Correlations In Initial State Research Articles

Double ionization of He and Li by 95-MeV/amu N7+ impact.

The cross-section ratio for double-to-single ionization has been investigated for collisions of 95-MeV/amu ${\mathrm{N}}^{7+}$ with He and Li target atoms. The measured values for Li and He are equal within the experimental uncertainties. First-order perturbation theory suggests that double ionization of Li is dominated by electron-nuclear interaction, whereas double ionization of He is dominated by electron-electron interactions such as shake-off and initial-state correlation. First-order perturbation theory can describe the ratio of double to single ionization of ${\mathrm{N}}^{7+}$+Li at 95 MeV/amu within the experimental uncertainties.

Angular distribution in the 1 s → 3 p coherently excited resonant KLL Auger spectrum in neon

Angular anisotropies, energies, and relative intensities have been studied for the 1 s → 3 p resonant KLL spectrum in neon. The resonant excitation of the 1 s2 p 22 p 63 p configuration leads to a multiplet of four levels with J = 0, 1, 2, and an energy splitting ≤ 35 meV which is much smaller than the natural level widths of about 250 meV. Thus, the various states of the multiplet are excited (more or less) coherently. To obtain the angular distribution of the Auger lines, knowledge of the density matrix is required. This matrix includes all information about the specific excitation process, whereas the dynamics of the autoionization is described by the relative intensities and Auger angular parameters A 2. Multiconfiguration Dirac-Fock wave functions have been used to calculate this set of coefficients in an intermediate coupling scheme including initial and final state correlations. The use of these data in the interpretation of an angular distribution measurement is briefly discussed.

Sixfold differential cross sections for atomic helium, magnesium, and calcium in ( gamma,2e) experiments.

We have calculated sixfold differential (\ensuremath{\gamma},2e) double-photoionization cross sections (6DCS) for helium and for the alkaline-earth atoms Mg and Ca. We use configuration-interaction wave functions for the initial state and two sets of wave functions for the final state: (1) smoothly joined final-state wave functions corresponding to the Coulomb potential at large r and to a pseudopotential at small r and (2) wave functions that are the same as (1) but multiplied by the factor [1-exp(-${\mathit{r}}_{12}$/${\mathit{r}}_{\mathit{C}}$)] to account for the singularity at ${\mathit{r}}_{12}$=0 and the short-range correlation in the final state. To see the effects of the initial-state correlation on the 6DCS, sample calculations are performed with Hartree-Fock initial-state wave functions. In contrast to the results of Le Rouzo and Dal Cappello [Phys. Rev. A 43, 318 (1991)], our 6DCS plots for cases in which both electrons escape with equal energy \ensuremath{\varepsilon}=\ensuremath{\varepsilon}'=15 eV differ significantly from the cross sections for the case in which the electrons escape with different energies \ensuremath{\varepsilon}=5 eV and \ensuremath{\varepsilon}'=25 eV. The results show that approximate correlation by means of inclusion of a Coulomb hole into the final-state wave function has a significant effect in some cases for Mg and Ca, but has little effect in the cases studied for He. Comparison with the results of a very recent experiment is made.

Triply differential (e,2e) cross sections for He from threshold to 50 eV above

Distored wave calculations of the triply differential cross sections for electron-impact ionization of He are presented for electrons sharing ≤50 eV excess energy (E x ) and having the coplanar, θ 12 =π geometry. The results are in good agreement with absolute experimental measurements of T. Rosel et al. [Phys. Rev. A 46 (1992) 2539-2552] and of A. J. Murray, M. B. Woolf, and F. H. Read [J. Phys. B 25 (1992) 3021-3036]. For final state electrons sharing 2 eV excess energy equally, many-body perturbation theory corrections to the author's first order (e,2e) triply differential cross sections [Phys. Rev. A 45 (1992) 4588-4603] are also presented. These results indicate that singlet-triplet interchannel coupling effects in the final state are very significant; that initial state correlations are significant near the perpendicular plane, i.e., θ 1 =θ 2 =π/2; and that the polarization effects we include are insignificant. Finally, comparison of our first order results with the semiclassical quantal theory results of D. S. F. Crothers [J. Phys. B 19 (1986) 463-483] shows excellent agreeement for excess energies E x ≥2 eV and for θ 1 =θ 2 =π/2; for E x <2 eV, the two results diverge as E x →0, indicating that experimental tests of the Wannier-Peterkop-Rau theory of three-body Coulomb breakup should be carried out in this energy region

Recent Advances in Electron Momentum Spectroscopy

Abstract The flexibility of the (e, 2e) technique or "electron momentum spectroscopy" (EMS) in obtaining information on the electronic structure of atoms, molecules, and solids is demonstrated. High-resolution EMS measurements for argon, including the first measurements of momentum profiles belonging to the 2P0 and 2De -manifolds, are used to demonstrate the technique for atomic targets. The d-wave transitions in argon are entirely due to initial-state correlations. The first (e, 2e) measurements on an excited target, and also on an oriented target, are discussed. Sodium atoms are pumped to the ml = +1 state of the excited 3p-state by σ+ -light from a laser. The (e, 2e) measurements on this excited state are in excellent agreement with the momentum density given by the 3p (ml - 1) Hartree-Fock wavefunction. The recent measurements of the valence-electron momentum distributions for ethyne, as well as some earlier results for water, are used as an example of the application of EMS to the study of molecules. The application of the EMS technique to measure spectral momentum densities in condensed-matter targets is demonstrated by some recent results on amorphous carbon.

Correlation in the photoionization process: the relaxed Hartree-Fock method

Various concepts which arise in connection with correlation effects in photoionization are examined through a simple example: the He Is cross-section calculation. The classification of correlation is examined from the viewpoint of the frozen orbital and relaxed Hartree-Fock models. It is demonstrated that within the frozen orbital model the definition of initial and final ionic state correlation is somewhat arbitrary. Within the relaxed Hartree-Fock framework bound state correlation naturally subdivides into three categories: initial state, relaxation, and final ionic state. The He diagram photoionization cross section, calculated at various levels of approximation from hv = 26 to 54 eV, is presented and discussed. It is shown that the inclusion of initial state correlation and relaxation are necessary for accurate results.

Electron momentum spectroscopy of atoms, molecules and solids

Electron Momentum Spectroscopy (EMS) is the application of the (e,2e) technique to obtain detailed information on the dynamic structure of atoms, molecules, and condensed matter. The ability of EMS to provide wavefunction mapping, in terms of the independent particle representation of a manybody system in momentum space, is discussed for valence electrons. The quantitative measurement of correlation effects in both the initial and final electron states is demonstrated. Correlations can significantly change the momentum density distribution, as well as giving rise to transitions forbidden in the independent particle approximation. The case of argon is discussed in some detail since both initial state correlations (d-wave correlations) and final state correlations (mainly in the 3s −1 manifold) are present. The influence of relativistic effects in outer valence momentum densities is demonstrated for Xe and Pb. The importance of correlations in the outer valence orbitals of some molecules is discussed with particular reference to H 2O. The first (e,2e) results on an excited target and also an oriented target are discussed, as are some recent high resolution measurements on amorphous carbon.

Angular distributions in the double ionization of helium by electron impact.

Electron-impact double ionization of helium is investigated theoretically for the case of high incident energies (5--10 keV). An {ital ab} {ital initio} calculation is proposed, which includes almost full correlation in the initial state and partial correlations in the final state. The results of this model are compared with those given by other theories in the framework of the wave-function approach. We show that the correlations in the final state must be taken into account for the evaluation of the angular distributions.

How to Explain the Difference between (?, e) and (e, 2e) Spectroscopic Factors

It is shown that the relative line intensity of the main and satellite lines in the atomic shell ionisation spectrum depends significantly on the mechanism responsible for the removal of the electron. This dependence is explained by the influence of many-electron correlations in the initial state of the atom to be ionised, which is considerable when the momentum transferred to the ion is large. This is the case for photoionisation, i.e. the (y, e) reaction under the condition of large photon energy. On the contrary, in electron momentum spectroscopy, such as the symmetric noncoplanar (e, 2e) reaction, the momentum transferred to the ion is typically small and the initial atomic state correlations are negligible. It follows from this that the spectroscopic factors of the different final states of the ion, as defined in the usual way, can be measured only for the (e,2e) reaction, whereas a more involved interpretation is necessary for the (y, e) reaction. Comparison of the calculated spectroscopic factors of Ar II and Xe II 2S ion eigenstates with recent (Y,e) and (e,2e) experimental data has confirmed this conclusion.

Initial- and final-state correlation in the valence-shell Auger spectrum of Rb.

The ${\mathit{M}}_{4,5}$NO and ${\mathit{M}}_{4,5}$NN Auger spectra in Rb have been studied both experimentally and theoretically in order to understand the effect of the outermost 5s electron on the valence-shell hole states in Rb. Transition energies were obtained from extensive multiconfiguration Dirac-Fock calculations and the line intensities from our relativistic single-channel Auger-rate code. The ${\mathit{M}}_{4,5}$NO transitions were reproduced by intermediate-coupling calculations quite well indicating that the initial-state correlation with the 5s electron present is weak. For the ${\mathit{M}}_{4,5}$NN transitions our single-channel calculations revealed dramatic effects of the 5s electron on the configuration interaction in the final ionic states. Even the most elaborate calculations failed, however, to give a basis for complete identification of the observed spectral features.

(e,2e) Studies of Atoms ? Some Recent Developments

Some recent work on (e,2e) collisions in atoms is reported. The first (e,2e) results on an excited target and also on an oriented target are discussed. Sodium atoms are pumped to the m/ = +1 state of the excited 3p state by 0"+ light from a laser. The (e,2e) measurements are then performed on this excited state. The results are in excellent agreement with the momentum density profile given by the 3p(m/ = 1) Hartree-Fock wavefunction. High resolution electron momentum spectroscopy measurements are reported for argon. The first momentum profiles for excited Ar ion states belonging to the 2po and 20e manifolds are obtained. The latter are entirely due to initial state correlations. Comparison is made with several many-body calculations. The importance of core quadrupole (10) excitations is demonstrated. Although the 2se manifold is dominated by final state correlations, the momentum profile to the 4s 2S ion state in the 2Se manifold also shows the influenee of initial state correlation effects. The third series of measurements examines correlations in the autoionising region of helium, encompassing the (2s2)1 S, (2s2p)3p, (2p2)! 0 and (2s2p)! P resonances, at 100, 200 and 400 eV incident electron energies. Measurements, with an energy resolution of 150 meV, were taken at a number of scattered electron angles over an extended range of ejected electron angles, encompassing both the binary and recoil regions. The data show very strong correlations between the resonance amplitudes and the direct ionisation amplitudes.

Satellite structure in the argon valence shell by electron-momentum spectroscopy.

Momentum distributions and spectroscopic factors are obtained in a high-resolution study of argon at 500, 1000, and 1500 eV by electron-momentum spectroscopy. The shapes and relative magnitudes of the 1500-eV cross sections are in excellent agreement with the results of a distorted-wave impulse approximation calculation. The final states belonging to the $^{2}\mathrm{S}^{\mathrm{e}}$ and $^{2}\mathrm{P}^{\mathrm{o}}$ manifolds are identified and their spectroscopic factors (pole strengths) are obtained. These are found to be independent of energy and momentum in the range 0.1--1.9 a.u. within experimental error, although some momentum dependence is observed for the spectroscopic factor leading to the 4s $^{2}S$ ion state due to initial-state correlations. The first momentum profiles for excited states belonging to the $^{2}\mathrm{P}^{\mathrm{o}}$ and $^{2}\mathrm{D}^{\mathrm{e}}$ manifolds are obtained. The latter are entirely due to initial-state correlations. Comparison is made with several many-body calculations. The data show the importance of core quadrupole ${(}^{1}$D) excitations in describing electron correlations in both the initial Ar ground state and in the final ionic states.

Multiphoton ionization of negative ions in the presence of a dc FIELD. Application to Li −

We present results from the application of a nonperturbative, many-electron, many-photon (MEMP) theory of ionization to Li −, in the presence and absence of an external dc field. In conjunction with published theoretical and experimental data, our calculations suggest that although initial-state electron correlation influences the absolute values of the multiphoton ionization cross-sections, much of the essential physics of negative ions in strong external ac and dc fields is caused by final-state effects (atomic structure of the core plus field-perturbed free electron).

Near-threshold K-shell absorption cross section of argon: Relaxation and correlation effects.

A detailed theoretical study has been made of the effects of core relaxation and electron-electron correlation on the near-threshold absorption cross section of argon, and the results are compared with previous calculations and experiment. The key results are the following: (1) Within the Hartree-Fock approximation, core relaxation must be included to obtain realistic cross sections; (2) final-state calculations are extremely sensitive to the way in which exchange effects are included in the calculations; (3) although electron-electron correlations produce only small changes in the single-electron cross section, they can account for the two-electron resonances which have been observed immediately above the ionization threshold. In particular, the main resonance above threshold appears to be 1s3${p}^{5}$3${d}^{2}$, which can be reached from the ground state via initial-state correlation.

Perturbation expansion and initial-state correlations in non-equilibrium thermo-field dynamics

A perturbation scheme in non-equilibrium thermo-field dynamics is developed by taking into account the initial-state correlations. Two methods are proposed: in the first method the time dependence of amplitudes and their initial values are evaluated by two independent perturbation schemes while in the second method the two perturbation schemes are combined by use of a fictitious past.

The multiconfigurational spin-tensor electron propagator method for determining vertical principal and shake-up ionization potentials for open shell and highly correlated atoms and molecules

We propose and develop the multiconfigurational spin-tensor electron propagator (MCSTEP) technique for the theoretical determination of vertical ionization potentials (IPs) and electron affinities (EAs) for general open-shell and highly correlated atoms and molecules. We obtain these equations from a Green’s function or electron propagator approach where we properly couple electron removal and addition tensor operators to a multiconfigurational tensor state. To account for important shake-up effects and to achieve a ‘‘balance’’ in initial and final state correlation corrections, we include in MCSTEP ionization and electron affinity operators analogous to the ‖c〉〈0‖ state transfer operators necessary in multiconfigurational linear response. In repartitioned MCSTEP (RMCSTEP) we augment the MCSTEP operator manifold with operators of the form a+iajak by first employing partitioning theory to estimate their contributions and then repartitioning only the important operators into the primary space. In this way, important shake-up processes to diffuse orbitals are accurately and reliably handled with RMCSTEP at the same level of approximation, i.e., as part of the primary space operator manifold . Initial application of these methods is extremely encouraging for both principal and shake-up IPs. Using a 〈5s5pld〉 contracted Gaussian valence basis set augmented with two diffuse s, two diffuse p, and two diffuse d functions, the RMCSTEP ionization potentials to the low-lying (&amp;lt;∼24 eV) 2S and 2P bound ionic states (including diffuse states) for Be are calculated within ±0.07 eV of experiment. The IP to the lowest 2D state is calculated 0.14 eV from experiment.

Atomic photoionization by the complex-basis-function expansion method: Application to ground-state and metastable Mg.

We present photoionization cross sections for the ground and metastable (3s3p) /sup 3/P states of atomic magnesium, using ab initio many-electron wave functions in the LS-coupling scheme. The effects of initial-state correlation and channel coupling are incorporated in a straightforward manner with use of configuration-interaction methods. The selective use of complex basis functions obviates the need for explicit construction of continuum wave functions. This method also provides a convenient way of incorporating the effects of autoionization into atomic photoionization cross sections.

Kaon-induced deuteron disintegration with two-body final states

Integrated cross sections for the reactions K −d → Σ −p and K −d → Λn have been obtained within a simple model that involves excitation of an S = − l, I = 0 or 1 resonance (Y ∗) followed by a pseudoscalar meson exchange that deexcites the resonance and transfers momentum to the other nucleon. The model incorporates the eight well-established Y ∗ below 1700 MeV with coupling strengths estimated from partial decay widths and SU(3) symmetry relations. Initial-state correlations are included through the deuteron wave function, obtained with the Reid NN interaction, while final-state correlations are ignored. When examined as functions of the laboratory kaon momentum, the cross sections computed with form factors omitted exhibit two prominent features: a narrow structure centred at 385 MeV/ c, due almost entirely to Λ(1520) excitation, and a broader peak around 700 MeV/ c, that is associated with several overlapping resonances above 1650 MeV. In principle, these two structures could provide coupling-strength information within a more quantitative model. Both peaks are quite sensitive to the inclusion of form factors, however, and may be difficult to detect if the phenomenologically required form factors are as long-ranged as the sparse data presently available indicate.

On the physics and modeling of small semiconductor devices—IV. Generalized, retarded transport in ensemble Monte Carlo techniques

It is shown that the ensemble Monte Carlo technique, in which an ensemble of electrons is utilized and all averages of dynamic variables are computed as ensemble averages, is a numerical solution to generalized equations of motion involving memory effects. Balance equations are also obtained having the same feature. Moreover, these show the importance of initial-state correlations in delaying the initial accelerative effect of the fields.

Nonunitary effects in the time evolution of one-body observables

We present a formal derivation of the exact dynamics of the one-body density matrix. Its essential ingredients are shown to be the following: (a) a mean field unitary time evolution; (b) irreducible nonunitary corrections to the unitary evolution (collision effects); and (c) effects due to the time evolution of initial state correlation (which contribute to both (a) and (b)). In the weak coupling limit the collision effects give rise to a term of Boltzmann form. A qualitative discussion of the importance of collision effects for the expectation values of one-body operators and a quantitative illustration in the framework of an exactly soluble model are given. In this case one finds large nonunitary contributions.