Quantum-statistical mechanics of a system of charged particles at high temperatures

If a quantum-mechanical potential is introduced the calculation of the quantummechanical binary distribution function for a system with Coulomb interaction is reduced to the well-known mathematical formalism of classical statistical mechanics in the case ofnλ³?1 (λ being the thermal wavelength). The two-particle quantummechanical potential is determined by the two-particle Slater sum. In this paper we calculated the two-particle Slater sum using an expansion according toe ² and the resolvent formalism. From the binary distribution function the correlation energy and the free energy as well were determined up to ordere ⁶. Symmetry effects were taken into account.     

Radiative charge transfer and radiative association of protons colliding with Na at low energies

Using the fully quantum-mechanical approach, the radiative charge transfer for H⁺ + Na(3s) collisions has been investigated. The charge transfer emission spectra are analyzed at resonant and non-resonant collision energies. The radiative association cross sections, obtained by subtracting the radiative charge transfer part from total radiative decay cross sections calculated by the optical potential method, are presented in the energy range 10⁻⁶-1 eV.     

Bremsstrahlung spectrum for α decay and quantum tunneling

Spectra of the electromagnetic radiation arising during α decay of atomic nuclei as a consequence of the motion of the α particle through a Coulomb potential barrier and in the Coulomb field of the daughter nucleus are calculated via a quantum-mechanical approach. The contributions of the E1 and E2 multipoles are calculated. Model problems of emission during motion of a charged particle through a spherically symmetric, rectangular potential barrier and a “cut-off” Coulomb barrier are treated. Numerical calculations are performed for ^210,214Po and ²²⁶Ra nuclei. Emission spectra are derived for an α particle propagating along classical trajectories in these potentials. Zh. éksp. Teor. Fiz. 116, 390–409 (August 1999)     

Group-theoretical classification of angular momentum coherences in hydrogen

Results of photon-scattered atom coincidence measurements are presented for Mg-inert gas collisions. A polarisation analysis of the collision induced Mg(3¹ P-3¹ S) photons emitted perpendicular to the scattering plane was carried out at 1 keV collision energy as a function of the impact parameter. From these data the quantum-mechanical scattering amplitudes for the excitation of one of the two available Mg 3s-valence electrons are derived. The results are compared with the corresponding ones for the Mg⁺-inert gas collisions. A good qualitative understanding of the mechanism can be obtained.     

Reaction-rate approach to impurity dipole reorientation in RbBr:Ag+

The temperature dependence of optical relaxation time of impurity dipoles (Ag⁺ in RbBr) is calculated using the quantum-mechanical theory of reaction rates in condensed media. A good agreement between theory and experiment is found.     

Evaluation of the single ionisation transition amplitude using the CDW-EIS model within the framework of the impact-parameter method

The continuum distorted-wave model with an eikonal initial state for ionisation is discussed within the framework of the impact-parameter method. Particular attention is paid to the surface term, which describes the transition by a distorting potential, and which has been omitted in all of the previous calculations performed using the model. However, this term is included in the transition amplitude in a recent application of the model based upon a quantum-mechanical treatment. The present study, in which the surface term is evaluated within the impact-parameter method, shows that this term does not contribute to the transition amplitude. In describing the electron-ejection mechanism for a p^±–H collision, the cross-sections evaluated using the impact-parameter model show numerical agreement with those determined in the quantum-mechanical version. This agreement indicates that the contribution of the surface term calculated in the wave treatment is negligible over the region in which the impact-parameter model is valid.     

Bremsstrahlung emission accompanying the α -decay of 214Po

We analyze the bremsstrahlung emission obtained by the α -γ coincidence measurements to investigate on the α -decay dynamics of the ²¹⁴ Po nucleus. We performed the experiment using a radioactive ²²⁶ Ra source leading, by α -decays, to the ²¹⁴ Po nucleus, and the apparatus with the Si detector for α -particles, the NaI(Tl) detector able to collect photons with energies up to about 1 MeV. We compare the experimental data with the quantum-mechanical calculations and find a good agreement between theory and experiment for photon energies up to 765 keV. In the experimental data of the bremsstrahlung spectrum one can see the presence of slight oscillations.     

Photodetachment cross section of S^- in electric and magnetic fields＊

In this paper, the quantum-mechanical photodetachment cross section of S^- in uniform electric and magnetic fields at arbitrary angles is presented. It compares the quantum-mechanical cross section with the quantum source formalism cross section. The results show that at large angle, the two results have good agreements, however, with the decrease of the angles, they deviate obviously from each other. The reasons for this discrepancy are also discussed.     

Hole mobility in a homogeneous nucleotide chain

The conductivity of molecular DNA-based conductors has been calculated. Charge motion is described by quantum-mechanical equations, and macromolecular vibrations are described by classical equations of motion with dissipation and a source of temperature fluctuations. In a homogeneous sequence of G-C nucleotide pairs, the calculated hole mobility at T=300 K equals ≈2cm² V^?1 s^?1.     

New approaches to the generalized WKB approximation. III

The problem of particle transmission through a one-dimensional potential barrier of arbitrary shape is considered within the new generalized WKB method, developed in [1, 2]. A number of properties of the matrix F(S, S_t), needed to solve specific quantum-mechanical problems, is indicated.     

Ab initio potential energy curve for the helium atom pair and thermophysical properties of the dilute helium gas. II. Thermophysical standard values for low-density helium

A helium–helium interatomic potential energy curve determined from quantum-mechanical ab initio calculations and described with an analytical representation considering relativistic retardation effects (R. Hellmann, E. Bich, and E. Vogel, Molec. Phys. (in press)) was used in the framework of the 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. The second pressure virial coefficient as well as the viscosity and thermal conductivity coefficients, the last two in the so-called limit of zero density, were calculated for ³He and ⁴He from 1 to 10 000 K and the third pressure virial coefficient for ⁴He from 20 to 10 000 K. The transport property values can be applied as standard values for the complete temperature range of the calculations characterized by an uncertainty of ±0.02% for temperatures above 15 K. This uncertainty is superior to the best experimental measurements at ambient temperature.     

Analogs of de Finetti's theorem and interpretative problems of quantum mechanics

It is argued that the characterization of the states of an infinite system of indistinguishable particles satisfying Bose-Einstein statistics which follows from the quantum-mechanical analog of de Finetti's theorem ⁽²⁾ can be used to interpret the nonuniqueness of the resolution into a convex combination of pure states of a quantum-mechanical mixed state.     

Electron spin relaxation of gadolinium (III) complexes in dimethylformamide solution

The characteristics of spontaneous Raman scattering from solutions of diatomic molecules are reviewed, especially with regard to what they may tell one about the dynamics of molecular motion. In the limit of extreme motional narrowing the polarized component of the Q branch is a lrentzian with a width which depends upon the rate (τ^-1) of dephasing of the molecular vibrations. An approximate, closed, quantum-mechanical expression for the contribution of ‘translational-translational’ quasielastic scattering to τ^-1, called τ_ph ^-1(T-T), is derived. The translational states of the liquid are determined by invoking the Lennard-Jones-Devonshire (LJD) cell model. The full LJD cell potential is replaced by an harmonic approximation thereto. The dependence of the τ_ph(T-T) upon thermodynamic variables and microscopic properties is discussed. The derived expression for τ_ph ^-1 (T-T) is then used to compute upper bounds on τ for liquid N₂ and O₂, for which experimental data are available. It is concluded that the T-T quasielastic scattering mechanism is essentially negligible and that other mechanisms must be dominant in determining τ. In particular, it is suggested that solvent-induced vibrational-reorientational coupling may be quite important.     

Anharmonic Oscillator and Double-Well Potential: Approximating Eigenfunctions

A simple uniform approximation of the logarithmic derivative of the ground state eigenfunction for both the quantum-mechanical anharmonic oscillator and the double-well potential given by V=m ² x ²+g x ⁴ at arbitrary g ≥ 0 for m ²>0 and m ²<0, respectively, is presented. It is shown that if this approximation is taken as unperturbed problem it leads to an extremely fast convergent perturbation theory Mathematics Subject Classifications(2000) 34L40, 34B08, 41A99     

Nonradiative charge transfer in collisions of protons with rubidium atoms

The nonradiative charge-transfer cross sections for protons colliding with Rb(5s) atoms are calculated by using the quantum-mechanical molecularorbital close-coupling method in an energy range of 10 3 keV-10 keV.The total and state-selective charge-transfer cross sections are in good agreement with the experimental data in the relatively low energy region.The importance of rotational coupling for chargetransfer process is stressed.Compared with the radiative charge-transfer process,nonradiative charge transfer is a dominant mechanism at energies above 15 eV.The resonance structures of state-selective charge-transfer cross sections arising from the competition among channels are analysed in detail.The radiative and nonradiative charge-transfer rate coefficients from low to high temperature are presented.     

A comparison of foreign gas broadening and shift of neon and argon emission lines

Foreign gas broadening and shift coefficients for Ne and Ar emission lines produced in a high pressure (0·5-2·0 atm) He discharge have been measured. The shift coefficients vary significantly for different transitions. This variation results from the differing excited state potentials for the He-Ne¹ and He-Ar¹ collision pairs, which must be included in any reasonable quantum-mechanical calculation of line shifts. Even the small differences in broadening coefficients demonstrate the inadequacy of calculation of broadening from equations based on the Lindholm⁽¹⁾-Foley⁽²⁾ theory of collision broadening.     

Exact and approximate solutions to the Schrödinger equation for the harmonic oscillator with a singular perturbation

I obtain exact solutions for the quantum-mechanical harmonic oscillator with a perturbation potential which belongs to a class of polynomial functions of 1/r. I show that some of the eigenfunctions enable the calculation of expectation values in closed form and are therefore suitable trial functions for the application of the variational method to related nonsolvable problems.     

Calculation of the integrated band intensities of NO

The integrated intensities for the 5.3-μ fundamental vibration-rotation band and for the first and second overtone bands of NO have been calculated within a quantum-mechanical framework. The dipole moment of NO was determined over a wide range of internuclear separations as an expectation value calculated with an accurate configuration-interaction electronic wavefunction and, in part, from experimental data. Our calculated value for the 5.3-μ fundamental band is 134±2 cm^-2 atm^-1 at S.T.P.     

Reaction and inelastic processes in the collision O () + O ()

A reduced dimensionality model is used to study the reaction OO O ₃ ( X1A1 ) + O( ³ P ) by means of time-dependent and time-independent quantum-mechanical methods. State-selected probabilities and rate constants are obtained for the reactive process as well as for the inelastic collision in which the vibrationally excited oxygen loses one or more quanta. It is found that the experimentally observed jump in depletion rates above a critical value of v could be partially explained by the vibrational relaxation rather than reaction. Reaction only becomes important for relatively high translational energies and therefore the calculated rates are too small at the temperatures of interest. It is concluded, however, that the reaction saddle point region in the potential energy surface plays a crucial role in the enhancement of vibrational relaxation. Received: 3 February 1998 / Revised: 27 March 1998 / Accepted: 15 May 1998