Realistic Energies Research Articles

Behaviour of the complex dielectric function and energy loss spectrum of copper in the [110] direction in the energy range 2 < ?? ? 4 Rydberg

The complex wave vector- and frequency-dependent dielectric function,e (q,ω) =ɛ1 (q,ω) +e2 (q,ω), for copper is calculated using realistic band energies and wave functions. The Bloch statesψbk (r) are obtained from the modified augmented plane wave method (MAPW) with the Chodorow potential. Results are presented for the principal direction ofq, [110]. About 70 bands and 60 plane waves at 10k-points in the 1/48th of the Brillouin zone are considered. An additional peak was found at the energy loss spectrum of copper whose centre is situated near 2.1 Rydberg, its centre moves gradually to the high energy side with increasing |q|. According to our knowledge, it is the first time this result has been calculated theoretically or even measured experimentally in the [110] direction for copper.

Nonlinear theory of domain walls and domain effective interactions in intercalation compounds

A nonlinear theory of Daumas-H\'erold dislocations in intercalation compounds is presented. Purely elastic effects in a nonequilibrium partly intercalated situation, and also the case of equilibrium with a guest reservoir are considered. In the first case, the local deformations of the host show spatially damped oscillations which give rise to strong interference effects in the domain-wall energetics. They provide a stabilizing mechanism against island conglomeration during intercalation and help to explain the persistence of domains in these compounds. Realistic domain-wall energies and energy barriers to relative motion of intercalate domains are calculated for the entire range of guest species intercalating into graphite. The calculations presented include different host-layer stacking arrangements and wall configurations for stage-2 compounds. The dependence of the energetics on intercalate guest and wall configurations is complex and unexpected, profoundly affecting the kinetics of intercalation. This suggests an explanation to the unusual behavior of sodium and other guest species with slow kinetics and imperfect intercalation. In the second case, samples in equilibrium with the guest reservoir are considered by the inclusion in the energetics of the chemical potential. The main effect is to reduce the domain-wall widths and remove energy barriers. Other experimental implications of this model are also discussed.

Asymmetric stretching of a symmetrically loaded elastic sheet

This consideration of the stretching of a square of thin elastic sheeting by equal tensile forces acting in dead loading on the edges of the square is motivated by some early observations of Treloar. For any reasonable elastic materials the loading will certainly correspond to some symmetric stretching but, it is shown here that depending on the form of the strain energy function and for some values of load an asymmetric stretching can equilibrate the symmetric loading as well as the more obvious symmetric stretching. Furthermore, the asymmetric response, when it is a dynamical possibility, is stable while the symmetric response is unstable. The phenomenon does not occur for neo-Hookean rubbers but does occur for the elastic materials corresponding to many realistic strain energies. Mooney-Rivlin rubbers for example.

Nonlinear theory of domain walls and the anomalies of intercalation kinetics.

A nonlinear theory of domain walls in intercalation compunds is presented. Realistic domain-wall energies and barriers to the relative motion of intercalate domains are calculated for the entire range of guest species intercalating into graphite. The different stackings of host layers found in stage-2 compounds are studied. The dependence of the energetics on stacking and intercalate thickness is both unexpected and complex and should profoundly affect the intercalation kinetics. An explanation is proposed for the anomalous behavior of sodium and some other guest species.

Symplectic shell-model calculations for 20Ne with horizontal configuration mixing

The symplectie shell model, which incorporates vertical (2n h ̵ ω; n = 1, 2…) major shell configuration mixing as dictated by a quadrupole interaction, is augmented with horizontal (0ħω) mixing induced by realistic single-particle energies and a monopole-pairing interaction. The excitation spectrum and B(E2) rates of the 20Ne ground band are accurately reproduced without the use of an effective charge. The degree of horizontal and vertical mixing is found to be on the order of 20% in the ground state and up to as much as 50% for the 8 + level.

Independent particle description of mass and charge transfer in deep inelastic collisions

A model is presented for the description of mass transfer in the dinuclear system formed during a deep inelastic process. The relative motion is treated classically while the transfer is described in terms of independent particle motion as due to the mean fields of the two colliding nuclei, in the same spirit of the so called time-dependent single-particle model (TDSPM). Particle-hole excitations, apart from those arising from the transfer, are phenomenologically included via friction forces in the hamiltonian for the relative motion. The results suggest that by using appropriate conservative and friction forces in describing the ion-ion relative motion, together with realistic single-particle energies, it is possible to get reasonable values of the average number of transferred nucleons. Poorer results are obtained for the variance, showing the necessity of taking into account two-body correlations. Comparison with TDHF calculations and experimental results is discussed.

Hydrogen recycling properties of stainless steels

The hydrogen retention and release characteristics of stainless steels that contribute to plasma-wall recycling of a magnetically confined plasma are reviewed. Details are presented on laboratory measurements of hydrogen reflection, desorption, trapping and release. Critical data needs are shown to include reflection below 100 eV, desorption cross sections at realistic energies, hydrogen surface coverage, and molecular recombination rates for characterized first wall surfaces.

Dielectric function of hexagonal metals: II. Beryllium

AbstractThe longitudinal dielectric function ϵ(q,ω) of beryllium is calculated using realistic wave functions and band energies. Comparison with experiment is performed in the optical properties (including anisotropy), plasmon dispersion relation, and half width of the plasmon peak. The relaxation times for inclusion of damping are fitted. The experimentally observed peak splitting of the loss function is explained as a band structure effect.

Dielectric matrix for aluminum

The dielectric screening matrix ${\ensuremath{\epsilon}}_{G{G}^{\ensuremath{'}}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ for aluminum is evaluated using realistic band energies and wave functions. The Bloch states are obtained from a self-consistent tight-binding calculation in which Gaussian orbitals are used as basis functions. Results are presented for three principal directions of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$, [100], [110], and [111], with 15 values for the reciprocal-lattice vectors $\stackrel{\ensuremath{\rightarrow}}{\mathrm{G}}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{G}}}^{\ensuremath{'}}$. It is found that the off-diagonal elements are, in general, small compared to the diagonal terms and that the diagonal terms show some directional effect in their monotonic decrease as $|\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}+\stackrel{\ensuremath{\rightarrow}}{\mathrm{G}}|$ increases.

Study of the electronic structure of molecules. XXII. Correlation energy corrections as a functional of the Hartree-Fock type density and its application to the homonuclear diatomic molecules of the second row atoms

A semiempirical functional of the Hartree-Fock type density, previously obtained for the Hartree-Fock atomic functions and applied with good success to the second row hydrides (in paper XXI of this series), is now applied to the molecules H2(X 1Σg+), Li2(X 1Σg+), Be2(1Σg+), B2(X 3Σg−), C2 (x1 Σg+), N2(X 1Σg+), O2(X 3Σg−), and F2(X 1Σg+). For each molecule the potential energy curve is computed from the repulsive region to large internuclear distances. In order to follow the dissociation to the correct limits, we have added to the Hartree-Fock configuration of each molecule those configurations which are needed for describing proper dissociation (HFPD functions). It is found that for certain molecules (Li2, B2, C2, and O2) there are configurations which contribute quite significantly in the bonding regions and must be added to the HFPD function to reach a proper reference state function as previously defined (see paper XXI). With our functional of the density applied to the HFPD functions, the calculated dissociation energies are, with the experimental values given in parentheses, 4.69 eV (4.75 eV), 0.65 eV (1.14 eV), 1.64 eV (3.0 eV), 3.48 eV (6.36 eV), 9.34 eV (9.91 eV), 3.75 eV (5.21 eV), and 1.37 eV (1.66 eV) for H2, Li2, B2, C2, N2, O2, and F2, respectively. More realistic dissociation energies are obtained for Li2 (1.03 eV), B2 (3.06 eV), C2 (5.21 eV), and O2 (4.64 eV) if we use the proper reference state functions. The Σg+1 state of Be2 arising from the ground state atoms is repulsive. The agreement with the experimental dissociation energy is satisfactory but not as good as what we have previously obtained for the second row hydrides. However, owing to the extreme simplicity of the method it appears in a preliminary way that the combination of a Hartree-Fock type function and the functional of its density (of the form that we have proposed) is capable of yielding sufficiently reliable results for very little computational and human effort. Since the parametrization of the density functional was made for the atomic systems and not changed in the molecular formation, our method does not suffer from the need of variation of parameters introduced ad hoc and differing from molecule to molecule.

Densities of states and the complex partition function

A Fourier transform technique based on the method of Dubner and Abate is here applied to the energy-level density problem for quantum partition functions. It is shown that, for typical molecular systems at realistic energies, the integrated level count, W(E), is obtainable to near ‘spectroscopic’ accuracy and in reasonable computing time. A smooth Fourier resolution of the simple density function, g(E), is likewise possible. Though somewhat less economical, this procedure entirely removes the slight discrepancies found in the steepest-descent method and can reasonably be claimed to dispose once and for all of the problem of quantum level-density computations in molecular rate theory.

Investigations of parity deformation in spherical nuclei

The possibility of parity deformation for spherical structures is investigated from various viewpoints. We use several criteria of stability for the spherical Hartree-Fock solution (Thouless condition, critical 0 − states in different approximations) as well as different types of two-body forces (a realistic effective interaction and the OPEP) and single-particle spectra (HF, oscillator, Woods-Saxon and experimental) in order to obtain a complete survey. The result is that parity deformation can be excluded in practically all cases. In addition, the positions of the two critical 0 − states of 16O are in good numerical agreement with experiments if realistic forces and experimental single-particle energies in connection with the random phase or Tamm-Dancoff approximation are used.

Investigation of heavy nuclei with sharp seniority wave functions and comparison to the BCS approximation

Within a realistic model for heavy spherical nuclei, a numerical comparison of the results of the BCS approximation and the seniority 0 and 1 approximation is performed in a detailed way. It is shown that for the characteristic pairing properties there is a good agreement between both computational methods for this range of nuclei if one takes realistic single-particle energies and pairing matrix elements into account.

Effective velocity-dependent potentials for use in large nuclei

The criteria for developing an effective velocity-dependent nucleon-nucleon potential which gives realistic energies for large nuclei are discussed, and two such potentials are constructed. One is successful while the other gives too large values for the surface and symmetry energies. The reasons for the differences are investigated. The potentials are used to find the energy-density relationship for the neutron gas.