Solution of the Energy Level of Hydrogen-Like Atom for the Debye Shielding Potential

The first-order revision and the approximation analytical formula of the energy levels for hydrogen-like atoms under the condition of Debye shielding potential are achieved by means of the Rayleigh–Schr?dinger perturbation theory; meanwhile, the corresponding recurrence relations are obtained from the use of the solution of power series. Based on the above solutions and with the use of energy consistent method the equivalent value of second-order reversion under the condition of Debye shielding potential is produced as well and the result is compared with the data obtained by the numerical method. Besides, the critical bond-state and corresponding cut-off conditions are discussed.

Solution of the Energy Level of Hydrogen-Like Atom for the Debye Shielding Potential

The first-order revision and the approximation analytical formula of the energy levels for hydrogen-likeatoms under the condition of Debye shielding potential are achieved by means of the Rayleigh-Schrodinger perturbationtheory; meanwhile, the corresponding recurrence relations are obtained from the use of the solution of power series. Basedon the above solutions and with the use of energy consistent method the equivalent value of second-order reversion underthe condition of Debye shielding potential is produced as well and the result is compared with the data obtained by thenumerical method. Besides, the critical bond-state and corresponding cut-off conditions are discussed.

Spin Dependent Selection Rules for Photonic Transitions in Hydrogen-Like Atoms

Spin dependent selection rules for photonic transitions in hydrogen-like atoms is derived by using the solution of Dirac equation for hydrogen-like atoms. It is shown that photonic transitions occur when [ Δj=0,±1,±2, while Δmj=0,±1,±2 ]. By applying the spin dependent selection rules, we can explain the observed (6s→7s) transition in Cesium (Cs) atom.

Electromagnetic Radiation Reaction and Stability of the Hydrogen-Like Atoms

Based on a suitable linear combination of the physical and un-physical electromagnetic potentials, the radiation reaction potentials have been calculated. Through the near zone expansion of the potentials, it has been shown that in either of the relativistic and non-relativistic cases the outgoing (radiated) energy of the electrons orbiting the nucleus is substituted by incoming (electromagnetic radiation reaction) energy. This means that energy is conserved and the classical hydrogen-like atoms are stable.

Quasi-Relativistic Description of Hydrogen-Like Atoms

Using a novel wave equation, which is Galileo invariant but can give precise results up to energies as high as mc2, exact quasi-relativistic quantum mechanical solutions are found for the Hydrogen atom. It is shown that the exact solutions of the Grave de Peralta equation include the relativistic correction to the non-relativistic kinetic energies calculated using the Schrödinger equation.

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems

The mechanical angular momentum and magnetic moment of the electron and proton spin have been calculated semiclassically with the aid of the uncertainty principle for energy and time. The spin effects of both kinds of the elementary particles can be expressed in terms of similar formulae. The quantization of the spin motion has been done on the basis of the old quantum theory. It gives a quantum number n = 1/2 as the index of the spin state acceptable for both the electron and proton particle. In effect of the spin existence the electron motion in the hydrogen atom can be represented as a drift motion accomplished in a combined electric and magnetic field. More than 18,000 spin oscillations accompany one drift circulation performed along the lowest orbit of the Bohr atom. The semiclassical theory developed in the paper has been applied to calculate the doublet separation of the experimentally well-examined D line entering the spectrum of the sodium atom. This separation is found to be much similar to that obtained according to the relativistic old quantum theory.

Motion Characteristics of Single Electrons of Atoms of Atomic Gas of Hydrogen and Single Electrons of Hydrogen-Like Ions in Form Gas or Vapour during Decays of Such Atoms and Ions. Emission Line Spectra

For the first time the vector differential equation of central motion of single electron in electric field of an atomic nucleus as in external central electric field is set up and solved. Here the following findings are reported. Each of single electrons of a part of atoms of atomic gas of hydrogen and a part of hydrogen-like ions in the form of a gas or a vapour revolves around corresponding atomic nucleus in a flat spiral which has an interior maximum of turns density. The distance between each of these single electrons and corresponding atomic nucleus increases while a speed of single electron decreases. Such motion of single electrons takes place with no expenditures of external energy and points to decays of foregoing parts of atoms and ions. The electric field strength of the atomic nuclei of atoms of atomic gas of hydrogen and hydrogen-like ions in the form of a gas or a vapour is inversely proportional to the distance between the atomic nucleus and the corresponding single electron by greater than the power of 3. Calculated cyclic frequency (rough value 3.5×1014 s-1) of revolution of the electron around the nucleus of atom of atomic gas of hydrogen (in interior maximum of turns density of the flat spiral), which moves at speed 2.2×106 ms-1, and central cyclic frequency of α-line of Balmer series (4.5×1014 s-1) have the same order of magnitude. This fact and line structure of experimental emission line spectra confirm the formation of all lines of these spectra by continuous slight emission of light front by single electrons. The formation of series of lines of emission line spectra is linked to repeated creations of atoms of atomic gas of hydrogen and hydrogen-like ions in the form of a gas or a vapour.

Intensities and shifts of Lyman and Balmer lines of hydrogen-like ions in high density plasmas

The spectral line intensities and line shifts of Lyman and Balmer series for transitions up to n=5 of hydrogen-like ion are studied in plasmas with densities and temperatures in the ranges n_(c)~10^(18)-10^(21)cm^(-3),T_(e)=0.3e1.2 eV respectively.The screened potential used to describe the interaction between charged particles includes the electron exchange-correlation and finite-temperature gradient effects and is valid for both weakly and strongly coupled plasmas.The dependencies of alpha,beta and gamma line shifts of Lyman and Balmer series on plasma density(for fixed temperature)and temperature(for fixed density)are investigated.The results for the H_(a)line shifts are compared with the available high-density experimental data.

Metal-organic framework-based single-atom electro-/ photocatalysts: Synthesis, energy applications, and opportunities

Single-atom catalysts(SACs)have gained substantial attention because of their exceptional catalytic properties.However,the high surface energy limits their synthesis,thus creating significant challenges for further development.In the last few years,metal–organic frameworks(MOFs)have received significant consideration as ideal candidates for synthesizing SACs due to their tailorable chemistry,tunable morphologies,high porosity,and chemical/thermal stability.From this perspective,this review thoroughly summarizes the previously reported methods and possible future approaches for constructing MOF-based(MOF-derived-supported and MOF-supported)SACs.Then,MOF-based SAC's identification techniques are briefly assessed to understand their coordination environments,local electronic structures,spatial distributions,and catalytic/electrochemical reaction mechanisms.This review systematically highlights several photocatalytic and electrocatalytic applications of MOF-based SACs for energy conversion and storage,including hydrogen evolution reactions,oxygen evolution reactions,O_(2)/CO_(2)/N_(2) reduction reactions,fuel cells,and rechargeable batteries.Some light is also shed on the future development of this highly exciting field by highlighting the advantages and limitations of MOF-based SACs.

Single-atom Pt on carbon nanotubes for selective electrocatalysis

Utilizing supported single atoms as catalysts presents an opportunity to reduce the usage of critical raw materials such as platinum,which are essential for electrochemical reactions such as hydrogen oxidation reaction(HOR).Herein,we describe the synthesis of a Pt single electrocatalyst inside single-walled carbon nanotubes(SWCNTs)via a redox reaction.Characterizations via electron microscopy,X-ray photoelectron microscopy,and X-ray absorption spectroscopy show the single-atom nature of the Pt.The electrochemical behavior of the sample to hydrogen and oxygen was investigated using the advanced floating electrode technique,which minimizes mass transport limitations and gives a thorough insight into the activity of the electrocatalyst.The single-atom samples showed higher HOR activity than state-of-the-art 30%Pt/C while almost no oxygen reduction reaction activity in the proton exchange membrane fuel cell operating range.The selective activity toward HOR arose as the main fingerprint of the catalyst confinement in the SWCNTs.

Strong synergy between physical and chemical properties:Insight into optimization of atomically dispersed oxygen reduction catalysts

Atomically dispersed catalysts exhibit significant influence on facilitating the sluggish oxygen reduction reaction(ORR)kinetics with high atom economy,owing to remarkable attributes including nearly 100%atomic utilization and exceptional catalytic functionality.Furthermore,accurately controlling atomic physical properties including spin,charge,orbital,and lattice degrees of atomically dispersed catalysts can realize the optimized chemical properties including maximum atom utilization efficiency,homogenous active centers,and satisfactory catalytic performance,but remains elusive.Here,through physical and chemical insight,we review and systematically summarize the strategies to optimize atomically dispersed ORR catalysts including adjusting the atomic coordination environment,adjacent electronic orbital and site density,and the choice of dual-atom sites.Then the emphasis is on the fundamental understanding of the correlation between the physical property and the catalytic behavior for atomically dispersed catalysts.Finally,an overview of the existing challenges and prospects to illustrate the current obstacles and potential opportunities for the advancement of atomically dispersed catalysts in the realm of electrocatalytic reactions is offered.

Analytical expressions of non-relativistic static multipole polarizabilities for hydrogen-like ions

Analytical formulas for the static multipole polarizabilities of hydrogen-like ions are derived by using the analytical wave functions and the reduced Green function and by applying a numerical fitting procedure.Our results are then applied to the studies of blackbody radiation shifts to atomic energy levels at different temperatures.Our analytical results can be served as a benchmark for other theoretical methods.

Precise construction of RuPt dual single-atomic sites to optimize oxygen electrocatalytic behaviors for high-performance Zn-air batteries

The development of redox bifunctional electrocatalysts with high performance,low cost,and long lifetimes is essential for achieving clean energy goals.This study proposed an atom capture strategy for anchoring dual single atoms(DSAs)in a zinc-zeolitic imidazolate framework(Zn-ZIF),followed by calcination under an N_(2) atmosphere to synthesize ruthenium-platinum DSAs supported on a nitrogendoped carbon substrate(RuPt DSAs-NC).Theoretical calculations showed that the degree of Ru 5dxz-~*O 2p_x orbital hybridization was high when^(*)O was adsorbed at the Ru site,indicating enhanced covalent hybridization of metal sites and oxygen ligands,which benefited the adsorption of intermediate species.The presence of the RuPtN_6 active center optimized the absorption-desorption behavior of intermediates,improving the electrocatalytic performance of the oxygen reduction reaction(ORR)and the oxygen evolution reaction(DER),RuPt DSAs-NC exhibited a 0.87 V high half-wave potential and a 268 mV low overpotential at 10 mA cm^(-2)in an alkaline environment.Furthermore,rechargeable zinc-air batteries(ZABs)achieved a peak power density of 171 MW cm^(-2).The RuPt DSAs-NC demonstrated long-term cycling for up to 500 h with superior round-trip efficiency.This study provided an effective structural design strategy to construct DSAs active sites for enhanced electrocata lytic performance.

Atom substitution of the solid-state electrolyte Li_(10)GeP_(2)S_(12)for stabilized all-solid-state lithium metal batteries

Solid-state electrolyte Li_(10)GeP_(2)S_(12)(LGPS)has a high lithium ion conductivity of 12 mS cm^(-1)at room temperature,but its inferior chemical stability against lithium metal anode impedes its practical application.Among all solutions,Ge atom substitution of the solid-state electrolyte LGPS stands out as the most promising solution to this interface problem.A systematic screening framework for Ge atom substitution including ionic conductivity,thermodynamic stability,electronic and mechanical properties is utilized to solve it.For fast screening,an enhanced model Dop Net FC using chemical formulas for the dataset is adopted to predict ionic conductivity.Finally,Li_(10)SrP_(2)S_(12)(LSrPS)is screened out,which has high lithium ion conductivity(12.58 mS cm^(-1)).In addition,an enhanced migration of lithium ion across the LSr PS/Li interface is found.Meanwhile,compared to the LGPS/Li interface,LSrPS/Li interface exhibits a larger Schottky barrier(0.134 eV),smaller electron transfer region(3.103?),and enhanced ability to block additional electrons,all of which contribute to the stabilized interface.The applied theoretical atom substitution screening framework with the aid of machine learning can be extended to rapid determination of modified specific material schemes.

Optimizing high-coordination shell of Co-based single-atom catalysts for efficient ORR and zinc-air batteries

Atom-level modulation of the coordination environment for single-atom catalysts(SACs)is considered as an effective strategy for elevating the catalytic performance.For the MNxsite,breaking the symmetrical geometry and charge distribution by introducing relatively weak electronegative atoms into the first/second shell is an efficient way,but it remains challenging for elucidating the underlying mechanism of interaction.Herein,a practical strategy was reported to rationally design single cobalt atoms coordinated with both phosphorus and nitrogen atoms in a hierarchically porous carbon derived from metal-organic frameworks.X-ray absorption spectrum reveals that atomically dispersed Co sites are coordinated with four N atoms in the first shell and varying numbers of P atoms in the second shell(denoted as Co-N/P-C).The prepared catalyst exhibits excellent oxygen reduction reaction(ORR)activity as well as zinc-air battery performance.The introduction of P atoms in the Co-SACs weakens the interaction between Co and N,significantly promoting the adsorption process of ^(*)OOH,resulting in the acceleration of reaction kinetics and reduction of thermodynamic barrier,responsible for the increased intrinsic activity.Our discovery provides insights into an ultimate design of single-atom catalysts with adjustable electrocatalytic activities for efficient electrochemical energy conversion.

Generation and Detection of a Directed Monoenergetic Neutrino Beam with Hydrogen-Like Ions

We consider two possible schemes for generation and detection of a monoenergetic directed beam of neutrinos which may have application to neutrino communication. First, we consider generation of a directed neutrino beam using electron capture beta decay in hydrogen-like ions. Next, we suggest detection of a directed neutrino beam using resonant absorption of a neutrino by a bare nucleus with the generation of a bound electron. This reaction is inverse to electron capture beta decay, and we call it “Bound State Inverse Beta Decay (BSIBD)”. We show that the recoil effect can be eliminated by an appropriate choice of velocities for the ions and bare nuclei. Finally, we consider a combination of a solid state source of a directed mono-energetic neutrino beam and its detection using BSIBD.

Synthesis and Modulation of Low-Dimensional Transition Metal Chalcogenide Materials via Atomic Substitution

In recent years,low-dimensional transition metal chalcogenide(TMC)materials have garnered growing research attention due to their superior electronic,optical,and catalytic properties compared to their bulk counterparts.The controllable synthesis and manipulation of these materials are crucial for tailoring their properties and unlocking their full potential in various applications.In this context,the atomic substitution method has emerged as a favorable approach.It involves the replacement of specific atoms within TMC structures with other elements and possesses the capability to regulate the compositions finely,crystal structures,and inherent properties of the resulting materials.In this review,we present a comprehensive overview on various strategies of atomic substitution employed in the synthesis of zero-dimensional,one-dimensional and two-dimensional TMC materials.The effects of substituting elements,substitution ratios,and substitution positions on the structures and morphologies of resulting material are discussed.The enhanced electrocatalytic performance and photovoltaic properties of the obtained materials are also provided,emphasizing the role of atomic substitution in achieving these advancements.Finally,challenges and future prospects in the field of atomic substitution for fabricating low-dimensional TMC materials are summarized.

A frequency servo SoC with output power stabilization loop technology for miniaturized atomic clocks

A frequency servo system-on-chip(FS-SoC)featuring output power stabilization technology is introduced in this study for high-precision and miniaturized cesium(Cs)atomic clocks.The proposed power stabilization loop(PSL)technique,incorporating an off-chip power detector(PD),ensures that the output power of the FS-SoC remains stable,mitigating the impact of power fluctuations on the atomic clock's stability.Additionally,a one-pulse-per-second(1PPS)is employed to syn-chronize the clock with GPS.Fabricated using 65 nm CMOS technology,the measured phase noise of the FS-SoC stands at-69.5 dBc/Hz@100 Hz offset and-83.9 dBc/Hz@1 kHz offset,accompanied by a power dissipation of 19.7 mW.The Cs atomic clock employing the proposed FS-SoC and PSL obtains an Allan deviation of 1.7×10^(-11) with 1-s averaging time.

Atomically dispersed Ni electrocatalyst for superior urea-assisted water splitting

Urea oxidation reaction(UOR) has been selected as substitution for oxygen evolution reaction ascribing to its low thermodynamic voltage as well as utilization of nickel as electrocatalyst.Herein,we report the formation of nickel single atoms(Ni-SAs) as exceptional bifunctional electrocatalyst toward UOR and hydrogen evolution reaction(HER) in urea-assisted water splitting.In UOR catalysis,Ni-SAs perform a superior catalytic performance than Ni-NP/NC and Pt/C ascribing to the formation of HOO-Ni-N_(4) structure evidenced by in-situ Raman spectroscopy,corresponding to a boosted mass activity by 175-fold at 1.4 V vs.RHE than Ni-NP/NC.Furthermore,Ni-SAs requires only 450 mV overpotential to obtain HER current density of 500 mA cm^(-2).136 mA cm^(-2) is achieved in urea-assisted water splitting at1.7 V for Ni-SAs,boosted by 5.7 times than Pt/C-IrO_(2) driven water splitting.

Building Feedback-Regulation System Through Atomic Design for Highly Active SO_(2)Sensing

Reasonably constructing an atomic interface is pronouncedly essential for surface-related gas-sensing reaction.Herein,we present an ingen-ious feedback-regulation system by changing the interactional mode between single Pt atoms and adjacent S species for high-efficiency SO_(2)sensing.We found that the single Pt sites on the MoS_(2)surface can induce easier volatiliza-tion of adjacent S species to activate the whole inert S plane.Reversely,the activated S species can provide a feedback role in tailoring the antibonding-orbital electronic occupancy state of Pt atoms,thus creating a combined system involving S vacancy-assisted single Pt sites(Pt-Vs)to synergistically improve the adsorption ability of SO_(2)gas molecules.Further-more,in situ Raman,ex situ X-ray photoelectron spectroscopy testing and density functional theory analysis demonstrate the intact feedback-regulation system can expand the electron transfer path from single Pt sites to whole Pt-MoS_(2)supports in SO_(2)gas atmosphere.Equipped with wireless-sensing modules,the final Pt1-MoS_(2)-def sensors array can further realize real-time monitoring of SO_(2)levels and cloud-data storage for plant growth.Such a fundamental understanding of the intrinsic link between atomic interface and sensing mechanism is thus expected to broaden the rational design of highly effective gas sensors.