Finite Binding Energy Research Articles

Critical exponents of a multicomponent anisotropict?J model in one dimension

A recently presented anisotropic generalization of the multicomponent supersymmetric $t-J$ model in one dimension is investigated. This model of fermions with general spin-$S$ is solved by Bethe ansatz for the ground state and the low-lying excitations. Due to the anisotropy of the interaction the model possesses $2S$ massive modes and one single gapless excitation. The physical properties indicate the existence of Cooper-type multiplets of $2S+1$ fermions with finite binding energy. The critical behaviour is described by a $c=1$ conformal field theory with continuously varying exponents depending on the particle density. There are two distinct regimes of the phase diagram with dominating density-density and multiplet-multiplet correlations, respectively. The effective mass of the charge carriers is calculated. In comparison to the limit of isotropic interactions the mass is strongly enhanced in general.

Monte Carlo Simulation of Particle Coagulation and Sintering

A Monte Carlo simulation has been developed to describe the gas phase coagulation and sintering of nan-oclusters. The cluster-cluster aggregation model is modified to include a finite interparticle binding energy. Particle restructuring and densification (sintering) are incorporated into the model by modifying Kadanoff's algorithm for random particle walks on the surface of the cluster. The effect of sintering on aggregate size distribution and fractal dimension has been investigated in simulations of two-dimensional clusters. The binding energy and the relative rates of aggregation and sintering are the primary variables affecting particle structure. In the initial stages, the sintering process results in aggregates which are compact on small length scales. As time progresses and the aggregates become larger, the sintering process slows down and the fractal dimension of the aggregates decreases. The model is able to track the effect of reactor residence time and temperature on the specific surface area a...

Effects of finite pair binding energy in a model of a superconductor with local electron pairing

Abstract A simple model of a superconductor with very short coherence length is studied for arbitrary electron density. The tight binding hamiltonian consists of the inter-site charge exchange term J , determining the hopping of electron pairs, and the effective on-site interaction U . The evolution of phase diagrams, superconducting critical temperature T c and critical fields are determined as functions of interaction parameters and electron density, and the temperature dependences of the electron pair concentration, magnetic susceptibility and specific heat are established. There are two well defined regimes of the model. In the local pair limit i.e. for large pair binding energies E b ( E b / k B T c ⪢1) the superconducting transition occurs through Bose condensation of preexisting pairs, whereas in the opposite case, i.e. for E b / k B T c ≲1, the transition is determined by pair breaking excitations and there are essentially no preformed pairs above T c . It turns out that a crossover between the two regimes, occurring with increasing U , is smooth.

Magneto-optical studies of screened excitons in GaAs/AlxGa1-xAs modulation-doped quantum wells.

Asymmetric GaAs/Al x Ga 1-x As quantum wells were studied by photoconductivity and photoluminescence in magnetic fields up to 15 T. The sample chosen had only one occupied electric subband, with a high density of 8.2×10 12 cm -2 , which allowed a study of the empty E2-H1 transitions by photoconductivity. This showed that there was a small but finite binding energy of 1.5±0.5 meV for the 1s state, which increased very rapidly at high fields in agreement with theory, due to the changing effects of the screening on the exciton

THE APPLICATIONS OF ANOMALOUS DIFFRACTION IN POWDER DIFFRACTOMETRY

An atom scatters X-ray with an amplitude and a phase that can be represented by the complex number ; ftof (K,E) = fo (K) + f' (K,E)+ if (K, E) . fo(K) represents the atomic scattering factor for the radiations with frequencies smaller than the absorption edge frequencies. The anomalous scattering terms f' and f, which are functions of the wavelength, describe the in-phase an out phase components of the change due to finite binding energies of the electrons .in the atom. Near an absorption edge of an atom, where the x-ray energy is close to the binding energy of an inner shell electron both f' and vary rapidly with wavelength , jumps rapidly up to a maximum while f' dips and then rises again as the x-ray energy goes from below the edge to above it. The term results in breaking of Friedel's law, this effect has long been used to find the solution of the crystallographic phase problem. Very few applications were performed to show the useful aspect of anomalous dispersion on the powder dif f ractometry . Even though the principle is simple and straight forword the implementation was not a trivia tasK. The main difficulty was to obtain reliable data. As the energy dependence of diffraction intensity is usually small then a very high accurancy of measurments were required. The recent availability of synchrotron radiation as a tunable source of x-ray, with very high intensity made it possible to use this effect to obtain structural information from a powder diffractometry. For this purpose a powder automated diffractometer has been designed to be adapted to such new sources (L.U.R.E. DCI) . This diffractometer consistes of three main parts :

Reversible-growth model: Cluster-cluster aggregation with finite binding energies.

Reversible-growth model: Cluster-cluster aggregation with finite binding energies.

Classical wall formula and quantal one-body dissipation

Within the quantal, self-consistent RPA description of the dissipation of nuclear collective energy, a specific set of assumptions is shown to reduce the RPA system to a vibrating potential model which, with the stipulation of certain additional assumptions, yields precisely the dissipation rate given by the Swiatecki wall formula. This correspondence is utilized to explore the explicit and the implicit assumptions of the wall model. Various implications emerge, the most important of which is the fact that, for finite nucleonic binding energy, the true one-body dissipation rate of giant resonance states is reduced by about an order of magnitude from the wall formula value. The wall formula overestimate is due mostly to the fiction it assumes ab initio that all particles are totally reflected at the wall, whereas realistically only bound particles can be totally reflected. In addition, the self-consistency of the quantal description implies that no dissipation occurs to the bound one-particle one-hole subspace from which the RPA phonon is constructed, imposing an absolute prohibition of one-body dissipation for phonon energies less than the nucleonic binding energy. Finally, the quantal dissipation rate exhibits an explicit, but relatively weak, dependence upon the collective phonon energy, ħω. The result is that the wall formula yields a gross overestimate of the quantal one-body dissipation rate over the whole range of realistic nuclear situations.

Effect of random potential fluctuations on electron transport in n-type InSb.

A number of previous investigators have concluded that the low-temperature transport properties of n-type InSb can only be understood by assuming the existence of an impurity band which is separated from the conduction band by a finite binding energy. However, we show that the experimental results are fully consistent with a one-band interpretation as long as the effects of potential fluctuations due to random inhomogeneities in the impurity concentration are considered. Single-site electron mobilities are compared with a large body of experimental data from the literature covering the temperature range 1.3 to 80 K. Experiment and theory are found to agree well as long as the magnitude of the fluctuations \ensuremath{\gamma} is small compared to the thermal energy of the electrons ${E}_{0}$. However, when \ensuremath{\gamma}\ensuremath{\gg}${E}_{0}$ in compensated samples at low temperatures, the experimental mobilities fall far below the results of the single-site theory (which ignores the fluctuations). This behavior is consistent with that observed for one-band conduction in other semiconductors. Also considered are effects of the potential fluctuations in the alternative case where an impurity band is assumed to be present.

Bound states in the field of several noncollapsing inverse square potentials

Depending on the value of β, a single attractive inverse square potential (−β/r2) has either no discrete bound states at all (if β< 1/8 atomic units), or has a discrete spectrum with infinitely low eigenvalues (if β> 1/8 ). The latter case is usually interpreted as the collapse of the particle towards the center. Here we consider the problem of several ‘‘noncollapsing’’ inverse square potentials, none of which separately have a discrete spectrum. We give a simple demonstration that such spatial superposition provides an intermediate case when the discrete level(s) exists and yet there is no collapse of the particle to the center. The ground state with the finite binding energy continues to exist even if the separation between individual potential wells increases indefinitely.

Generalized Fermi sea for plane-wave Hartree-Fock theory: One dimensional model calculation

The Hartree-Fock theory for many fermions with plane-wave orbitals but with abnormal occupation is studied. A one-dimensional problem with an interparticle interaction of finite range which saturates the $N$ body system at a fixed density and finite binding energy is solved explicitly. A direct variation of the resulting Hartree-Fock energy with respect to the additional variational parameters introduced is carried out numerically and results reminiscent of a gas-to-liquid phase transition are found.NUCLEAR STRUCTURE plane-wave Hartree-Fock; model calculation; nuclear matter.

Some Properties of a Quartic Potential with a Finite Binding Energy

Abstract A potential energy function is proposed which exhibits a quartic dependence on (r - re), where re is the equilibrium interparticle distance, in the neighbourhood of re, and has a finite binding energy. To study the pattern of the eigenvalues, the WKBJ method is applied to the third order, and the relevant integrals are evaluated analytically. Results are shown graphically for a few sets of parameters. The number of vibrational states that the potential can support is determined for a range of values of the parameters. Some suggestions as to the possible applications of the proposed potential are also made.

Detailed study of relativistic strings

Presented is a detailed analysis of the dynamics of the relativistic vortex by means of the boson transformation method. General formulas for the energy and momentum of the string are derived. It is shown that a vortex of finite length creates a superposition of a short-range field associated with the body of the vortex and a field coming from the end points. This end-point field decomposes into a short-range and a long-range component, and the latter can be eliminated by attaching Dirac magnetic monopoles at the end points. It turns out that the monopole-string system has a finite negative binding energy.

Compton scattering by bound electrons

Abstract : The deviation in the Compton effect due to the finite binding energy of the atomic electrons was experimentally determined for K-shell electrons of tantalum, gold, and uranium. The differential cross section for scattering of 662 keV photons by K-shell electrons was obtained by measurements of the scattered photons in coincidence with the accompanying K X-ray and compared with the Klein-Nishina cross section for scattering by free electrons. The behavior of the ratio of the two cross section ratios was determined for scattering angles varying from 20 degrees to 70 degrees. The results indicate that the cross section ratio approaches zero as the photon scattering angle decreases to zero, and becomes >1 for scattering angles greater than 40 degrees for Ta and 50 degrees for Au. (Author)