Helium-antihydrogen interaction: the Born-Oppenheimer potential energy curve

The interaction of atomic antihydrogen with helium has been studied within the Born-Oppenheimer approximation. The linear combination of explicitly correlated Gaussian functions was used as the ansatz for the wave function of light particles. The potential energy curve with the minimum at 3.63 bohr and the barrier at 2.42 bohr has been obtained.     

A variational method for calculating the energies and widths of resonances

We present a variational method which employs complex wave-functions and yields both the energy and the width of resonances.     

Microscopic approach to calculating cross sections and optical potentials for nucleus-nucleus interaction at intermediate energies

Nucleus-nucleus scattering is considered in the high-energy approximation and on the basis of Glauber-Sitenko microscopic theory in the optical limit. Analytic expressions for eikonal phase shifts are given for the case of Fermi-type realistic potentials and nuclear-density distributions. The effect of taking into account the distortions of the trajectories of the nuclei involved and the nuclear-density dependence of nucleon-nucleon forces on the total reactions cross sections is illustrated. The sensitivity of the reaction cross sections to the choice of model for the ⁶He projectile nucleus, which involves a neutron halo, is explored. Semimicroscopic optical potentials are introduced in order to describe differential cross sections for elastic scattering. The results of the present calculations are compared with available experimental data.     

Effective surface potential method for calculating surface states

A novel formalism (the effective surface potential method) is developed for calculating surface states. Like the Green function method of Kalkstein and Soven and the transfer matrix method of Falicov and Yndurain, the technique is exact for simple tight binding Hamiltonians. As well as offering an alternative viewpoint, the present method provides a simple analytic expression describing the surface states. At each point k_s in the surface Brillouin zone the semi-infinite solid is viewed as an effective linear chain where each element of the chain is a planar layer. The solution to the linear chain problem can be expressed in terms of an effective potential h(k_s,E) at each energy E. A number of examples are presented in detail; “sp^d” Hamiltonians for a linear chain (d = 1), the honeycomb lattice (d = 2), the 111 surface of silicon (d = 3), and a dissected Bethe lattice. Various exact results are given, e.g. the extremities of surface state bands and the surface density of states of p-like (delta function) bands. The results of Kalkstein and Soven for the 100 surface of a simple cubic solid with a perturbation on the surface layer are rederived.     

Improved potential energy curve and vibrational energies for the electronic ground state of the hydrogen molecule

The potential energy curve for the electronic ground state of the hydrogen molecule has been recomputed for intermediate and large internuclear separations. for 2.4 ≤ R ≤ 8.0a.u. the previous potential energy curve has been improved. The largest improvement amounts to 5.5 cm^?1, and was obtained in the vicinity of R = 4.4a.u.. Using the new potential energy curve, and the adiabatic and relativistic corrections, the vibrational and rotational energy levels have been calculated for H₂, HD, and D₂. The deviations of the calculated energy levels G(v) of H₂ and D₂ from the observed values follow very closely the nonadiabatic corrections resulting from the Van Vleck formula.     

The potential curve of the He-α-quartz surface interaction

One of the fundamental problems for gas-surface interaction physics is to relate the pairwise gas atom-surface atom interaction characteristics to that of the aggregate collision complex. One method of studying the problem on a microscopic scale is to model the surface lattice structure and calculate the interaction characteristics using the Monte Carlo technique. We describe the calculation of the He-α-quartz (SiO₂) interaction potential applying this method assuming pairwise He-surface atom Lennard-Jones (12, 6) potentials. The results show that the interaction potential follows a (13.5, 3.8) shape function in the gas-surface interaction range below 8 Å, and an asymptotic dependence with 3.8 < m < 6 for the region beyond 8 Å. This potential well shape function differs substantially from the (9, 3) function suggested by earlier work. The calculated potential curve shows a weak dependence on surface and gas temperature. The potential well depth of the gas-surface interaction shows a strong nonlinear relationship to the equilibrium internuclear distance of the HeSi pair potential applied to the calculation. We find that the empirically determined parameters for the HeSi pair potential provide resultant gas-surface potentials with well depth remarkably close to those required by the measured heat of adsorption.     

New formula for calculating coulomb energies in the liquid-drop model

A new transformation of double volume integrals into double surface integrals is presented. A simple regular method for deriving integrands in a surface integral is proposed. This method is used to calculate the Coulomb energy of a nucleus within the model of a liquid drop with a sharp boundary. Numerical results obtained on the basis of the new formula are compared with those calculated by one of the formulas employed previously.     

A new method for calculating three-particle interaction in the theory of modulus elasticity

We propose a new method for calculating the potential of multiparticle interaction. Our method considers the energy symmetry for clusters that contain N identical particles with respect to permutation of the number of atoms and free rotation in three-dimensional space. As an example, we calculate moduli of third-order rigidity for copper considering only the three-particle interaction. We analyze nine models of energy dependence on the polynomials that form the integral rational basis of invariants (IRBI) for the group G ₃ = O(3) ? P ₃. In this work, we use only the simplest relation between energy and the invariants forming the IRBI: \(\varepsilon \left( {\left. {i,k,l} \right|j} \right) = \sum\nolimits_{i,k,l} {\left[ { - A_1 r_{ik}^{ - 6} + A_2 r_{ik}^{ - 12} + Q_j I_j^{ - n} } \right]}\), where I _j is the invariant number j (j = 1, 2,..., 9). The results are in good agreement with the experimental values. The best agreement is observed at n = 2, j = 4: \(I_4 = \left( {\vec r_{ik} \vec r_{kl} } \right)\left( {\vec r_{kl} \vec r_{li} } \right) + \left( {\vec r_{kl} \vec r_{li} } \right)\left( {\vec r_{li} \vec r_{ik} } \right) + \left( {\vec r_{li} \vec r_{ik} } \right)\left( {\vec r_{ik} \vec r_{kl} } \right)\).     

Ab initio method for calculating electron-phonon scattering times in semiconductors: application to GaAs and GaP

We propose a fully ab initio approach to calculate electron-phonon scattering times for excited electrons interacting with short-wavelength (intervalley) phonons in semiconductors. Our approach is based on density functional perturbation theory and on the direct integration of electronic scattering probabilities over all possible final states with no ad hoc assumptions. We apply it to the deexcitation of hot electrons in GaAs, and calculate the lifetime of the direct exciton in GaP, both in excellent agreement with experiments. Matrix elements of the electron-phonon coupling, and their dependence on the wave vector of the final state and on the phonon modes, are shown to be crucial ingredients of the evaluation of electron-phonon scattering times.     

A new method for calculating potential curves in the zero-order approximation of a generalized WKB method

A new method, different from that of [1 ], is proposed for plotting potential curves from vibrational-rotational levels in the zero-order approximation in Planck's constant of a generalized WKB method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 7, pp. 127–129, July, 1973.     

On the cluster approach for calculating electronic energies of solid surfaces

A scheme for calculating electronic energy states of infinite solid surface systems by a cluster approach under the framework of the method of linear combinations of atomic orbitals is presented. The basis functions consist of atomic-like orbitals confined within a cluster whereas the Hamiltonian is that of the infinite solid. The latter circumvents the difficulty arising from the auxiliary boundary of the cluster which is not the true surface of the solid. All the multicenter integrals appearing in the Hamiltonian matrix can be evaluated exactly by means of the technique of Gaussian orbitals. This cluster-basis method is applied to the chlorine-adsorbed silicon (111) surface using several different clusters. The results are compared with those of the same Hamiltonian with basis functions extending over the entire solid in the Bloch-sum form. Criteria for optimal selection of clusters are suggested.     

New method for calculating the potential energy of deformed nuclei within the liquid-drop model

The method that we previously developed for going over from double volume integrals to double surface integrals in calculating the Coulomb energy of nuclei that have a sharp surface is generalized to the case of nuclei where the range of nuclear forces is finite and where the nuclear surface is diffuse. New formulas for calculating the Coulomb and the nuclear energy of deformed nuclei are obtained within this approach. For a spherically symmetric nucleus, in which case there is an analytic solution to the problem in question, the results are compared with those that are quoted in the literature, and it is shown that the respective results coincide identically. A differential formulation of the method developed previously by Krappe, Nix, and Sierk for going over from double volume integrals to double surface integrals is proposed here on the basis of the present approach.     

Landau-Zener problem for energies close to potential crossing points

We examine a previously overlooked aspect of the well-known Landau-Zener (LZ) problem, namely, the behavior in the intermediate, i.e., close to a crossing point, energy region, when all four LZ states are coupled and should be taken into account. We calculate the 4×4 connection matrix in this intermediate energy region, possessing the same block structure as the known connection matrices for the tunneling and in the over-barrier regions of the energy and continuously matching those in the corresponding energy regions. Applications of the results may concern various systems of physics, chemistry, or biology, ranging from molecular magnets and glasses to Bose condensed atomic gases.     

Efficient compact model for calculating the surface potential of carbon-nanotube field-effect transistors using a curve-fitting method

This paper presents an analytical method to compute the surface potential of ballistic metal-oxide semiconductor field-effect transistor (MOSFET)-like carbon-nanotube field-effect transistors (CNFETs). The proposed compact model considers the surface potential as functions of the carbon-nanotube diameter, gate insulator thickness, gate voltage and drain voltage. One of the advantages of this model is that there is no need to refer to the numerical model to recalculate the surface potential each time nanotube diameter or insulator thickness is changed. Instead of using a constant smoothing parameter regardless of the device size and applied bias voltages, a parameter calculated for the specific situations is employed to provide the simulation results with higher accuracy. The validity of the proposed model was verified by comparing the simulated output characteristics of three CNFETs with those of the numerical model and the previous compact model.