Construction of Different Kinds of Atomic and Molecular Orbitals Using Complete Orthonormal Sets of ψ^α-ETO in Single Exponent Approximation

Using complete orthonormal sets of ψ^α-exponential type orbitals in single exponent approximation the new approach has been suggested for construction of different kinds of functions which can be useful in the theory of linear combination of atomic orbitals. These functions can be chosen properly according to the nature of the problems under consideration. This is rather important because the choice of the basis set may be play a crucial role in applications to atomic and molecular problems. As an example of application, different atomic orbitals for the ground states of the neutral and the first ten cationic members of the isoelectronic series of He atom are constructed by the solution of Hartree-Fock-Roothaan equations using ψ^1, ψ^0 and ψ^-1 basis sets. The cMculated results are close to the numerical Hartree-Fock values. The total energy, expansion coefficients, orbital exponents and virial ratio for each atom are presented.     

The factorization approximation for the Master Equation

We examine the validity of the application of the Factorization Approximation to derive the Master Equation for a microscopic system coupled to a reservoir. We developed a formal perturbation expansion for the time evolution of the system reduced density matrix. We employed a diagrammatic schemes to produce each term of the perturbation series. The diagrams in the time domain provide a distinct criteria to distinguish the diagrams which survive the Factorization Approximation. The Feynmann-like diagrams in the energy domain, originated from the Resolvent method, are used for execution of diagram summations to estimate their overall contributions. We demonstrated that for a two level atomic system, interacting with a thermal reservoir, the summation over the diagrams which survived the Factorization Approximation, yields the proper time evolution of the system, in agreement with the solution of the Master Equation. The summation of the diagrams which are excluded by applying the Factorization Approximation are characterized by a dimensionless parameter: Γ/ω₀, where ω₀ is the frequency of the transition line, and Γ is the line width. The Factorization Approximation is thus rigorously justified when this expansion parameter is very small.     

Calculation of Elastic Scattering Properties in an Ultra-Cold ^85Rb-^85Rb Vapour

We report the calculation of the same-species elastic scattering properties for the ultracold rubidium-rubidium (^85Rb-^85Rb) system and the results are compared with other theoretical and experimental results in detail. We present an improved potential for triplet ground states of the Rb2 molecule, and calculate the scattering lengths αt and the effective range re using WKB and Numerov methods for two rubidium-85 collisions in the triplet state. Also, we investigate the convergence of these scattering properties, i.e. the dependence on core radius and K^0 parameter using quantum defect theory and the analytic calculations of scattering length obtained by Szmytkowski. In addition, we present evaporative cooling and other results that include phase shift and cross section at zero energy limit.     

Rotational and Vibrational State Distributions of CsH and Relative Reactivity in Reactions of Cs（6^2D,7^2D） with H2

By using a pump-probe technique, the nascent rotational and vibrational state distributions of CsH are obtained in the Cs（6^2 D,7^2 D） plus H2 reaction. The nascent CsH molecules are found to populate the lowest two vibrational （v″ = 0 and 1） levels of the ground electronic state. By comparing the spectral intensities of the CsH action spectra with those of pertinent Cs atomic fluorescence excitation spectra, the relative reactivity with 1-12 is in an order of6^2D3/2 〉 6^2D5/2 〉 7^2D3/2 〉 7^2D5/2. The rotational temperatures are found to be slightly below the cell temperature. The relative fractions （〈fV〉, 〈fR〉, 〈fT〉） of average energy disposal are derived as （0.2,0.12,0.68）, （0.2,0.12,0.68）, （0.07,0.04,0.89） and （0.07,0.04,0.89） for the 6^2D3/2, 6^2D5/2, 7^2D3/2 and 7^2D5/2, respectively. The major available energy is released as translation. These results support that the reaction mechanism of Cs（6^2 D,7^2 D） plus 112 is primarily a eollinear abstraction and not an insertion.     

Three-body decay of a rubidium Bose–Einstein condensate

We have measured the three-body decay of a Bose–Einstein condensate of rubidium (⁸⁷Rb) atoms prepared in the doubly polarized ground state F=m _F =2. Our data are taken for a peak atomic density in the condensate varying between 2×10¹⁴ cm^-3 at initial time and 7×10¹³ cm^-3, 16 s later. Taking into account the influence of the uncondensed atoms on the decay of the condensate, we deduce a rate constant for condensed atoms L=1.8 (±0.5) ×10^-29 cm⁶ s^-1. For these densities we did not find a significant contribution of two-body processes such as spin dipole relaxation. Received: 24 November 1998 / Revised version: 26 June 1999 / Published online: 8 September 1999     

Observations of anomalous “quantum jumps” in a single ion trap

Cooled positive barium ions, proposed for new frequency standards, cease scattering cooling radiation for anomalously long periods in the presence of carbon dioxide or water. The probable mechanism is the attraction of a gas molecule to the ion as a result of the dipole induced in the molecule by the ion, followed by the formation of a weak chemical bond between the two. The mechanism seems applicable to any ion.     

Characterization of an ethylene free jet

The rotational population distribution in a free molecular jet of ethylene, C₂H₄, is found to be thermal over a range of distances below the nozzle (z/d=0.5–13.2, nozzle diameter d=0.50 mm). Results for on-axis rotational temperature, number density and flow velocity are presented. The average number of gas-kinetic collisions experienced by any molecule in travelling some distance along the jet axis is calculated.     

Light-induced effect on the density distribution in a sample of cold trapped atoms

As it is known [1] an intense laser field can induce atom-atom interaction according to a dipole-dipole R ^–3 law. Such an interaction depends on the angle between light polarization and interatomic vector-position R. This angular dependence may produce an anisotropy in the spatial density distribution of the confined sample of cold atoms. We develop the main relations and apply them to the case of an atomic cloud of cold trapped neutral atoms with the density higher than or of the order of ^–3, where is the wavelength of light. The results presented here show the effect of such an interaction in a density regime of high experimental interest.     

Effective Atomic Numbers for Fe-Mn Alloy Using Transmission Experiment

The effective atomic numbers （Zeff ） and effective electron density （Ne ） for Fe-Mn alloy with different Mn contents are calculated using the mass attenuation coefficients μ/p obtained via XCOM in the photon energy range of i keV-1 GeV. The results are compared with the values measured at the photon energy of 662, 1170 and 1332keV.     

Photoionization cross sections of Fe XXI

Total and partial photoionization cross sections for (Fe XXI+hν→Fe XXII+e) are presented for the ground and excited bound states with n?10 and l?9. Fe XXI is prevalent in high-temperature astrophysical plasmas as well as in photoionized plasmas excited by hard X-rays. Results are reported for the first time for the high-energy photoionization with core excitations to n=2,3 states. Details of photoionization, especially the high-energy features that often dominate considerably over the low energy ones, are illustrated. These prominent features will affect the photoionization and the recombination rates in high-temperature plasmas. Calculations are carried out in the close coupling (CC) approximation using the R-matrix method. A large CC wavefunction expansion for Fe XXII which includes the ground and 28 excited core states from n=2 and 3 complexes and spans over a wide energy range is used. A total of 835 discrete bound states of Fe XXI in the singlet, triplet, and quintet symmetries are obtained. Total photoionization cross sections, σ_PI(nLS), for ionization into all 29 states are presented for all 835 final bound states and partial photoionization cross sections, σ_PI(g,nLS), for ionization into the ground ²P⁰ state of the core are presented for 685 states. While the n=2 core excitations are at relatively lower energy range (within 15 Ry from the ionization threshold), the n=3 excitations lie at considerably higher energy, 73 Ry and above, yet introduce resonant features and enhancements more prominent than those of n=2 states. Larger numbers of resonances are formed due to Rydberg series of autoionizing states converging on to the 29 core states. However, most noticeable structures are formed in the excited state cross sections by the photoexcitation-of-core (PEC) resonances in the photon energy range of 73-82 Ry. All these high-energy features are absent in the currently available results. The present results should enable more accurate modeling of the emission spectrum of highly excited plasma from the optical to far-ultraviolet region.     

Electron-ion recombination and photoionization of Fe XXI

Results for electron-ion recombination and photoionization of , with emphasis in high-temperature region, are presented from ab initio unified method. The unified method, based on close coupling (CC) approximation and R-matrix method, (i) subsumes both the radiative recombination (RR) and dielectronic recombination (DR), (ii) enables self-consistent sets of photoionization and recombination cross sections from using an identical wavefunction for both the processes, and (iii) provides state-specific recombination rates of a large number of bound states. A large CC wavefunction expansion, which includes the ground and 28 core excitations of n=2 and 3 complexes and span a wide energy range, has been used. Compared to Δn=2-2, Δn=2-3 core excitations are found to introduce strong resonant structures and enhance the background photoionization cross sections (σ_PI) in the high-energy region. These features along with prominent photoexcitation-of-core (PEC) resonances at n=3 core thresholds have increased the unified total recombination rate coefficients (α_R(T)) at temperatures , region of maximum abundance of the ion in collisional equilibrium, by a factor of 1.6 over previous calculations. State-specific recombination rate coefficients α_R(nLS), which include both the RR and DR, are presented for the first time for 685 bound states with n?10 and l?9. The unified total recombination rate with photoelectron energy α_R(E) is presented and the role of low-energy near-threshold fine structure resonances is illustrated. The present results should provide a reasonably complete self-consistent set of recombination rates and photoionization cross sections for astrophysical modelings of high-temperature plasmas from optical to far-ultraviolet wavelength regions.     

Ion formation in laser-irradiated cesium vapor

We study theoretically the formation of Cs⁺ and during cw laser radiation resonant with 6s-7p transition of Cs atomic vapor. This is done by numerically solving rate equations for the evolution of atomic state and electron populations. The results of calculations for the atomic and molecular ions density at different values of laser power clarified that the associative ionization and Penning ionization process play an important role for producing the and Cs⁺, respectively, during the plasma formation. Also, the results showed that laser power of the order of 150 mW and 40-50 ns irradiation time are optimal in producing a fully ionized plasma.