Dispersion and polarization interactions of the strontium atom

Dispersion coefficients involving the 5s ^{2 1} S ^e and 5s5p ^1,3P ^o states of strontium are determined from a large basis configuration interaction calculation. Dispersion coefficients are presented for the strontium dimer and also for strontium interactions with hydrogen and the rare gases. Polarizabilities and oscillator strengths from some low lying states are also given. The ground state polarizability and that of the 5s5p ¹P ^o and 5s4d ¹D ^e states are very similar in size.     

Effect of strongly coupled plasma on the doubly excited states of heliumlike ions

The effect of strongly coupled plasma occurring in astrophysical context has been studied for the first time to estimate the energy levels of the autoionizing states of highly stripped astrophysically important ions Al¹¹⁺, Si¹²⁺, P¹³⁺, S¹⁴⁺ and Cl¹⁵⁺ and also C⁴⁺ isoelectronic to helium. The transition energies corresponding to 1s ²:¹S^e → 2s ²:¹S^e, 2p ²:¹D^e, 2s2p:¹P^o, 2s3d:¹D^e and 2p3d:¹F^o are analyzed with respect to different plasma densities using the ion sphere (IS) model of strongly coupled plasma. Transition energies are obtained from the position of the poles of a variational functional based on frequency dependent perturbation calculation probing the collective oscillation modes of the plasma embedded two electron ions. For the free ions corresponding to zero plasma coupling our calculated data agree well with those obtained from spectroscopic data while for the plasma embedded ions the data are new but follow systematic trend. The work has been performed in the domain of linear response theory. The analytical wave function of the doubly excited states have been obtained and may be useful for calculating various transition properties of the plasma embedded ions and also for estimating the rate coefficients for dielectronic recombination processes which play a major role in maintaining equilibrium in high temperature astrophysical or laser produced plasmas.     

Radiative lifetime and oscillator strength determination in Mg-like potassium (K VIII)

Theoretical transition probabilities have been obtained for 54 n = 3 transitions depopulating the 3s3p ¹P^o, 3p^{2 3}P, ¹D, ¹S, 3s3d ¹D, ³D and 3p3d ³P^o, ³D^o, ³F^o, ¹F^o, ¹D^o, ¹P^o levels, including 14 transitions not yet observed. Some of these predictions have been compared with experimental lifetimes obtained by beam-foil spectroscopy for four n = 3 levels of K⁷⁺. An excellent agreement is observed between theory and experiment for all the levels. Received 23 January 2002 / Received in final form 23 April 2002 Published online 19 July 2002     

Computational study of collisional energy transfer and quasi-continuous population inversions in laser-pumped Ca vapor

A computational study of population inversion between several pairs of excited states viz 3d4p ³ F-4s3d ³ D, 4s5s ³ S-4s4p ³ P and 4s3d ³ D-4s4p ³ P in Ca vapor pumped on the 4s ^{2 1} S ₀-4s4p ³ P ₁ transition is presented. The main aim is to investigate the influence of various atomic processes in creating and sustaining the population inversion for long times after the excitation pulse. The delicate interplay between superelastic energy transfer to free electrons, energy pooling collisions and cascaded recombination is particulary examined. It is noted that quasi-continuous population inversion can be readily excited on the 4s3d ³ D-4s4p ³ P transitions; and under some conditions, also on the 4s5s ³ S-4s4p ³ P transitions. Furthermore, inversion on the 3d4p ³ F-4s3d ³ D transitions can also be excited for a considerable length of time. The results may be useful in designing and developing quasi-cw metal vapor lasers.     

Two-electron excitation in helium-like ions by electron impact

Calculation of cross-sections for the two-electron excitation in helium-like ions by electron impact employing Coulomb-Born-Oppenheimer (CBO) approximation is presented. Analytical expressions for the differential and total scattering cross-sections without using partial wave expansion of the wavefunction reported earlier have been used. The total and differential scattering cross-sections for each of the excitations 1s ^{2 1} S* → 2s ^{2 1} S ^e , 2s2p ^1.3 P ⁰, 2p ^{2 1} S ^e ,³ P ^e,¹ D ^e in Be²⁺ and B³⁺ are computed. Results for Li⁺ reported earlier are also included for comparison.     

Triple differential cross section of electron impact ionisation of Na(3s, 3p, 3d)

The fivefold differential cross section (5DCS) of the ionisation by electron impact of atomic sodium is determined theoretically for its fundamental 3s(² S) state and the excited 3p(² P) and 3d(² D) states by a procedure which employs in the transition matrix element of the first order Born approximation, the correlated double continuum (3C) wave function. This permits us to determine the statistical M-state population and the orientation and alignment tensors in (e,2e) detection. It is also shown that, the use of Gamow correlation term, in the independent particle (2C) model, reproduces, only in some situations, the shape of the angular distribution of the 5DCS obtained by the (3C) wave function. Received: 17 November 1997 / Received in final form: 16 March 1998 / Accepted: 21 March 1998     

Calculation of the Hyperfinestructure and gJ-Values of the 3d 4s 4p-Configuration of Scandium

Wave functions for the 3d 4s 4p, 3d² 4p and 4s² 4p configurations of ScI are calculated, taking into account departures from SL-coupling and configuration interaction and on fitting the radial integrals to the experimental fine structure energies. Using these wave functions g J -values are derived. The intermediate coupled hfs matrix elements of the 3d 4s 4p configuration are reduced to the unknown electron coupling constants a_s, a_p and a_d and calculated on estimating these constants from the spin-orbit coupling constants and fitting them to some experimental A-values. By this way the absolute phases of the experimental A((¹P)²D)- and A((¹P)²F)-values are obtained. Good agreement between calculated and most experimental data has been achieved.     

Wavelengths for 2pnp 1Pe→2pnd 1Do and 2pnp 3Pe→2pnd 3Do transitions in Li II,Be III,B IV,C V using correlated exponential wave functions

Doubly-excited ^1,3P^e and ^1,3D^o states of Li II, Be III, B IV, C V are calculated using highly correlated exponential wave functions within the framework of Ritz variational principle. The wavelengths for the 2pnp ¹P^e→2pn′d ¹D^o (n, n′≤7) and 2pnp ³P^e→2pn′d ³D^o (n, n′≤7) transitions are reported. Our present results for the 2pnp ^1,3P^e and 2pnd ^1,3D^o states energies are accurate in precision compared to the results of previous calculations. Comparisons are also made with the experimental results. The effective quantum numbers (n^?) for the 2pnp ^1,3P^e and 2pnd ^1,3D^o states are also reported.     

Energy levels, oscillator strengths and lifetimes in Ar V

We have calculated the excitation energies, oscillator strengths and transition probabilities for electric-dipole-allowed and intercombination transitions among the 46 LS levels belonging to the configurations 3s ²3p ², 3s3p ³, 3s ²3p3d, 3p ⁴, 3s ²3p4s, 3s ²3p4p, 3s3p ²(² S)4s, 3s3p ²(² P)4s, 3s3p ²(⁴ P)4s, 3s3p ²(² D)4s, 3s ²3p4d and 3s ²3p4f of Si-like Argon. These states are represented by extensive Configuration-Interaction (CI) wavefunctions obtained using the CIV3 computer code of Hibbert. From our transition probabilities we have also calculated the radiative lifetimes of singlet and triplet states of Ar V. Our results are compared with other available theoretical calculations and experimental data. To assess the importance of relativistic effects on our calculated values, we have also carried out calculations in the intermediate-coupling scheme using the Breit-Pauli Hamiltonian. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made so that the energy splittings are as close as possible to the experimentally compiled energy values of the National Institute for standards and Technology (NIST). The energy splitting of 85 fine-structure levels, the oscillator strengths and transition probabilities for electric-dipole-allowed and intercombination transitions and the lifetimes of some fine-structure levels are presented and compared with available experimental and other theoretical values. In this calculation, we also predict new data for several fine-structure levels where no other theoretical and experimental results are available.     

Van der Waals attraction between cylinders,rods or fibers

In a first step, we calculate the van der Waals energy between two cylinders by pairwise integration of unscreenedr ⁻⁶ interactions between any two molecules. It turns out proportional tod ^−3/2 at small separations and proportional tod ⁻⁵ at large separationsd of the cylinders. In a second step, we use an integration method for multiplet interactions, which relates the latter to screening and represents the van der Waals energy by macroscopic reaction fields. We expand these reaction fields in terms of modified Bessel functions. The van der Waals energy evolves from a sum over the numberl of field reflections, from a frequency integral over the dielectric constants involved, and from a wave number integral over the radii and the separation of the cylinders. The lowest order term verifies the results found by integration of pair interactions, yet replaces the unscreened polarizabilities of the atoms by the screened dielectric constants of the media. The higher order reflection termsl≧2 likewise turn out to be proportional tod ^−3/2 at small separationsd, but decrease in weight more rapidly than 1/l ³. Their contribution at large separation is proportional tod ^−(4l+1). From a comparison of our results with those obtained for spheres and half-spaces, we conclude that retardation entails ad ^−5/2 and ad ⁻⁶ law at small and large separations, respectively. This suggestion is confirmed by preliminary calculations based on the Helmholtz equation.     

Photoionization of Al IV (neon-type) from its ground 2s 22p 6 1 S e and excited 2s 22p 53p 3,1 P 0 3 S e states using the R-matrix method

The R-matrix method is used to calculate the total photoionization cross-sections from the ground 2s ²2p ^{6 1} S ^e and the first three excited 2s ²2p ⁵3p ^3,1 S ^e states of Al IV, for photon energies ranging from the first ionization threshold to just above the second threshold of the residual ion Al V. The two lowest LS terms of Al V − 2s ²2p ^{5 2} P ⁰, 2s2p ^{6 2} S ^e, 2s2p ^{6 2} S ^e, represented by sophisticated configuration interaction wavefunctions, are included in the R-matrix calculation. The resulting cross-sections are affected by Rydberg series of resonances converging to the 2s2p ^{6 2} S ^e excited threshold.     

Transition wavelengths for helium atom in weakly coupled hot plasmas

We have investigated the effect of surrounding plasmas on several singly excited and doubly excited meta-stable bound states of helium atom using highly correlated basis functions for singly excited S, P, D states and CI-type basis functions for doubly excited meta-stable D states. Plasma effect is taken care of by using a screened Coulomb (Yukawa) potential obtained from the Debye model that admits a variety of plasma conditions, and such a model plays an important role in plasma spectroscopy. The wavelengths for transitions from the 1snp ¹P° (n=2,3)→1s²¹S^e, 1snp ³P° (n=2,3)→1s2s ³S^e, 2pnp ¹P^e (n=3,4)→1s2p ¹P°, 2pnp ³P^e (n=2,3)→1s2p ³P°, 2pnd ¹D° (n=3,4)→1s3d ¹D^e, 2pnd ³D° (n=3,4)→1s3d ³D^e, 2p3p ¹P^e→2pnd ¹D° (n=3,4), 2pnd ¹D°(n=3, 4)→2p4p ¹P^e, 2pnp ³P^e (n=2,3)→2p3d ³D°, and 2pnp ³P^e (n=2,3)→2p4d ³D° of helium atom in plasmas for various Debye lengths are reported.     

Excitation of the Li isoelectronic sequence

Summary The inner-shell excitation 1s ²2s ² S ^e→1s2s ²² S ^e, which leads to autoionization (Auger transition), as well as the outer-shell excitation 1s ²2s ² S ^e→ 1s ²2p ² P ⁰ transitions have been investigated in Li, Be⁺, B²⁺ and C³⁺ ions of the lithium isoelectronic sequence employing the configuration interaction wave functions for both the initial and final states involved in the transition matrix element. Results are compared with other available theoretical predictions and experimental observations. Comparison shows that our present theoretical results are encouraging. A part of this work was done while the author was Research Director and Professor, CNRS Laboratory, University of Paris-Sud, Paris and Observatoire de Paris, Meudon, Paris, France.     

Fine-structure energy levels,oscillator strengths and lifetimes in Mg-like chromium

Excitation energies from ground state for 86 fine-structure levels as well as oscillator strengths and radiative decay rates for all fine-structure transitions among the levels of the terms (1s²2s²2p⁶)3s²(¹S), 3s3p(^1,3P^o), 3s3d(^1,3D), 3s4s(^1,3S), 3s4p(^1,3P^o), 3s4d(^1,3D), 3s4f(^1,3F^o), 3p²(¹S, ³P, ¹D), 3p3d(^1,3P^o, ^1,3D^o, ^1,3F^o), 3p4s(^1,3P^o), 3p4p(^1,3S, ^1,3P, ^1,3D), 3p4d(^1,3P^o, ^1,3D^o, ^1,3F^o), 3p4f(^1,3D, ^1,3F, ^1,3G) and 3d²(¹S, ³P, ¹D, ³F,¹G) of Cr XIII are calculated using extensive configuration-interaction (CI) wave functions obtained with the CIV3 computer code of Hibbert. The important relativistic effects in intermediate coupling are included through the Breit-Pauli approximation via spin-orbit, spin-other-orbit, spin-spin, Darwin and mass correction terms. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made. The mixing among several fine-structure levels is found to be very strong. Our excitation energies, including their ordering, are in excellent agreement (better than 0.5%) with the available experimental results. From our transition probabilities, we have also calculated radiative lifetimes of some fine-structure levels. Our calculated lifetime for the longer-lived level 3s3p(³P₁) is found to be in excellent agreement with the experimental result of Curtis compared to other theoretical calculations.     

Stark effect,hyperfine structure and isotope shifts in highly excited states of BaI and CaI

The electric dipole polarizabilities of 9 even-parity barium states (6s8s ¹ S ₀,³ S ₁; 6s7d ¹ D ₂,³ D _1,2; 5d7s ¹ D ₂ and 6p ^{2 3} P _0,1,2) in the interval 33,800–35,800 cm^?1 have been measured with high resolution laser-atomic-beam spectroscopy. Simultaneously, values of isotope shifts and hyperfine coupling constants for theJ=1 states have been obtained. Comparison of the experimental polarizabilities with calculated values as well as inspection of the data on isotope shifts and hyperfine structure from the present and earlier work strongly suggests erroneous assignments of theJ=2 states, with an exception for the 5d 7s ¹ D ₂ state. The influence of an electric field on the 3d ^{2 3} P _0,1,2 states of calcium has also been studied. A marked departure from a quadratic Stark effect has been observed at relatively small field strengths. This can be attributed to the large polarizabilities of neighbouring Rydberg states. The low field data allow the determination of admixtures of Rydberg states into the 3d ^{2 3} P-states as small as 0.02%.     

Relativistic and nonrelativistic oscillator strengths in the Na isoelectronic sequence

We report the general trend of the nonrelativistic Hartree-Fock relativistic Hartree-Fock, nonrelativistic configuration-interaction, and relativistic configuration-interaction length form of the oscillator strengths for the resonance excitation 1s ²2s ²2p⁶3s ² S _J ^e 1s ²2s ²2p ⁵3s ^{2 2} P _J ^o . transition, which leads to autoionization (Auger transition), in Na, Mg¹⁺, Al²⁺, Si³⁺, P⁴⁺, S⁵⁺, Cl⁶⁺, Ar⁷⁺, K⁸⁺, Ca⁹⁺, Sc¹⁰⁺, Ti¹¹⁺, Fe¹⁵⁺, Cu¹⁸⁺, Zn¹⁹⁺, Br²⁴⁺, and Kr²⁵⁺ ions of the sodium isoelectronic sequence.     

Multiconfiguration Hartree-Fock calculations in Cr5+, Mn6+ and Fe7+

The multiconfiguration Hartree-Fock (MCHF) method is used to calculate the excitation energies and oscillator strengths, of both the length (f _L) and velocity (f _V) forms, for 1s²2s²2p⁶3s²3p⁶3d² D→1s²2s²2p⁶3s²3p⁵3d^{2 2} P ⁰,² D ⁰,² F ⁰ transitions in Cr⁵⁺, Mn⁶⁺ and Fe⁷⁺ ions of the potassium isoelectronic sequence. Comparison is made with our earlier relevant results obtained by employing the configuration interaction (CI) method which is closely related to the MCHF method. Our present investigation demonstrates that the MCHF method is more accurate than the CI method in all ions of present consideration.     

One-photon two-electron transitions for metastable helium

We have obtained very accurate excitation energies for helium corresponding to the transitions 2p^{2 3}P^e ↦nln’l’ ³D^o using highly correlated Hylleraas-type wave functions. The doubly excited 2p^{2 3}P^e metastable bound state energy is obtained using Ritz variational principle. The upper bound of 2p^{2 3}P^e energy is –0.7105001556783 a.u., which is close to the best results –0.71050015567833 [R. Hilger et al., Chem. Phys. Lett. 262, 400 (1996)]. We employ complex-coordinate rotation method to obtain ³D^o resonances. The ³D^o resonance energies and widths along with one-photon two-electron transition energies are reported.     

电子与类铍N3+和O4+离子碰撞激发截面的相对论扭曲波计算

采用全相对论扭曲波方法,系统地计算了类铍N³⁺和 O⁴⁺离子从基态到2s2p和2p² 的各激发态以及从亚稳态到2p²各激发态的电子碰撞激发截面,详细地讨论了靶态的关联效应对激发截面的影响.结果表明：对于2s-2p的单电子激发,在低能碰撞时,靶态的电子关联效应起非常重要的作用,且使得激发截面降低;而高能碰撞时,靶态波函数的描述对连续态波函数的影响比较小,对激发截面影响也比较小.对于2s²-2p²的双电子激发,其中基态2s²¹S₀到J=0的2p²³P₀,¹S₀的激发截面较大,其主要原因是末离子态波函数与基组态波函数的混合,但是其他几个激发的激发截面较小. 关键词： 全相对论扭曲波方法 电子碰撞激发 电子关联效应