Doubly-excited States Research Articles

Theory and computation of the attosecond dynamics of pairs of electrons excited by high-frequency short light pulses

By defining and solving from first principles, using the state-specific expansion approach, a time-dependent pump-probe problem with real atomic states, we show computationally that, if time resolution reaches the attosecond regime, strongly correlated electronic ``motion'' can be probed and can manifest itself in terms of time-dependent mixing of symmetry-adapted configurations. For the system that was chosen in this study, these configurations, the $\text{He}\phantom{\rule{0.3em}{0ex}}2s2p,2p3d,$ and $3s3p\phantom{\rule{0.3em}{0ex}}^{1}P^{o}$, whose radials are computed by solving multiconfigurational Hartree-Fock equations, label doubly excited states (DES) of He inside the $1s\ensuremath{\epsilon}p\phantom{\rule{0.3em}{0ex}}^{1}P^{o}$ scattering continuum and act as nonstationary states that mix, and simultaneously decay exponentially to $1s\ensuremath{\epsilon}p\phantom{\rule{0.3em}{0ex}}^{1}P^{o}$ via the atomic Hamiltonian, ${H}_{A}$. The herein presented theory and analysis permitted the computation of attosecond snapshots of pairs of electrons in terms of time-dependent probability distributions of the angle between the position vectors of the two electrons. The physical processes were determined by solving ab initio the time-dependent Schr\odinger equation, using as initial states either the $\text{He}\phantom{\rule{0.3em}{0ex}}1{s}^{2}$ or the $1s2s\phantom{\rule{0.3em}{0ex}}^{1}S$ discrete states and two femtosecond Gaussian pulses of $86\phantom{\rule{0.3em}{0ex}}\text{fs}$ full width at half-maximum, having frequencies in resonance with the energies of the correlated states represented by the $2s2p$ and $2p3d$ configurations. We calculated the probability of photoabsorption and of two-photon resonance ionization and of the simultaneous oscillatory mixing of the configurations $2s2p,2p3d,3s3p,$ and $1s\ensuremath{\epsilon}p\phantom{\rule{0.3em}{0ex}}^{1}P^{o}$, within the attosecond scale, via the interactions present in ${H}_{A}$. Among the possible channels for observing the attosecond oscillations of the occupation probabilities of the DES, is the de-excitation path of the transition to the $\text{He}\phantom{\rule{0.3em}{0ex}}1s3d\phantom{\rule{0.3em}{0ex}}^{1}D$ discrete state, which emits at $6680\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$.

Fine structure and hyperfine structure of some excited states of helium

The fine structure and the hyperfine structure for some singly-excited and doubly-excited states of helium atom are calculated using Rayleigh-Ritz variational method with multi-configuration-interaction wave functions. The calculated results of the fine structure for the Rydberg series are in good agreement with other theoretical and experimental data. The hyperfine parameters and the hyperfine coupling constants of 3He are also obtained for this system.

Total cross sections and molecular frame photoelectron angular distributions in the N 1s photoionization of N2: An investigation of electron correlation effects

Multichannel scattering calculations have been performed to study the electron correlation effects in the N 1s photoionization of nitrogen molecules. Both the Hartree–Fock and configuration–interaction methods were applied in the calculations of target states, therefore the role of electron correlation effects in the target states can be investigated. Both single- and multichannel calculations have been performed to study the interchannel coupling effects. With correlated target states and coupled channels in the calculations, our calculated cross sections and asymmetry parameters are in good agreement with the experiments. The shape resonance is very well reproduced in our calculation, and we found weak coupling between channels leading to the 1σg−1 and 1σu−1 states, which agrees well with more recent experimental results by Hergenhahn et al. [J. Phys. Chem. 105, 5704 (2001)], but contradicts the random phase approximation results. The molecular frame photoelectron angular distributions obtained from our calculations are also in agreement with experiments. Our calculations also suggest an autoionization process via a double-excited state of the character of 1σg−11πu−11πg2, which is located near the threshold as observed by the experiments. Dynamics of the shake-up channels are also studied and compared with the experiments.

Transferionization and total electron emission for 25 keV amu-1He2+ colliding on He and H2

We have investigated electron emission for transfer ionization(TI) and total electron emission, for He and H2targets. Double differential cross sections in angle and energy of the ejected electrons have been obtained covering the angularrange from 0° to 175° and energies from2 to 140 eV. Pure ionization differential cross sections,derived by subtraction, show an increasing contribution to theelectron emission at low energies. The main observed structure,a cusp in the forward direction for electrons emitted withvelocities close to the incident projectile velocity, presents asymmetric shape for TI. This fact, togetherwith the similar shape of the cusp for both He and H2targets, suggest the presence of a two-electron intermediatestate centred at the projectile leading to cusp formation inTI. The cusp for pure ionization, in contrast, shows a strong asymmetry, and a different shape foreach target. The differential electron emission measurementsallow us to estimate the cross sections for capture to doublyexcited states resulting in autoionization of the projectile,which contributes to the TI channel. Weobtained a much larger cross section value for H2 than for Hetargets, in contrast with known cross sections for true doublecapture having the same order of magnitude for both targets.

Degrees of validity ofmodels for the description of doubly excited states of H-and He

There are models for the description of doubly excited states(DES) of H- and He whose degrees of validity can be testedby comparing their results to those from theory based on thesolution of the Schrödinger equation with the fullHamiltonian. Such comparisons are meaningful and definitivewhen a reasonably wide range of data are available. We presentresults for the energies and the nature of the wavefunctions of the four lowest 1Po DES of H- and of He foreach hydrogenic manifold from N = 6 up to 25. These are usedto establish the degree and range of validity of thequantum number n2 introduced by Herrick and Kellman (Herrick D Rand Kellman M E 1980 Phys. Rev. A 21 418) in their triatomicmodel for qualitative description of the spectra of DES, aswell as of two classification schemes, as a function of levelof excitation and of type of state. According to the model, thenumber n2 is equal to the number of nodes of the density ρ(θ12) of the corresponding DES. We presentresults of calculations of ρ(θ12) usingcorrelated wavefunctions for the four lowest states in theN = 10 and 25 manifolds. These show for the first time forsuch highly excited states how the angle opens as excitationincreases. Furthermore, they indicate that n2 provides a valid picture even up to N = 25. The first of the twoclassification schemes examined here is the (K,T) scheme, introducedby Herrick and Sinanoglu (Herrick D R and Sinanoglu O1975 Phys. Rev. A 11 97). It is shown quantitatively that itdeteriorates as N increases and Z decreases. The secondscheme is the (F,T) scheme, introduced by Komninos et al (Komninos Y,Themelis S, Chrysos M and Nicolaides C A 1993 Int. J. Quantum Chem. Suppl. 27 399), where F = N-K-1 and N,K arenot good numbers anymore. It is shown that it constitutes aconsistently better representation, especially as the relative significance of electron correlation increases, as inthe high-lying DES of H-. For the lowest intrashell andintershell states of each N-manifold, for which thecalculation incorporates the effects of electron correlation tovery high accuracy, the (F,T) `purity' coefficient is very high, close to one.

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 ↦∞.

Diagnostics of Electron Temperature and Ions Distribution in Expanding Al Plasmas Pumped by a ns-Pulsed 1.06μm Laser

Resonance lines are extensively used to diagnose electronic temperature Te and ions distribution. However, the analysis of the x-ray spectroscopy emitted from plasmas produced by a ns laser usually needs the help of a code or some assumptions. In this paper, a diagnostic idea of using line-pairs emitted from a doubly-excited state is proposed. By using the method presented in this paper, Te and the fractional population ratio of bare nuclei and H-like ions are directly obtained from the emission intensity ratios.

The effect of correcting the size-extensivity error in singles and doubles configuration interaction excitation energies

The size-consistent self-consistent singles and doubles configuration interaction method (SDCI) has been used to get size-extensive excitation energies into the framework of the SDCI space. The method is applied through a matrix dressing operator that usually accounts for the dressing effects carried by the doubles. This operator has been modified to take into account the dressing effects of singles too. The new operator is relevant when MOs other than the canonical SCF ones are used. The extensivity error correction is analyzed depending on the nature of the MOs, the inclusion or not of singles dressing, and the single or diexcited nature of the excited states. Excited states of BH, CH +, SiH 2 and CH 2 are used as FCI reference benchmarks for comparison. The addition of the singles correction appears to be chiefly relevant for doubly-excited states. The importance of the extensivity correction is evidenced in systems with a larger number of correlated electrons, such as cis-butadiene and cyclopentadiene.

Line shapes of Heβ including higher-order satellite lines for Arions in dense plasmas

We have calculated the Stark broadening of Heβ of dopant Ar ionsincluding higher-order satellite lines. Since spectator electrons are bound inhigh-lying orbitals, the higher-order satellite lines are unresolved from theparent lines. The total intensity of the higher-order satellite lines dependson the population of doubly-excited states. The probabilities for theexistence of high-lying orbitals in dense plasmas have been considered. In thespectral calculation of the higher-order satellite lines, the Stark broadeningis limited by the critical field strength, above which a bound state cannotexist, of the outermost orbital. The critical field strengths for Rydbergspectator orbitals are lower than those of low-lying orbitals. The resultsshow that the higher-order satellite lines modify total line shapes.

The band structure of double excited states for a linear chain

The energy band structure in the case of double excited states of finite spin systems (s= 1 2 ) has been investigated. A geometrical construction based on the Bethe Ansatz method for determining eigenstates has been proposed. The formula for energy spectrum in the center and at the border of Brillouin zone has been obtained. Classification of energy bands has been elaborated on and approximated dispersion law for bounded states given. Some problems with application of the Bethe Ansatz in the case of finite system has been pointed out.

Doubly-Excited States of Beryllium-Like Ions

The resonance energies and widths for doubly-excited (1s23d2, 3p4f, 3d4d) 1Ge states of beryllium-like ions are determined by calculating the density of resonance states using the stabilization method. A model potential is used to represent the interaction between the outer electrons and the core electrons. Products of Slater Orbitals are used to represent the two-electron wave functions. We present results for some lower-lying doubly-excited states for Z = 5-10. Comparisons are made with other calculations in the literature.

The role of autoionization in (1+2′)-photon above-threshold ionization of H2 molecules: Study of photoelectron energy spectrum

We have theoretically studied the effect of autoionization through doubly-excited autoionizing states on the photoelectron energy spectrum in (1+2′)-photon above-threshold ionization (ATI) of H2 molecules. We have considered excitation from the ground X 1Σg(v″=0 ,j″) state to the dissociation continuum of autoionizing states of 1Σu and 1Πu symmetry, via the intermediate resonant B 1Σu(v′=5, j′) state. These autoionizing states decay to form molecular ions in the dissociation continuum (dissociative autoionization) and in the bound vibrational levels (nondissociative autoionization) of the ionic ground state (X 2Σg), as well as free electrons carrying extra energy. We have found that the photoelectron spectrum (PES) is mainly determined by the autoionization from the doubly-excited autoionizing states of ungerade symmetry, and that it is oscillatory in nature and shows a structure similar to that observed in a recent experiment by Rottke et al. [J. Phys. B 30, 4049 (1997).]

Resonance-enhanced ionization spectroscopy of laser-cooled rubidium atoms

We report the utilization of resonance-enhanced ionization to perform high-resolution spectroscopy on laser-cooled atoms. The technique is applied to the 5S1/25P3/25DJ (J = (3/2), (5/2)) optical double resonances of rubidium atoms in a magneto-optical trap. Ions generated when atoms in the double excited state absorb a single photon are detected, together with the induced fluorescence. The two detection channels are compared for this class of high-resolution spectroscopy experiment.

New interseries interferences in doubly-excited helium

Abstract We present spectra of doubly-excited 1Po states in helium below the N=4, 6, 8, and 9 ionization thresholds measured with a resolution of ΔE≅2.0 meV. A number of hitherto unobserved interseries interferences are reported. The spectra below the N=8 and 9 ionization thresholds are assigned and analyzed using theoretical results obtained with the complex rotation method and diagonalization of sparse matrices. The resonances below the N=9 ionization threshold reveal unexpected high values and strong fluctuations of the Fano parameter q.

Spin-effects in the ionisation-with-excitation of krypton atoms by polarised electrons

Ionisation-with-excitation has been studied for the krypton excited ionic 5p 4 P 3/2 4 P 5/2 and 4 D 7/2 states which decay by emission of photons of wavelengths 465.9, 473.9 and 435.6 nm, respectively, to the lower ionic 5s 4 P 5/2 state. The integrated Stokes parameters of these photons are measured near threshold with polarised electrons and the coincidence counts between the scattered electrons and the decay photons as a function of the ejected electron energy and scattering angles are measured with unpolarised electrons. The integral polarisation data indicate that the residual ions can be aligned and oriented. The electron exchange process plays a significant role and the spin-orbit interactions are less important than the exchange process near threshold. The coincidence measurements show the interference between ionisation-with-excitation and excitation of doubly-excited states.

Potential curves for the ground states and some excited states of MgNe, Mg+Ne, and Mg+2Ne van der Waals complexes

We have estimated the potential curves of the Mg(3s2)⋅Ne(1Σ+), Mg(3s3p)⋅Ne(3Π,3Σ+), Mg(3p2)⋅Ne(3Σ−), Mg+(3s)⋅Ne(2Σ+), Mg+(3p)⋅Ne(2Π), and Mg+2(2p6)⋅Ne(1Σ+) van der Waals states by means of ab initio calculations. Similar to the analogous doubly-excited states of MgAr and MgKr, the Mg(3pπ3pπ)⋅Ne(3Σ−) state is found to be unusually strongly bound, De=548 cm−1, a bond strength which is more than 20 times that of the singly-excited Mg(3s3pπ)⋅Ne(3Π) state and even more than three times that of the Mg+(3s)⋅Ne ion. The strong bonding is attributed primarily to the lack of a Mg(3s) electron, so that all the attractive van der Waals forces can extend to smaller internuclear distances because there is no Mg(3sσ)/Ne(2pσ) exchange repulsion.

Studies of the photophysics and spectroscopy of alloxazine and related compounds in solution and in the solid state

The absorption and emission spectra and the fluorescence lifetimes and quantum yields of alloxazine and several of its N- and C- methyl-substituted derivatives, including two isoalloxazines, have been measured in a nonpolar solvent (1,2-dichloroethane), a polar aprotic solvent (acetonitrile), and a polar protic solvent (ethanol). The excited state decays are all single exponential, suggesting that only one emitting species is present in all cases. The spectroscopic data show that the emitting species is the π,π* electronic excited state corresponding to the ground state of the absorbing molecule; there is no evidence of excited state proton transfer for any of these solutes in any of the three solvents. The longer lifetimes and larger fluorescence quantum yields of the isoalloxazines compared with the alloxazines can be attributed exclusively to significantly slower rates of radiationless relaxation in the excited isoalloxazines. The remission and emission spectra of these same compounds adsorbed on cellulose are similar to the corresponding absorption and emission spectra in homogeneous solution, suggesting that the emitting species are the same in the adsorbed state as they are in homogeneous solution. However, the adsorbed excited species exhibit non-exponential temporal decay, attributed to inhomogeneities in the binding of the chromophore to cellulose. The emission spectra of polycrystalline samples of alloxazine and lumichrome suggest the possible occurrence of double intermolecular excited state proton transfer, but this interpretation is not supported by the further photophysical data obtained here.Key words: photophysics, spectroscopy, alloxazine, lumiflavin, cellulose.

28a-ZC-9 低速多価イオン衝突におけるAuger電子の角度分布測定

28a-ZC-9 低速多価イオン衝突におけるAuger電子の角度分布測定

Inherent Nodal Structures in Doubly-Excited Intrashell States of Atoms

Quantum mechanical systems are strongly constrained by symmetry. Consequently, inherent nodal surfaces are imposed on the wave functions. In this paper, the inherent nodal surfaces existing in the doubly-excited intrashell states of atoms have been investigated. The decisive effect of these surfaces on low-lying states has been demonstrated. The feature of the spectra has been explained.

Studies of the photophysics and spectroscopy of alloxazine and related compounds in solution and in the solid state

The absorption and emission spectra and the fluorescence lifetimes and quantum yields of alloxazine and several of its N- and C- methyl-substituted derivatives, including two isoalloxazines, have been measured in a nonpolar solvent (1,2-dichloroethane), a polar aprotic solvent (acetonitrile), and a polar protic solvent (ethanol). The excited state decays are all single exponential, suggesting that only one emitting species is present in all cases. The spectroscopic data show that the emitting species is the π,π* electronic excited state corresponding to the ground state of the absorbing molecule; there is no evidence of excited state proton transfer for any of these solutes in any of the three solvents. The longer lifetimes and larger fluorescence quantum yields of the isoalloxazines compared with the alloxazines can be attributed exclusively to significantly slower rates of radiationless relaxation in the excited isoalloxazines. The remission and emission spectra of these same compounds adsorbed on cellulose are similar to the corresponding absorption and emission spectra in homogeneous solution, suggesting that the emitting species are the same in the adsorbed state as they are in homogeneous solution. However, the adsorbed excited species exhibit non-exponential temporal decay, attributed to inhomogeneities in the binding of the chromophore to cellulose. The emission spectra of polycrystalline samples of alloxazine and lumichrome suggest the possible occurrence of double intermolecular excited state proton transfer, but this interpretation is not supported by the further photophysical data obtained here.Key words: photophysics, spectroscopy, alloxazine, lumiflavin, cellulose.