Energy Epsilon Research Articles

The activation energy of hopping transport with sequential correlations of hops due to Coulomb interactions

The authors study the effects of correlations in successive jumps on the reduction of the activation energy epsilon 3 in impurity conduction at low concentrations. These correlation effects are considered within a mean-field theory, and a dielectric approach is used. They find that epsilon 3 is reduced by about 30% with respect to previous calculations that do not include relaxation. The new value is in better agreement with the experimental results and with Monte Carlo calculations by Nguyen and co-workers (1979). Their value for intermediate compensation still exceeds experimental values by about 50%.

Mechanism of cluster emission in nucleon-induced preequilibrium reactions

A model is proposed for the preequilibrium emission of light composite particles in the framework of the exciton model. The model contains two new points: One is the calculation of the formation factor F/sub l/,m(epsilon) which stands for the probability that the composite particle of an energy epsilon is composed of l particles above the Fermi level and m particles below. Information of the intrinsic wave function of the composite particle is incorporated in the F/sub l/,m(epsilon). Another new point is the inclusion of the pickup type contribution in the particle emission mechanism. We allow some nucleons which constitute the emitted composite particle to come from levels below the Fermi energy. This model is applied to six kinds of (p,..cap alpha..) reactions of incident energies of several tens of MeV on /sup 54/Fe, /sup 118/Sn, and /sup 120/Sn targets. Calculated results reproduce nicely the high energy part of the experimental energy spectra and indicate that its main component is the ''three-particle pickup'' reaction coming from 2p-1h and 3p-2h, but ''two-particle pickup'' also contributes substantially.

Metastable states in anisotropic spin glasses. I. Cubic anisotropy

The numbers and properties of the metastable states of an infinite-range spin glass at T=0 with cubic spin anisotropy are investigated. The author evaluates the 'direct average' (Ns)J over the bond distribution rather than (lnN)J, leading to results which are exact above a critical energy epsilon c. He finds no gaps in the Hessian or spin-wave spectra, the latter result being in conflict with the numerical work of L.R. Walker and R.E. Walstedt (1980). He speculates that their result is due to finite-size effects.

Exact second Born exchange amplitude for elastic electron-hydrogen scattering

An exact calculation of the (plane-wave) second Born exchange amplitude for elastic electron-hydrogen scattering at 30 eV is reported. It is shown that exchange coupling to excited states is as important as exchange with the 1s state (at 30 eV) and that in the forward angular region it acts in the opposite direction to 1s exchange (at least in perturbation theory). A closure approximation to the second-order exchange amplitude is compared with the exact numbers. Poor agreement is obtained but it is not clear whether this results from a bad choice of average energy epsilon or is an intrinsic failing of the closure method. If the closure approximation can be made to work then a value of epsilon greater than -1/18 au would seem to be indicated. The Glauber approximation to the exchange amplitude is criticised on the basis that it involves using a closure approximation with epsilon = epsilon 1s=-1/2 au. An exploratory calculation shows that second-order exchange does exert a pronounced effect on the differential cross section.

The SCF-Ξα-SW method: the one-electron eigenvalues and total energies for even-Z atoms, Ne to Ar

Including electron self-interaction in the Hamiltonian of the Xalpha method gives the Hamiltonian of the Xi alpha method, which gives one-electron energies epsilon Xi alpha for the even-Z atoms, Ne to Ar, in good agreement with epsilon HF. The total energies E in the Xalpha , Xi alpha and HF schemes are compared.

A continuous one-dimensional fluid as the limit of a lattice fluid

The basic model treated is a linear fluid in which each molecule has a hard core of length a and there is an interaction energy epsilon (r) when the hard cores of two molecules are separated by a distance r, for r<a. In the lattice version the hard core of each molecule occupies n sites and there is an interaction energy epsilon q when there are q vacant sites between the hard cores of two neighbouring molecules, for q<n. The constant-pressure partition function is constructed for a general value of n and the equation of state deduced. It is shown that, with the epsilon q appropriately related to the function epsilon (r), the equation of state of the lattice fluid tends to that of the continuous fluid when the mesh of the lattice becomes infinitely fine (n to infinity ), with the hard-core length kept constant. For rectangular-well interactions it is shown that the difference between the equation of state of the continuous fluid and that of the lattice fluid for any value of n depends solely on hard-core effects. Three models displaying the water-like property of a maximum on density isobars in a low-pressure range are treated. Density isobars for lattice models with various values of n are compared with those of the continuous fluid. The relative magnitude of hard-core and attractive interaction effects in the lattice 'error' is considered for a parabolic well fluid.

Composition of the positive column of a helium glow discharge at intermediate pressures

The composition of the plasma on the axis of the positive column of a helium glow discharge is investigated. Four rate equations for the concentration of atomic and molecular ions and metastables can be written. For conditions of gas pressure between 5 and 40 Torr and currents between 10 mA and 200 mA, the equations can be simplified and solved. Rate coefficients for different processes were taken from afterglow measurements. Rates of excitation to the metastable level 23S and of step ionisation were calculated. The distribution at energies epsilon lower than the excitation energy epsilon 1 of level 23S is near maxwellian with a temperature Te, while for epsilon > epsilon 1 it decreases much faster. The relative number of atomic ions is maximal at the pressure p=5 Torr, increases with current and decreases with pressure. At the pressure p=5 Torr and currents i>or=100 mA practically all ions are atomic. The proportion of molecular ions decreases with current and increases with pressure. At the pressure p=40 Torr and currents i<or=40 mA practically all ions are molecular.

A modified antiferroelectric six-vertex model

A modified antiferroelectric model (MF-model) is introduced. It is shown that the general solution of this model, whose basic ingredients are two energies epsilon 1 and epsilon 2, includes as special cases the F-model ( epsilon 1= epsilon 2= epsilon ) and the Ising model ( epsilon 1= epsilon , epsilon 2= infinity ). The MF-model has a polymer equivalent in which a polymer bond can assume one of three available states, one trans state (energy zero) and two gauche states with energies epsilon 1 and epsilon 2.

On the role of the electron impact ionisation and electron scattering cross-section in the breakdown strength of dielectric gases

Discusses the role of the electron impact ionisation cross-section sigma i( epsilon ) and the electron scattering cross-section sigma sc( epsilon ) as a function of electron energy epsilon in the breakdown strength of gases/mixtures. Four gases (Ne, Ar, N2 and SF6) were chosen for which sigma i( epsilon ) and sigma sc( epsilon ) at low energies are known. Direct-current breakdown strength measurements on Ne, Ar, (Ne+SF6), (Ar+SF6), (N2+Ne+SF6) and (N2+Ar+SF6) were made and are reported, using sphere-on-sphere to sphere and square-rod to plane electrode geometries. On the basis of these measurements and the data on sigma sc( epsilon ) and sigma i( epsilon ) it was concluded that the magnitude of sigma sc( epsilon ) at subionisation ( epsilon <I) and especially at subexcitation ( epsilon <energy of lowest excited electronic state) energies is much more significant in effecting a high dielectric strength than is sigma i( epsilon ). The effect of perfluorination and static polarisability on sigma i( epsilon ) is also discussed.

Frequency dependence of the alternating current method for measuring the electron energy distribution function in plasmas

In the alternating current method for measuring the electron energy distribution function f(E) in plasmas, the influence of the frequency f of the superimposed signals is studied. When f is near the electron plasma frequency fpe, the second derivative of the probe characteristics, ip", is seriously affected, particularly near the space potential, and the distortion of ip" due to a resonance effect gives a false estimation of the average energy epsilon toward a higher value by more than 20%. The relative error in ip" is estimated to be of the order of f2/fpe2 at a relatively deep bias, so that except near the space potential f(E) may still be measured accurately with a frequency far above the ion plasma frequency fpi. Increasing the frequency results in better resolution as the scan rate of the probe voltage becomes rapid.

Impurity band structure in lightly doped semiconductors

The density of states and the position of the Fermi level in the impurity band at zero temperature have been studied by Monte Carlo computer simulation over a wide range of degrees of compensation. The impurity concentration is thought to be so small that the electron states of the impurity band are localised. The density of states has a soft Coulomb gap in the vicinity of the Fermi level, and its behaviour in this region is shown to have a universal character. In the cases of extremely small and extremely close compensation the simulation results agree with the theoretical ones obtained earlier. The increase in the activation energy epsilon 1 of the band conductivity at high degrees of compensation is computed and agrees with the experimental results. However, the computed value of hopping conductivity activation energy epsilon 3 is four times as large as the experimental one.

Theory of surface excitations of liquid helium four

The wavefunction proposed by Chang and Cohen (see Phys. Rev. B, vol.11, p.1059 (1975)) for surface excitations of a quantum fluid is used to calculate the excitation energy epsilon (k). A general relation epsilon (k)<or=h(cross)2k2/2mS*(k) is obtained, where S* (the surface structure factor) is determined in terms of the density profile and the pair correlation function. If one assumes that the liquid has bulk properties right up to the surface, the theory leads rigorously to epsilon (k)= pi h(cross)ck/(ln(2/ka)+constant) in the long wavelength limit. This expression is in qualitative agreement (for intermediate values of k) with the semiclassical theory of Edwards, Eckardt and Gasparini, and with the numerical work of Chang and Cohen. The authors discuss the proposal that the inclusion in the groundstate of correlations due to the zero-point motion of the surface modes would lead to the classical dispersion relation epsilon approximately k32/.

Cross sections for excitation and ionization in e-He(21,3S) collisions

Cross sections for the 23S-n3L(n=2-5, L=S-F) excitations and for single ionization in e-He(21,3S) collisions are determined by using the Born approximation. For a given n, the 23S-n3D transitions dominate at intermediate energies and this trend is continued for transitions to the near continuum. For larger energies epsilon of the ejected electron, higher angular momentum l waves progressively dominate. While up to nine partial waves are in general required for convergence of the bound-free form factor, as many as 30 are needed when momentum changes are in the vicinity of the Bethe ridge for large epsilon . Binary-encounter results for ionization are also obtained and agree with the Born values at intermediate energies.

Cross sections for ionization of metastable rare-gas atoms (Ne*, Ar*, Kr*, Xe*) and of metastableN2*, CO* molecules by electron impact

Cross sections for the collisional ionization of the metastable atoms Ne*, Ar*, Kr*, and Xe* by electrons with impact energy E in the range 6 < E < 250 eV are determined in the Born and binary-encounter approximations. For low energies epsilon of ejection, the s-d and s-f bound-free transitions dominate the associated form factor, while transitions to continuum states with progressively higher angular momentum gain importance with increasing epsilon. While up to nine partial waves are normally sufficient for convergence of the bound-free form factor at a given energy epsilon and momentum change K of the ejected electron, as many as 30 are required for those K in the vicinity of the Bethe ridge at large epsilon. These properties are the origin of the overall closeness obtained between the Born and binary-encounter cross sections. Also inner-shell ionization, as described by the binary-encounter treatment, becomes increasingly important as the target atom becomes more complex. Cross sections for ionization of metastable N/sub 2/* and CO* are also determined. Good agreement with available measurements (for Ne* and Ar*) is obtained. (AIP)

The active center of methemoglobin Hb(H2O) investigated by Mössbauer and susceptibility experiments.

A fast freezing technique using liquid propane was used to obtain frozen solutions of methemoglobin at pH 7. With this method it was possible to eliminate largely the presence of a low spin component which is usually found in slowly frozen solutions but not present in the sample at room temperature. The magnetic susceptibility and Mössbauer spectra of Hb(H2O) in the temperature range 4.2 K less than or equal to T less than or equal to 250 K have been measured. The data of the high spin compound of Hb(H2O) were evaluated with a Hamiltonian comtaining the Coulomb repulsion of the five 3d-electrons of the Fe3+ ion, a crystal electric field of C2V symmetry and the spin orbit coupling. The term describing the crystal electric field depends on five energy parameters epsilon1, epsilon2, epsilon3, D, and E which are determined by least squares fits to the experimental data. The most relevant parameters epsilon 2 and epsilon 3 which equal the energies of the antibonding single 3d-electron orbitals 3dz2 and 3dx2-y2 with respect to the 3dxy orbital are compared with earlier results of these energies epsilon 2 and epsilon 3 of the high spin compound of Mb(H2O). From this comparison conclusions regarding the different spatial arrangements of Fe3+ in Hb(H2O) and Mb(H2O) are drawn.

Structural changes and fluctuations of proteins. II. Analysis of the denaturation of globular proteins.

The statistical thermodynamic model of protein structure proposed in paper I is developed with special attention to the hydrophobic interaction. Calorimetric measurements of the thermal denaturation of five globular proteins, ribonuclease A, lysozyme, alpha-chymotrypsin, cytochrome c, and myoglobin, are quantitatively analyzed using the model. The thermodynamic parameters obtained by the least squares method reflect the global, average properties of proteins and are in good agreement with the expected values estimated from experimental and theoretical studies for model peptides. The average bond energy epsilon is well related to the tertiary structure of each protein. However, the difference in the parameters between different proteins is not observed for the cooperative energy ZJ and the chain entropy alpha. The individuality of a protein as far as its structural stability is concerned, is mainly reflected by the parameter gamma specifying the hydrophobic nature of a protein. The model is further applied in the analysis of several aspects of the structural stability of globular proteins. Denaturation induced by denaturants, salts, and pH are also explained by the model in a unified manner.

Swarm-determined electron attachment cross sections as a function of electron energy

An unfolding procedure is described whereby the known electron energy distribution function in the swarm F(( epsilon ), epsilon ) at each mean electron energy ( epsilon ) is used as the 'smearing out' function to unfold the monoenergetic attachment rate M( epsilon ) from the experimentally determined electron attachment rate functions Rexp(( epsilon )). From the monoenergetic attachment rate the absolute electron attachment cross section as a function of electron energy epsilon is calculated. The cross section functions determined from the unfolding of swarm data for a number of molecules compare well with those obtained using quasi-monoenergetic electron beams. This successful unfolding of swarm data enhances the potential of the electron swarm method in electron attachment studies.

Approximations and interpolation rules for ranges and range stragglings

Abstract Approximations and interpolation rules for ranges and stragglings in amorphous substances are presented. Two energy regions, termed low and intermediate energies, corresponding to the dimensionless energy epsilon being in the intervals 0.002<∊<0.1 and 0.5<∊<10, respectively, are defined. For low energies the projected range is approximately proportional to E2/3 , and for intermediate energies approximately proportional to E. For low energies, approximate stragglings are also obtained. The agreement of the results with accurate range-calculations is better than ∼10 per cent.

Investigation of fine structure in the steps observed in the intermolecular activation energy of viscous flow of ethylene glycol

Previous experiments had shown that, whereas the steps in the intermolecular activation energy epsilon of viscous flow of water are sharp and separated by intervals of nearly 6 °C, the steps in ethylene glycol occur at about 12 °C intervals and the drop from one to the next is very gradual (Qurashi and Ahsanullah 1961, Rauf and Qurashi 1959). The measurements on ethylene glycol, using the equation Δ ln η/ΔT = - (/κ)/T2, have now been repeated with more refined techniques working at intervals of 1 °C (with temperature control to 0.002 °C) in the range 2-92 °C, and the gradual drop is in each case found to break up into two short and sharp steps. The results have an accuracy to the order of 0.2% in /κ and indicate the presence of two regular series of steps, out of phase with each other by a slowly varying temperature difference. To study the possible effects of impurities on these phenomena, the experiments have been repeated with three different grades of ethylene glycol, namely (i) commercial grade, (ii) technical grade and (iii) laboratory reagent grade. The graph for the purest grade, (iii), exhibits pairs of steps of equal height, Δ/κ similar 100, while that for (i) shows some large irregularities and the curve for (ii) shows only small deviations from regularity. This confirms the general reproducibility of the phenomena and establishes that they are characteristic of pure ethylene glycol. The refined graphs for glycol now show several similarities with those for water, and quantitative and graphical comparison indicates that /κ for water runs very close to 0.6 × /κ for ethylene glycol, both in regard to the temperatures at the discontinuities and the values of the energy jumps, so that the phenomena are to be associated with the two effective OH groups in ethylene glycol and water. A tentative quantitative interpretation is attempted on the basis of existing theories of molecular association, with some measure of success. Data on other related liquids are being obtained for further elucidation.

Ground-State Energy of an Electron Gas in a Lattice of Positive Point Charges

The ground state energy epsilon of an electron gas in a rigid lattice of positive point charges is calculated as a function of the Bohr radius between electrons, by quantum statistical methods. The couplings between pairs of electrons, and between electrons and lattice points, are taken into account. The value of epsilon in a positive continuum is derived as a special case. As an example, epsilon is calculated for an H lattice. (T.F.H.)