Electron impact ionization cross sections of beryllium and beryllium hydrides

We report calculated electron impact ionization cross sections (EICSs) for beryllium (Be) and some of its hydrides from the ionization threshold to 1 keV using the Deutsch-Märk (DM) and the Binary-Encounter-Bethe (BEB) formalisms. The positions of the maxima of the DM and BEB cross sections are very close in each case while the DM cross section values at the maxima are consistently higher. Our calculations for Be are in qualitative agreement with results from earlier calculations (convergent close-coupling, R matrix, distorted-wave and plane-wave Born approximation) in the low energy region. For the various beryllium hydrides, we know of no other available data. The maximum cross section values for the various compounds range from 4.0 × 10^?16 to 9.4 × 10^?16 cm² at energies of 44 to 56 eV for the DM cross sections and 3.0 × 10^?16 to 5.4 × 10^?16 cm² at energies of 40.5 to 60 eV for the BEB cross sections.     

Lattice dynamics of beryllium

Phonon frequencies in beryllium along the principal symmetry directions have been determined by means of the slow neutron inelastic scattering technique. The data are analysed in terms of a six-neighbour force constant model and the force constants are evaluated. It is concluded that strong tensor forces are present in beryllium and the importance of this finding to basic theories of lattice dynamics is pointed out.     

The beryllium atom and beryllium positive ion in strong magnetic fields

The ground and a few excited states of the beryllium atom in external uniform magnetic fields are calculated by means of our 2D mesh Hartree-Fock method for field strengths ranging from zero up to 2.35×10⁹ T. With changing field strength the ground state of the Be atom undergoes three transitions involving four different electronic configurations which belong to three groups with different spin projections S _z = 0, - 1, - 2. For weak fields the ground state configuration arises from the 1s ²2s ², S _z = 0 configuration. With increasing field strength the ground state evolves into the two S _z = - 1 configurations 1s ²2s2p _-1 and 1s ²2p _-13d _-2, followed by the fully spin polarised S _z = - 2 configuration 1s2p _-13d _-24f _-3. The latter configuration forms the ground state of the beryllium atom in the high field regime γ > 4.567. The analogous calculations for the Be ⁺ ion provide the sequence of the three following ground state configurations: 1s^22s and 1s ²2p _-1 (S _z = - 1/2) and 1s2p _-13d _-2 (S _z = - 3/2). Received 2 October 2000 and Received in final form 8 January 2001     

The absorption spectrum of beryllium

Energy terms, dipole oscillator strengths and photoionization cross-sections from the ground state are calculated. Autoionizing state transition energies and line widths for the ¹P⁰ resonances in the continuum are also obtained. The configuration interaction method for initial and final states is used, and atomic orbitals are generated through angular-momentum-dependent, scaled Thomas-Fermi-Dirac potentials.     

The high-temperature resistivity of beryllium

The band structure of body-centered cubic beryllium is reported, both at the Hartree and exact-exchange Hartree-Fock level. There is no gap immediately above the valence band. This is consistent with the resistivity experiments by Amonenko et al. which rises sharply, but not discontinuously above the h.c.p.-to-b.c.c. phase transition at 1254°C.     

Creep of beryllium. I

Creep characteristics of beryllium have been determined in the temperature range 600–800°C and the stress range 0.25–5 kgf/mm². The rate of the process is controlled by the Herring —Nabarro mechanism in the range of stresses less than 1 kgf/mm². The creep activation energy (39±1 kcal/mole) hence agrees with the energy of self-diffusion. The creep rate for stresses greater than 1 kgf/mm² is determined by the simultaneous progress of dislocation creep and slip, where the slip contribution grows with the increase in stress. An approximate picture of the deformation mechanisms of creep is constructed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 68–73, March, 1976.     

On the cleavage plane of beryllium

Gilman's criterion erroneously predicts the most probable cleavage plane of Be. The formula is refined in order to take into account anisotropy of the interaction range between atoms in various planes. The pseudopotential approximation is used, and the cleavage plane is now correctly predicted.     

Autoionization states of the beryllium atom

Using the modified Feshbach method, the^1,3S^e,^1,3P^o,^1,3D^e,^1,3S^o autoionization states of the beryllium atoms are calculated in the region of the first ionization threshold. The energies and widths of the autoionization states of Be are obtained. The results obtained are compared with experimental data and the results of existing theoretical calculations. The good agreement between the results obtained and the experimental data and other theoretical calculations is pointed out.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 23–28, March, 1984.     

Condensation effects of excitons

The theory of the electronic excitations in a highly excited semiconductor is presented. The relaxation processes, the formation of excitons and excitonic molecules, the interaction among the various forms of electronic excitations, as well as their optical and thermodynamical properties are analyzed. At low temperatures one expects condensations into the quantum statistically degenerate phases of the excitonic molecules and of the electron-hole plasma. The physical properties of these low temperature phases are investigated. Possibilities and previous attempts to observe the Bose-Einstein condensation in excitonic systems are discussed critically. The experimental observations of the electron-hole liquid phase transition are reviewed.     

Condensation of lattice gases

Techniques due toR. L. Dobrushin andR. Griffiths are combined to prove the existence of a first order phase transition at low temperature for a class of lattice systems with non nearest-neighbour interaction.     

Observation of diamagnetic domains in beryllium

We have observed diamagnetic domains (Condon domains) in a beryllium single crystal in magnetic fields H⩽3 T (H∥[0001]) at liquid-helium temperatures. The formation of the domain structure was determined according to magnetic-breakdown quantum oscillations of the resistance thermoelectric power as well as according to the splitting of the resonance peak of the free spin precession frequency of muons (μSR). The alternation of a uniform state (with one μSR peak) and a state with domain structure (with two peaks) is consistent as regards the periodicity with the de Haas-van Alphen effect, the period is ΔH≅78 Oe, and the range of existence of domains and the difference in their magnetizations are ΔB=4πΔM=B ₂−B ₁≅30 Oe. Fiz. Tverd. Tela (St. Petersburg) 40, 524–526 (March 1998)     

Multiple scattering of muons in beryllium

The defocussing and the depolarization of a high energy muon beam in a beryllium filter, often used to eliminate accompanying pions, have been studied. The quantum mechanical transport equation of Waldmann, which can also be used to describe the multiple scattering of Dirac particles, is solved with a distorted wave Born approximation. Calculations are done for both the Thomas-Fermi and the Hartree-Fock potential of the beryllium atom. It is shown that the Hartree-Fock potential leads to a less divergent beam. The depolarization of a longitudinally polarized muon beam in passage through a thin beryllium foil is also studied.     

Calculation of threshold exponents for beryllium metal

The threshold exponents related to the singularities in the X-ray spectra of solid beryllium has been calculated using a nonseparable scattering potential. An appreciable d-wave contribution is obtained.     

Photoexcitation of K-shell and L-shell hollow beryllium

We have observed K-shell and L-shell hollow beryllium atoms (2s(2)2p3s and 1s3s(2)3p) created by photoexcitation using synchrotron radiation. Resonance shapes were fitted to the Fano profile and the parameters were deduced. A Dirac-Fock calculation was performed to identify the configuration of the peaks and to predict other hollow atomic peaks. The results of the calculation were in good agreement with the experimental data. The comparison of the transition strength has revealed that the three-electron photoexcitation to the 1s3s(2)3p configuration is stronger than the two-electron photoexcitation to the 2s(2)2p3s configuration. This is attributed to the large overlap between the 2s orbital of the ground state (1s(2)2s(2)) with the orbital of the L-shell hollow state (1s3s(2)3p).     

Heating of ultracold neutrons on beryllium surfaces

The temperature dependence of the loss factor for ultracold neutrons owing to heating at thermal energies on the surface of a beryllium sample is studied. The probability of heating ultracold neutrons is anomalously high throughout the entire measured temperature interval, but especially at low temperatures. Zh. éksp. Teor. Fiz. 114, 786–797 (September 1998)     

Computer simulation of proton channelling in beryllium

The channelling of protons through a thin beryllium crystal is simulated in a computer. The angular dependence of the momentum density is computed using particle trajectory approximation and is reported as the transmission spectra. In obtaining the spectra, the energy loss suffered by protons due to electron multiple scattering is considered and the effect of thermal vibrations treated separately. The spectra obtained are characteristic of the hcp structure of Be. Positions of the major dips in the transmission spectra are found to correlate well with the directions of neighbouring strings. Variations in the angle of incidence of the beam and in its initial azimuthal angle bring about modifications in the spectra depending on the transverse kinetic energy of the incident particles and the crystalline structure of Be. Thermal vibration of the lattice does not modify the spectra appreciably.     

Ab initio hartree-fock investigation of beryllium slabs

An analysis of the electronic structure in beryllium slabs with an ab initio LCAO HF method is presented. Band structure, electronic density and density of states were determined for thin films of 1 to 4 atomic layers of Be. A comparison of the electronic structure in films of different thickness with the situation found for bulk Be and Be clusters shows strong modifications in the surface region and a progressive reconstruction of the bulk bonds.     

Thermoluminescence and low-temperature luminescence of beryllium oxide

Beryllium oxide in the forms of either single crystals (pristine, additively-colored) or hot-pressed ceramic samples was studied in the energy range of 1.2–6.2 eV using both the thermoluminescence (TL) and steady-state X-ray induced luminescence (XRL) techniques. The XRL emission spectra were recorded at 6 and 293 K, whereas TL glow curves were studied after X-ray exposure at T₀ = 6 K upon linear heating in the temperature range from 6 to 293 K. A search for TL manifestations of shallow trapping centers was carried out using a sensitive channel for TL registration in the range of more than six decades of change in intensity. The participation of shallow trapping centers in the process of recombination luminescence excitation at 6–293 K; branching electronic excitations between different recombination channels; the dominance of the self-trapped exciton and F-center emissions in spectra of the low-temperature recombination luminescence in BeO at 6–293 K were discussed.