Calculations of D‐wave bound states and resonance states of the screened helium atom using correlated exponential wave functions

We have investigated the effects of screened Coulomb (Yukawa) potentials on the bound ^1,3D states and the doubly excited ^1,3 D^e resonance states of helium atom using highly correlated exponential basis functions. The Density of resonance states are calculated using stabilization method. Highly correlated exponential basis functions are used to consider the correlation effect between the charged particles. A total of 18 resonances (nine each for ¹ D^e and ³ D^e states) below the n = 2 He ⁺ threshold has been calculated. For each spin states, this includes four members in the 2pnp series, three members in the 2snd series, and two members in 2pnf series. The resonance energies and widths for various screening parameters ranging from infinity to a small value for these ^1,3 D^e resonance states are reported along with the bound‐excited 1s3d ^1,3 D state energies. Overall behavior of the spectral profile of 1s3d ¹D state of helium atom due to electron‐electron and electron‐nucleus screening are also presented. Accurate resonance energies and widths are also reported for He in vacuum. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Complex‐scaling calculations for resonance states of he with screened coulomb potentials

The doubly excited ¹S^e, ¹P^o, and ¹D^e resonance states of helium atom with screened Coulomb potentials are investigated. The complex scaling method with configuration interaction type basis functions are employed to extract the resonances associated with the He⁺(N = 2, 3, and 4) thresholds. 18 resonances (six below each of the He⁺ threshold) for each angular‐momentum state are calculated. The results lying below the He⁺(N = 2) threshold are in good agreement with previous calculations by the stabilization method with correlated basis wave functions. The ¹P^o and ¹D^e resonance states lying below the He⁺(N = 3 and 4) thresholds in the screening environment are reported for the first time. © 2013 Wiley Periodicals, Inc.     

Doubly-excited 1,3Po autoionization states of He between the N = 4 and N = 6 thresholds of He+ ions

The method of complex-coordinate rotation is used to investigate the doubly-excited ^1,3P^o autoionization states of He between the N = 4 and N = 6 thresholds of He⁺ ions. Resonance energies and total widths for 51 ¹P^o and 51 ³P^o states are reported in the present work. For the singletspin and triplet-spin states, lower-lying resonances for all nine Rydberg series converging on the He⁺ (N = 5) threshold are calculated. For resonances below the He⁺ (N = 6) threshold, we report lower-lying states for eleven and ten Rydberg series for the singlet-spin states and triplet-spin states, respectively. Our results are compared with the experimental observations and with other theoretical calculations when available.     

Resonances in helium atoms associated with theN=4 andN=5 He+ thresholds

Some doubly excited autoionising states of helium atoms converging on theN=4 andN=5 He⁺ thresholds are calculated by use of a method of complex-coordinates. States withL≧2 and with parities of (?1) ^L and (?1) ^L+1 are calculated by using products of Slater-orbital type wave functions with expansion lengths up to 319 terms. Resonance parameters (both resonance energy and autoinoisation width) are calculated for states with angular momentum up toL=7 forN=4 resonances, andL=8 forN=5 resonances.     

Effect of Debye plasma on the doubly excited states of highly stripped ions

Pilot calculations have been performed to study the effect of surrounding plasma on several doubly excited states for a few astrophysically important, highly stripped ions of helium isoelectronic sequence Al¹¹⁺, Si¹²⁺, P¹³⁺, S¹⁴⁺, and Cl¹⁵⁺. The transitions from 1s²:¹S^e → 2s²:¹S^e, 2p²:¹D^e, 2s2p:¹P^o, 2s3d:¹D^e and 2p3d:¹F^o are studied. The effect of the plasma background is taken care of using the Debye screening model which admits of a wide variety of plasma conditions. Transition energies as well as the analytical wave functions of the doubly excited states have been obtained from a study of the pole positions of the collective oscillation modes in the two‐electron charge cloud under a time‐dependent harmonic perturbation. The response properties of the system are analyzed from the linearized version of a suitably constructed variational functional. Most of the calculated data are new. Our results agree well with the relatively few existing experimental and theoretical data for the free ions. The general trend of the results show systematic behavior with respect to increased plasma strength, and the data may be useful from the astrophysical viewpoint. The doubly excited state wave functions have been used to calculate the Coulomb repulsion integrals to check their consistency and may be useful for evaluating other physical properties connected with transitions and also estimating the rate coefficients for dielectronic recombination processes, which play a major role in the diagnostic determination of high‐temperature plasmas. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Periodic orbits in atomic hydrogen exposed to circularly polarised laser light

Exact circular periodic orbits for a hydrogen atom in a strong circularly polarised laser field are derived. A stability analysis shows one orbit to be stable or unstable depending on the laser parameters, whereas the other orbit is always unstable. These orbits are expected to manifest themselves as resonances in laser assistede ^? ?H ⁺ scattering. The binding mechanism for these resonances is provided by the trapping of the quantum mechanical wave function onto the neighbourhood of a classical periodic orbit. This mechanism is analogous to that for a Wannier ridge resonance in a doubly excited two-electron atom.     

Fock space multireference coupled cluster theory: Study of shape resonance

The complex absorbing potential along with correlated independent particle potential (CIP) Fock space multireference coupled cluster method is used for the study of resonances. We have studied shape resonance of e^?‐ F₂, e^?‐ N₂O and e^?‐CO molecules. In particular, we have studied e^?‐ F₂ scattering at different bond lengths to know whether is bound at the equilibrium bond length of F₂. © 2013 Wiley Periodicals, Inc.     

Calculations of the energies of resonances for atoms and ions with two and three electrons by the stabilization method

An approach to calculating the energies and widths of resonances for atoms and ions with two and three electrons was developed on the basis of the stabilization method. The energies of 28 resonances of ⁿ S symmetry with the spin multiplicities n = 1, 2, 3, and 4 were calculated for H^?, He, Li⁺, He^?, and Li. The energies of several resonances were obtained for the first time. Four resonance widths for H^?, He, and He^? were determined. The calculation results are compared with experimental data and calculations performed by other authors. Very close agreement was obtained for resonance energies (uncertainties of from 0.005 to 0.5 eV) and widths (uncertainties of ～10–20%).     

Resonance photoionisation of the metastable 21,3 S helium near then=2 andn=3 excitation thresholds of He

Diagonalisation calculations of line profile parametersq for a few^1,3 P resonances in the photoionisation of singlet and triplet metastable helium are performed near then=2 andn=3 excitation thresholds of He⁺. From the analysis and comparison of calculated values, the symmetric and asymmetric characters of resonance lines near then=2 andn=3 thresholds respectively are shown. In addition, near then=3 excitation threshold, a comparison is made with helium ground-state photoionisation for a few¹ P resonances, together with a discussion on the character of changes occurring in the line profile parameters.     

Doubly excited3Se,3De and3Ge states of two-electron atomic systems

Summary Time-dependent perturbation theory has been applied to calculate the doubly excited triplet statesNsns:³S^e,Npnp:³D^e andNdnd:³G^e (N=2, 3, 4,n=N+1, ... ,5) for He, Li⁺, Be²⁺ and B³⁺. A time-dependent harmonic perturbation causes simulataneous excitation of both the electrons with a change of spin state. The doubly excited energy levels have been identified as the poles of an appropriately constructed linearized variational functional with respect to the driving frequency. In addition to the transition energies, effective quantum numbers of these doubly excited states have been calculated and analytic representations of their wave functions are obtained. These are utilized to estimate the Coulomb repulsion term for these states which checks the consistency of the wave functions. These wave functions may also be used for calculating other physical properties of the systems.     

Triple differential generalized oscillator strength of direct and resonance He(e, 2e)He+ reaction at high incident energies

The triple differential cross section and triple differential generalized oscillator strength of the direct and resonance He(e, 2e)He⁺ reaction in the first Born approximation for incident energiesE ₀≥4keV are calculated. For the direct (e, 2e) process our results obtained in definite structure models of the atom are found to be in good agreement with the available experimental data and theoretical estimates. The resonance profiles calculated in these models exhibit a complicated structure formation of overlapping¹ P and¹ D autoionization states (AIS) excited in the (e, 2e) reaction. The specific kine-matical conditions, when the overlap and interference of the¹ P and¹ D resonances are small and the¹ P and¹ D AIS yields can be measured separately, are discussed. It is also shown that in a certain range of ejection angles and at large momentum transfers (Q>2au) the yield of the¹ D AIS dominates over the¹ P resonance yield.     

Bound states of helium atom in dense plasmas

We have obtained the bound 1s^{2 1}S, 1s2s ^1,3S, and 1s2p ^1,3P states energies of helium atom in dense plasma environments in accurate variation calculations. A screened Coulomb potential to represent the Debye model is used for the interaction between the charged particles. A correlated wave function consisting of a generalized exponential expansion has been used to take care of the correlation effect. The 1s^{2 1}S, 1s2s ^1,3S, and 1s2p ^1,3P states energies along with the ionization potential, the energy splitting between the 1s2s ³S, and 1s2s ¹S states, transition energies between the ground state and low‐excited states of He estimated for various Debye lengths, are reported. The results show high degree of accuracy even under strong plasma conditions. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

High lying energy positions of doubly (2pns) P° and (2pnd) P° excited states of the beryllium atom

The Screening Constant by Unit Nuclear Charge (SCUNC) method is used to study (2pns) ^1,3P° and (2pnd) ^1,3P° autoionizing states of the beryllium atom. Energy positions are reported up to n=20. In addition, resonance widths of the (2pns) ¹P° states also presented. The current results compared very well to available theoretical and experimental literature values up to n=15. The accurate data presented in this work may be of interest for future experimental and theoretical studies in the photoabsorption spectrum of Be.     

Exploiting the analyticity of Schrödinger operators: Theory and the computation of partial cross sections

The idea of dilation, or dilatation, analyticity with respect to complex scaling of the interparticle distances for nonrelativistic atomic or molecular electronic Hamiltonians is now over 20 years old and the first major reviews are just over 10. The method continues to be a fruitful source of new theoretical and computational results. Under the scale transformation r → re^iθ, the usual “spectrum” of bound states is exactly preserved, and scattering continua are “rotated” off the real axis by an angle of −2Re(θ) about their respective thresholds. Useful features of this transformation are (1) that resonances are exposed, and, thus, (complex) resonance eigenvalues are easily calculated as the wave functions are L², and standard results of Kato-type perturbation theory can thus be applied to them; (2) that utilization of this technique to study atoms in ac and dc fields was an early, and still evolving extension of the original theory; and (3) the fact that the “continua” are rotated off the real energy axis allows scattering information to be extracted from computations carried out entirely L² in bases as the usual resolvents of scattering theory are no longer singular on the real axis. After a brief survey of the technique and its applications, these ideas are illustrated by discussion of positive energy-bound states and resonances, the extension of the theory to include the dc Stark effect, and a review of the resolution of the initially perplexing problem of atomic and molecular bound states in continua. These theoretical results are followed by a discussion of some very recent computational results, allowing computation of atomic partial photoionization cross sections with no specific coordinate space enforcement of boundary conditions, a highly advantageous situation for calculation of the partial cross section for three-body breakup, as in the process ℏ ω + He → He²⁺ + e⁻ + e⁻. © 1996 John Wiley & Sons, Inc.     

Ground state for two‐electron and electron‐muon three‐body atomic systems

In this article, the angular correlated configuration interaction method previously introduced by some of the authors is extended to three‐body atomic systems with general masses. A recently proposed angularly correlated basis set is used to construct ground state wave functions which: (i) satisfy exactly Kato cusp conditions at the two‐body coalescence points; (ii) have only linear coefficients; and (iii) show a fast convergency rate for the energy. The efficiency of the construction is illustrated by the study of the negatively charged hydrogen‐like systems (^∞H^?, T^?, D^?, ¹H^?, and Mu^?), neutral helium‐like systems (e^?e^{? ∞}He⁺²,e^?e^{? 4}He⁺², e^?e^{? 3}He⁺², e^?μ^{? ∞}He⁺², e^?μ ^?4He⁺², and e^?μ^{? 3}He⁺²), and positively charged lithium‐like systems (e^?e^{? ∞}Li⁺³, e^?e^{? 7}Li⁺³, e^?e^{? 6}Li⁺³, e^?μ^{? ∞}Li⁺³, e^?μ^{? 7}Li⁺³, and e^?μ^{? 6}Li⁺³). The ground state energies and other mean values are compared with those given in the literature, when available. Wave functions with a moderate number of (20 maximum) linear coefficients are given explicitly; they are sufficiently simple and accurate to be used in practical calculations of atomic collision in which multidimensional integrations are involved. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Study of nonradiative decay properties following resonant double excitation to the [1s2p]nln′l′ states of Ne atom using soft X-ray undulator radiation

We investigate the nonradiative decay properties of resonantly photoexcited [1s2p]nln′l′ (n,n′≧3) states of Ne atom, where square brackets indicate hole states, using soft X-ray undulator radiation. Partial ion-yield spectra for the Ne²⁺–Ne⁴⁺ ions were measured in the region of double excitation resonance by means of time-of-flight spectrometry. The Ne³⁺ partial ion-yield spectrum has been found to reveal resonant enhancements at the energy positions of doubly excited states, which implies the most plausible decay channels leading to the third step Auger processes. Energy diagram of the excited and relaxed states associated with the [1s2p](³P)3p² doubly excited state of the neutral Ne as well as the Ne ions was calculated based on the multiconfiguration Dirac–Fock (MCDF) method in order to interpret the possible nonradiative decay channels. The low-energy electron spectrum originated from the second/third step Auger processes was preliminarily measured to show a rich structure induced at the [1s2p](³P)3p² double excitation resonance.     

Theoretical investigation on the detailed mechanism of the OH‐initiated atmospheric photooxidation of o‐xylene

The reaction mechanism for o‐xylene with OH radical and O₂ was studied by density functional theory (DFT) method. The geometries of the reactants, intermediates, transition states, and products were optimized at B3LYP/6‐31G(d,p) level. The corresponding vibration frequencies were calculated at the same level. The single‐point calculations for all the stationary points were carried out at the B3LYP/6‐311++G(2df,2pd) level using the B3LYP/6‐31G(d,p) optimized geometries. Reaction energies for the formation of the aromatic intermediate radicals have been obtained to determine their relative stability and reversibility, and their activation barriers have been analyzed to assess the energetically favorable pathways to propagate the o‐xylene oxidation. The results of the theoretical study indicate that OH addition to o‐xylene forms ipso, meta, and para isomers of o‐xylene‐OH adducts, and the ipso o‐xylene adduct is the most stable among these isomers. Oxygen is expected to add to the o‐xylene‐OH adducts forming o‐xylene peroxy radicals. And subsequent ring closure of the peroxyl radicals to form bicyclic radicals. With relatively low barriers, isomerization of the o‐xylene bicyclic radicals to more stable epoxide radicals likely occurs, competing with O₂ addition to form bicyclic peroxy radicals. The study provides thermochemical data for assessment of the photochemical production potential of ozone and formation of toxic products and secondary organic aerosol from o‐xylene photooxidation. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Doubly excited1 P 0 resonances in He

Doubly excited¹ P ⁰ autoionizating states in He below then=2 threshold of He⁺ ions are calculated by use of a method of complex-coordinate rotation. Hylleraas type wave functions are used to calculate resonance parameters for intrashell states (the two electrons occupy the same shell), and products of Slater-orbitals are used for intershell states (the two electrons occupy different shells). A total of 15 resonances below then=2 He⁺ thresholds are reported in this work. This includes six members in the 2snp ₊ (2≦n≦7) series, five members in the 2snp _? (3≦n≦7) series, and four members in the 2pnd (3≦n≦6) series. Comparisons are made with other theoretical calculations and with experimental observations.     

Low‐lying singlet excited states of isocyanogen

Recent photofragment fluorescence excitation (PHOFEX) spectroscopy experiments have observed the ùA″ singlet excited state of isocyanogen (CNCN) for the first time. The observed spectrum is not completely assigned and significant questions remain about the excited states of this system. To provide insight into the energetically accessible excited states of CNCN, optimized geometries, harmonic vibrational frequencies, and excitation energies for the first three singlet excited states are determined using equation‐of‐motion coupled‐cluster theory with singles and doubles (EOM‐CCSD) and correlation‐consistent basis sets. Additionally, excited state coupled‐cluster methods which approximate the contributions from triples (CC3) are utilized to estimate the effect of higher‐order correlation on the energy of each excited state. For the ùA″ state, our best estimate for T₀ is about 42,200 cm^?1, in agreement with the experimentally estimated upper limit for the zero‐point level of 42,523 cm^?1. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008