Effect of the longitudinal momentum of electrons on their surfatron acceleration by an electromagnetic wave in space plasma

By numerically calculating the second-order nonlinear time-dependent equation for the wave phase on a particle trajectory, the effect of the longitudinal (with respect to the external magnetic field) momentum of electrons on the dynamics of their surfatron acceleration by an electromagnetic wave propagating across the external magnetic field in space plasma is analyzed. It is shown that, for strongly relativistic initial values of the longitudinal component of the electron momentum (the other parameters of the problem being fixed), the electrons are trapped into the ultrarelativistic regime of surfatron acceleration within a definite interval of the initial wave phase Ψ(0) on the particle trajectory. It was assumed in the calculations that Ψ(0) ≤ π. For the initial wave phases lying within the interval of 0 < Ψ(0) ≤ π, the electrons are immediately trapped by the wave, whereas at π ≤ Ψ(0) ≤ 0, no electron trapping is observed even at long computation times. This result substantially simplifies estimates of the wave damping caused by particle acceleration. The dynamics of the velocity components, momentum, and relativistic factor of electrons in the course of their ultrarelativistic acceleration are considered. The obtained results present interest for the development of modern concepts of the mechanisms for the generation of ultrarelativistic particles in space plasma, correct interpretation of experimental data on the flows of such particles, explanation of possible reasons for the deviation of the fast particle spectra observed in the heliosphere from the standard power-law scaling, and analysis of the relation between such deviations and the space weather.     

On the cause of variability of the cosmic ray spectrum in the knee region

Cosmic ray (CR) energy spectra for H, He, Si, and Fe nuclei with energy-to-charge number ratios ?/Z in the range from 10 to 5 × 10⁷ GeV are studied using observational data obtained at different times in different energy ranges: AMS-02, CREAM, Tibet ASγ, Tibet (hybrid), GRAPES-3, KASCADE, and KASCADE-Grande. Comparison of the H and He CR fluxes according to the KASCADE and KASCADE-Grande data (for different models of deconvolving CR spectra) with the Tibet ASγ and Tibet (hybrid) data obtained at another time in the range of ?/Z ～ 3 × 10⁶ GeV demonstrates space weather-caused variability of the CR flux. This feature of CR energy spectra in the Tibet ASγ data is most clearly observed in the spectra of heavier nuclei (Si and Fe) according to the KASCADE-Grande and GRAPES-3 data. The variability in the energy spectra of all CRs in the vicinity of the “knee” is shown in the data of Yakutsk EAS, CASA-BLANCA, and Tibet-III experiments. The variability of the CR flux on a time scale on the order of several years exists only if the source corresponding to the peak in the energy spectrum is situated at a distance of no more than 1 pc from the Sun. Rapid surfatron acceleration of CRs may result from colliding interstellar clouds nearest to the Sun (LIC and G). This acceleration mechanism allows one to explain the variability of the CR spectrum in the range 10³ GeV < ?/Z < 10⁸ GeV. Conditions for the trapping of strongly relativistic Fe nuclei by an electromagnetic wave, the dynamics of the components of the particle velocity and momentum, and the dependence of the particle acceleration rate on the initial parameters of the problem are analyzed using numerical calculations. The structure of the phase plane of the accelerated Fe nuclei is examined. Optimal conditions for the implementation of ultrarelativistic surfatron acceleration of Fe nuclei by an electromagnetic wave are formulated.     

On the reason for the kink in the rigidity spectra of cosmic-ray protons and helium nuclei near 230 GV

A three-component phenomenological model describing the specific features of the spectrum of cosmic-ray protons and helium nuclei in the rigidity range of 30–2×10⁵ GV is proposed. The first component corresponds to the constant background; the second, to the variable “soft” (30–500 GV) heliospheric source; and the third, to the variable “hard” (0.5–200 TV) source located inside a local bubble. The existence and variability of both sources are provided by the corresponding “surfatron accelerators,” whose operation requires the presence of an extended region with an almost uniform (in both magnitude and direction) magnetic field, orthogonally (or obliquely) to which electromagnetic waves propagate. The maximum energy to which cosmic rays can be accelerated is determined by the source size. The soft source with a size of ～100 AU is located at the periphery of the heliosphere, behind the front of the solar wind shock wave. The hard source with a size of >0.1 pc is located near the boundary of an interstellar cloud at a distance of ～0.01 pc from the Sun. The presence of a kink in the rigidity spectra of p and He near 230 GV is related to the variability of the physical conditions in the acceleration region and depends on the relation between the amplitudes and power-law exponents in the dependences of the background, soft heliospheric source, and hard near galactic source. The ultrarelativistic acceleration of p and He by an electromagnetic wave propagating in space plasma across the external magnetic field is numerically analyzed. Conditions for particle trapping by the wave and the dynamics of the particle velocity and momentum components are considered. The calculations show that, in contrast to electrons and positrons (e ⁺), the trapped protons relatively rapidly escape from the effective potential well and cease to accelerate. Due to this effect, the p and He spectra are softer than that of e ⁺. The possibility that the spectra of accelerated protons deviate from standard power-law dependences due to the surfatron mechanism is discussed.     

Surfatron accelerator in the local interstellar cloud

Taking into account results of numerous experiments, the variability of the energy spectra of cosmic rays (protons and helium nuclei) in the energy range of 10 GeV to ~10⁷ GeV is explained on the basis of a hypothesis of the existence of two variable sources close to the Sun. The first (soft) surfatron source (with a size of ~100 AU) is located at the periphery of the heliosphere. The second (hard) surfatron source (with a size of ~1 pc) is situated in the Local Interstellar Cloud (LIC) at a distance of <1 pc. The constant background is described by a power-law spectrum with a slope of ~2.75. The variable heliospheric surfatron source is described by a power-law spectrum with a variable amplitude, slope, and cutoff energy, the maximum cutoff energy being in the range of E _СН/Z < 1000 GeV. The variable surfatron source in the LIC is described by a power-law spectrum with a variable amplitude, slope, and cut-off energy, the maximum cut-off energy being E _СL/Z ≤ 3 × 10⁶ GeV. The proposed model is used to approximate data from several experiments performed at close times. The energy of each cosmic-ray component is calculated. The possibility of surfatron acceleration of Fe nuclei (Z = 26) in the LIC up to an energy of E _CL ~ 10¹⁷ eV and electron and positrons to the “knee” in the energy spectrum is predicted. By numerically solving a system of nonlinear equations describing the interaction between an electromagnetic wave and a charged particle with an energy of up to E/Z ~ 3 × 10⁶ GeV, the possibility of trapping, confinement, and acceleration of charged cosmic-ray particles by a quasi-longitudinal plasma wave is demonstrated.     

Nonquasineutral relativistic current filaments and their X-ray emission

Nonquasineutral electron current filaments with the azimuthal magnetic field are considered that arise due to the generation of electron vorticity in the initial (dissipative) stage of evolution of a current-carrying plasma, when the Hall number is small (σB/en _e c ? 1) because of the low values of the plasma conductivity and magnetic field strength. Equilibrium filamentary structures with both zero and nonzero net currents are considered. Structures with a zero net current type form on time scales of t < t _sk = (r ₀ω _pe /c)² t _st, where t _sk is the skin time, t _st is the typical time of electron-ion collisions, and r ₀ is the radius of the filament. It is shown that, in nonquasineutral filaments in which the current is carried by electrons drifting in the crossed electric (E _r ) and magnetic (B _θ) fields, ultrarelativistic electron beams on the typical charge-separation scale r _B = B/(4πen _e ) (the so-called magnetic Debye radius) can be generated. It is found that, for comparable electron currents, the characteristic electron energy in filaments with a nonzero net current is significantly lower than that in zero-net-current filaments that form on typical time scales of t < t _sk. This is because, in the latter type of filaments, the oppositely directed electron currents repel one another; as a result, both the density and velocity of electrons increase near the filament axis, where the velocities of relativistic electrons are maximum. Filaments with a zero net current can emit X rays with photon energies ? ω up to 10 MeV. The electron velocity distributions in filaments, the X-ray emission spectra, and the total X-ray yield per unit filament length are calculated as functions of the current and the electron number density in the filament. Analytical estimates of the characteristic lifetime of a radiating filament and the typical size of the radiating region as functions of the plasma density are obtained. The results of calculations are compared with the available experimental data.     

Adiabatic Heating of Electrons in the Magnetospheric Current Sheet

Electron dynamics and acceleration in an electromagnetic field configuration modeling the current sheet configuration of the Earth’s magnetotail region is investigated. A focus is made on the role of the dawn?dusk magnetic field component B_y in the convection electron heating by an electric field E_y. For numerical integration of a large number of test particle trajectories over long time intervals, the equations of motion written in the guiding center approximation are used. It is shown that the presence of a B_y ≠ 0 magnetic field significantly changes the electron heating and allows electrons with small pitch angles to gain energy much more efficiently than the equatorial electrons. As a result, the convection heating in the current sheet with B_y ≠ 0 leads to the formation of an accelerated anisotropic population of particles with energies higher than a few hundred electronvolts. The obtained results and spacecraft observations in the Earth’s magnetotail are compared, and possible limitations in the proposed model approaches are discussed.     

Trapping of high-energy electrons into regime of surfatron acceleration by electromagnetic waves in space plasma

The phenomenon of trapping of weakly relativistic charged particles (with kinetic energies on the order of mc ²) into a regime of surfatron acceleration by an electromagnetic wave that propagates in plasma across a weak external magnetic field has been studied using nonlinear numerical calculations based on a solution of the relativistic equations of motion. Analysis showed that, for the wave amplitude above a certain threshold value and the initial wave phase outside the interval favorable for the surfing regime, the trajectory of a charged particle initially corresponds to its cyclotron rotation in the external magnetic field. For the initial particle energies studied, the period of this rotation is relatively short. After a certain number (from several dozen to several thousand and above) of periods of rotation, the wave phase takes a value that is favorable for trapping of the charged particle on its trajectory by the electromagnetic wave, provided the Cherenkov resonance conditions are satisfied. As a result, the wave traps the charged particle and imparts it an ultrarelativistic acceleration. In momentum space, the region of trapping into the regime of surfing on an electromagnetic wave turns out to be rather large.     

Solitary waves in dusty plasmas with weak relativistic effects in electrons and ions

Two distinct classes of dust ion acoustic (DIA) solitary waves based on relativistic ions and electrons, dust charge Z _d and ion-to-dust mass ratio Q’ = m _i /m _d are established in this model of multicomponent plasmas. At the increase of mass ratio Q’ due to increase of relativistic ion mass and accumulation of more negative dust charges into the plasma causing decrease of dust mass, relativistic DIA solitons of negative potentials are abundantly observed. Of course, relativistic compressive DIA solitons are also found to exist simultaneously. Further, the decrease of temperature inherent in the speed of light c causes the nonlinear term to be more active that increases the amplitude of the rarefactive solitons and dampens the growth of compressive solitons for relatively low and high mass ratio Q’, respectively. The impact of higher initial streaming of the massive ions is observed to identify the point of maximum dust density N _d to yield rarefactive relativistic solitons of maximum amplitude.     

Study of Electromagnetic Electron Cyclotron Waves for Kappa Distribution with AC Field in the Magnetosphere of Saturn

Parallel propagating electromagnetic electron cyclotron (EMEC) waves in the extended plasma sheet (~12R_S) and in the outer magnetosphere (~18R_S) of Saturn have been studied. A dispersion relation for parallel propagating relativistic EMEC waves has been applied to the magnetosphere of Saturn, and comparisons have been made with the data of Voyager 1 at these radial distances. The detailed investigations for EMEC waves have been done in the presence of the perpendicular AC electric field, using the kappa distribution function. The relativistic temporal growth rate is calculated by the method of characteristic solution with the data provided by Voyager 1. The effect of the suprathermal electron density, temperature anisotropy, frequency of AC electric field, thermal energy of ions, and relativistic factor on the temporal growth rate of EMEC wave emission has been studied. The simulation results show that the growth of parallel propagating EMEC waves is significantly affected by variations in the temperature anisotropy, electron density, ion thermal energy, and relativistic factor in both the extended plasma sheet and the outer magnetosphere of Saturn. The temperature anisotropy (T⊥/T_║), ion thermal energy (K_BT_║i), and electron density (n₀) have been found to be a major source of free energy for parallel propagating EMEC waves in both regions.     

Nonlinear dynamics of beam–plasma instability in a finite magnetic field

The nonlinear dynamics of beam–plasma instability in a finite magnetic field is investigated numerically. In particular, it is shown that decay instability can develop. Special attention is paid to the influence of the beam?plasma coupling factor on the spectral characteristics of a plasma relativistic microwave accelerator (PRMA) at different values of the magnetic field. It is shown that two qualitatively different physical regimes take place at two values of the external magnetic field: B ₀ = 4.5 kG (Ω ~ ωB _p ) and 20 kG (Ω _B ? ω_p). For B ₀ = 4.5 kG, close to the actual experimental value, there exists an optimal value of the gap length between the relativistic electron beam and the plasma (and, accordingly, an optimal value of the coupling factor) at which the PRMA output power increases appreciably, while the noise level decreases.     

Changes in leaf hydraulic conductance correlate with leaf vein embolism in<Emphasis Type="Italic"> Cercis siliquastrum</Emphasis> L.

The impact of xylem cavitation and embolism on leaf (K _leaf) and stem (K _stem) hydraulic conductance was measured in current-year shoots of Cercis siliquastrum L. (Judas tree) using the vacuum chamber technique. K _stem decreased at leaf water potentials (Ψ_L) lower than ?1.0 MPa, while K _leaf started to decrease only at Ψ_L L K _leaf changes. Field measurements of leaf conductance to water vapour (g _L) and Ψ_L showed that stomata closed when Ψ_L decreased below the Ψ_L threshold inducing loss of hydraulic conductance in the leaf. The partitioning of hydraulic resistances within shoots and leaves was measured using the high-pressure flow meter method. The ratio of leaf to shoot hydraulic resistance was about 0.8, suggesting that stem cavitation had a limited impact on whole shoot hydraulic conductance. We suggest that stomatal aperture may be regulated by the cavitation-induced reduction of hydraulic conductance of the soil-to-leaf water pathway which, in turn, strongly depends on the hydraulic architecture of the plant and, in particular, on leaf hydraulics.     

Physical Parameters of a Reactor-Stellarator with Small Ripples of the Helical Magnetic Field

The paper describes the calculation data on the physical parameters of a reactor-stellarator, where the nonuniformities of the helical field are smaller than the toroidal magnetic field nonuniformities: ε_h < ε_t. Unlike the previous studies, where the ion-component transport coefficients had the collision frequency dependence proportional to ν^1/2, this being equivalent to the ε_h > ε_t case, in the present calculations, these coefficients were assumed to be in proportion to the first power of the collision frequency, D_i ∝ ν for ν_eff < 2ω_E, and to D_i ∝ ν^?1 for the inverse inequality. Here, ω_E is the rotation frequency of plasma in the radial electric field. As before, the plasma electrons corresponded to the mode of D_e ∝ ν^?1. As initial parameters for numerical calculations, a reactor with R = 8 m, r_p = 2 m, and B₀ = 5 Т was taken. A numerical code was used to solve the set of equations that describes the plasma space?time behavior in the reactor-stellarator under the conditions of equal diffusion fluxes. The start of reactor operation in the mode of thermonuclear burning was provided by heating sources with a power of several tens of megawatts. Steady-state operating conditions of a self-sustained thermonuclear reaction were attained by maintaining the plasma density through DT fuel pellet injection into the plasma.     

A generalized theory of particulate electron conduction enzymes applied to cytochrome oxidase. A theory of coupled electron and/or ion transport applied to pyruvate carboxylase

A previously developed theory of particulate electron conduction enzymes was based on a model of an enzyme particle catalyzing the oxidation-reduction of two different substrates at two different enzymatic sites on the same particle with conduction of electrons between the two sites through the enzyme particle. Using the simplifying assumption that the percent reduction of the second substrate is held constant, there was previously shown to be a hyperbolic relationship between the first order rate constant (k′) and the sum (C _x ) of oxidized plus reduced substrate, of the formk′=α/(C _x +β), where α and β are positive constants. It is shown here that if this simplifying assumption is omitted, a positive constant is added to the right hand side of this equation, which describes exactly the experimental data of Smith and conrad on cytochrome oxidase. If electron transport is assumed to be coupled to ion transport, this equation becomesk′=(α/C _x )?γ (where γ is a positive constant) which describes the experimental data of Eadie and Gale on pyruvic carboxylase of yeast. It seems probable that the same theory is applicable to coupled ion-ion transport and coupled electron-electron transport in both membranous systems, and in particulate preparations consisting of membrane fragments.     

The mathematical model of concentration polarization coefficient in membrane transport and volume flows

In this paper, the authors investigate the membrane transport of aqueous non-electrolyte solutions in a single-membrane system with the membrane mounted horizontally. The purpose of the research is to analyze the influence of volume flows on the process of forming concentration boundary layers (CBLs). A mathematical model is provided to calculate dependences of a concentration polarization coefficient (ζ _s ) on a volume flux (J _vm ), an osmotic force (Δπ) and a hydrostatic force (ΔP) of different values. Property ζ _s ?=?f(J _vm ) for J _vm ?>?0 and for J _vm ?≈?0 and property ζ _s ?=?f(ΔC ₁) are calculated. Moreover, results of a simultaneous influence of ΔP and Δπ on a value of coefficient ζ _s when J _vm ?=?0 and J _vm ?≠?0 are investigated and a graphical representation of the dependences obtained in the research is provided. Also, mathematical relationships between the coefficient ζ _s and a concentration Rayleigh number (R _C ) were studied providing a relevant graphical representation. In an experimental test, aqueous solutions of glucose and ethanol were used.     

Reexamination of structures,stabilities, and electronic properties of holmium-doped silicon clusters HoSi<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 12–20)

The total energies, growth patterns, equilibrium geometries, relative stabilities, hardnesses, intramolecular charge transfer, and magnetic moments of HoSi _n (n?=?12–20) clusters have been reexamined theoretically using two different density functional schemes in combination with relativistic small-core Stuttgart effective core potentials (ECP28MWB) for the Ho atoms. The results show that when n?=?12–15, the most stable structures are predicted to be exohedral frameworks with a quartet ground state, but when n?=?16–20, they are predicted to be endohedral frameworks with a sextuplet ground state. These trend in stability across the clusters (gauged from their dissociation energies) was found to be approximately the same regardless of the DFT scheme used in the calculations, with HoSi₁₃, HoSi₁₆, HoSi₁₈, and HoSi₂₀ calculated to be more stable than the other clusters. The results obtained for cluster hardness indicated that doping the Ho atom into Si₁₃ and Si₁₆ leads to the most stable HoSi _n clusters, while doping Ho into the other Si _n clusters increases the photochemical sensitivity of the cluster. Analyses of intracluster charge transfer and magnetic moments revealed that charge always shifts from the Ho atom to the Si _n cluster during the creation of exohedral HoSi _n (n?=?12–15) structures. However, the direction of charge transfer is reversed during the creation of endohedral HoSi _n (n?=?16–20) structures, which implies that Ho acts as an electron acceptor when it is encapsulated in the Si _n cage. Furthermore, when the most stable exohedral HoSi _n (n?=?12–15) structures are generated, the 4f electrons of Ho are virtually unchanged and barely participate in intracluster bonding. However, in the most stable endohedral HoSi _n (n?=?16–20) frameworks, a 4f electron does participate in bonding. It does this by transferring to the 5d orbital, which hybridizes with the 6s and 6p orbitals and then interacts with Si valence sp orbitals. Meanwhile, the total magnetic moments of the HoSi _n (n?=?16–20) clusters are considerably higher than those of HoSi _n (n?=?12–15). Interestingly, the endohedral HoSi₁₆ and HoSi₂₀ clusters can be viewed as the most suitable building blocks for novel high-density magnetic storage nanomaterials and for novel optical and optoelectronic photosensitive nanomaterials, respectively.     

On the minimum electron transport coefficients in tokamaks in the range of low collision frequencies

There are two close empirical scalings, namely, the T-11 and neo-Alcator ones, that provide correct estimates for the energy confinement time in tokamaks in ohmic heating regimes in the linear part of the dependence τ _E (\(\bar n_e \)) in the range of low values of \(\bar n_e \) and 〈ν _e ^* 〉 ≤ 1. The similar character of electron energy confinement in this range, which expands with increasing magnetic field B ₀, has stimulated the search for dimensionless parameters and simple physical models that would explain the experimentally observed dependences χ _e ～ 1/n _e and τ _Ee ～ \(\bar n_e \). In 1987, T. Okhawa showed that the experimental data were satisfactorily described by the formula χ_e⊥ = (c ²/ω _pe ² )ν _e /qR, in deriving of which the random spatial leap along the radius r on the electron trajectory was assumed to be the same as that in the coefficient of the poloidal field diffusion, while the repetition rate of these leaps was assumed to be ν _e /qR. In 2004, J. Callen took into account the decrease in the fraction of transient electrons with increasing toroidal ratio ? = r/R and corrected the coefficient c ²/ω _pe ² in Okhawa equation by the factor σ _‖ ^Sp /σ _‖ ^neo . If one takes into account this correction and assumes that the frequency of the stochastic process is equal to the reciprocal of the half-period of rotation of a trapped electron along its banana trajectory, then the resulting expression for χ_e⊥ will coincide with the T-11 scaling: χ _e ^an ∞ ?^1.75(T _e /A _i )^0.5/(n _e qR) at A i = 1. If the same stochastic process also involves ions, it may result in the opening of the orbit of a trapped ion at the distance ～(c/ω _pe )(m _i /m _e )^1/4. In this case, the calculated coefficient of electron and ion diffusion D is close to D ^an ≈ χ _e ^an /2.     

Theoretical study of the NMR chemical shift of Xe in supercritical condition

In this work we investigate the level of theory necessary for reproducing the non-linear variation of the ¹²⁹Xe nuclear magnetic resonance (NMR) chemical shift with the density of Xe in supercritical conditions. In detail we study how the ¹²⁹Xe chemical shift depends under supercritical conditions on electron correlation, relativistic and many-body effects. The latter are included using a sequential-QM/MM methodology, in which a classical MD simulation is performed first and the chemical shift is then obtained as an average of quantum calculations of 250 MD snapshots conformations carried out for Xe _n clusters (n =?2 ? 8 depending on the density). The analysis of the relativistic effects is made at the level of 4-component Hartree-Fock calculations (4c-HF) and electron correlation effects are considered using second order Møller-Plesset perturbation theory (MP2). To simplify the calculations of the relativistic and electron correlation effects we adopted an additive scheme, where the calculations on the Xe _n clusters are carried out at the non-relativistic Hartree-Fock (HF) level, while electron correlation and relativistic corrections are added for all the pairs of Xe atoms in the clusters. Using this approach we obtain very good agreement with the experimental data, showing that the chemical shift of ¹²⁹Xe in supercritical conditions is very well described by cluster calculations at the HF level, with small contributions from relativistic and electron correlation effects.     

Analysis of ionization and recombination processes under the coronal equilibrium conditions by using a statistical atomic model

Ionization and recombination processes accompanying collisions of free electrons with plasma ions are considered using a statistical atomic model in which ionization and recombination are regarded as the processes of pair electron collisions in the electron gas of an atom. An expression for the ionization rate as a function of the ionization energy I and temperature T is derived. According to this expression, the ionization rate at I ? T is proportional to exp(?I/T). The statistical atomic model provides an estimate of the recombination rate for an ion with an arbitrary nuclear charge number Z, whereas more exact calculations of the recombination rate can be performed only for large Z. The model explains relatively low values of I/T (as compared to those given by the Saha equation) under the coronal equilibrium conditions and predicts a reduction in I/T with increasing Z. The values of I/T and the average ion charge number obtained from the balance equation for multielectron ions with the use of one fitting coefficient agree with the tabulated data calculated in the multilevel coronal model.     

Stability and electronic properties of praseodymium-doped silicon clusters PrSin (<Emphasis Type="Italic">n</Emphasis> = 12–21)

The neutral PrSi _n (n = 12–21) species considering various spin configurations were systematically studied using PBE0 and B3LYP schemes in combination with relativistic small-core potentials (ECP28MWB) for Pr atoms and cc-pVTZ basis set for Si atoms. The total energy, growth-pattern, equilibrium geometry, relative stability, hardness, charge transfer, and magnetic moments are calculated and discussed. The results reveal that when n < 20, the ground-state structure of PrSi _n evaluated to be prolate clusters. Starting from n = 20, the ground-state structures of PrSi _n are evaluated to be endohedral cagelike clusters. Although the relative stabilities based on various binding energies and different functional is different from each other, the consensus is that the PrSi₁₃, PrSi₁₆, PrSi₁₈, and PrSi₂₀ are more stable than the others, especially the PrSi₂₀. Analyses of hardness show that introducing Pr into Si _n (n = 12–21) elevates the photochemical sensitivity, especially for PrSi₂₀. Calculated result of magnetic moment and charge transfer shows that the 4f electrons of Pr in the clusters are changed, especially in endohedral structures such as PrSi₂₀, in which one electron transfers from 4f to 5d orbital. That is, the 4f electron of Pr in the clusters participates in bonding. The way to participate in bonding is that a 4f electron transfers to 5d orbital. Although the 4f electron of Pr atom participates in bonding, the total magnetic moment of PrSi _n is equal to that of isolated Pr atom. The charge always transfers from Pr atom to Si _n cluster for the ground state structures of PrSi_n (n = 12–19), but charge transfer is reverse for n ≥ 20. The largest charge transfer for endohedral structure reveals that the bonding between Pr and Si _n is ionic in nature and very strong. The fullerenelike structure of PrSi₂₀ is the most stable among all of these clusters and can act as the building blocks for novel functional nanotubes.     

The Suitable Condition of Using LSPR Model in SERS: LSPR Effect Versus Chemical Effect on Microparticles Surface-Modified with Nanostructures

The conditions under which the localized surface plasmon resonance (LSPR) model can be applied to the calculation of surface-enhanced Raman scattering (SERS) enhancement factors have been questioned because the chemical effect presents simultaneously with LSPR effect, resulting in calculations that are not always consistent with the measured data. The SERS spectra of crystal violet (CV) molecules on single, dimer, trimer, and aggregates of silver microparticles surface-modified with nanostructures (MSMN) were obtained. It is found that the chemical effect is determined by the chemical adsorption behavior of CV molecules on single particle. As more particles are introduced as amplifiers, to assemble dimer, trimer, and aggregates, no new SERS signals related to the chemical effect can be observed, except for the further enhancement to the original signals. The further enhancement is attributed to the LSPR effect from the electromagnetic coupling with introduced particles. This is also demonstrated by dark field scattering. The LSPR theoretical values of single, dimer, trimer, and aggregates of MSMNs should fit the measured enhancement factor (G _LSPR) after correcting the SERS enhancement factor (G _SERS) with the chemical enhancement factor on the single particle (G _Chem-Sgl), i.e., G _LSPR?=?G _SERS/G _Chem-Sgl. Tip-enhanced Raman spectroscopy with a gold nanoparticle further implies that this could be extended to nanoparticle systems. This work provides an effective and simple route, whereby only the chemical effect from a single particle needs to be considered when studying the fit between the LSPR model and the measured LSPR enhancement factor.