Energies and widths of triply excited states of lithiumlike oxygen and neon

Seven low-lying triply exited states of lithium-like oxygen and neon are calculated with the multichannel saddle-point and saddle-point complex-rotation methods. The term energies are given for these excited states, along with level shifts and partial Auger widths from dominant decay channels. The mass polarization effect and relativistic corrections are included. The radiative transition rates are also calculated. These results are compared with other theoretical data in the literature. Received: 25 May 1998 / Revised: 28 July 1998 / Accepted: 25 August 1998     

Triply excited three-electron systems--semiclassical model

We calculate rovibronic intrashell spectra of the triply highly excited atomic hydrogen dianion, helium anion and lithium atom, within a simple semiclassical model. Zero-order electronic energy levels and half-lives are calculated for a number of principal quantum numbers and approximate thresholds for the appearance of vibronic modes are estimated. Since no quantum-mechanical and experimental data are available for the highly excited levels (N > 5), where the semiclassical models apply, no comparison with other results are possible at present. The problem of comparing semiclassical and quantum-mechanical calculations for moderately large quantum numbers, which seem attainable by the present day experimental technique, has been discussed. Received: 16 September 1998 / Received in final form: 16 March 1999     

Properties of doubly excited states of H- and He associated with the manifolds from N = 6 up to N = 25

This paper discusses theory and results on ¹P⁰ doubly excited states (DES) in He and in H^- of very high excitation, up to the N = 25 manifold. Our calculations employed full configuration interaction (CI) with large hydrogenic basis sets and produced correlated wavefunctions for the four lowest roots at each hydrogenic manifold by excluding open channels and the small contribution of series belonging to lower thresholds. The suitability of the hydrogenic basis sets for such calculations is justified, apart from their practicality, by the fact that, by computing from them natural orbitals, the results were shown to be the same with those of earlier multiconfigurational Hartree-Fock (MCHF) calculations on low-lying DES. In total, 160 states were computed, most of them for the first time. Their energy spectrum should be of use to possible future photoabsorption experiments. For certain low-lying DES up to N = 13, for which previous reliable results are available, comparison of the calculated energies shows good agreement. The correlated wavefunctions contain systematically chosen single and double excitations from each hydrogenic manifold of interest. From their analysis, we determined the “goodness" of different quantum numbers and the geometry (average angles and radii) as a function of excitation. For the Sinano lu-Herrick ( K , T ) classification scheme, whose basis is a restricted CI with hydrogenic functions and which has thus far been tested only on low-lying DES, we established that, whereas T remains a good index as energy increases, K does not. Consequently, a more flexible than K quantum number is needed in order to account for most of the additional correlation. This number, represented by F = N - K - 1, where N and K are not good numbers anymore, produces consistently a much higher degree of purity than the ( K , T ) scheme does, especially as N increases and as the relative significance of various virtual excitations due to electron correlation increases. Among the four states of each manifold, in all cases in H^- and in most cases in He, the three are of the intrashell type and one is of the intershell type with ( F , T ) = (0, 0). The lowest intrashell states and the lowest intershell states exhibit a wide angle geometry tending to 180 ^° as N ↦∞. Received 10 September 2001 and Received in final form 12 November 2001     

Ionic transitions and oscillator strengths in Debye plasma - a case study

Stability and energy of the excited states of the ion in plasmas are investigated theoretically using the Debye model. The transition energies of and transitions are seen to follow completely opposite trends of variation with the plasma screening strength. The dependence of absorption oscillator strength values on the screening strength is also discussed. Received: 22 October 1997 / Accepted: 9 January 1998     

Investigation of auto-ionizing states in xenon by resonantly enhanced multi-photon ionization

We have examined the autoionization spectrum of xenon by resonantly enhanced three-photon ionization (2 + 1 REMPI) involving intermediate states 5p ⁵6p[J = 0, 2]. The properties of the observed autoionization resonances change significantly with the choice of the intermediate state. For ionization via an intermediate state with predominantly 5p ⁵(²P_3/2) core character, a strong continuum with embedded window-type 5p ⁵(²P _1/2)nd'-autoionization resonances is observed. For intermediate states, predominantly with 5p ⁵(²P_1/2) core character, both 5p ⁵(²P _1/2)nd'- as well as 5p ⁵(²P _1/2)ns'-resonances are present in the spectrum as overlapping, nearly symmetric peaks on a rather weak continuum. Calculations confirm the significant dependence of the spectral lineshapes upon the excitation pathway to the autoionizing state. The ionization data are compared with spectra obtained by monitoring third-harmonic generation via autoionizing states without resonant excitation of intermediate states. These spectra also exhibit the signature of both the nd'- and ns'-resonances. Received 30 September 2002 Published online 28 January 2003 RID="a" ID="a"Permanent address: Rostov State University of Transport Communication, 344038, Rostov-on-Don, Russia. RID="b" ID="b"e-mail: halfmann@physik.uni-kl.de     

On the implicit integral character of Roothaan's expansion

The molecular generator coordinate Hartree-Fock method is reviewed. The connection between a quadrature solution of the generator coordinate Hartree-Fock equations and Roothaan's equations is stressed. The relation between linear expansion coefficients and generator coordinate weight functions is discussed and a numerical and analytical example is provided for the 1s orbital of the hydrogen atom represented as the integral transform of a Gaussian function. For the same example, the Gauss-Labatto quadrature is employed to emphasize the implicit integral character of Roothaan's equations. As a major conclusion, the interpretation that every LCAO calculation is actually performing integrations of the Griffin-Wheeler equations is advanced. Basis sets are therefore abscissas of the implicit quadrature used in the integration, whereas the linear coefficients automatically incorporate the corresponding weights. Subsequently, it is shown how to extract the generator coordinate weight function from the LCAO coefficients which has the advantage of being a characteristic of the physical system under study and not of the particular calculation being carried out. As such, basis set design becomes how to efficiently sample the weight function. Received: 13 June 1998 / Received in final form: 12 August 1998 / Accepted: 14 September 1998     

Near threshold photoionization of excited alkali atoms Ak(np) (Ak = Na, K, Rb, Cs; n = 3-6)

The effect of the polarization of the atomic core by the outer electron on near threshold photoionization of excited alkali atoms Ak(np) (Ak = Na-Cs; n=3-6) is investigated. Partial and total cross-sections for photo-ionization of the np-electron were computed utilizing the configuration interaction technique with Pauli-Fock atomic orbitals (CIPF) and including the long range core polarization potential (CP). To calculate the core polarization potential the variational principle is applied. Comparison with previous theoretical results and with available experimental data is made for the total cross-section , for the electron angular distribution parameter , for the ratio of the reduced electric dipole matrix elements and for the phase shift difference , associated with the d-wave and s-wave continua, respectively. In the comparison, new experimental results for , , and , measured for laser-excited, polarized ³⁹K(4p _3/2) atoms, have been included. Received 21 July 1999 and Received in final form 14 October 1999     

Vitamin E models

The molecular conformations of shortened molecular models of vitamin E (tocopherol and tocotrienol) and their sulfur and selenium congeners were studied computationally at the DFT level of theory [B3LYP/6-31G(d)]. The sequence of stabilization by the various heteroatoms was found to be the following: O∼Se > S. On the basis of the present structural results it seems that the seleno-congener of vitamin E is a distinct possibility. Received 9 May 2002 / Received in final form 9 July 2002 Published online 13 September 2002     

Ionization of barium through a coherent excitation of two bound intermediate states

We have investigated theoretically the asymmetrical photoionization yields into the 6s _1/2, 5d _3/2 and 5d _5/2 continuum channels of atomic barium observed by Wang, Chen and Elliott [Phys. Rev. Lett. 77, 2416 (1996)] in the study of coherent control through two-color resonant interfering paths. The atomic parameters obtained from a theoretical approach based on a combination of jj-coupled eigenchannel R-matrix and Multichannel Quantum Defect Theory are used to analyze the photoionization spectra from the and 6s7p states with polarized light beams. The studied energy range includes the 6p7p autoionizing resonances. The dynamics of the two-color photoionization is governed by the coherent excitation of the 6s6p and intermediate states. This excitation is described as an adiabatic process in the rotating wave approximation. The influence of the radiative decay, spatial distribution of the intensities of the laser beams and hyperfine interaction is discussed. Received 28 September 1999     

Sextet levels in the phosphorus-like ion Cu

Delayed spectra of foil-excited fast Cu ions have been studied to find a number of 3s3p⁴, 3 s2 3 p2 3 d and 3s3p^33d levels in the P-like ion Cu¹⁴⁺ (spectrum Cu XV). Among these are 3 s 3 p3 3 d ⁶ D levels, which have never been observed before, although they are the lowest excited states that have the same parity as the ground configuration. The investigation combined theory and experiment. The calculations used the Cowan code with semi-empirically scaled parameters and extensive MCDF computations. Received: 14 April 1998 / Accepted: 18 April 1998     

Rydberg states in the condensed phase studied by fluorescence depletion spectroscopy

Higher Rydberg states of NO trapped in rare gas matrices have been studied by inducing Rydberg-Rydberg transitions from the lowest Rydberg state and detecting its fluorescence depletion. This technique unravels Rydberg states, which cannot be accessed by ground state absorption. However, no clear cut Rydberg series show up. The data show a compression of the n-(n + 1) splittings between Rydberg states, as well as of the splittings. The results are rationalised in terms of the quantum defect model and the lack of extended Rydberg series is due to the compression of high-n Rydberg states in a tiny energy region below the ionisation potential. Finally, fluorescence depletion data of NO trapped in amorphous sites (the so-called red sites) of solid Ar can be interpreted in terms of the gas phase NO-Ar van der Waals data. A general discussion on the fate of Rydberg states in van der Waals complexes, in liquids, and in solids is presented in an attempt to relate the data in these different media. Received 28 July 1999 and Received in final form 8 November 1999     

How to get access to long range states of highly excited molecules

Due to competition between ionic and covalent dissociation, the excited potential curves of the alkali dimers display long range structures, leading in some cases to secondary wells. We discuss the possibility of populating the well (with a depth of 1614.8 cm^-1, located at R _e = 30.5a ₀ ) that is present in the Na₂ potential curve and propose detection schemes. Received: 28 May 1998 / Revised: 5 August 1998 / Accepted: 24 September 1998     

Angular dependence of double electron capture in collisions of C4+ with He

In charge-transfer collisions of C⁴⁺(1s^{2 1}S) with He (1s^{2 1}S), the process of double electron capture into the ground state C²⁺ is well-known to dominate other channels by an order of magnitude for projectile energies below 10 keV. This work presents a calculation of differential cross-sections resolved in the angle and energy gain variables, based on an ab initio treatment of electronic states, and compares with the measurements published in the literature (projectile energy E=270, 400, and 470 eV). We also briefly discuss the semi-empirical two-state models developed by experimentalists for this process.     

Molecular ions in ultracold atomic gases: computed electronic interactions for MgH<Superscript>+</Superscript>(X<Superscript>1</Superscript>Σ<Superscript>+</Superscript>) with Rb

The electronic structures of the manifold of potential energy surfaces generated in the lower energy range by the interaction of the MgH⁺(X¹Σ⁺)  cationic molecule with Rb(²S)  neutral atom are obtained over a broad range of Jacobi coordinates from strongly correlated ab initio calculations which use a Multireference (MR) wavefunction within a Complete Active Space (CAS) approach. The relative features of the lowest five surfaces are analyzed in terms of possible collisional outcomes when employed to model the ultracold dynamics of ionic molecular partners.     

All electron ab initio investigations of the electronic states of the FeC molecule

The low-lying electronic states of the molecule FeC have been investigated by performing all electron ab initio multi-configuration self-consistent-field (CASSCF) and multi reference configuration interaction (MRCI) calculations. The relativistic corrections for the one-electron Darwin contact term and the relativistic mass-velocity correction have been determined in perturbation calculations. The electronic structure of the FeC molecule is interpreted as antiferromagnetic couplings of the localized angular momenta of the ions and resulting in a triple bond in the valence bond sense. The electronic ground state is confirmed as being . The spectroscopic constants for the ground state and eleven excited states have been derived from the results of the MRCI calculations. The spectroscopic constants for the ground state have been determined as and ,and for the low-lying state as and . The values for the ground state agree well with the available experimental data. The FeC molecule is polar with charge transfer from Fe to C. The dipole moment has been determined as in the ground state and as 1.51 D in the state. From the results of the MRCI calculations the dissociation energy, , is determined as 2.79 eV, and D₀ as 2.74 eV. Received: 2 October 1998 / Received in final form: 30 March 1999     

Ab initio calculation of excited state dipole polarizability - Application to the first 1, 3 Σ + g,u states of Li 2

Firstly, imaginary frequency-dependent dipole polarizabilities of Li in its ² S ground state and the first ² P excited state are calculated from a time-dependent gauge-invariant method using effective core pseudo-potentials and the multi-configuration one-electron wave function. C₆ dispersion coefficients of the 2 s + 2 s and 2 s + 2 p dissociations are deduced and also compared with all-electron values. Then, static polarizabilities of Li₂ in its ground and first excited ^{1, 3} Σ ⁺ _g,u states are obtained at interatomic distance corresponding to the energy minimum of each state. Received 10 May 2001 and Received in final form 14 September 2001     

Magnetization of Gd cluster: Anomalous thermal behavior

Theoretical studies of the temperature (T) dependence of magnetization of Gd₁₃ clusters have been carried out within a classical Heisenberg model using Monte-Carlo simulations. It is shown that for a broad range of values of , defined as the ratio between competing ferro and anti-ferro magnetic couplings, the cluster magnetization increases with T in the low T region, as seen in experiment. The clusters are also shown to exhibit a wide distribution of moments at a given T, which broadens significantly with increasing T. It is suggested that this may affect the observed magnetic behavior of magnetic clusters in Stern-Gerlach experiments. Received 29 May 1999 and Received in final form 5 September 1999     

Number of electrons active in slow collisions of and with

Resonant excitation or resonant electron scattering is a two step process in which Auger rates are involved in both steps. First an electron is captured into a bound state and a bound electron is excited (inverse Auger effect). Then an Auger transition leads to the emission of the electron from the ion. The corresponding cross-sections are very sensitive to the Auger rates and allow a detailed study of the Breit interaction which is a current-current contribution to the static electron-electron interaction. The contribution of the Breit interaction to the cross-section of resonant excitation on hydrogen-like uranium ions is discussed and shown that it is roughly twice as large as in the case of dielectronic recombination. Received 4 August 1999 and Received in final form 29 September 1999     

A pseudopotential study of molecular spectroscopy in rare gas matrices: absorption of NO in argon

We present a pseudopotential method to study the absorption spectroscopy of NO in an argon matrix modeled by a large albeit finite cluster. The excited states of NO are described with the virtual orbitals of a NO⁺ Hartree-Fock calculation plus a core-polarization operator to account for the electron-NO⁺ correlation. The argon atoms of the matrix are replaced by pseudopotentials for the repulsive contributions and core-polarization operators to account for matrix polarization and correlation with the excited electron. The model is shown to account for the matrix-induced transition shifts and also for the cut-off of the Rydberg series for n >3 reported in absorption experiments from the ground state. Received: 6 March 1998 / Revised: 1st June 1998 / Accepted: 16 June 1998