Thermionic field emission of electrons from metals and explosive electron emission from micropoints

We suggest a general approach to considering the thermionic, field, and thermionic field emissions of electrons from metals. For this purpose, based on the standard model of free electrons in a metal, we suggest a numerical method for determining the transmission coefficient through the potential barrier at the metal-vacuum interface suitable for an arbitrary barrier. This method is free both from the approximations based on the saddle-point approximation and characteristic of the analytical models for thermionic emission and from the approximations for the tunneling coefficient through the potential barrier characteristic of the models for field emission. Based on numerical simulations, we determine the thermal effect of the emission and ascertain that a very sharp transition from surface cooling by electron emission to heating occurs at certain electric field and temperature. We explain the triggering mechanism of the explosive electron emission observed during micropoint explosions by this phenomenon. The explosive emission is shown to begin when the level of the potential barrier at the micropoint tip drops below the Fermi level in the metal.     

Role of barrier penetration in complete fusion of heavy ions

The relevance of tunneling in determining the cross section for complete fusion is explored. The classical model with frictional forces is used for the determination of the trajectory of two heavy ions up to the classical turning point. The penetrability of the barrier is calculated quantum mechanically. It is shown that the so calculated transmission coefficient differ from the sharp cut-off approximation, but yield cross section for complete fusion which are not significantly different from the cross section neglecting quantum mechanical effects.     

Three-Body Phase Shift in One-Dimensional 2 + 1 Scattering

For a model of three particles on a line, subject to attractive delta-function interactions, we consider the phase shift. We do this from the point of view of the calculation of the S-matrix in a hyperspherical adiabatic basis (an adiabatic S-matrix), and for energies ranging from the (negative) energy of the two-body bound state to a total energy of zero. We derive analytical expansions and present numerical work, for different approximations, and compare with the exact results that we obtain from the work of McGuire, whose model we have borrowed. We show that the simplest adiabatic approximation gives results that are qualitatively wrong, but that better approximations yield, for most of our range, excellent agreement with the exact result. Understanding the threshold behaviour, however, requires a zero-energy three-body bound state, or resonance, previously unsuspected for this model. The methods developed for the case of the simplest adiabatic approximation also yield threshold and low-energy results applicable to the two-body problem in two dimensions. Received December 23, 1996; revised May 13, 1997; accepted for publication June 19, 1997     

Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers

In analogy with the definition of resonant or quasi-bound states used in three-dimensional quantal scattering, we define the quasi-bound states that occur in one-dimensional transmission generated by twin symmetric potential barriers and evaluate their energies and widths using two typical examples: (i) twin rectangular barrier and (ii) twin Gaussian-type barrier. The energies at which reflectionless transmission occurs correspond to these states and the widths of the transmission peaks are also the same as those of quasi-bound states. We compare the behaviour of the magnitude of wave functions of quasi-bound states with those for bound states and with the above-barrier state wave function. We deduce a Breit-Wigner-type resonance formula which neatly describes the variation of transmission coefficient as a function of energy at below-barrier energies. Similar formula with additional empirical term explains approximately the peaks of transmission coefficients at above-barrier energies as well. Further, we study the variation of tunnelling time as a function of energy and compare the same with transmission, reflection time and Breit-Wigner delay time around a quasi-bound state energy. We also find that tunnelling time is of the same order of magnitude as lifetime of the quasi-bound state, but somewhat larger.     

Transmission of Correlated Gaussian Packets Through a Delta-Potential

We study the evolution of the most general initial Gaussian packet with nonzero correlation coefficient between the coordinate and momentum operators in the presence of a repulsive delta-potential barrier, using the known exact propagator of the time-dependent Schrödinger equation. For the initial packet localized far enough from the barrier, we define the transmission coefficient as the probability of discovering the particle in the whole semi-axis on the other side of the barrier. It appears that the asymptotical transmission coefficient (calculated in the large time limit) depends on two dimensionless parameters: the normalized ratio of the potential strength to the initial mean value of momentum and the ratio of the initial momentum dispersion to the initial mean value of momentum. For small values of the second parameter, the result is reduced to the well-known formula for the transparency of the delta barrier, obtained in the plane-wave approximation by solving the stationary Schrödinger equation. For large values of the second parameter, the transmission coefficient can be much larger than that calculated in the plane-wave approximation. For a fixed initial spread of the packet in the coordinate space, the initial correlation coefficient influences the transparency of the barrier only indirectly, through the increase in the initial momentum dispersion.     

Generalized dependences of the reflection coefficient of ions from a relief surface

Dependences of the reflection coefficient of ions on their energy and the height and geometry of surface asperities obtained while studying ion beam interaction with targets by the Monte Carlo method have been analyzed. The dependences of the reflection coefficient on the height of asperities with a specified geometry under bombardment with ions of different energies, on the height of asperities for different angles of inclination of lateral walls at a specified energy of ions, and on the angle of inclination of walls for different ion energies at a fixed height have been considered. Generalized curves for reflection coefficients have been obtained, and analytical approximations have been calculated.     

Some aspects of heavy ion fusion-fission dynamics

Study of heavy ion induced fusion-fission reactions at near and below barrier energies has attracted a great deal of attention in recent years, due to the observations of anomalous features in the fragment angular distributions for many target-projectile systems. Additionally there are also measurements of the fragment spin distributions and time-scales of the fusion-fission reactions, which have provided important information on the dynamics of these processes. In the present paper, the emphasis would be to highlight some of the recent experimental findings and their implications on the dynamics of the fusion-fission reactions in heavy ion collisions at near and above barrier energies.     

Integral equation approximations for fluids of hard spheres with linear quadrupoles

In this paper we solve numerically several integral equation theories for the dense quadrupolar hard-sphere fluid. Closure approximations obtained by expanding the hypernetted-chain equation are shown to give pair-correlation functions and internal energies in good agreement with Monte Carlo calculations. The mean spherical approximation, however, is found to be extremely poor.     

Gaseous ion mobility and diffusion in electric fields of arbitrary strength

In a previous paper we presented the first kinetic theory of gaseous ion mobility which is valid for electric fields of arbitrary strength and for arbitrary ion-neutral interaction potentials and mass ratios. In this paper we extend this theory to gaseous ion diffusion and systematize it so as to greatly decrease the effort involved in computing high approximations to the transport coefficients. Analytical results in low approximation are discussed, as are scaling rules for ion mobilities and diffusion coefficients. An extensive study of the convergence of the successive approximations of this theory is given for model systems, from which it is concluded that the theory is accurate, particularly in third and higher approximation, when applied to ion mobility and mean kinetic energy. When applied to diffusion, the theory is less successful in some circumstances, but it is still the best general theory currently available.     

Do thermal fluctuations destroy the concept of a critical angular momentum?

We estimate the influence of thermal fluctuations in heavy-ion induced deep inelastic and fusion reactions by means of a one-dimensional Fokker-Planck equation. Approximating the fusion barrier by an inverted harmonic oscillator, we find an expression for the range of angular momenta ΔJ over which the transmission coefficient falls from 1 to 0. Numerically, ΔJ is fairly but not insignificant, and becomes larger for incident energies near the barrier.     

Comparison of models for the Gaunt factor for free-free absorption

Within the dipole approximation to the radiation field for the free-free Gaunt factor, we compare various models of the electron-atom (ion) collisional process. These models range in sophistication from the static-exchange to the simple Born, point-charge representation. We also consider a number of local potential models such as the Thomas-Fermi and Free-Electron-Gas. The Born approximation is shown to be singularly unreliable for electron and photon energies between 10 and 100 eV. Of the local potential models, the FEG gives the most accurate results.     

Analytic approach to the motion of cosmological phase transition fronts

We consider the motion of planar phase-transition fronts in first-order phase transitions of the Universe. We find the steady state wall velocity as a function of a friction coefficient and thermodynamical parameters, taking into account the different hydrodynamic modes of propagation. We obtain analytical approximations for the velocity by using the thin wall approximation and the bag equation of state. We compare our results to those of numerical calculations and discuss the range of validity of the approximations. We analyze the structure of the stationary solutions. Multiple solutions may exist for a given set of parameters, even after discarding non-physical ones. We discuss which of these will be realized in the phase transition as the stationary wall velocity. Finally, we discuss on the saturation of the friction at ultra-relativistic velocities and the existence of runaway solutions.     

Tunneling of slow quantum packets through the high Coulomb barrier

We study the tunneling of slow quantum packets through a high Coulomb barrier. We show that the transmission coefficient can be quite different from the standard expression obtained in the plane wave (WKB) approximation (and larger by many orders of magnitude), even if the momentum dispersion is much smaller than the mean value of the momentum.     

Energy barriers for vortex nucleation in dipolar condensates

We consider singly-quantized vortex states in a condensate of ⁵²Cr atoms in a pancake trap. We obtain the vortex solutions by numerically solving the Gross-Pitaevskii equation in the rotating frame with no further approximations. The behavior of the condensate is studied under three different situations concerning the interactions: only s-wave, s-wave plus dipolar and only dipolar. The energy barrier for the nucleation of a vortex is calculated as a function of the vortex displacement from the rotation axis in the three cases. These results are compared to those obtained for contact interaction condensates in the Thomas-Fermi approximation, and to a pseudo-analytical model, showing this latter a very good agreement with the numerical calculation.     

An analytic approach to tunnelling magnetoresistance

We present an analytic model for the barrier transmission coefficient that can be used to calculate the tunnelling magnetoresistance (TMR) for metal-insulator-metal systems. It removes the approximations inherent in the Simmons’ and Brinkman models currently used to fit experimental systems that give much lower predictions of the barrier height than would be expected. The model is accurate enough to directly relate to the experiment and hence device optimisation by predicting junction parameters that are in line with bulk properties.     

Determining reflections for beam propagation algorithms

Reflections occur whenever different waveguide sections are concatenated. In this paper, we will give approximate formulas for determining the reflection coefficient. Starting with generalized transmission line equations we will derive general formulas where suitable approximations are introduced. These approximations allow the determination of the reflections with low numerical effort. The expressions were implemented in an FD-BPM algorithm to determine the field distribution in waveguide devices. For an application in CAD systems the reflection coefficient of the fundamental mode was computed with the approximate formulas. Numerical results were obtained for various concatenations of different waveguide sections. A comparison with the method of lines, a semi-analytic algorithm, shows a good agreement.     

CSR能区重离子反应中的介子产生

重离子反应中介子产生的观测对于认识重离子反应动力学和核物质性质具有重要的意义 .讨论了重离子反应中阈能附近介子产生的一些特点和研究现状 ,特别讨论了π介子产生和K+ 介子产生 .在我国兰州重离子冷却储存环上开展这方面的实验研究具有可能性 ,可望得到很有意义的结果 .及时开展这方面实验研究和相应的理论研究是必要的.It is important to measure meson productions in heavy ion collisions in order to understand the dynamics of heavy ion reactions and the properties of nuclear matter. In this paper we review the characteristic and present status of meson productions near the threshold energies in heavy ion collisions. Especially the pion and K + productions are discussed. We point out that it is meaningful and possible to carry out the experimental studies at the CSR. It is necessary to carry out timely the...     

Discrete anchoring: Bulk-substrate coupling in lattice models

We formulate the anchoring problem for discrete-state lattice models. Anchoring is the selection of a bulk equilibrium state from a degenerate set of equivalent equilibrium states in semi-infinite samples in contact with a substrate, a phenomenon widely discussed in the context of liquid crystalline displays. As a concrete example we consider this problem for the three-state Potts model employing two different approximations, viz., a layered mean-field approximation and a Bethe lattice approach. The anchoring behaviour of the model is shown to be completely determined by the symmetry properties of the Hamiltonian.