Electron mean free path and conduction-band density of states in solid argon

In this paper, we apply a theoretical model developed by Plenkiewicz et al. for analyzing the current I_t transmitted by an ultrathin dielectric film as a function of incident electron energy E for solid argon. The analysis of I_t(E) in the elastic scattering region (0–12 eV) allows one to determine the electronic conduction-band density of states and to calculate the electron scattering mean free path as a function of energy. Comparison of our results with various solid argon band structure calculations is also presented.     

Detection limits in Auger electron spectroscopy

The sources of background noise in Auger electron microanalysis are analyzed in order to evaluate the minimum detectable concentration x_m and the minimum number of detectable atoms y_m that can be reached. The best choices of operating conditions (the energy E₀, intensity I₀, and spot size d₀ of the incident electron beam, and the duration of the experiment t_e) are deduced for bulk and thin film analysis. The main results are: (i) The choice of E₀ is not very stringent, at least when E₀ ? 5E_i(A), where E_i(A) is the ionization energy, (ii) For a given electron dose received by the sample, x_m is improved by the use of the largest incident spot size while y_m is improved by the use of the finest spot size. The results also hold for other microanalytical techniques such as electron energy loss spectroscopy or electron probe microanalysis. (iii) Chemical identification of a single atom will be possible on samples able to tolerate very large electron doses by using incident electron beams 10 nm or less in diameter. The expected performance of a coincidence technique first suggested by Wittry is also discussed.     

Approximately linear relations between two-nucleon and three-nucleon parameters

The correlation between the triton binding energyE _t and then-d scattering length² a and the zero energy singlet and triplet wound integral I_os and I_ot is investigated, with phaseequivalent separableNN interactions obeying all the important off-shell constraints. It is found that the correlation betweenE _t and² a is stronger than betweenE _t (² a) andI _os ,I _ot separately. A strong correlation is also found between the percentageD-state in the deuteronP _d andI _ot . Fixing all the other off-shell parameters but allowing variations ofI _os andI _ot leads to surprisingly accurate linear relations betweenE _t(² a) andI _os ,I _ot (P _d). These relations depend strongly on the other off-shell parameters.     

Ionization cross sections and rate coefficients for the ground state of AsI-like ions

Detailed level-by-level calculations of cross sections and rate coefficients for electron impact direct ionization and excitation-autoionization of AsI-like ions in the 3d ¹⁰4s ²4p ³ (⁴S_3/2) ground state have been performed. The cross sections are presented in the energy range near the threshold for the five ions Mo⁹⁺, Xe²¹⁺, Pr²⁶⁺, Dy³³⁺ and W⁴¹⁺. The rate coefficients are given for all the ions from Sr⁵⁺ to U⁵⁹⁺ in the AsI sequence at the seven electron temperatures (k T _e = 0.1E _I ,0.3E _I ,0.5E _I ,0.7E _I ,E _I ,2E _I and 10E _I , where E _I is the first ionization energy). The calculations include the contribution of direct ionization (DI) calculated using the Lotz formula approximation and the contributions of excitation-autoionization (EA) computed in the framework of the Distorted Wave (DW) approximation for the 4s ? nl, 3d ? nl and 3p ? nl resonant inner-shell excitations. The ionization enhancement due to the EA channels is presented as a function of Z along the AsI isoelectronic sequence. The present results show the great importance of the EA processes; an ionization enhancement factor of up to 6.5 is predicted for instance for Dy³³⁺ (Z = 66) at electron temperature of coronal equilibrium maximum abundance.     

The electronic conductivity of lead fluoride and the D.C. Polarization theory

The electronic conduction characteristics of solid lead fluoride were investigated using the Wagner d.c. polarization technique. It was found that when the (?) Pb/PhF₂/graphite ( + ) cell was polarized at potentials much below a critical value, E_c, the steady state current, I, as a function of the polarization potential, E, behaves in accordance with the Wagner equation. The log I vs E plots gave straight lines with slopes having the theoretical value of F/2.303 RT. On the other hand, when the polarization potential was equal or higher than E_c, an anomalous behavior was observed. Slopes with values less than the theoretical were obtained from the log I vs E plots. This anomalous behavior was attributed to the high concentration of electron holes at the PbF₂/graphite interface resulting from the high polarization potential. The critical potential was defined as the applied potential where the electron hole concentration at the PbF₂/graphite interface becomes so high that the electronic conductivity is equal to the ionic conductivity which contradicts the assumptions for the Wagner equation. Consequently, the Wagner equation is not applicable under these conditions.     

Optimized t-expansion method for the Rabi Hamiltonian

A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E₀ of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E₀ is assumed to be stationary with respect to the free parameters. A high accuracy of E₀ estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than ¹⁰−4 (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E₁, with the relative error smaller than ¹⁰−2 (1%).     

Nuclear levels in152Eu

The transitional nucleus¹⁵²Eu has been studied using the (n, e), (n, γ), (n _res,γ), (n, γγ), (d, p), (d, t) and (p, d) reactions. The experiments have been performed at nine different laboratories. A model independent level scheme was established including 95 levels below 510 keV and nearly 900 transitions by combination of low energy transitions and reaction data. More than 20 additional levels result from gamma rays and/or charged particle reactions. The level scheme is interpreted in terms of the Nilsson model indicating that¹⁵²Eu is a deformed nucleus. Seven rotational bands and Nilsson configurations are established. An additional 27 rotational bands are tentatively or speculatively assugned. Gallagher-Moszkowski splittings are discussed. The neutron binding energy was determined as 6305.2±0.5 keV. The energy of the 9.3 h 0^? isomer is 45.599 keV. The lifetimes of four levels were measured. Nuclear Reactions¹⁵¹Eu(n,γ),E _n =thermal and resonance; measuredE _γ ,I _γ ,E _c.e.,I _c.e.,γγ Coinc.,γγΔt coinc.;¹⁵¹Eu(d, p),E=12MeV and 14MeV;¹⁵³Eu(d, t),E=12MeV;¹⁵³Eu(p, d),E =18MeV; deduced level scheme of¹⁵²Eu,J, π, T _1/2,cc, Nilsson configurations. Magnetic electron spectrometer, curved crystal spectrometer, Ge(Li) and Si(Li) detectors, magnetic spectrographs. Enriched targets.     

Valence quark effects in beam remnants in high Et proton-proton collisions at s=27.4 GeV

Charged particle trajectories have been reconstructed in pp collisions with transverse energies (E_t) ranging from 1 GeV to 20 GeV. Data were collected by triggering on E_t in a highly segmented calorimeter with full azimuthal coverage. Minimum bias triggers were also used. Valence quark effects are known to appear at low E_t in the differences between positive and negative particle multiplicities in the forward direction. We reproduce these known prominent effects at low E_t, but find them not present in the collisions with large E_t, disappearing by about E_t=8 GeV. Furthermore, events with high planarity do not show a strong forward net flow of charge and disagree with the predictions of ISAJET. The results suggest that for the triggers studied, more than a single pair of proton constituents scatter at this energy.     

Nuclear rotation for low and high spin values

It is shown that a rigorous application of the Peierls-Yoccoz angular momentum projection method leads, in the case ofK=0 rotational bands, to a simple exact expression for the projected energyE _I , which may be especially suitable for numerical calculations. On the basis of this energy law and without making any assumption for the overlapsn(Β) andh(Β), a finite expansion ofE _I in powers ofI( _I +1) is obtained and discussed. Using this finite series a microscopical variable moment of inertia model is presented.     

The relationship between the transition voltage of the I–V curve of the ferroelectrics and the coercive field of the P–V hysteretic curve

The relationship between the transition voltage of the I–V curve of the ferroelectrics and the coercive field of the P–V hysteretic curve is calculated. The first mathematical analysis to explain the relation between the transition voltage V_t and the coercive voltage V_c is obtained. The origin of the interrelation between the transition voltage of the I–V curve and the coercive field is that the height of the boundary barrier is inversely proportional to the effective dielectric constant of the near-boundary region, which is dependent on a derivative of polarization on the electric field, ∂P/∂E. The term ξ(eV_t) plus the term (en_b²δ/dN_dP_s)(eV_c) equals a constant. V_t is the function of E_g, P_s, V_c, and E. There is a linear relation between V_c and V_t. This relationship will induce the matchable relations between the I–V curve and the E–P loop. As long as the V_c of the V–P loop exists, the correspondent V_t of I–V curve will certainly exist. It will be the foundation of a new ferroelectric memory, which operates by the I–V characteristics. These relations are the conditions that can enable nonvolatile memory and nondestructive readout.     

Fixed-J level densities beyond spin cut-off approximation

It is well known that the expression for fixed-J level densityI _?(E, J)=?I(E) $\frac{\partial }{{\partial M}}$ I(M|E)| _M=J+1/2 reduces to familiar Bethe’s formula provided the conditionalM-distributionI(M|E) is approximated by a Gaussian form, so called spin cut-off approximation (M is thez-component of total angular momentumJ andE is the excitation energy). After a detailed analysis, we find that the Bethe’s formula which overestimatesI?(E, J) at highJ values, in particular near the yrast line, can be significantly improved by including a few higher-order moment terms in a suitable expansion forI(M|E) with the lowest-order term to be a Gaussian, e.g., Edgeworth expansions. We also find that, except at very low excitation energies, reasonable values (close to exact) of the moments ofI(M|E) can easily be obtained when multiple Laplace-back transform of the partition function for grand canonical ensemble is evaluated within the saddle point approximation. Furthermore, we study the effects of shell structure as well as residual interaction on the excitation energy dependence of these moments.     

Plasmons in semiconductors and insulators: A simple formula

Based on the dielectric function of an excitonic system, a simple model dielectric function is constructed. The high energy zero of this function yields the plasma frequency, and is given by: (hω_x)² = (hω_f)² + E_x² where ω_f is the free electron plasma frequency and E_x the lowest exciton energy. It is argued that this formula is valid for both, Frenkel and Wannier excitons, and comparison is made with experiments on a variety of crystals, ranging from InSb to Ar. In all cases, surprisingly good agreement is found.     

Effect of kink-rounding barriers on step edge fluctuations

The effect that an additional energy barrier E_kr for step adatoms moving around kinks has on equilibrium step edge fluctuations is explored using scaling arguments and kinetic Monte Carlo simulations. When mass transport is through step edge diffusion, the time correlation function of the step fluctuations behaves as C(t)=A(T)t^1/4. At low temperatures the prefactor A(T) shows Arrhenius behavior with an activation energy (E_det+3?)/4 if E_kr<? and (E_det+E_kr+2?)/4 if E_kr>?, where ? is the kink energy and E_det is the barrier for detachment of a step adatom from a kink. We point out that the assumption of an Einstein relation for step edge diffusion has lead to an incorrect interpretation of step fluctuation experiments, and explain why such a relation does not hold. The theory is applied to experimental results on Pt(1 1 1) and Cu(1 0 0).     

Excitation-autoionization cross sections and rate coefficients for Ga-like ions

Detailed level-by-level calculations of cross sections and rate coefficients for electron impact direct and indirect ionization of ions belonging to the GaI isoelectronic sequence (ground 3d ¹⁰4s ²4p) have been performed. The cross sections are presented in the energy range near the threshold for the five ions Kr⁵⁺, Mo¹¹⁺, Xe²³⁺, Pr²⁸⁺ and Dy³⁵⁺. The rate coefficients are given for ions from Kr⁵⁺ to U⁶¹⁺ in the GaI sequence at seven electron temperatures (kT _e = 0.1E _I , 0.3E _I , 0.5E _I , 0.7E _I ,E _I , 2E _I and 10E _I , where E _I is the first ionization energy). The calculations include the contribution of direct ionization (DI) calculated using the Lotz formula approximation and the contributions of excitation-autoionization (EA) computed in the framework of the distorted wave (DW) approximation for the 4s-nl, 3d-nl and 3p-nl resonant inner-shell excitations. The ionization enhancement due to the EA channels is presented as a function of Z along the GaI isoelectronic sequence. The present results show the great importance of the EA processes; an ionization enhancement factor of up to 10 is predicted for instance for La²⁶⁺ (Z = 57) at electron temperature of coronal equilibrium maximum abundance.     

Scaling and fragmentation distributions of beam remnants in high Et proton-proton collisions at √s =27.4 GeV

Charged particle trajectories have been reconstructed in pp collisions triggered by transverse energies (E_t) ranging from 1 GeV to 20 GeV. The forward fragmentation function of negative particles in the beam jet is found to scale with E_t in variable x=2p_L/√s−E_t, and the slope is near to that found for small jet triggers in an earlier experiment. Above about E_t=8 GeV, positive particles scale and for 0.5<x<1.0 the ratio of positives to negatives is 1.73±0.2. The forward fragmentation functions at high E_t do not show the behavior expected from the fragmentation of diquarks and are more like that from quarks.Multiplicity and energy flow in various forward polar angle regions are also presented; they are compared to the beam jet predictions of ISAJET and found to be greater at wide angles and less at small.     

Influence of the boundary conditions on the fermi energy and density of states in a free-electron solid of sub-micron dimensions

Asymptotic expressions for the distribution of the eigenvalues of the Helmholtz-Schrödinger equation are used to anlyze the dependence of the Fermi energy, E_F, and the density of states, ρ(E), on sample size, shape, and electron density, in a free-electron model with Dirichlet boundary conditions. It is found that for very small samples E_F is increased relative to its asymptotic (i.e., bulk) value and ρ(E) is decreased relative to its bulk value. These effects are more pronounced for samples with low electron density and with a large surface-to-volume ratio. In general E_F and ρ(E_F) deviate significantly from their bulk values only for systems with fewer than 50,000 electrons and/or with linear dimensions of 100 Å or less. The use of smoothing functions to represent the density of states obtained from the exact eigenvalue distribution is also discussed. It is shown that an oscillating density of states leads to small cusps in the plot of E_F as a function of sample size. This is in qualitative agreement with the results of experiments on size-dependent oscillations in field emission from thin metallic films. Comparison is also made between photoemission experiments from thin films and other results obtained in this study.     

Transient behaviour of the mechanoluminescence induced by impulsive deformation of fluorescent and phosphorescent crystals

When a crystal is fractured impulsively by the impact of a moving piston, then initially the mechanoluminescence (ML) intensity increases quadratically with time, attains a peak value and later on it decreases with time. Considering that the solid state ML and gas discharge ML are excited due to the charging and subsequent production of electric field near the tip of moving cracks, expressions are derived for the transient ML intensity I, time t_m and intensity I_m corresponding to the peak of ML intensity versus time curve, respectively, the total ML intensity I_T, and for fast and slow decays of the ML intensity. It is shown that the decay time for the fast decrease of the ML intensity after t_m, is related to the decay time of the strain rate of crystals, and the decay time of slow decay of ML, only observed in phosphorescent crystals, is equal to the decay time of phosphorescence. The value of t_m decreases with the increasing impact velocity, I_m increases with the increasing impact velocity, and I_T initially increases and then it tends to attain a saturation value for higher values of the impact velocity. The values of t_m, I_m and I_T increase linearly with the thickness, area of cross-section and volume of the crystals, respectively. So far as the rise, attainment of ML peak, and fast decay of ML are concerned, there is no any significant difference in the time-evolution of solid state ML, gas discharge ML, and the ML emission consisting of both the solid state ML and gas discharge ML. From the time-dependence of ML, the values of the time-constant for decrease of the surface area created by the movement of a single crack, the time-constant for the decrease of strain rate of crystals, and the decay time of phosphorescence of crystals can be determined. A good agreement is found between the theoretical and experimental results. The importance of fracto ML induced by impulsive deformation of crystals is discussed.     

Inelastic mean free paths for electrons in bulk jellium

Bulk inelastic mean free paths, λ, of electrons in jellium are given in graphical form as a function of the electron spacing parameter r_s and the electron energy E, based on self-energy results of Lundqvist. The results are suggested as a useful guide to the dependence of λ on the material in the energy range near the minimum of λ.     

The energy dependence of nuclear reaction cross sections

The reaction cross section σ_R^pA(E) for proton-nucleus collisions varies with energy as the total cross section σ_t^pN(E) does for proton-nucleon scattering in the energy regime 100 MeV ? E ?400 GeV. We propose several empirical relations, and test them by a χ² analysis of various data. Within the framework of Glauber theory, the parameters in the relations can be linked to the cross section for a single inelastic collision.     

Statistical mechanics of rotating systems

A microcanonical distribution function depending on the total energyE and thez-componentM of the total angular momentum of a rotating system is examined. ForM=0 the generalized microcanonical ensemble is found to give the same entropy as the usual microcanonical ensemble. The moment of inertia of a rotating gas is calculated, and the kinetic energy of rotation is given as a power series in the small parameterM ²/2I ₀E_int, whereI ₀ is the moment of inertia of the gas at rest andE _int the internal energy.