Large Number Of Excited States Research Articles

Orbital Kondo behavior from dynamical structural defects

The interaction between an atom moving in a model double-well potential and the conduction electrons is treated using renormalization group methods in next-to-leading logarithmic order. A large number of excited states is taken into account and the Kondo temperature $T_K$ is computed as a function of barrier parameters. We find that for special parameters $T_K$ can be close to $1 {\rm K}$ and it can be of the same order of magnitude as the renormalized splitting $\Delta$. However, in the perturbative regime we always find that $T_K \alt \Delta $ with a $T_K \alt 1 {\rm K}$ [Aleiner {\em et al.}, Phys. Rev. Lett. {\bf 86}, 2629 (2001)]. We also find that $\Delta$ remains unrenormalized at energies above the Debye frequency, $\omega_{\rm Debye}$.

Magneto-optical studies of Er3+ in stoichiometric LiNbO3

Various slightly differing Er3+ sites in stoichiometric LiNbO3 have been characterised using optical measurements of the Zeeman effect and of the magnetic circular dichroism of the absorption (MCDA), together with the optical detection of the EPR by microwave-tagging of the MCDA. For three distinct Er3+ sites the g∥-values have been determined for the ground and a large number of excited states. The technical requirements for directly correlating site-selective optical and EPR spectroscopic data have been clarified for arbitrary directions of the magnetic field B relative to the crystal main axis.

Lifetimes of metastable states in Sr II

The lifetimes of the 4d 2D 3/2,5/2 levels of Sr+ have been determined both experimentally and theoretically. The experiment was performed at an ion storage ring utilising collinear laser excitation. The calculation was performed by the Hartree-Fock method including relativistic effects and core polarisation. The obtained lifetimes (which are about 0.4 s) are discussed in detail and compared with earlier published results. In addition, calculated lifetimes of a large number of excited states in Sr+ are included.

Intermediate Hamiltonian Fock-space coupled-cluster method

An intermediate Hamiltonian Fock-space coupled-cluster method is presented, following the formalism developed by Malrieu in the context of perturbation theory. The method is expected to be applicable to many states not accessible by traditional FSCC. A pilot application to a large number of excited states of Sc+ shows good convergence and agreement with experiment to a few hundredths of an eV, whereas the usual FSCC iterations diverge for all but the few lowest states.

A theoretical study of the electronic spectrum of s-tetrazine

The vertical electronic spectrum of s-tetrazine has been studied using multiconfigurational wavefunctions (CASSCF) and second-order perturbation theory (CASPT2) to include effects of dynamic electron correlation. The spectrum is complex with a large number of excited states at low energies (10 singlet valence states between 2eV and 6eV). They include n → π* and π → π* excited states, but also two doubly excited states of the n, n → π*, π* type. The lowest doubly excited state appears already at 4.37 eV. In all, 47 excited states have been characterized, comprising both valence (singlet and triplet) and Rydberg states. The calculations are complicated due to strong correlation effects in the four lone-pairs and between the lone-pairs and the π electrons. Thus large active spaces were needed. In some cases it was necessary to use the multi-state CASPT2 method to unravel mixing of valence and Rydberg states at the reference CASSCF level. The computed energies have been used to assign the electronic spectrum and good agreement between computed and experimental vertical transition energies is found, the largest deviation being 0.3 eV.

Fully relativistic density functional calculations of the ground and excited states of Yb, YbH, YbF, and YbO

Fully relativistic density functional calculations using the recently developed Beijing 4-component density functional program package (BDF) were performed for a large number of excited states of the ytterbium atom and the spectroscopic constants of the ground and some excited states of the diatomic molecules YbH, YbF and YbO. It is shown that in a relativistic framework based on the Dirac–Coulomb Hamiltonian modern (nonrelativistic) density functionals work fairly well even for the rather compact 4f shell, i.e., they quantitatively reproduce the excitation energies due to the occupation changes in the 4f shell, in contrast to previous statements made by other authors. The nondegeneracy induced by the approximate density functionals to the degenerate open 4f shell is found to be almost independent of the occupancy of outer shells as well as Hund’s coupling and of the same order as that for the first transition metals. After subtracting the unphysical nondegeneracy we obtain reasonable patterns of excited states due to different occupations of the 4f spinors for the molecules studied here. Although the spectroscopic constants for YbH and YbF obtained by this and other theoretical work are all in good agreement with available experimental data, the theoretical results for YbO show remarkable disagreement with each other and experiment. The present calculations favor a Ω=0+ ground state with a leading f14σ0 configuration, which is in agreement with the interpretation of experimental data.

Electron‐Ion Recombination Rate Coefficients, Photoionization Cross Sections, and Ionization Fractions for Astrophysically Abundant Elements. I. Carbon and Nitrogen

We present a comprehensive and self-consistent set of new atomic data for ionization balance in radi- atively and collisionally ionized astrophysical plasmas. Complex resonant phenomena resulting in rapid energy variation in the cross sections for photoionization and recombination require accurate and large- scale calculations, as reported. Another new development is the consideration of the uni-ed nature of the recombination process in an ab initio manner, via resonances embedded in the electron-ion continua, which have been heretofore considered as separate processes of radiative recombination and dielectronic recombination. A single set of total electron-ion recombination rate coefficients is thereby obtained as a function of electron temperature. The present calculations also meet the hitherto neglected, but theoreti- cally essential, criterion of self-consistency between the rates for the inverse processes of photoionization and recombination, ensured by describing all atomic processes with an identical set of eigenfunction expansion within the close-coupling approximation using the R-matrix method. Photoionization cross sections and total electron-ion recombination rate coefficients for the carbon and nitrogen isonuclear sequences, C IEC VI and N IEN VII, are presented. Ionization fractions in coronal equilibrium are also computed. The present photoionization cross sections have been calculated using more extensive eigen- function expansions than those in the Opacity Project. In addition to the total photoionization and recombination data, state-speci-c cross sections are also obtained for a large number of excited states for non-LTE models. Complete data sets are available electronically. Subject headings: atomic data E atomic processes E plasmas

Interstellar silicon–nitrogen chemistry. III. The spectral signatures of the H2SiN+ molecular ion

The recent detection of SiN in the outer envelope of the IRC+10216 carbon star has renewed the interest for the gas phase interstellar silicon chemistry. In this contribution, we present a theoretical study of the H2SiN+ molecular ion, the silicon hydrogenated counterpart of the previously studied SiNH+2. On many points, the differences relative to the SiNH+2 isomer have been found to be dramatic. As an example, the dipole moment is computed to be 3.8 D while being only 0.5 D in SiNH+2. The radio, infrared and electronic signatures have been evaluated at a quantitative level. The rotational constants and vibrational frequencies have been determined using Möller–Plesset MPn (n=2,3,4), coupled cluster (CCSDT) and complete active space self-consistent field (CASSCF) methods for H2SiN+ and some of its isotopomers. These quantities have been corrected using a scaling procedure derived from previous studies on the HNSi, HSiN, HSiNH2, H2SiNH, and SiNH+2 species in order to provide quantitative results. The failure of single-reference perturbation theories to predict a relevant infrared spectrum is discussed. Intense bands around 550, 950, and 2300 cm−1 are predicted. The electronic spectrum has been obtained using a coupled multiconfiguration SCF–perturbation treatment (MC/P): It is characterized by a large number of excited states, none of them having a strong transition moment. The lowest excited state is predicted to lie 0.54 eV above the ground state, but the first allowed transition having a nonnegligible oscillator strength has to be searched at 6.44 eV.

Analysis of the Large Hyperpolarizabilities of Push-Pull Quinonoid Molecules

Donor-acceptor substituted quinonoid molecules have been investigated very tittle in connection with nonlinear optical (NLO) applications. We present a theoretical analysis of the hyperpolarizability, β, of a model push-pull quincnold molecule as a function of the quinonoid-benzenoid character (QBC). β is found to be quite large at all geometries except the quinonoid extreme; it results from appreciable contributions from a large number of excited states.

Spin–orbit coupling in the copper monoxide molecule

Diagonal as well as off-diagonal spin–orbit matrix elements were calculated for the ground state and a large number of excited states of CuO. They are based on previously calculated CI wave functions and energies. The spin–orbit splitting of the ground state X 2Π is analyzed in detail. The excitation energies for a large number of excited states are predicted, for Ω quantum numbers 1/2, 3/2, 5/2, and 7/2. They are compared with experimentally observed states. The results suggest a new designation of the ‘‘δ 2Σ− ’’ state as 4Π contaminated by spin–orbit effects. Also ‘‘k 4Σ− ’’ is most likely the Ω=1/2 component of 2 4Π.

Role of doubly excited states in calculations of optical activity

AbstractIt is shown that doubly excited states play an important role in calculations of the optical activity of molecules with well‐conjugated electron systems, such as the DNA bases. In some significant cases it is necessary to include a large number of excited states in the configuration interaction (CI) to obtain a reliable, converging result. A new version of the CNDO/OPTIC method, which includes doubly excited states in the CI, is proposed. As an application, the electric transition moments in different pyrimidines are considered. The calculated results agree with experimental data and results obtained from ab initio calculations and INDO calculations using doubly excited states in the CI.

Strongly bound multiply excited states of B+2 and B2

The potential curves, transition energies (Te), and spectroscopic constants (Re, ωe) of several low-lying electronic states of B+2 and selected doubly excited states of B2 are given. The data have been obtained by using a multireference single- and double-excitation (MRD) configuration interaction (CI) approach and a triple-zeta plus polarization AO basis set. The B+2 ground state, which is found here to be X 2Σ+g, shows a rather shallow potential curve (Re =4.015 bohr, ωe =423 cm−1) when compared with that of X 3Σ−g of B2(Re =3.00 bohr, ωe =1051 cm−1, exptl.). The first excited state of B+2, namely 1 2Πu, lies at Te =0.30 eV. Moreover, double excitations relative to X 2Σ+g are essential for the description of a large number of excited states, such as σuσg→π2u(1 4Σ−u, 1 2Σ−u, 1 2Δu, 1 2Σ+u) and σ2u→π2u(1 4Σ−g, 1 2Σ−g, 1 2Δg, 1 2Σ+g). Similarly, 2 2Πu arises from the triple excitation σ2uσg→π3u. In the same order as given above, such multiple excitations lead to a significant gain in bond strength (i.e., shorter Re, larger ωe) as a result of the simultaneous depopulation and population of strongly antibonding and bonding MOs, respectively. For neutral B2, similar features are observed for the excitation σ2u→π2u relative to X3Σ−g (leading to 3 1Σ+g) and 1 3Πu (leading to 2 3Πu). As a result of the loss of the two πu electrons, the ground state dissociation energy (De) of B+2(X 2Σ+g), with a calculated value of 1.94 eV, is about 1.12 eV smaller than the experimental De of B2 (X 3Σ−g).

Electron shake-up and correlation satellites and continuum shake-off distributions in X-Ray photoelectron spectra of the rare gas atoms

The rare gases H, He, Ne, Ar, Kr and Xe have been studied in the gas phase at low pressure by means of high resolution photoelectron Spectroscopy. Monochromatized Al Kα radiation at 90° was used to excite the photoelectrons. Extended energy regions of all valence electron spectra and the most interesting core electron spectra have been recorded. The spectra contain a large number of correlation satellites and shake-up as well as double shake-up satellites which originate from unknown highly excited, singly ionized states. The energies and intensities of these discrete satellites have been determined and several states are identified. The assignments rely partly on results from relativistic MCSCF calculations, and partly on comparisons with optical data and recent Auger electron data. Relativistic MCSCF energies for a large number of excited states in Kr + and Xe + are reported. Extended shake-off continua in both the valence region and in the core electron regions have been recorded. The shake-off continua of Ne and Ar reveal several Fano-like resonance states. The resonances occur when shake-up photoionization channels, involving inner valence electron excitation or multiple valence excitation, have the same energies and symmetries as photoionization channels for outer valence electron shake-off. A theoretical model for this type of resonance is presented and some numerical results are obtained and compared with experimentally determined Fano parameters for the most prominent resonance in the Nels shake-off spectrum.

Statistical formalism for particle emission

A simple transparent formalism is presented for following the ensemble averaged evolution of an excited system as it statistically emits particles. The formalism provides spectra and multiplicities for the emitted particles. It permits consideration of large numbers of emitted particle species, including those of medium mass, and a large number of excited states. The time developments of temperature, mass, charge, Coulomb barrier, and recoil velocity are investigated with regard to their influence on multiplicity and spectra. Emission of resonant states is limited to those with decay rates, $\frac{\ensuremath{\hbar}}{\ensuremath{\Gamma}}$, slow compared with emission rates which are readily calculable with the formalism.NUCLEAR REACTIONS Developed ensemble averaged formalism for statistical decay of excited nuclear system. Time evolution of nuclear temperature, mass, charge, Coulomb barrier, recoil velocity; emission of light, medium mass particle stable, unstable composite fragments; multiplicities, energy spectra calculated.

Energy Levels of Atomic Nitrogen Calculated in a Multiconfiguration Optimized Potential Model

The method of carrying out configuration interaction calculations using orbitals that are derived from a variationally optimized potential [K. Aashamar, T. M. Luke, J. D. Talman, J. Phys. B: Atom. Molec. Phys. 12, 3455 (1979), 14, 803 (1981)] is studied by applying it to the ground state and a considerable number of excited states of the nitrogen atom. The results of applying the method, using several correlation configurations, to the ground state multiplet are only slightly less satisfactory than the corresponding multiconfiguration Hartree-Fock results. It is shown furthermore that it is possible to obtain a unified description of a large number of excited states within the model using quite restricted configuration sets which are chosen in a reasonable way. Wavelengths and oscillator strengths for a large number of transitions are calculated and compared with experiment.

Theoretical Helium i Emission-Line Intensities for Quiescent Prominences

Self-consistent solutions of the combined statistical equilibrium and transfer equations have been carried out for a rather complete multilevel, multi-ion model helium atom in model quiescent prominences. The excitation and ionization of both He I and He II were considered simultaneously, and detailed calculations of the radiative transfer in the resonance lines and ground-state continua of both these ions were made, allowing for the effects of overlapping hydrogen transitions. A large number of excited states have been included in the computation, so that a fairly comprehensive set of predicted subordinate line intensities are now available for comparison with observation. A preliminary comparison of the predicted values with published singlet/triplet ratio observations shows good agreement for all the pairs of lines considered.

Effective Mass Approximation for Acceptor States in Silicon

AbstractThe effective mass equations for acceptors in silicon have been solved approximately for a large number of excited states. The variational approach used by Schechter was followed, but with more general trial functions that allow the treatment of a larger number of excited states. More recently measured valence band parameters were also used. Energies and wave functions were calculated for all of the lower excited states. Several energy levels were found between the levels treated by Schechter. The energy values obtained from the new valence band parameters do not agree as well with experiment as those obtained with the older parameters. However, the new distribution of levels does yield a better agreement between the theoretical and experimental symmetries of the excited state wave functions.

Structure of the Alkali Hydroxides. I. Microwave Spectrum of Gaseous CsOH

The microwave spectra of gaseous CsOH and CsOD have been studied in a high-temperature spectrometer. The spectrum indicates a linear or near-linear molecule with a large-amplitude, low-frequency bending vibration. A large number of excited states involving the bending mode and the Cs–O stretching mode have been identified. The rotational constant Bv shows an unusual variation as the bending mode is excited; the cause is not yet understood. The Cs–O bond length is found to be 2.40±0.01 Å and the O–H distance is probably about 0.97 Å. The electric dipole moment is 7.1±0.5 D. Relative intensity measurements indicate a Cs–O stretching frequency of 400±80 cm−1 and a bending frequency in the neighborhood of 300 cm−1. All of the evidence supports a highly ionic cesium—oxygen bond.

Scattering of 40.5-MeV Alpha Particles byC12,C13,N14,N15,O16, andO18

Elastic and inelastic scattering of 40.5-MeV \ensuremath{\alpha} particles from targets of ${\mathrm{C}}^{12}$, ${\mathrm{C}}^{13}$, ${\mathrm{N}}^{14}$, ${\mathrm{N}}^{15}$, ${\mathrm{O}}^{16}$, and ${\mathrm{O}}^{18}$ was studied. Angular distributions were measured for a large number of excited states. It was found that the shape of the angular distribution depends on the nature of the single-particle transition involved. Six examples of quadrupole transitions involving promotion of a ${p}_{\frac{3}{2}}$ nucleon to the ${p}_{\frac{1}{2}}$ shell were found. Although the cross sections varied over a tenfold range, the shapes of the angular distributions remained very similar. Six examples of the dipole transition ${p}_{\frac{1}{2}}\ensuremath{\rightarrow}2{s}_{\frac{1}{2}}$ and seven examples of the octupole transition ${p}_{\frac{1}{2}}\ensuremath{\rightarrow}{d}_{\frac{5}{2}}$ were also observed. The dipole transitions gave angular distributions of a characteristic and unusual shape. Excitation of the ${\mathrm{N}}^{14}$ levels at 9.41, 9.71, 10.22, and 10.55 MeV suggests that they are all $T=0$. The levels at 6.05, 6.70, 7.40, and 7.60 MeV were not observed; probably they do not exist. A weak level at 10.85 MeV and two strongly excited levels (or groups of levels) at 11.3 and 12.9 MeV were observed in ${\mathrm{N}}^{14}$. The angular distribution of particles scattered from the 4.45-MeV level of ${\mathrm{O}}^{18}$ suggests strongly that this level is 1-rather than 3+. Several unnatural parity states were observed, but no states known to have isotopic spin different from the ground state. The angular distributions for several scattered particle groups were compared with distorted-wave Born approximation calculations and very approximate reduced transition probabilities for excitation of the levels were obtained. For the quadrupole and octupole excitations the results are in reasonably good agreement with values measured by electromagnetic methods.

Neutron Groups fromK(α, n)Sc

Neutron groups resulting from the alpha-particle bombardment of separated isotopes of potassium were observed. Ground-state Q values of -3.42 plus or minus 0.06 Mev for K/sup 4//sup 1/( alpha ,n)Sc/sup 4//sup 4/ and -7.16 plus or minus 0.06 Mev for s/sup 9/( alpha ,n)Sc/sup 4//sup 2/ were obtained. A large number of excited states or groupings of states were also observed. The presence of chlorine in one of the targets permitted measurement of the Cl/sup 3// sup 7/( alpha ,n)K/sup 4//sup 0/ reaction as well. A ground-state Q value of - 3.86 plus or minus 0.06 Mev was obtained. A tentative value of -5.89 plus or minus 0.06 Mev was given for the Cl/sup 3//sup 5/ ( alpha ,n)K/sup 3//sup 8/ ground state. (auth)