Path integral treatment for the generalized Ginocchio potentials

The solution for the generalized Ginocchio potentials is exactly constructed by the path integral approach combined to the summation of the spectral representation. The energy spectrum and the wave functions of bound and scattering states are explicitly evaluated. The scattering functionS _l for each angular momentuml is also deduced.     

Algebraic expressions for effective potential characteristic parameters in heavy ion scattering

In this paper, we obtain reliable expressions to calculate the barrier and pocket positions of the real part of the effective phenomenological optical potential having Woods-Saxon form factor, for different partial waves. The comparison of the results obtained from these formulae, when compared with the numerical results obtained using Newton-Raphson iterative procedure are found to be quite accurate, with error less than 1%. We also obtain algebraic expressions for estimatingl _poc, the angular momentum at which the potential pocket vanishes, the accuracy of which is tested with the exact calculations, using self-consistent iterative procedures. These and other expressions deduced in this paper provide simple and useful methods for calculating critical parameters of heavy ion effective potentials like barrier and pocket positions, curvatures at the barrier and pocket positions,l _poc and the grazing angular momentuml _g to carry out the analysis of heavy ion scattering.     

Study on the electronic structure and Fermi surface of 3d-transition-metal disilisides CoSi2

We have investigated the electronic structure, the momentum density distribution ρ(p), and the Fermi surface FS of single crystals of the Pyrite-type 3d-transition-metal disilisides CoSi₂. The band structure calculations, the density of states DOS, and the FS, in vicinity of Fermi level, have been carried out using the full-potential linearized augmented plane wave FP-LAPW method within generalized gradient approximation GGA for exchange and correlation potential. The measurements have been performed via the 2D angular correlation of annihilation radiation ACAR experiments. ρ(p) has been reconstructed by using the Fourier transformation technique. The FS has been reconstructed within the first Brillion zone BZ through the Locks, Crisp, and West LCW folding procedures. The analysis confirmed that Si 3sp states hybrid with both Co 3d–t _2g and Co 3d–e _g states around Γ and X points, respectively. The dimensions of the FS of CoSi₂ have been compared to the present calculations as well as to the earlier results.     

Pressure-volume calculation in bcc metals using Born stability criteria

A simple analytical two-body potential φ(r) = −Ar ⁻ⁿ + B exp(−pr ^m) is considered for P-V calculations in bcc metals using Born stability criteria. It is shown that the stability of bcc metals can be expressed uniquely as a function of a parameter q (discussed in the text). The P-V calculations are done in ten bcc metals. The calculations are compared with the experimental data of shock-wave measurements and also with other potential available. It is found out that the present potential is better than the other two-body potentials in case of bcc metals. Further, the calculations done for TOEC and the first pressure derivative of SOEC are found in good agreement with the reported results.     

An ab initio study of PuO<Subscript>2±0.25</Subscript>, UO<Subscript>2±0.25</Subscript>, and U<Subscript>0.5</Subscript>Pu<Subscript>0.5</Subscript>O<Subscript>2±0.25</Subscript>

Hybrid density functional theory has been used to systematically study the electronic, geometric, and magnetic properties of strongly correlated materials PuO_2±x , UO_2±x , and U_0.5Pu_0.5O_2±x with x = 0.25. The calculations have been performed using the all-electron full- potential linearized augmented plane wave plus local orbitals basis (FP-L/APW+lo) method. Each compound has been studied at the ferromagnetic (FM) and anti-ferromagnetic (AFM) configurations with and without spin-orbit coupling (SOC) and full geometry optimizations. The optimized lattice constants, bulk moduli, and band gaps are reported. Total energy calculations indicate that the ground states are AFM for all compounds studied here and the band gaps are typically higher than 1.0 eV, characteristic of semiconductors. The total energy is lowered significantly and the band gaps increase with the inclusion of SOC. The chemical bonds between the actinide metals and oxygen atoms are primarily ionic in character.     

Dirac coupled-channels analysis of inelastic scattering of 800 MeV polarized protons from 16O, 24Mg and 26Mg

Coupled-channels calculations using the Dirac phenomenology have been performed to analyse cross sections and analyzing power data for inelastic scattering of 800 MeV protons from low-lying states in ¹⁶O, ²⁴Mg and ²⁶Mg. Large negative reals scalar potentials, large positive real vector potentials and large negative imaginary vector potentials were obtained. Considerable improvements were obtained using the Dirac equation compared to the classical Schrödinger calculations. These best fits have been found compatible with an imaginary scalar potential equal to zero (U_sⁱ=0) and therefore with less parameters (nine) than usually required in the classical calculations (twelve).     

Oscillatory modes of interaction of supersonic overexpanded jets with barriers

The self-oscillatory interaction of supersonic jets with barriers has mainly been studied for under-expanded jets. There are only a few experimental studies examining the case of overexpanded jets, with little computational work done in this direction. To fill this gap, we performed numerical simulations of overexpanded supersonic jets with barriers. The calculations were performed by the Godunov method on fine grids using parallel programming techniques. In the course of numerical simulations, the gasdynamic parameters of the jet and the geometric parameter of the barrier were varied. The barrier had the shape of a cylindrical cavity of depth l = (0 − 18)r _a , where r _a is the nozzle exit radius (the case l = 0 corresponds to a flat-end barrier). Based on the results of the numerical simulations, the conclusion on whether the self-oscillation process occurs was drawn and the dependence its characteristics (frequency and amplitude) on the governing gasdynamic and geometric parameters were obtained. Good agreement with experimental data on the fundamental tone frequency was demonstrated. A low-frequency oscillation mode was mostly realized. In this case, the jet experienced periodic suctions into and ejections from the cavity, counter the oncoming jet flow, with the formation of a structure consisting of three discontinuity surfaces (two shock waves and a separating surface contact).     

Crossing of the πd<Subscript>5/2</Subscript> and πg<Subscript>7/2</Subscript> orbitals in the <Subscript>51</Subscript>Sb isotopes

Self-consistent calculations using the D1S Gogny force have been performed in order to study the mechanism involved in the crossing of the πd _5/2 and πg _7/2 orbitals in the Sb isotopes. This inversion is well predicted by the HFB + blocking calculations with spherical symmetry performed for the odd-A Sb isotopes. In addition, several HFB and HF calculations have been performed for even-even nuclei of the five neighbouring isotopic chains (Z = 46 to 54, from the proton dripline to N = 82). The results obtained for the binding energies of the two proton orbitals indicate that the radii of the systems play an important role in the crossing, even though some particular πν interactions also give a contribution. The spin-orbit interaction, which is known to be concentrated mainly at the nuclear surface, is proposed to be the main responsible of the crossing.     

A model for viscosity coefficients of gases with potentials differing in form

A recent theory of non-conformal interactions has been very succesful in providing effective spherical potentials for the pressure of more than 40 real gases and many of their binary mixtures. Here, this theory is applied to deal with low-density viscosity coefficients. In its simplest form, the approximate non-conformal (ANC) theory introduces, besides the usual corresponding states parameters-energy ? and distance r_m-a softness parameter s to account for the form of a particular potential function. We investigate the effects of the potential form on the temperature behaviour of the viscosisty coefficient η. It is shown that the softer potentials, with wider attractive wells, have larger viscosities and an explicit expression for η (T, ?, r_m, s) is obtained. The ANC potentials are tested in their capacity to reproduce the temperature dependence of η for the heavier noble gases (Ar, Kr and Xe), diatomics (H₂, N₂, O₂ and CI₂) and a dozen small polyatomics. It is found that the ANC model η (T, ?, r_m, s), with only three substance-dependent parameters, reproduces experimental 7 data within their estimated error.     

Construction of muffin-tin potentials for liquid metals

We propose a method of constructing muffin-tin potentials for liquid metals in which the structure of the liquid is explicitly incorporated through the pair-correlation function. It is shown that for the liquid alkalis, the structure has a significant effect on the potential, however, the muffin-tin potentials of liquid noble and transition metals like Cu, Fe, and Ni are insensitive to the structure. Our structure based potentials for the liquid alkalis give resistivities in much better agreement with experiment compared to those calculated from the conventionally constructed potentials.     

Charge density of Ga<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Al<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Sb

Charge density calculations and electronic band structures for Ga _x Al_{1 − x} Sb with x = 1.0, 0.5 and 0.0 are presented in this work. The calculations are performed using the empirical pseudopotential method. The charge density is computed for a number of planes, i.e. z = 0.0, 0.125 and 0.25 A ₀ by generating the potential through a number of potential parameters available in the literature. The virtual crystal approximation was applied for the semiconducting alloy. The characteristics of the band structure and charge density are observed to be affected by the potential parameters. Calculated band gaps and the nature of gaps are in good agreement with the experimental data reported. The ionicity is also reasonably in good agreement with other scales proposed in the literature; however the formulation needs to be improved. The present work also demands indirect experimental band gap for the alloy.      

Heterogenization of supercritical fluids and nonvariant critical equilibria in ternary systems with one volatile component (for water-salt systems as examples)

The phase equilibria in ternary systems with one volatile component and a homogeneous supercritical fluid (SCF) region in one of the binary subsystems (with two critical end-points p and Q) were analyzed. Heterogenization of SCFs, extending from the 2d′ boundary subsystem into a ternary system, starts with monovariant critical phenomena in saturated solutions (l₁ = l₂-s) or (g = l−s), which pass through the extremal parameters of the temperature or composition to form special critical equilibria such as double critical end-points DCEs (l₁ = l₂-s, g = l-s, l₁ = l₂-g) or double homogeneous points DHPs (l₁ = l₂-s ↔ g = l-s). Ternary nonvariant critical points (l₁ = l₂ = g, l₁ = l₂-g-s, and l₁ = g-l₂-s) appear at the intersections of the monovariant critical and noncritical curves.     

Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

We investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ ₀, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ ₀ r ², we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ ₀, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.     

Improvement of modified analytic embedded atom method potentials for noble metals and Cu

The modified analytic embedded atom model (EAM) potentials considering farther neighbor atoms are improved for the noble metals (Ag, Au, Pt, Pd, Rh) and Cu. We not only adopt an end processing function and an enhanced smooth continuous condition for the pair potential, but also adjust the model parameters of multi-body potential by fitting a cohesive energy, a mono-vacancy formation energy, the Rose equation curve for the cohesive energy as a function of lattice parameter, a structure energy difference, elastic parameters and an equilibrium condition of crystal. The calculation results of structure energy differences misfit the experiment data for the noble metals and Cu in the unimproved EAM, because anyone of these differences have not been considered in the calculation of its model parameters. After the modification, the model showed better simulation results for the noble metals and Cu.     

Note on the calculation of electrostatic lattice potentials

We reconsider the problem of calculating electrostatic lattice potentials, or in fact potentials of the type |r|^βφ_l(r), where φ_l(r) is the lth derivative of the l/|r|^p potential. According to Ewald, and generalized by Nijboer and de Wette, the slowly converging potential can be expressed in two screened potentials, one on the original lattice and the other on the reciprocal lattice, which are rapidly converging. In general these screenings are related by a type of Hankel transform. The request of (asymptotic) symmetry between the screenings then leads to the well-known screenings as the best possible. Detailed formula needed for calculations are given.     

Delocalization transition of two-dimensional disordered systems in a strong magnetic field

The delocalization transition in two-dimensional systems and a strong magnetic field is investigated with respect to its dependence on the Landau band indexj and on the type of disorder. The generation of random potentials according to a given correlation functionf and for a chosen correlation lengthd is described. The spectral properties of random eigenvalue sequences are examined as measures for the extension of wavefunctions and indicate a nonuniversal delocalization behaviour in higher Landau bands for short ranged correlated potentials. The critical exponents of the localization length of wavefunctions are determined for rapidly varying potentials in the second lowest Landau band (j=1) and depend on the correlation lengthd of the disorder. This different critical behaviour compared to that in the lowest band is confirmed by calculations for the density-density correlations of wavefunctions at the centers of the Landau levels. Calculations in different geometries also show that the critical systems of delocalized states are conformal invariant in the case of the nonuniversal delocalization transition (dl ₀), whereas such local rescaling properties cannot be expected for slowly varying potentials.     

Interaction potentials,spectroscopy and transport properties of RG+–He (RG=Ar–Rn)

High-level ab initio potential energy curves are calculated for the RG⁺–He complexes (RG=Ar–Rn). RCCSD(T) calculations are employed with large basis sets, and taking account of spin–orbit coupling. The calculated spectroscopic parameters are compared with experimentally determined values, with other high-level ab initio results, and with results from potentials that were obtained by fitting to experimental data. The gas-phase mobilities of RG⁺ ions in He are calculated from our potentials and compared, graphically and statistically, with the experimental mobilities as a function of E/n ₀ at several temperatures. We conclude that more precise experimental data are required in order to discriminate between potentials with more certainty. In addition, we discuss previously reported, unexpectedly large drops in experimental mobility values for RG⁺ in He at 4.35 K as E/n ₀ → 0.     

Structure of some liquid transition metals using integral equation theory

We present the results of calculations of the structure factorS(q) of some liquid 3d transition metals using the self consistent hybridized mean spherical approximation (HMSA) integral equation. The local pseudopotential used is composed of the empty core model and a part that takes care of s-d mixing through an inverse scattering approach to model the interionic pair potential. The results presented are in very good agreement with experiment for most of the systems investigated near freezing, as well as for the noble metals Cu, Ag and Au, thus, confirming the reliability of the pseudopotential in the present integral equation scheme.     

High-level theoretical spectroscopic parameters for three ions of astrochemical interest

The equilibrium geometry and rovibrational spectroscopic parameters of the three astrochemical ions l-C₃H⁺, l-SiC₂H⁺, and C₃N^? and some of their isotopologues are obtained from high-level quantum chemical calculations. A composite approach based on the explicitly correlated coupled-cluster method CCSD(T)-F12b, that further includes core correlation, scalar-relativistic effects and most importantly higher order correlation beyond CCSD(T) is used to set-up the near-equilibrium potential energy surface (PES). The spectroscopic parameters of these linear tetra-atomic ions are then extracted from these PESs by vibrational perturbation theory of second order (VPT2). Calculation of absolute intensities is also carried out for the stretching frequencies of the cations in order to identify the bands that are most likely to be detected. The importance of the accurate calculation of the rotational constants B₀ and D₀ for astrochemistry is discussed as well as the limits of VPT2 in this context and reasons for these limitations.