Ab initio pair potential energy curve for the argon atom pair and thermophysical properties of the dilute argon gas. I. Argon–argon interatomic potential and rovibrational spectra

An argon–argon interatomic potential energy curve was derived from quantum-mechanical ab initio calculations using basis sets of up to d-aug-cc-pV(6+d)Z quality supplemented with bond functions and ab initio methods up to CCSDT(Q). In addition, corrections for relativistic effects were determined. An analytical potential function was fitted to the ab initio values and utilised to compute the rovibrational spectrum. The quality of the interatomic potential function was tested by comparison of the calculated spectrum with experimental ones and those derived from other potentials of the literature. In a following paper the new interatomic potential is used to determine selected thermophysical properties of argon by means of quantum-statistical mechanics and the corresponding kinetic theory considering two-body and three-body interactions.     

Production of π0 mesons and charged hadrons in\bar v neon and ν neon charged current interactions

The average multiplicities of charged hadrons and of π⁺, π^? and π⁰ mesons, produced in \(\bar v\) Ne and νNe charged current interactions in the forward and backward hemispheres of theW ^±-nucleon center of mass system, are studied with data from BEBC. The dependence of the multiplicities on the hadronic mass (W) and on the laboratory rapidity (y _Lab) and the energy fraction (z) of the pion is also investigated. Special care is taken to determine the π⁰ multiplicity accurately. The ratio of average π multiplicities \(\frac{{2\left\langle {n_{\pi ^O } } \right\rangle }}{{[\left\langle {n_{\pi ^ + } } \right\rangle + \left\langle {n_{\pi ^ - } } \right\rangle ]}}\) is consistent with 1. In the backward hemisphere \(\left\langle {n_{\pi ^O } } \right\rangle \) is positively correlated with the charged multiplicity. This correlation, as well as differences in multiplicities between \(\mathop v\limits^{( - )} \) and \(\mathop v\limits^{( - )} \) , \(\mathop v\limits^{( - )} \) scattering, is attributed to reinteractions inside the neon nucleus of the hadrons produced in the initial \(\mathop v\limits^{( - )} \) interaction.     

Ab initio potential energy curve for the helium atom pair and thermophysical properties of dilute helium gas. I. Helium–helium interatomic potential

A helium–helium interatomic potential energy curve was determined from quantum-mechanical ab initio calculations. Very large atom-centred basis sets including a newly developed d-aug-cc-pV8Z basis set supplemented with bond functions and ab initio methods up to full CI were applied. The aug-cc-pV7Z basis set of Gdanitz (J. Chem. Phys. 113, 5145 (2000)) was modified to be more consistent with the aug-cc-pV5Z and aug-cc-pV6Z basis sets. The diagonal Born–Oppenheimer corrections as well as corrections for relativistic effects were also calculated. A new analytical representation of the interatomic potential energy was fitted to the ab initio calculated values. In a following paper this potential model will be used in the framework of quantum-statistical mechanics and of the corresponding kinetic theory to calculate the most important thermophysical properties of helium governed by two-body and three-body interactions.     

Investigation of the mode crossing resonance shape of the 1.52 μm and 633 nm neon transitions

The shape of zero field mode crossing resonances has been investigated both theoretically and experimentally. Taking into account the effect of collisions, the resonance shape is given generally by superposition of four Lorenzians. Two of them are caused by the aligned laser levels (ifJ≧1), the other two are produced by phase destroying collisions. Investigations of the zero field mode crossing resonances of the 2s ₂→2p ₁(λ=1.52μm) and 3s ₂→2p ₄ (λ=633nm) Ne laser transition revealed deviations of the measured data from a Lorentz profile. By computer fitting both the alignment relaxation rate \(\gamma _{2s_2 } \) (2) and the relaxation rate of the optical coherence \(\gamma _{2s_2 ,2p_1 } \) was obtained from one resonance curve. An investigation of the relaxation rate of the optical coherence as a function of the Ne pressure yields the pressure broadening constant (7±3) MHz/Torr and the natural linewidth 1/2 \(\tfrac{1}{2}(\gamma _{2s_2 } + \gamma _{2p_1 } ) = (18.8 \pm 1.7)\) MHz which are in agreement with inverted Lamb dip measurements.     

An alternative scheme for calculating the unrestricted Hartree–Fock equation: Application to the boron and neon atoms

We present an alternative scheme for calculating the unrestricted Hartree–Fock (HF) equation. The scheme is based on the variational method utilizing the sophisticated basis functions that include no adjustable parameters. The validity of the present scheme is confirmed by actual calculations of the boron and neon atoms. The total energy of the present scheme is lower than that of the conventional restrictive HF equation, but higher than that of the CI method. Also, the resultant wave function satisfies the electron–nucleus cusp condition.     

Temperature effects on the width,shift and asymmetry of 748.8 nm self-broadened neon line

The influence of temperature on the shape of the self-broadened 748.8 nm Ne line emitted from the low pressure glow discharge of neon was investigated with a Fabry-Perot interferometer. Detailed analysis showed departures of the registered line shapes from the ordinary Voigt profile. These departures were consistent with fits of the speed-dependent asymmetric Voigt profile to experimental profiles. The values of the pressure broadening, shifting and collision-time asymmetry were determined and compared with those calculated in the adiabatic approximation for the van der Waals and Lennard-Jones potentials.     

Positron scattering and ionization of neon atoms—theoretical investigations

Although positron scattering with inert gas atoms has been studied in theory as well as in experiment, there are discrepancies. The present work reports all the major total cross sections of e+-neon scattering at incident energies above ionization threshold, originating from a complex potential formalism. Elastic and cumulative inelastic scatterings are treated in the complex spherical e+-atom potential. Our total inelastic cross section includes positronium formation together with ionization and excitation channels in Ne. Because of the Ps formation channel it is difficult to separate out ionization cross sections from the total inelastic cross sections. An approximate method similar to electron-atom scattering has been applied to bifurcate ionization and cumulative excitation cross sections at energies from threshold to 2000 eV. Comparisons of present results with available data are made. An important outcome of this work is the relative contribution of different scattering processes, which we have shown by a bar-chart at the ionization peak.     

Changes in the structure and composition of the surface of a cathode upon long-term interaction with helium‒neon plasma

The findings of an investigation into the impact of ions on the atomic state of the upper layer of He?Ne laser cathodes are presented. The research results are obtained using electron-probe microscopy, X-Ray photoelectron spectroscopy, and Auger spectroscopy, including the scanning mode. Changes in the surface compositions of the cathodes and active-element mirrors of lasers are revealed before and after tests.     

Ratchet potential in d.c. SQUID’s and reduced two-junction interferometer models

For finite values of the parameter and in the presence of small structural asymmetry and inhomogeneity of the junctions parameters, the two-junction interferometer model can be described by means of a single non-linear differential equation in such a way that a ratchet potential for SQUIDs can be deduced. The resulting dynamical equation, derived for first-order corrections with respect to a symmetric and homogeneous model with =0, presents an additional second-harmonic term and a cosine term in the expression for the effective current-phase relation. For opportune values of the perturbation parameters a ratchet potential with pre-definite characteristics can be obtained.     

An improved approximation scheme for the centrifugal term and the Hulthén potential

We present a new approximation scheme for the centrifugal term to solve the Schrödinger equation with the Hulthén potential for any arbitrary l -state by means of a mathematical Nikiforov-Uvarov (NU) method. We obtain the bound-state energy eigenvalues and the normalized corresponding eigenfunctions expressed in terms of the Jacobi polynomials or hypergeometric functions for a particle exposed to this potential field. Our numerical results of the energy eigenvalues are found to be in high agreement with those results obtained by using the program based on a numerical integration procedure. The s -wave (l = 0analytic solution for the binding energies and eigenfunctions of a particle are also calculated. The physical meaning of the approximate analytical solution is discussed. The present approximation scheme is systematic and accurate.     

The heavy quark potential and the ϒ, J/ψ systems

A new heavy quark potential is proposed which incorporates the two concepts of asymptotic freedom and linear quark confinement in a unified manner. It is shown that this potential reproduces the spectroscopy of the triplet $c\overline{c}$ system charmonium and the triplet $b\overline{b}$ system upsilonium. The only parameters other than a scale size Λ, are the quark masses.     

Resonances and antibound states for the dressed one-dimensional δ-function potential

We calculate resonances, antibound states and two new light induced states of the dressed one-dimensional attractive δ-function potential, as function of α₀ — the free electron quiver motion amplitude in a monochromatic electromagnetic field, in the range 0<α₀<150 a.u. We describe also our method, adequate to the numerical solution of the Schrödinger equation for this particular potential.     

Eigen solutions of the D-dimensional Schrӧdinger equation with inverse trigonometry scarf potential and Coulomb potential

The approximate analytical solutions of the D-dimensional space of the Schrӧdinger equation is studied with a newly proposed potential model. The proposed potential is a combination of Coulomb potential and inverse trigonometry scarf-type potential. The energy equation and the corresponding wave function are obtained using parametric Nikiforov–Uvarov method. The energy equations for Coulomb potential and inverse trigonometry scarf-type potential are respectively obtained by changing the numerical values of the potential strengths. It is found that the results obtained are equivalent to that previously obtained for Hellmann potential which is a combination of Coulomb potential and Yukawa potential. It is also found that the results for inverse trigonometry scarf potential are equivalent to the results previously obtained for Yukawa potential. Also, the Onicescus information energy of a system under the influence of the newly proposed potential is investigated in detail.     

Recursion-transform method and potential formulae of the m × n cobweb and fan networks

In this paper, we made a new breakthrough, which proposes a new recursion–transform(RT) method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.     

On the zero fluctuation of the “microscopic free energy” and its potential use

The fluctuations of the microscopic free energy calculated with the ensemble probability are shown to be zero. We suggest that this result be used for estimating approximate free energies calculated on the basis of the minimum free energy principle. As an example the estimation is performed with respect to a certain computer simulation of the square Ising lattice. The zero fluctuations also can be used to obtain relations among fluctuations with the accurate ensemble probability distribution.     

Taking the “naive” and “non-relativistic” out of the quark potential model

Some recent results are highlighted and synthesized which place the quark potential model on a more solid foundation within the context of quantum chromodynamics.     

Ab initio potential surfaces for the à and states of HCN+

Ab initio configuration interaction calculations for the à ²Σ⁺ and states of HCN⁺ are presented. Minima occur at r _CH = 2·03 a ₀, r _CN = 2·25 a ₀ (à ²Σ⁺) and r _CH = 2·75 a₀, r _CN = 2·26 a ₀ (). The potential surface for the state has a local maximum as the hydrogen atom is pulled away from CN. The barrier height is calculated to be 0·27 eV.     

Differential cross section and related integrals for the molière potential

The Molière potential is widely used in radiation damage simulation studies. It is not much used in analytical transport theory calculations because of the awkward expression for the differential cross section corresponding to the potential. We follow a two step process to obtain a useful cross section: adopting the Lindhard, Nielsen and Scharff (LNS) approximations in order to generate a simpler form of the Molière cross section and then creating a simple, easy-to-use, fit to that approximate form. Within the framework of the LNS treatment of atomic cross sections, our fit is accurate to 6%. Simple forms for the total cross section and several related quantities are presented.     

Excitation of 1+ AND 2− states in the neon isotopes

High resolution inelastic proton scattering is used to study the excitation of 1⁺ states in ²⁰Ne and ²²Ne. By comparing these results with those from gamma-ray fluorescence measurements, the strong role of the orbital contribution in the electromagnetic transitions, predicted by the theory, is confirmed. Shell model predictions of the 1⁺ strength are compared to the measured strength in ²⁰Ne and ²²Ne. The (p, p′) excitation of 2⁻ states in ²⁰Ne is compared to (π⁻, γ) and (e, e′) results.     

Effects of the close approach of potential curves in photoabsorption by diatomic molecules—I. Theory and computational procedures

A procedure is given for the calculation of continuum photoabsorption cross sections of diatomic molecules in a spectral region corresponding to the avoided crossing of molecular potentials. The technique involves the simultaneous solution of coupled Schrödinger equations and the numerical procedures adopted for their solution are outlined. Results of calculations using simple analytic potentials similar to those of the B³Σ^-_u and E³Σ^-_u states of oxygen are presented. It was found that non-adiabatic effects are significant as much as 1 eV below the crossing energy.