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.

Efficient loading of cesium atoms in a magnetic levitated dimple trap

We report a detailed study of magnetically levitated loading of ultracold ^(133)Cs atoms in a dimple trap.The atomic sample was produced in a combined red-detuned optical dipole trap and dimple trap formed by two small waist beams crossing a horizontal plane.The magnetic levitation for the ^(133)Cs atoms forms an effective potential for a large number of atoms in a high spatial density.Dependence of the number of atoms loaded and trapped in the dimple trap on the magnetic field gradient and bias field is in good agreement with the theoretical analysis.This method has been widely used to obtain the Bose–Einstein condensation atoms for many atomic species.

Advances of Synergistic Electrocatalysis Between Single Atoms and Nanoparticles/Clusters

Combining single atoms with clusters or nanoparticles is an emerging tactic to design efficient electrocatalysts.Both synergy effect and high atomic utilization of active sites in the composite catalysts result in enhanced electrocatalytic performance,simultaneously provide a radical analysis of the interrelationship between structure and activity.In this review,the recent advances of single-atomic site catalysts coupled with clusters or nanoparticles are emphasized.Firstly,the synthetic strategies,characterization,dynamics and types of single atoms coupled with clusters/nanoparticles are introduced,and then the key factors controlling the structure of the composite catalysts are discussed.Next,several clean energy catalytic reactions performed over the synergistic composite catalysts are illustrated.Eventually,the encountering challenges and recommendations for the future advancement of synergistic structure in energy-transformation electrocatalysis are outlined.

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

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.

Geometric properties of the first singlet S-wave excited state of two-electron atoms near the critical nuclear charge

The geometric structure parameters and radial density distribution of 1s2s1S excited state of the two-electron atomic system near the critical nuclear charge Z_(c)were calculated in detail under tripled Hylleraas basis set.Contrary to the localized behavior observed in the ground and the doubly excited 2p^(23)Pe states,for this state our results identify that while the behavior of the inner electron increasingly resembles that of a hydrogen-like atomic system,the outer electron in the excited state exhibits diffused hydrogen-like character and becomes perpendicular to the inner electron as nuclear charge Z approaches Z_(c).This study provides insights into the electronic structure and stability of the two-electron system in the vicinity of the critical nuclear charge.

Achieving Negatively Charged Pt Single Atoms on Amorphous Ni(OH)_(2)Nanosheets with Promoted Hydrogen Absorption in Hydrogen Evolution

Single-atom(SA)catalysts with nearly 100%atom utilization have been widely employed in electrolysis for decades,due to the outperforming catalytic activity and selectivity.However,most of the reported SA catalysts are fixed through the strong bonding between the dispersed single metallic atoms with nonmetallic atoms of the substrates,which greatly limits the controllable regulation of electrocatalytic activity of SA catalysts.In this work,Pt-Ni bonded Pt SA catalyst with adjustable electronic states was successfully constructed through a controllable electrochemical reduction on the coordination unsaturated amorphous Ni(OH)_(2)nanosheet arrays.Based on the X-ray absorption fine structure analysis and first-principles calculations,Pt SA was bonded with Ni sites of amorphous Ni(OH)_(2),rather than conventional O sites,resulting in negatively charged Pt^(δ-).In situ Raman spectroscopy revealed that the changed configuration and electronic states greatly enhanced absorbability for activated hydrogen atoms,which were the essential intermediate for alkaline hydrogen evolution reaction.The hydrogen spillover process was revealed from amorphous Ni(OH)_(2)that effectively cleave the H-O-H bond of H_(2)O and produce H atom to the Pt SA sites,leading to a low overpotential of 48 mV in alkaline electrolyte at-1000 mA cm^(-2)mg^(-1)_(Pt),evidently better than commercial Pt/C catalysts.This work provided new strategy for the control-lable modulation of the local structure of SA catalysts and the systematic regulation of the electronic states.

Microwave electrometry with Rydberg atoms in a vapor cell using microwave amplitude modulation

We have theoretically and experimentally studied the dispersive signal of the Rydberg atomic electromagneticallyinduced transparency(EIT)Autler–Townes(AT)splitting spectra obtained using amplitude modulation of the microwave(MW)electric field.In addition to the two zero-crossing points interval△f_(zeros),the dispersion signal has two positive maxima with an interval defined as the shoulder interval△f_(sho),which is theoretically expected to be used to measure a much weaker MW electric field.The relationship of the MW field strength E_(MW)and△f_(sho)is experimentally studied at the MW frequencies of 31.6 GHz and 9.2 GHz respectively.The results show that△f_(sho)can be used to characterize the much weaker E_(MW)than that of△f_(zeros)and the traditional EIT–AT splitting interval△f_(m);the minimum E_(MW)measured by△f_(sho)is about 30 times smaller than that by△f_(m).As an example,the minimum E_(MW)at 9.2 GHz that can be characterized by△f_(sho)is 0.056 mV/cm,which is the minimum value characterized by the frequency interval using a vapor cell without adding any auxiliary fields.The proposed method can improve the weak limit and sensitivity of E_(MW)measured by the spectral frequency interval,which is important in the direct measurement of weak E_(MW).

Optical PAM-4/PAM-8 generation via dual-Raman process in Rydberg atoms

A scheme of optical four-level pulse amplitude modulation(PAM-4) is proposed based on dual-Raman process in Rydberg atoms. A probe field counter-propagates with a dual-Raman field which drives the ground and the excited states transition, respectively, and the Rydberg transition is driven by a microwave(MW) field. A gain peak appears in the probe transmission and is sensitive to the MW field strength. Optical PAM-4 can be achieved by encoding an MW signal and decoding the magnitude of a probe signal. Simulation results show that the differential nonlinearity and the integral nonlinearity of the proposed scheme can be reduced by 5 times and 6 times, respectively, compared with the counterparts of previous scheme, and the ratio of level separation mismatch is close to the ideal value 1. Moreover, the scheme is extended to optical PAM-8 signal, which may further improve the spectral efficiency.

Simulation of space heavy-ion induced primary knock-on atoms in bipolar devices

Bipolar junction transistors(BJTs) are often used in spacecraft due to their excellent working characteristics. However,the complex space radiation environment induces primary knock-on atoms(PKAs) in BJTs through collisions, resulting in hard-to-recover displacement damage and affecting the performance of electronic components. In this paper, the properties of PKAs induced by typical space heavy ions(C, N, O, Fe) in BJTs are investigated using Monte Carlo simulations. The simulated results show that the energy spectrum of ion-induced PKAs is primarily concentrated in the low-energy range(17eV–100eV) and displays similar features across all tested ions. The PKAs induced by the collision of energetic ions have large forward scattering angles, mainly around 88°. Moreover, the distribution of PKAs within a transistor as a function of depth displays a peak characteristic, and the peak position is linearly proportional to the incident energy at a certain energy range. These simulation outcomes serve as crucial theoretical support for long-term semiconductor material defect evolution and ground testing of semiconductor devices.

Multifunctional Film Assembled from N‑Doped Carbon Nanofiber with Co–N_(4)–O Single Atoms for Highly Efficient Electromagnetic Energy Attenuation

Single-atom materials have demonstrated attractive physicochemical characteristics.However,understanding the relationships between the coordination environment of single atoms and their properties at the atomic level remains a considerable challenge.Herein,a facile waterassisted carbonization approach is developed to fabricate well-defined asymmetrically coordinated Co–N_(4)–O sites on biomass-derived carbon nanofiber(Co–N_(4)–O/NCF)for electromagnetic wave(EMW)absorption.In such nanofiber,one atomically dispersed Co site is coordinated with four N atoms in the graphene basal plane and one oxygen atom in the axial direction.In-depth experimental and theoretical studies reveal that the axial Co–O coordination breaks the charge distribution symmetry in the planar porphyrin-like Co–N_(4) structure,leading to significantly enhanced dielectric polarization loss relevant to the planar Co–N_(4) sites.Importantly,the film based on Co–N_(4)–O/NCF exhibits light weight,flexibility,excellent mechanical properties,great thermal insulating feature,and excellent EMW absorption with a reflection loss of−45.82 dB along with an effective absorption bandwidth of 4.8 GHz.The findings of this work offer insight into the relationships between the single-atom coordination environment and the dielectric performance,and the proposed strategy can be extended toward the engineering of asymmetrically coordinated single atoms for various applications.

Research of caged dynamics of clusters center atoms in Pd_(82)Si_(18) amorphous alloy

To date,there is still a lack of a comprehensive explanation for caged dynamics which is regarded as one of the intricate dynamic behaviors in amorphous alloys.This study focuses on Pd_(82)Si_(18)as the research object to further elucidate the underlying mechanism of caged dynamics from multiple perspectives,including the cage's lifetime,atomic local environment,and atomic potential energy.The results reveal that Si atoms exhibit a pronounced cage effect due to the hindrance of Pd atoms,resulting in an anomalous peak in the non-Gaussian parameters.An in-depth investigation was conducted on the caged dynamics differences between fast and slow Si atoms.In comparison to fast Si atoms,slow Si atoms were surrounded by more Pd atoms and occupied lower potential energy states,resulting in smaller diffusion displacements for the slow Si atoms.Concurrently,slow Si atoms tend to be in the centers of smaller clusters with coordination numbers of 9 and 10.During the isothermal relaxation process,clusters with coordination numbers 9 and 10 have longer lifetimes,suggesting that the escape of slow Si atoms from their cages is more challenging.The findings mentioned above hold significant implications for understanding the caged dynamics.

Bimetallic CoNi single atoms supported on three-dimensionally ordered mesoporous chromia:highly active catalysts for n-hexane combustion

Developing the alternative supported noble metal catalysts with low cost,high catalytic efficiency,and good resistance toward carbon dioxide and water vapor is critically demanded for the oxidative removal of volatile organic compounds(VOCs).In this work,we prepared the mesoporous chromia-supported bimetallic Co and Ni single-atom(Co_(1)Ni_(1)/meso-Cr_(2)O_(3))and bimetallic Co and Ni nanoparticle(Co_(NP)Ni_(NP)/mesoCr_(2)O_(3))catalysts adopting the one-pot polyvinyl pyrrolidone(PVP)-and polyvinyl alcohol(PVA)-protecting approaches,respectively.The results indicate that the Co_(1)Ni_(1)/meso-Cr_(2)O_(3)catalyst exhibited the best catalytic activity for n-hexane(C_(6)H_(14))combustion(T_(50%)and T_(90%)were 239 and 263℃ at a space velocity of 40,000 mL g^(-1)h^(-1);apparent activation energy and specific reaction rate at 260℃ were 54.7 kJ mol^(-1)and 4.3×10^(-7)mol g^(-1)_(cat)s^(-1),respectively),which was associated with its higher(Cr^(5+)+Cr^(6+))amount,large n-hexane adsorption capacity,and good lattice oxygen mobility that could enhance the deep oxidation of n-hexane,in which Ni_(1) was beneficial for the enhancements in surface lattice oxygen mobility and low-temperature reducibility,while Co_(1) preferred to generate higher contents of the high-valence states of chromium and surface oxygen species as well as adsorption and activation of n-hexane.n-Hexane combustion takes place via the Mars van Krevelen(MvK)mechanism,and its reaction pathways are as follows:n-hexane→olefins or 3-hexyl hydroperoxide→3-hexanone,2-hexanone or 2,5-dimethyltetrahydrofuran→2-methyloxirane or 2-ethyl-oxetane→acrylic acid→CO_x→CO_(2)and H_(2)O.

All-electron basis sets for H to Xe specific for ZORA calculations:Applications in atoms and molecules

A segmented basis set of quadruple zeta valence quality plus polarization functions(QZP)for H through Xe was developed to be used in conjunction with the ZORA Hamiltonian.This set was augmented with diffuse functions to describe electrons farther away from the nuclei adequately.Using the ZORA-CCSD(T)/QZP-ZORA theoretical model,atomic ionization energies and bond lengths,harmonic vibrational frequencies,and atomization energies of some molecules were calculated.The addition of core-valence corrections has been shown to improve the agreement between theoretical and experimental results for molecular properties.For atomization energies,a similar observation emerges when considering spin-orbit couplings.With the augmented QZP-ZORA set,static mean dipole polarizabilities of a set of atoms were calculated and compared with previously published recommended and experimental values.Performance evaluations of the ZORA and Douglas–Kroll–Hess Hamiltonians were made for each property studied.

Effects of surface chlorine atoms on charge distribution and reaction barriers for photocatalytic CO_(2)reduction

Photocatalytic CO_(2)reduction to produce high value-added carbon-based fuel has been proposed as a promising approach to mitigate global warming issues.However,the conversion efficiency and product selectivity are still low due to the sluggish dynamics of transfer processes involved in proton-assisted multi-electron reactions.Lowering the formation energy barriers of intermediate products is an effective method to enhance the selectivity and productivity of final products.In this study,we aim to regulate the surface electronic structure of Bi_(2)WO_(6)by doping surface chlorine atoms to achieve effective photocatalytic CO_(2)reduction.Surface Cl atoms can enhance the absorption ability of light,affect its energy band structure and promote charge separation.Combined with DFT calculations,it is revealed that surface Cl atoms can not only change the surface charge distribution which affects the competitive adsorption of H_(2)O and CO_(2),but also lower the formation energy barrier of intermediate products to generate more intermediate*COOH,thus facilitating CO production.Overall,this study demonstrates a promising surface halogenation strategy to enhance the photocatalytic CO_(2)reduction activity of a layered structure Bi-based catalyst.

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.

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.

Improved Plasmonic Hot‑Electron Capture in Au Nanoparticle/Polymeric Carbon Nitride by Pt Single Atoms for Broad‑Spectrum Photocatalytic H_(2)Evolution

ABSTRACT Rationally designing broad-spectrum photocatalysts to harvest whole visible-light region photons and enhance solar energy conversion is a“holy grail”for researchers,but is still a challenging issue.Herein,based on the common polymeric carbon nitride(PCN),a hybrid co-catalysts system comprising plasmonic Au nanoparticles(NPs)and atomically dispersed Pt single atoms(PtSAs)with different functions was constructed to address this challenge.For the dual co-catalysts decorated PCN(PtSAs–Au_(2.5)/PCN),the PCN is photoexcited to generate electrons under UV and short-wavelength visible light,and the synergetic Au NPs and PtSAs not only accelerate charge separation and transfer though Schottky junctions and metal-support bond but also act as the co-catalysts for H_(2) evolution.Furthermore,the Au NPs absorb long-wavelength visible light owing to its localized surface plasmon resonance,and the adjacent PtSAs trap the plasmonic hot-electrons for H_(2) evolution via direct electron transfer effect.Consequently,the PtSAs–Au_(2.5)/PCN exhibits excellent broad-spectrum photocatalytic H_(2) evolution activity with the H_(2) evolution rate of 8.8 mmol g^(−1) h^(−1) at 420 nm and 264μmol g^(−1) h^(−1) at 550 nm,much higher than that of Au_(2.5)/PCN and PtSAs–PCN,respectively.This work provides a new strategy to design broad-spectrum photocatalysts for energy conversion reaction.

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.