Maximum Number Of Electrons Research Articles

Cosmic-ray measurements with an array of Cherenkov telescopes using reconstruction of longitudinal profiles of air showers

We present a method to reconstruct the longitudinal profile of electrons in showers using Cherenkov telescopes. We show how the Cherenkov light collected by an array of telescopes can be transformed into the number of electrons as a function of atmospheric depth. This method is validated using air shower and simplified telescope simulations. The reconstruction of the depth in which the shower has the maximum number of electrons (Xmax) opens the possibility of cosmic ray composition studies with Cherenkov telescopes in the energy range from 10 to 100 TeV.

Рентгеновские фотоэлектронные спектры молекул кислорода, адсорбированных на нанопленках иттербия

The adsorption of oxygen molecules on ytterbium nanofilms of various thicknesses has been studied by X-ray photoelectron spectroscopy and contact potential difference measurements. It has been established that the maximum number of O2 molecules that can be adsorbed on the films increases with the film thickness. Such behavior is observed at thicknesses less than 10 monolayers. This size effect is ultimately due to the fact that an indispensable condition for the adsorption process at high doses of oxygen is the electron transfer from the film to molecules, and that the maximum number of electrons that can participate in this process depends on the nanolayer thickness. Localization of a negative charge on O2 molecules occurring in at high doses of adsorbate, causes a weakening of the bonding of 1s electrons in these molecules. In addition, it should lead to a weakening of the bond between oxygen atoms in O2 molecules.

X-ray photoelectron spectra of oxygen molecules adsorbed on ytterbium nanofilms

The adsorption of oxygen molecules on ytterbium nanofilms of various thicknesses has been studied by X-ray photoelectron spectroscopy and contact potential difference measurements. It has been established that the maximum number of O2 molecules that can be adsorbed on the films increases with the film thickness. Such behavior is observed at thicknesses less than 10 monolayers. This size effect is ultimately due to the fact that an indispensable condition for the adsorption process at high doses of oxygen is the electron transfer from the film to molecules, and that the maximum number of electrons that can participate in this process depends on the nanolayer thickness. Localization of a negative charge on O2 molecules occurring in at high doses of adsorbate, causes a weakening of the bonding of 1s-electrons in these molecules. In addition, it should lead to a weakening of the bond between oxygen atoms in O2 molecules. Keywords: oxygen, ytterbium, adsorbed molecules, nanofilms, X-ray photoelectron spectroscopy, work function.

Maximum Ionization in Restricted and Unrestricted Hartree-Fock Theory

In this paper, we investigate the maximum number of electrons that can be bound to a system of nuclei modelled by Hartree-Fock theory. We consider both the Restricted and Unrestricted Hartree-Fock models. We are taking a non-existence approach (necessary but not sufficient), in other words we are finding an upper bound on the maximum number of electrons. In giving a detailed account of the proof of Lieb’s bound [Theorem 1, Phys. Rev. A 29 (1984), 3018] for the Hartree-Fock models we establish several new auxiliary results, furthermore we propose a condition that, if satisfied, will give an improved upper bound on the maximum number of electrons within the Restricted Hartree-Fock model. For two-electron atoms we show that the latter condition holds.

Multi-Aperture-Based Probabilistic Noise Reduction of Random Telegraph Signal Noise and Photon Shot Noise in Semi-Photon-Counting Complementary-Metal-Oxide-Semiconductor Image Sensor.

A probabilistic method to remove the random telegraph signal (RTS) noise and to increase the signal level is proposed, and was verified by simulation based on measured real sensor noise. Although semi-photon-counting-level (SPCL) ultra-low noise complementary-metal-oxide-semiconductor (CMOS) image sensors (CISs) with high conversion gain pixels have emerged, they still suffer from huge RTS noise, which is inherent to the CISs. The proposed method utilizes a multi-aperture (MA) camera that is composed of multiple sets of an SPCL CIS and a moderately fast and compact imaging lens to emulate a very fast single lens. Due to the redundancy of the MA camera, the RTS noise is removed by the maximum likelihood estimation where noise characteristics are modeled by the probability density distribution. In the proposed method, the photon shot noise is also relatively reduced because of the averaging effect, where the pixel values of all the multiple apertures are considered. An extremely low-light condition that the maximum number of electrons per aperture was the only 2 was simulated. PSNRs of a test image for simple averaging, selective averaging (our previous method), and the proposed method were 11.92 dB, 11.61 dB, and 13.14 dB, respectively. The selective averaging, which can remove RTS noise, was worse than the simple averaging because it ignores the pixels with RTS noise and photon shot noise was less improved. The simulation results showed that the proposed method provided the best noise reduction performance.

Proposed Link between the Periodic Table and the Standard Model

The patterns of stable quantum states in the Periodic Table are inverted and extended to infinity in both directions to accommodate spatial variation relative to the nucleus. The upper end leads to a cut off point for white matter. The lower end represents quantum states in plasma. At 10-15 m to 10-20 m the interaction between weak strong and gravity forces results in suitable boundary conditions for the production of elementary particles. Chemical classification of the elements requires convergence of chemical properties and quantum states. By defining GROUP NUMBER as the maximum number of electrons in any one shell, Hydrogen and Helium are moved to the first set of 2(1)2 states first proposed by Janet. The atomic numbers are adjusted and mass number removed as it is an average of isotopes of each element produced in every supernova. This produces the: Roberts Janet Nuclear Periodic Table which proposes two zero states, a cut off and start point, of the electric field in attractive then repulsive modes. By symmetry of these fields energy states emerge in plasma with the counter intuitive property that the nearer the nucleus the greater the number of energy states. Fusion results and the consequential recycling implies a more rapid collapse than supernovae given sufficient energy density that could create an as yet unobserved interaction at 10-50 m to 10-65 m between the strong and gravity forces. String theory and extra dimensions may be required to explain such mechanisms and multiverses.

Multidirectional Angular Electronic Flux during Adiabatic Attosecond Charge Migration in Excited Benzene.

Recently, adiabatic attosecond charge migration (AACM) has been monitored and simulated for the first time, with application to the oriented iodoacetylene cation where AACM starts from the initial superposition of the ground state (φ0) and an electronic excited state (φ1). Here, we develop the theory for electronic fluxes during AACM in ring-shaped molecules, with application to oriented benzene prepared in the superposition of the ground and first excited singlet states. The initial state and its time evolution are analogous to coherent tunneling where φ0 and φ1 have different meanings; however, they denote the wave functions of the lowest tunneling doublet. This analogy suggests to transfer the theory of electronic fluxes during coherent tunneling to AACM, with suitable modifications which account for (i) the different time scales and (ii) the different electronic states, and which make use of (iii) the preparation of the initial state for AACM by a linearly polarized laser pulse. Application to benzene yields the multidirectional angular electronic flux with a pincer-motion type pattern during AACM: this unequivocal result confirms a previous working hypothesis. Moreover, the theory of AACM allows quantification of the electronic flux; that is, the maximum number of electrons (out of 42) which flow concertedly during AACM in benzene is 6 × 0.08 = 0.48.

Experimental investigation of time-resolved electron beam energy distributions generated in a transient hollow cathode discharge

In this paper, a retarding potential energy analyzer (RPEA) specific for pulsed electron beams within the pressure range of tens of mTorr is developed and used to investigate the energy of transient hollow cathode discharge produced electron beams. This RPEA has been applied in a pseudospark-based electron beam source at applied potential up to 20 kV. Experimental investigations under applied potential of 5 kV, 10 kV, 15 kV, and 20 kV were carried out and the time-resolved electron energy distributions are constructed. The numbers of electrons within various energy groups are calculated from the time-resolved electron energy spectra. Results show that the maximum number of electrons is emitted within the energy range of 40%–60% of the full applied potential on the pseudospark device, and varies from 22.5 ± 2.0% to 38.9±2.0% of the total number of emitted electrons. Additionally, the energy transformation efficiency of stored electrical energy to electron beam energy is calculated from presented data. The energy transformation efficiency increases from 11.4 ± 0.5% at 5 kV breakdown voltage to 23.2 ± 3.5% at 20 kV breakdown voltage.

Discontinuity of the exchange-correlation potential: Support for assumptions used to find it

It was shown by J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz [Phys. Rev. Lett. 49, 1691 (1982)]; J. P. Perdew and M. Levy [Phys. Rev. Lett. 51, 1884 (1983)]; and L. J. Sham and M. Schl\uter [Phys. Rev. Lett. 51, 1888 (1983)] that the exact Kohn-Sham exchange-correlation potential ${v}_{\text{xc}}(\stackrel{P\vec}{r})$ of an open system may jump discontinuously as the particle number crosses an integer, with important physical consequences. The original derivations of the size and nature of the discontinuity rely on an implicit assumption that, when $N\ensuremath{\rightarrow}J$ from above and below, the effective potential of the interacting system with particle number $N$ becomes identical (modulo a constant) to the effective potential at an integer particle number $J$ so that the Kohn-Sham orbitals change continuously as $N$ passes through $J$ at fixed external potential. We prove under mild assumptions that the noninteracting kinetic energy of the interacting system is a continuous function of the particle number (as is the density itself), and hence argue that the original assumption is likely correct; if so, then all energy components are continuous. A rigorous proof of the existence and size of the ${v}_{\text{xc}}$ discontinuity is presented in the special case where the particle number crosses 1, by showing that, even when the Levy-Lieb constrained search for a minimum kinetic energy expectation value is taken to go over ensembles instead of wave functions, the noninteracting kinetic energy is still given by the von Weizs\acker functional for all densities with real particle number $N$ between 0 and 2 inclusive. We also prove that the von Weizs\acker functional is a lower bound on the ensemble-search noninteracting kinetic energy for all real $Ng2$. To illustrate the ${v}_{\text{xc}}$ discontinuity and related results, we construct an analytic model density for the ${\text{H}}^{\ensuremath{-}}$ ion and plot the exchange-correlation potential as the particle number approaches 1 from above and below, and 2 from below. Finally, we discuss the behavior of the free-electron continuum as the particle number crosses an integer and the case where the particle number of a hydrogen or helium atom crosses $J=2$, the maximum number of electrons they can bind.

One-Dimensional Models for Atoms in Strong Magnetic Fields, II: Anti-Symmetry in the Landau Levels

Electrons in strong magnetic fields can be described by one-dimensional models in which the Coulomb potential and interactions are replaced by regularizations associated with the lowest Landau band. For a large class of models of these type, we show that the maximum number of electrons that can be bound is less than a Z + Z f(Z). The function f(Z) represents a small non-linear growth which is quadratic in log Z when the magnetic field strength grows polynomially with the nuclear charge Z. In contrast to earlier work, the models considered here include those arising from realistic cases in which the full trial wave function for N-electrons is the product of an N-electron trial function in one-dimension and an antisymmetric product of states in the lowest Landau level.

A one-dimensional model for many-electron atoms in extremely strong magnetic fields: maximum negative ionization

We consider a one-dimensional model for many-electron atoms in strong magnetic fields in which the Coulomb potential and interactions are replaced by one-dimensional regularizations associated with the lowest Landau level. For this model we show that the maximum number of electrons is bounded above by 2Z+1 + c sqrt{B}. We follow Lieb's strategy in which convexity plays a critical role. For the case of two electrons and fractional nuclear charge, we also discuss the critical value at which the nuclear charge becomes too weak to bind two electrons.

Molybdenum Cluster Chalcogenides: In Situ X-Ray Studies on the Formation of CuxMo6S8 via Electron/Ion Transfer

Systematic structural investigation have been performed on the formation of the ternary Chevrel phase system CuxMo6S8 by topotactic intercalation of copper into Mo6S8 via electron/ion transfer reactions. In high-temperature synthesis the homogeneity range of CuxMo6S8 formation corresponds to 1.8 ≤ x ≤ 3.66, while by galvanostatic or potentiostatic reduction of binary Mo6S8 at ambiet temperature in aqueous CuSO4 or aprotic CuCl/Ch3CN electrolyte the terminal rhombohedral phase Cu4Mo6S8 with the maximum number of electrons per Mo6 cluster can be obtained. The phase range 1 ≤ x ≤ 4 of CuxMo6S8 as obtained by galvanostatic reduction of Mo6S8 in aqueous CuSO4 electrolyte has been determined by in situ X-ray experiments. Warburg oxygen manometry has proved to be a new and powerful analytical tool for examination of the Cu content of ternary phase CuxMo6S8. Thermodiffractometry and 63 Cu NMR studies of Cu2Mo6S8 (high-temperature phase) reveal a phase-transition rhombohedral/triclinic in a broad temperature range between 285 and 200 K. Superconducting properties (temperature-dependent ac susceptibility) of high temperature and electrochemically prepared Cu phases are reported.

Colloidal Zn_1−xCdxS: optical saturation of the exciton band and primary photochemistry studied by subpicosecond laser flash photolysis

Quantum-size crystallites of Zn0.95Cd0.05S in an aqueous colloidal solution were optically excited using intense subpicosecond laser pump pulses tuned to the exciton band. Optical probing in the UV registered saturation and the kinetics of ground-state recovery due to carrier recombination, with lifetimes in the 0.8–30-psec range. Optical probing at 616 nm monitored the yield of Auger electron emission. The saturation and yield curves, as a function of pump fluence, are described by a simple kinetic model that involves the exciton lifetime before trapping (~30 fsec) and the maximum number of electrons (~16) that can be emitted per particle.

The restricted active space self-consistent-field method, implemented with a split graph unitary group approach

An MCSCF method based on a restricted active space (RAS) type wave function has been implemented. The RAS concept is an extension of the complete active space (CAS) formalism, where the active orbitals are partitioned into three subspaces: RAS1, which contains up to a given maximum number of hole; RAS2, where all possible distributions of electrons are allowed; and RAS3, which contains up to a given maximum number of electrons. A typical example of a RAS wave function is all single, double, etc. excitations with a CAS reference space. Spin-adapted configurations are used as the basis for the MC expansion

Ultrafast electron ejection and trapping in semiconductor colloids after multiple photon absorption

Quantum-size semiconductor microcrystallites of ZnCdS and CdS in aqueous and isopropanol solution were optically excited using intense sub-picosecond UV laser pump pulses. Broad-band optical probing monitored the yield of electron emission and the build-up of primary photochemical products. With typical pmp fluences of femtosecond light pulses multiple photons are absorbed by one quantum-dot leading to a quantum yield of up to 0.3 of photogenerated electrons. The yield curves, as a function of pump fluence, are described by a simple kinetic model which involves the trapping-rate constant and a maximum number of electrons which can be emitted per particle. This model is shown to be consistent with thermodynamic considerations.

Attachment of flame chemielectrons to inert, fine particles

Micron size alumina particles were introduced into low pressure methane-air flat flames on a matrix burner. By means of electrostatic probes the concentrations of chemiions were measured and also the number of electrons attaching to the particles at different positions in the flame, for different particle concentrations. The maximum number of electrons so attached seems larger than that to be expected from a steady state analysis in which electrons and positive ion currents to a particle are equal. Quite small concentrations of particles can be effective in removing electrons from the gas phase. Because the particles are charged, they are efficiently removed by collector anodes at quite moderate voltages.

Maximum Number of Electrons in an Atomic Bound State

Let $\ensuremath{\psi}$ be any normalizable energy eigenfunction for $N$ electrons in an atom having $Z$ protons in a fixed pointlike nucleus. It is shown that, for the state $\ensuremath{\psi}$, $N$ and $Z$ are rigorously related by $N<FZ+1$ with $F=4$. This is independent of any statistics. Evidence is presented that the result can be improved in the sense that $F=F(N)\ensuremath{\rightarrow}2$ for $N\ensuremath{\rightarrow}\ensuremath{\infty}$. A comparison is made with a recent result of Lieb.

Design Calculations for Ionization Spectrometers: Cascade Development

The total number of electrons has been calculated as a function of depth in air, glass, and iron absorbers. The nuclear interactions have been described by the model of Cocconi, Koester, and Perkins. The results help in the design of ionization spectrometers for the measurement of the total energy of ultrahigh energy particles. In particular, a correlation is established between the maximum number of electrons and the primary energy. Also, the amount of energy lost from ionization spectrometers due to limited depth can be derived from the results presented here.

Skin dose from a cobalt 60 teletherapy unit.

Because of its physical characteristics, high-energy radiation offers several advantages over radiation of lower energy in the treatment of deep-seated tumors. These are: (a) an increase in percentage depth dose, (b) a decrease in side-scatter, resulting in flatter isodose curves with a smaller penumbra, and (c) the establishment of electronic equilibrium at a greater depth, resulting in a smaller skin dose. With the Co60 unit under test at this laboratory, it was found that little could be done to affect (a) or (b), with the exception of a moderate dependence of penumbra on cone design. For short cone-to-skin distances, the third advantage is greatly affected by electrons scattered from the walls of the collimating system. This report is a study of the electron build-up region and the optimum cone design necessary to preserve the third advantage. When gamma rays enter tissue, they lose energy through interactions, and accelerated electrons are produced. These electrons in turn lose their energy as they penetrate tissue by radiation processes or by removing other electrons from their atoms (ionization). If the initial electron acquires a high energy from the gamma ray, thousands of electrons and positive ions are produced by this one electron along its path, since only a small amount of energy (about 32.5 ev) is lost in producing each ion pair. The accelerated electrons penetrate the tissue to an average depth corresponding to the energies given the electrons by the gamma rays. If the beam of gamma rays is completely free of electrons before entering the tissue and if there are no back-scattered gamma rays or electrons, the ionization at the surface will be zero. When the gamma rays enter the tissue, accelerated electrons are produced, and at Co60 energies the acceleration is predominantly in a forward direction. As the tissue is penetrated, additional electrons are accelerated with each increment of depth. Thus the number of electrons, and consequently the ionization, builds up with depth. This build-up progresses until a depth corresponding to the average range of the electrons is reached. At this depth, equilibrium has been established between the primary and secondary radiation, and the maximum number of electrons that can contribute to the dosage has been achieved. Beyond this depth, the number of gamma rays per unit area decreases due to the divergence of the beam and to interactions in the preceding layers of tissue. Hence, with further increase in depth, the ionization decreases relatively slowly. There are two other sources of radiation usually present which add to the ionization in the electron build-up region. The first is back-scattered gamma rays which produce additional ionization at all depths up to and including the surface. The second is electrons (from the collimating system or from air) that contaminate the gamma-ray beam. Several workers have studied the phenomenon of electron build-up.

On the Diurnal Variation of Ultra-Short Wave Wireless Transmission

An interpretation of ultra-short wave wireless phenomena is given which indicates that the maximum number of electrons per c.c. in the atmospheric ionized layer is of the order 105 to 106.