2p2 1D Research Articles

Energy calculations of the (2P2 1D); (3D2 1G) and (4F2 1I) doubly excited states of helium isoelectronic sequence (z ≤ 20) via the modified atomic orbital theory

We report in this paper the total energies of the 2p2 1D, 3d2 1G, 4f2 1I doubly excited states of Helium isoelectronic sequence with nuclear charge Z ≤ 20. Calculations are performed using the Modified Atomic Orbital Theory (MAOT) [1;2] in the framework of a variational procedure. The purpose of this study required a mathematical development of the Hamiltonian applied to Slater-type wave function [3] combining with Hylleraas-type wave function [4]. The study leads to analytical expressions which are carried out under special MAXIMA computational program. This proposed MAOT variational procedure, leads to accurate results in good agreement as well as with available other theoretical results than experimental data. In the present work, a new correlated wave function is presented to express analytically the total energies for each 2p2 1D, 3d2 1G, 4f 2 1I Doubly Excited States (DES) in the He-like systems. The present accurate data may be a useful guideline for future experimental and theoretical studies in the (nl2 ) systems.

Modified Atomic Orbital Calculations of Energy of the (2<i>s</i><sup>2</sup> <sup>1</sup><i>S</i>) Ground-State, the (2<i>p</i><sup>2</sup> <sup>1</sup><i>D</i>); (3<i>d</i><sup>2</sup> <sup>1</sup><i>D</i>) and (4<i>f</i><sup>2</sup> <sup>1</sup><i>I</i>) Doubly Excited States of Helium Isoelectronic Sequence from H<sup>-</sup> to Ca<sup>18+</sup>

We report in this paper the ground-state energy 2s2 1S and total energies of doubly excited states 2p2 1D, 3d2 1D, 4f2 1I of the Helium isoelectronic sequence from H- to Ca18+. Calculations are performed using the Modified Atomic Orbital Theory (MAOT) in the framework of a variational procedure. The purpose of this study required a mathematical development of the Hamiltonian applied to Slater-type wave function [1] combining with Hylleraas-type wave function [2]. The study leads to analytical expressions which are carried out under special MAXIMA computational program. This first proposed MAOT variational procedure, leads to accurate results in good agreement as well as with available other theoretical results than experimental data. In the present work, a new correlated wave function is presented to express analytically the total energies for the 2s2 1S ground state and each doubly 2p2 1D, 3d2 1D, 4f2 1I excited states in the He-like systems.The present accurate data may be a useful guideline for future experimental and theoretical studies in the (nl2) systems.

Classical Trajectory Monte Carlo simulation of coincidence experiments in electron impact ionization of helium

The state-to-state (exchange) interference of the autoionizing resonances of helium is studied in (e,2e) experiments. These studies are disturbed by the coincidence events caused by the direct ionization, so their decrease is desirable. For this reason, to mimic the experimental observation, we performed four-body classical trajectory Monte Carlo calculations. The calculations were done for 93.15 eV primary energy, where the exchange interference of the 2s2(1S) and 2p2(1D) autoionizing states of helium is expected. The yields of non-coincidence and coincidence events detected in various combinations of scattering geometry were calculated and compared with the experimental observations.Graphical abstract

Experimental study on the interference of autoionizing states of He

The interference of the low-lying doubly excited autoionizing states of helium (2s2(1S),2s2p(3P),2p2(1D) and 2s2p(1P)) is studied. In this paper we concentrate on the interference of the direct and indirect ionization (He+1s-1) in the neighborhood of the critical energy (93.15eV) of the possible state-to-state interference of the 2s2(1S) and 2p2(1D) resonances. The spectra of autoionizing and scattered electrons measured in three angular ranges at around 87–97eV primary energy are shown with the computer fitted parameters of the peaks.

(e,2e) coincidence study on the coherence of the 2s2(1S) and 2p2(1D) autoionizing states of He

SynopsisThe electron impact excitation of the autoionizing states of helium, their subsequent decay into the same He+1s-1 final ionic state, and the interference of these processes have been studied. A constant ionic state (e,2e) experiment (CIS) is performed, isolating the final state by keeping the sum of the energies of the scattered- ejected electron pairs constant. The focus of this work is on the exchange interference of the 2s2(1S) and 2p2(1D) autoionizing states of helium. At around the critical energy fast variations were observed in the CIS spectra, which indicates the presence of exchange interference effects.

State-Selective Differential Cross Section Measurements for the One-Electron Capture Process in C3+–He and C3+–Ne Systems at Elab = 33 eV

Using a crossed-beam apparatus, we measured the relative state-selective differential cross sections (DCSs) for the following reactions: C3+ (1s2 2s 2S) + He (1s2 1S) → C2+ (1s2 2s2p 1P) + He+ (1s 2S) + 10.6 eV and C3+ (1s2 2s 2S) + Ne (2p6 1S) → C2+ (1s2 2p2 1D) + Ne+ (2p5 2P) + 8.2 eV. The scattering angle studied in the laboratory frame, θlab, was from −3.0 to 24°, and the laboratory collision energy Elab was 33 eV. In both systems, the DCSs for the reaction are zero at the center-of-mass angle θcm = 0, and show a peak at a certain angle and a broad hump at larger angles. A classical trajectory analysis within the two-state approximation based on the ab initio potentials for (CHe)3+ revealed that these structures observed are ascribed to the reactions that occur in different trajectories. The peak corresponds to the reactions occurring in the outgoing part of the trajectory, and the hump is associated with the reactions occurring mainly in the incoming part of the trajectory.

Electron impact double-excitation of helium 2ℓ2ℓ' autoionizing states using the (e, 2e) technique

Coplanar (e, 2e) triple differential cross sections (TDCS) measurements are reported for the helium autoionizing doubly excited states, (2s2)1 S, (2p2)1D, and (2s2p)1P, for an incident electron energy of 250 eV and a scattering angle of −13°, corresponding to a momentum transfer of 1.06 a.u. The presence of autoionization results in a clearly visible recoil peak in the TDCS structure with a shape that is strongly dependent on the orbital angular momentum L of the resonance. The resonance contributions together with the strong background of direct ionization processes lead to a complicated asymmetric structure of the resonance profile in the TDCS.

The Stark effect in autoionizing doubly excited states of helium below the He+(n=2) threshold

In this paper, we have dealt with the problem of the effects of an external dc field on doubly excited autoionizing states of helium. The prototype 2s2 1S, 2s2p 1Po (ML=0, ML=±1), 2p2 1D (ML=0, ML=±1 and ML=±2) and 2p2 1S doubly excited states are considered. The major correlation effects and the coupling of the autoionizing states to field-induced open channels are taken into account. The complex eigenvalues of appropriately constructed non-Hermitian matrices are computed for both weak and strong electric fields. The smooth variation of the width Γ(n) as a function of the field strength F shows the influence of the nearby strongly coupled states. An analysis, based on second-order perturbation theory, shows that for small field strengths, the variation of Γ(n) is a quadratic function of F. The polarizabilities and hyperpolarizabilities of these states are also calculated.

(e, 2e) experiments on (2s2)1S, (2p2)1D and (2s2p)1P autoionizing levels of helium in the direction of the binary lobe

The (e, 2e) triple differential cross sections are measured for the electron-impact excitation of the (2s2)1S, (2p2)1D and (2s2p)1P autoionizing transitions in helium. The experiments were performed under coplanar asymmetric kinematics, at an incident electron energy of 250 eV, and for a scattered electron detection angle of −13° in the direction of the binary lobe. The results are compared with the two available experimental data sets under similar kinematical conditions, consequently removing questions raised by the theory on these earlier results. We present evidence that the spectrum for the (2p2)1D and (2s2p)1P states might be dependent on the energy resolution of the scattered-electron energy analyser, especially in the binary region, where the strong interference between the two processes results in the observed broad asymmetric profiles. This possible distortion is not solely related to the present work.

Complex Fano asymmetry parameters for helium L = 0, 1, 2 autoionizing levels excited by electron impact

Theoretical Fano q-parameters for He autoionizing states excited by electron impact are presented, as extracted from first- and second-order hybrid distorted-wave Born + R-matrix calculations. It is found that the q-parameters for (2s2)1S, (2p2)1D, and (2s2p)1P from the first-order calculations are essentially real quantities, while those from the second-order calculations are complex but with a real part similar to the first-order values. These findings are interpreted in terms of the relative phases of the first- and second-order amplitudes.

Recent out-of-plane (e,2e) experiments on autoionizing levels of helium

Out-of-plane (e, 2e) measurements and calculations are reported for the helium autoionizing levels (2s2)1S, (2p2)1D, (2s2p)1P, and for direct ionization [1]. While the recoil peak almost vanishes in the angular distribution for direct ionization, it remains significant for the autoionizing levels and exhibits a characteristic shape for each orbital angular momentum L = 0, 1, 2. These findings can qualitatively be explained by an L-dependent addition to the ionization amplitude, but only a second-order model in the projectile-target interaction can quantitatively reproduce the observed magnitudes of the recoil peaks. We present the data as both angular distributions and energy spectra for the resonances.The experimental part of this work is being carried out using an existing (e,2e) apparatus modied to allow the electron gun (see figure 1) to move on the surface of a (mathematical) cone [2]. This permits the measurement of out-of-plane (e,2e) angular distributions, for a full 360, using a special geometry that allows out-of-plane conditions to be combined with the binary peak in a single measurement. Details of the apparatus will be presented.

Calculation of the ground-state energy, the first ionization energy and the radial correlation expectation value for He-like atoms

Combining perturbation theory with the Ritz variation method, an analytical approach to the ground-state energy, the first ionization energy J(1S0) and the radial correlation expectation value ⟨r12−1 ⟩ (1S0) for He-like atoms is given in this paper. The possibility to extend our present analytical model to the doubly excited states (nl)2 is illustrated in this work by the calculation of the total energies and the radial correlation expectation value for the 2p2 1D, 3p2 1D, 4p2 1D and 5p2 1D singlet doubly excites states of He-like atoms with Z⩽12. The results presented in this paper indicate that the present analytical approach can usefully be performed to show quantitatively the importance of electron correlations in the ground-state and in the doubly excited states mainly for high-Z helium isoelectronic series.

The Singlet Doubly Excited (nl)2 States of Helium-Like Systems

The calculations of the energies of the singlet doubly excited states 2p2 1D, 3d2 1G, 4f2 1I of helium-like systems we have done in our previous paper [Biaye et al, Eur. Phys. J. D 13 21 (2001)] are extended to the other singlet doubly excited (nl)2 states with n ≤ 4. The energies are calculated in the framework of the variation method by using some special forms of Hylleraas-type wave functions with a real Hamiltonian. The results which we have obtained are in good agreement with some experimental data and other theoretical results.

Differential cross sections for double excitation of theautoionizing states of helium by 100-150 keV proton impact

Autoionizing (2s2) 1S, (2p2) 1D and (2s2p) 1P resonances in projectile energy loss spectra arestudied theoretically for protons scattered on atomic helium.The differential resonance yield, as a function of the scatteringangle, is the quantity of primary attention. The effects of theCoulomb interaction in the final state and the projectile-coreinteraction on the differential resonance yield are studied.Comparison with the experimental data of Schulz et al (1995)(Schulz M, Htwe W T, Gauss A D, Peacher J L and Vajnai T 1995 Phys. Rev. A 51 2140-50) is presented. Comparison is also made withcalculations for differential cross sections of doubleexcitation.

Zero-degreetarget electron spectroscopy: autoionizing resonances of heliumexcited by fast H+, He+ and He2+ impact

Two-electron excitation and decay of the autoionizing (2p2)1D and (2s2p)1P states of helium in collisionswith fast protons and helium ions have been studied usingzero-degree target electron spectroscopy. The energy resolution ofelectron emission spectra is 80 meV. Experimental spectra wereprocessed using a parametrization with allowance for theCoulomb interaction in the final state (CIFS) between theejected electron, the scattered ion and the recoil helium ion.The Shore formula was applied as well. Calculations have beencarried out with inclusion of CIFS in both direct and resonantionization amplitudes and within an expansion of a two-electronexcitation amplitude in powers of projectile-target interactionup to the second order. Influence of the three-body Coulombinteraction and effects of the charge and mass of theprojectiles are studied.

Excitation of lowest autoionizationstates in helium-like ions by photon scattering

High-frequency photon scattering by a two-electron ion withexcitation of singlet autoionization states located below thefirst excited level of the respective one-electron ion areconsidered. Angular distributions of scattered photons and totalcross sections are calculated for transitions to 2s2p(1P) and 2p2(1D) autoionization states (AIS)from the ground state of helium-like ions (the transitions totwo lower 1S AIS were investigated earlier). In the zeroapproximation electrons are described by Coulomb functions andthe inter-electron interaction is taken into account in thefirst perturbation order.

Electron Elastic Scattering Resonances in the Collision of Fast Hydrogenic Ions with Molecular Hydrogen

Absolute double differential cross sections for the electron production at zero degree laboratory observation angle were measured for high velocity hydrogenic carbon, nitrogen, oxygen and fluorine ions on molecular hydrogen. The energies of these ions were chosen so the elastic scattering resonance 2p2 1D for each case can be clearly observed near the peak of the binary encounter electron distribution. Close coupling R-matrix calculations of elastic differential cross sections of electron impact of these ions were related to the measured ion-atom cross sections by using the elastic scattering model (ESM). Excellent agreement was found between theory and experimental data.

Excitation of autoionizing states of helium by 100 keV proton impact: II. Excitation cross sections and mechanisms of excitation

Mechanisms of two-electron excitation of the (2s2)1S, (2p2)1D and (2s2p)1P autoionizing states of helium are studied both experimentally and theoretically. It is shown that an explicit introduction of a kinematic factor, with a process-specific phase leads to a productive parametrization of experimental cross sections of ionization, allowing one to extract cross sections of excitation of autoionizing states. Using a new fitting procedure together with the proposed parametrization made it possible to obtain the excitation cross sections and magnetic sublevel population from electron spectra as well as, for the first time, to resolve the contribution of resonance and interference components to resonance profiles. Interference with direct ionization is shown to contribute significantly into resonance formation even for backward ejection angles. We demonstrate theoretically that the excitation cross sections thus extracted from experimental electron spectra hold information about the interaction of autoionizing states with an adjacent continuum.

High resolution RTE measurements at 0° using a hemispherical analyser with lens and 2-D PSD

First high resolution measurements using a new electron spectrograph at 0° to the beam direction are reported. The new apparatus consists of a hemispherical analyser with a mean radius of 101.6 mm, a 4-element focusing lens and 40 mm diameter 2-D position sensitive detector (PSD). Electrons are decelerated and focused in the lens prior to analysis to improve the energy resolution. As a test of the apparatus in deceleration mode, we measured the differential cross section of the F7+(2p2)1D state produced by Resonance Transfer Excitation (RTE) in collisions of 21.78 MeV F8++ H2. An effective energy resolution of 0.25% was obtained using a deceleration factor of 4. Good agreement with known cross section values was found. Presently, our spectrograph with a maximum count rate of about 4 kHz (limited by dead-time considerations) is more than 15 times faster than the conventional tandem zero-degree spectrometer at Kansas State University, while using a factor of 20 lower intensity beams.

Double Excitation of Helium Atoms by Impact of Protons and Highly Charged Ions

The impact parameter version of the four body-symmetric Eikonal approximation (SE2) is introduced to study double excitation of dielectronic atoms by heavy ions at high impact energies. The total cross sections are calculated for double excitation to the 2p2 (1D) state and the sum of the 2p2 (1D) and 2s2p(1P) states of helium atoms by impact of protons, Cq+ (q = 4–6) and Fq+ (q = 7–9) ions. Theoretical results are compared with measurements and other existing calculations.