abstract
In research articles and patents several methods have been proposed for the extraction of zero-point energy from the vacuum. None of the proposals have been reliably demonstrated, yet they remain largely unchallenged. In this paper the underlying thermodynamics principles of equilibrium, detailed balance, [...] Read more.
In research articles and patents several methods have been proposed for the extraction of zero-point energy from the vacuum. None of the proposals have been reliably demonstrated, yet they remain largely unchallenged. In this paper the underlying thermodynamics principles of equilibrium, detailed balance, and conservation laws are presented for zero-point energy extraction. The proposed methods are separated into three classes: nonlinear processing of the zero-point field, mechanical extraction using Casimir cavities, and the pumping of atoms through Casimir cavities. The first two approaches are shown to violate thermodynamics principles, and therefore appear not to be feasible, no matter how innovative their execution. The third approach, based upon stochastic electrodynamics, does not appear to violate these principles, but may face other obstacles. Initial experimental results are tantalizing but, given the lower than expected power output, inconclusive. Full article
(This article belongs to the Special Issue Stochastic Electrodynamics)
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Open AccessArticle
Energy Considerations of Classical Electromagnetic Zero-Point Radiation and a Specific Probability Calculation in Stochastic Electrodynamics
Received: 16 February 2019 / Revised: 16 March 2019 / Accepted: 1 April 2019 / Published: 21 May 2019
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Abstract
The zero-point (ZP) radiation field in stochastic electrodynamics (SED) is considered to be formally infinite, or perhaps bounded by mechanisms yet to be revealed someday. A similar situation holds in quantum electrodynamics (QED), although there the ZP field is considered to be “virtual”. [...] Read more.
The zero-point (ZP) radiation field in stochastic electrodynamics (SED) is considered to be formally infinite, or perhaps bounded by mechanisms yet to be revealed someday. A similar situation holds in quantum electrodynamics (QED), although there the ZP field is considered to be “virtual”. The first part of this article addresses the concern by some about the related disturbing concept of “extracting energy” from this formally, enormous source of energy. The second part of this article introduces a new method for calculating probabilities of fields in SED, which can be extended to linear oscillators in SED. Full article
(This article belongs to the Special Issue Stochastic Electrodynamics)
Open AccessArticle
On the Spatial Uniformity of the Degree of Ionization in a Helium ECR Plasma Produced under a Simple Cusp Field
Received: 24 March 2019 / Revised: 10 May 2019 / Accepted: 13 May 2019 / Published: 17 May 2019
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Abstract
Production of a plasma that has a large degree of ionization (DOI), volume, and spatial and temporal uniformities is a challenge for the improvement of the performance of plasma-based vapor deposition processes. As a potential candidate for the discharge, we investigate plasma parameters [...] Read more.
Production of a plasma that has a large degree of ionization (DOI), volume, and spatial and temporal uniformities is a challenge for the improvement of the performance of plasma-based vapor deposition processes. As a potential candidate for the discharge, we investigate plasma parameters arising in helium electron cyclotron resonance (ECR) discharges due to a simple cusp field. Two-dimensional distributions of helium atom emission-line intensities were measured using spectroscopy with multiple viewing chords and then de-convoluted by Abel inversion. The local plasma parameters, including the atomic density, were evaluated using collisional-radiative model analysis. The DOI calculated from the electron and atomic densities reached up to 35% and, in most of the region inside the ECR surface, it was more than 10%. Full article
(This article belongs to the Special Issue Plasma Spectroscopy in the Presence of Magnetic Fields)
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Open AccessArticle
Measurement of the Magnetic Field in a Linear Magnetized Plasma by Tunable Diode Laser Absorption Spectroscopy
Received: 26 March 2019 / Revised: 5 May 2019 / Accepted: 6 May 2019 / Published: 15 May 2019
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Abstract
Tunable diode laser absorption spectroscopy (TDLAS) is a commonly used technique to measure the temperature and density of atoms or molecules in a gas. In this work, we demonstrate that the TDLAS diagnostics could be effectively applied to measure the magnetic field in [...] Read more.
Tunable diode laser absorption spectroscopy (TDLAS) is a commonly used technique to measure the temperature and density of atoms or molecules in a gas. In this work, we demonstrate that the TDLAS diagnostics could be effectively applied to measure the magnetic field in a low-density weakly magnetized plasma using the Zeeman splitting of the absorption spectrum of lines from noble gases. The laser wavelength is tailored to fit the 1 s 5 2 p 6 transition of atomic Ar with the wavelength λ = 763.51 nm . Two mechanisms of line broadening and splitting are observed: Doppler broadening and Zeeman effect. The latter is especially pronounced by applying polarization-selective observation of the absorption to the TDLAS measurements. By fitting the σ and π components of the absorption spectrum, the line-integrated magnetic field on the order of 30–50 mT is determined. The agreement between the measured values and the vacuum field (neglecting the impact of the plasma) calculations on the axis of the PSI-2 is found to be about 15–20%. Full article
(This article belongs to the Special Issue Plasma Spectroscopy in the Presence of Magnetic Fields)
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Open AccessArticle
On the Approximate Evaluation of Some Oscillatory Integrals
Received: 4 March 2019 / Revised: 27 April 2019 / Accepted: 29 April 2019 / Published: 5 May 2019
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Abstract
To determine the photon emission or absorption probability for a diatomic system in the context of the semiclassical approximation it is necessary to calculate the characteristic canonical oscillatory integral which has one or more saddle points. Integrals like that appear in a whole [...] Read more.
To determine the photon emission or absorption probability for a diatomic system in the context of the semiclassical approximation it is necessary to calculate the characteristic canonical oscillatory integral which has one or more saddle points. Integrals like that appear in a whole range of physical problems, e.g., the atom–atom and atom–surface scattering and various optical phenomena. A uniform approximation of the integral, based on the stationary phase method is proposed, where the integral with several saddle points is replaced by a sum of integrals each having only one or at most two real saddle points and is easily soluble. In this way we formally reduce the codimension in canonical integrals of “elementary catastrophes” with codimensions greater than 1. The validity of the proposed method was tested on examples of integrals with three saddle points (“cusp” catastrophe) and four saddle points (“swallow-tail” catastrophe). Full article
(This article belongs to the Special Issue Atomic and Ionic Collisions with Formation of Quasimolecules)
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Open AccessArticle
CHSH-Type Inequality Involving Commuting Continuous Variables
Received: 14 February 2019 / Revised: 21 April 2019 / Accepted: 23 April 2019 / Published: 25 April 2019
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Abstract
The correlation of projections of the momentum operators of two particles is used to derive a quantum inequality for continuous variables, which must be satisfied by any bipartite system in a pure state. This inequality resembles a Clauser–Horne–Shimony–Holt (CHSH)-type inequality except for additional [...] Read more.
The correlation of projections of the momentum operators of two particles is used to derive a quantum inequality for continuous variables, which must be satisfied by any bipartite system in a pure state. This inequality resembles a Clauser–Horne–Shimony–Holt (CHSH)-type inequality except for additional terms related to the imaginary component of the weak value of the momentum, which normally remains concealed in the usual quantum description but turns out to be of relevance for entangled states. Our results shed new light on the link between noncommutativity, entanglement and nonlocality of the quantum description. Full article
(This article belongs to the Special Issue Stochastic Electrodynamics)
Open AccessFeature PaperArticle
Towards an Improved Test of the Standard Model’s Most Precise Prediction
Received: 6 March 2019 / Revised: 9 April 2019 / Accepted: 10 April 2019 / Published: 25 April 2019
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Abstract
The electron and positron magnetic moments are the most precise prediction of the standard model of particle physics. The most accurate measurement of a property of an elementary particle has been made to test this result. A new experimental method is now being [...] Read more.
The electron and positron magnetic moments are the most precise prediction of the standard model of particle physics. The most accurate measurement of a property of an elementary particle has been made to test this result. A new experimental method is now being employed in an attempt to improve the measurement accuracy by an order of magnitude. Positrons from a “student source” now suffice for the experiment. Progress toward a new measurement is summarized. Full article
(This article belongs to the Special Issue High Precision Measurements of Fundamental Constants)
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Open AccessArticle
Frozen Core Approximation and Nuclear Screening Effects in Single Electron Capture Collisions
Received: 31 January 2019 / Revised: 28 March 2019 / Accepted: 4 April 2019 / Published: 12 April 2019
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Abstract
Differential cross sections (DCS) for single electron capture from helium by heavy ion impact are calculated using a frozen core 3-body model and an active electron 4-body model within the first Born approximation. DCS are presented for H+, He2+, [...] Read more.
Differential cross sections (DCS) for single electron capture from helium by heavy ion impact are calculated using a frozen core 3-body model and an active electron 4-body model within the first Born approximation. DCS are presented for H+, He2+, Li3+, and C6+ projectiles with velocities of 1 MeV/amu and 10 MeV/amu. In general, the DCS from the two models are found to differ by about one to two orders of magnitude with the active electron 4-body model showing better agreement with experiment. Comparison of the models reveals two possible sources of the magnitude difference: the inactive electron’s change of state and the projectile–target Coulomb interaction used in the different models. Detailed analysis indicates that the uncaptured electron’s change of state can safely be neglected in the frozen core approximation, but that care must be used in modeling the projectile–target interaction. Full article
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Open AccessArticle
Turbulent Intermittency in a Random Fiber Laser
Received: 30 January 2019 / Revised: 1 April 2019 / Accepted: 4 April 2019 / Published: 9 April 2019
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Abstract
In fluid turbulence, intermittency is the emergence of non-Gaussian tails in the distribution of velocity increments in small space and/or time scales. Intermittence is thus expected to gradually disappear as one moves from small to large scales. Here we study the turbulent-like intermittency [...] Read more.
In fluid turbulence, intermittency is the emergence of non-Gaussian tails in the distribution of velocity increments in small space and/or time scales. Intermittence is thus expected to gradually disappear as one moves from small to large scales. Here we study the turbulent-like intermittency effect experimentally observed in the distribution of intensity fluctuations in a disordered continuous-wave-pumped erbium-doped-based random fiber laser with specially-designed random fiber Bragg gratings. The intermittency effect is investigated as a crossover in the distribution of intensity increments from a heavy-tailed distribution (for short time scales), to a Gaussian distribution (for large time scales). The results are theoretically supported by a hierarchical stochastic model that incorporates Kolmogorov’s theory of turbulence. In particular, the discrete version of the hierachical model allows a general direct interpretation of the number of relevant scales in the photonic hierarchy as the order of the transitions induced by the non-linearities in the medium. Our results thus provide further statistical evidence for the interpretation of the turbulence-like emission previously observed in this system. Full article
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Open AccessArticle
Testing Quantum Coherence in Stochastic Electrodynamics with Squeezed Schrödinger Cat States
Received: 15 February 2019 / Revised: 20 March 2019 / Accepted: 2 April 2019 / Published: 5 April 2019
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Abstract
The interference pattern in electron double-slit diffraction is a hallmark of quantum mechanics. A long-standing question for stochastic electrodynamics (SED) is whether or not it is capable of reproducing such effects, as interference is a manifestation of quantum coherence. In this study, we [...] Read more.
The interference pattern in electron double-slit diffraction is a hallmark of quantum mechanics. A long-standing question for stochastic electrodynamics (SED) is whether or not it is capable of reproducing such effects, as interference is a manifestation of quantum coherence. In this study, we used excited harmonic oscillators to directly test this quantum feature in SED. We used two counter-propagating dichromatic laser pulses to promote a ground-state harmonic oscillator to a squeezed Schrödinger cat state. Upon recombination of the two well-separated wavepackets, an interference pattern emerges in the quantum probability distribution but is absent in the SED probability distribution. We thus give a counterexample that rejects SED as a valid alternative to quantum mechanics. Full article
(This article belongs to the Special Issue Stochastic Electrodynamics)
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Open AccessCommunication
New Solar Metallicity Measurements
Received: 5 March 2019 / Revised: 27 March 2019 / Accepted: 2 April 2019 / Published: 4 April 2019
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Abstract
In the past years, a systematic downward revision of the metallicity of the Sun has led to the “solar modeling problem”, namely the disagreement between predictions of standard solar models and inferences from helioseismology. Recent solar wind measurements of the metallicity of the [...] Read more.
In the past years, a systematic downward revision of the metallicity of the Sun has led to the “solar modeling problem”, namely the disagreement between predictions of standard solar models and inferences from helioseismology. Recent solar wind measurements of the metallicity of the Sun, however, provide once more an indication of a high-metallicity Sun. Because of the effects of possible residual fractionation, the derived value of the metallicity Z = 0.0196 ± 0.0014 actually represents a lower limit to the true metallicity of the Sun. However, when compared with helioseismological measurements, solar models computed using these new abundances fail to restore agreement, owing to the implausibly high abundance of refractory (Mg, Si, S, Fe) elements, which correlates with a higher core temperature and hence an overproduction of solar neutrinos. Moreover, the robustness of these measurements is challenged by possible first ionization potential fractionation processes. I will discuss these solar wind measurements, which leave the “solar modeling problem” unsolved. Full article
Open AccessArticle
Laser-Assisted (e, 2e) Collisions in the Symmetric/Asymmetric Coplanar Geometry
Received: 24 January 2019 / Revised: 6 March 2019 / Accepted: 9 March 2019 / Published: 2 April 2019
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Abstract
In this review, we present a comprehensive survey of laser-assisted (e, 2e) reactions. The influence of a laser field on the dynamics of (e, 2e) collisions in atomic hydrogen is analyzed in the symmetric and asymmetric coplanar geometries. Particular attention is devoted to [...] Read more.
In this review, we present a comprehensive survey of laser-assisted (e, 2e) reactions. The influence of a laser field on the dynamics of (e, 2e) collisions in atomic hydrogen is analyzed in the symmetric and asymmetric coplanar geometries. Particular attention is devoted to the construction of the dressed (laser-modified) target wave functions, in both the initial and final states. The calculation is performed in the framework of Coulomb-Volkov-Born approximation, where the initial and final electrons are described by Volkov wave functions, while the interaction of the incident electron with the target atom is treated in the first and the second Born approximation. The state of the ejected electron is described by a Volkov/Coulomb-Volkov wave function. A detailed account is also given of the techniques we have used to evaluate the scattering amplitudes. The influence of the laser parameters (frequency, intensity, and direction of polarization) on the angular distribution of the ejected electron is discussed, and a number of illustrative examples are given. The structure of the triple differential cross section in the vicinity of resonances is also analyzed. Full article
(This article belongs to the Special Issue Electron Scattering in Intense Laser Fields)
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Open AccessArticle
The Role of Vacuum Fluctuations and Symmetry in the Hydrogen Atom in Quantum Mechanics and Stochastic Electrodynamics
Received: 16 February 2019 / Revised: 25 March 2019 / Accepted: 27 March 2019 / Published: 31 March 2019
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Abstract
Stochastic Electrodynamics (SED) has had success modeling black body radiation, the harmonic oscillator, the Casimir effect, van der Waals forces, diamagnetism, and uniform acceleration of electrodynamic systems using the stochastic zero-point fluctuations of the electromagnetic field with classical mechanics. However the hydrogen atom, [...] Read more.
Stochastic Electrodynamics (SED) has had success modeling black body radiation, the harmonic oscillator, the Casimir effect, van der Waals forces, diamagnetism, and uniform acceleration of electrodynamic systems using the stochastic zero-point fluctuations of the electromagnetic field with classical mechanics. However the hydrogen atom, with its 1/r potential remains a critical challenge. Numerical calculations have shown that the SED field prevents the electron orbit from collapsing into the proton, but, eventually the atom becames ionized. We look at the issues of the H atom and SED from the perspective of symmetry of the quantum mechanical Hamiltonian, used to obtain the quantum mechanical results, and the Abraham-Lorentz equation, which is a force equation that includes the effects of radiation reaction, and is used to obtain the SED simulations. We contrast the physical computed effects of the quantized electromagnetic vacuum fluctuations with the role of the real stochastic electromagnetic field. Full article
(This article belongs to the Special Issue Stochastic Electrodynamics)
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