Table of contents

This paper extends to molecules the moment theory of ion traps and similar devices where the electric fields vary with both position and time. It is based on the Wang Chang–Uhlenbeck–de Boer equation and a series of successive approximations based on the Maxwell model and the assumption that all other moments of the ion distribution function vary much less rapidly with position and time than does the ion number density. Two versions of the theory are presented: a simpler one, based on spherical-polar basis functions, and a more comprehensive one, based on Cartesian functions.

Recent moment theories of ion motion in devices where the external fields vary with position and time are applied to non-ideal ion traps. In first approximation, the theories give differential equations with collision frequencies that vary with the effective temperature characterizing the relative kinetic energy of the ion–neutral collisions. Solutions of the set of coupled differential equations provide the ion number density, average velocities, average energies and average temperatures as functions of time and of position in the apparatus. Solutions of the coupled equations are discussed for the Maxwell model, rigid spheres and general ion–neutral interactions. A surprising finding is that ac fields on the endcaps lead to changes in the stability region for ion motion in traps, changes that can cause ion ejection both for small and large values of the ac field applied to the rings.

Formulating a quasiclassical approach we determine the cross section for the complete four-body break-up of the lithium ground state following single photon absorption from threshold up to 220 eV excess energy. In addition, we develop a new classification scheme for three-electron ionizing trajectories in terms of electron–electron collisions, thereby identifying two main ionization paths which the three electrons in the ground state of lithium follow to escape to the continuum. The dominant escape paths manifest themselves in a characteristic 'T-shape' break-up pattern of the three electrons which implies observable structures in the electronic angular correlation probability. This break-up pattern prevails for excess energies so low that the Wannier threshold law σ ∝ E^α describes already the triple ionization cross section, whose predicted value α = 2.16 we can confirm quantitatively.

Using the R-matrix Floquet approach, we have investigated ionization of the 1s2s ¹S and 1s3s ¹S states of He subjected to VUV radiation, following the absorption of two, three and four photons, with a focus on the influence of resonances on the state that the residual He⁺ ion is left in. For the 1s2s ¹S state, we find that final-state 3ℓnℓ' resonances enhance the relative probability that He⁺ is left in the n = 2 states. Intermediate 2ℓnℓ' resonances strongly enhance ionization following three-photon and four-photon absorption. The 2ℓ2ℓ' resonances enhance in particular the probability that He⁺ ion is left in n = 2, while higher 2ℓnℓ' enhance in particular the probability that He⁺ is left in n = 3, since photoionization of the 2ℓnℓ' resonances is dominated by emission of the inner 2ℓ electron. For the 1s3s ¹S state, we find a stronger influence of the final-state 3ℓnℓ' resonances on the relative probability that after two-photon absorption He⁺ is left in n = 2.

Based on the work of Görling and that of Levy and Nagy, a density-functional formalism for many fermionic excited states is explored through a careful and rigorous analysis of the excited-state density to external potential mapping. It is shown that knowledge of the ground-state density is a must to fix the mapping from an excited-state density to an external potential. This is the excited-state counterpart of the Hohenberg–Kohn theorem, where instead of the ground-state density the density of the excited state gives the true many-body wavefunctions of the system. Further, the excited-state Kohn–Sham system is defined by comparing its non-interacting kinetic energy with the true kinetic energy. The theory is demonstrated by studying a large number of atomic systems.

We create rotational wavepackets in deuterium molecules using 10 fs laser pulses, and observe the occurrence of rotational revivals and field-free alignment using Coulomb explosion imaging with intense 10 fs laser pulses.

Absolute differential cross sections have been measured for excitation of the v = 1–4 vibrational levels of the X³Σ_g⁻ ground state of molecular oxygen at an electron impact energy of 10 eV in a wide scattering angle range, from 15° to 180°. In the measurements, a recently constructed double hemispherical electron spectrometer has been used which employs the magnetic angle-changing technique to observe the backward scattering of electrons. The integral excitation cross sections for the above vibrational levels have been also determined through integration of the measured differential cross sections. A detailed comparison of the obtained cross sections has been made with the results of previous measurements.

Single ionization of helium by 102 eV electron impact has been studied by measuring the momentum vectors of all final-state particles, i.e., two electrons and the He⁺ ion, with an advanced reaction microscope. Fully differential cross sections for asymmetric scattering geometry, which have been normalized to an absolute scale, have been obtained covering a large range of emission angles for the emitted low-energy (E ⩽ 15 eV) electron and different scattering angles for the fast electron. Strong electron emission out of the projectile scattering plane is confirmed for electron impact, as was observed before for heavy-ion impact ionization. The data are compared with theoretical predictions from a three-Coulomb wavefunction model, first-order and second-order distorted-wave approaches, as well as a convergent close-coupling calculation.

New measurements of the three reduced Stokes parameters for 54.4 eV electron impact excitation of the 2p state of atomic hydrogen support convergent close coupling and propagating exterior complex scaling theoretical values within two standard deviations and over a larger angular range of 2°–140° than earlier work. Whereas the present measurements and theoretical values of the circular polarization Stokes parameter P₃ agree, they differ by up to about four standard deviations from the measurements by Gradziel and O'Neill (2004 J. Phys. B: At. Mol. Opt. Phys.37 1893) in the vicinity of 30° electron scattering angle and so do not support their explanation of an increased significance of electron exchange for this excitation process at 54.4 eV. We explore some variations in experimental methods and their implications for the measurements.

Differential and integral cross sections have been computed for elastic and rotationally inelastic collisions in (H⁻, H₂ (v = 0, j = 0, 1)) at four different relative translational energies (E_trans = 1.66, 2.03, 2.40 and 2.79 eV) on an accurate ab initio potential energy surface by a time-independent quantum mechanical approach (helicity basis truncated at k = 2). It is shown that the exchange reaction plays only a minor role when compared to the rotational inelastic process. The computed differential inelastic cross sections are in good agreement with the experimental results at E_trans = 1.66, 2.03 and 2.79 eV for j = 1. Although the elastic process plays only a minor role for j = 0, it is not negligible for j = 1.

We have developed the theory of the polarization of radiation emitted from an aligned ion in any one-photon transition involving two different electromagnetic multipoles. We have applied the theory to the line 1s2p ³P₂ → 1s²¹S₀, labelled x, emitted from He-like ions Sc¹⁹⁺ and ²⁰⁵Tl⁷⁹⁺ which are collisionally excited by an electron beam. In these ions with a non-zero nuclear spin, a mixture of magnetic quadrupole (M2) and hyperfine-induced electric dipole (E1) transitions occurs in the line x, the ratio of the E1 to M2 transition probability being equal to 0.350 for scandium and 0.118 for thallium. Our calculations show that quantum interference between the E1 and M2 channels has the effect of increasing the degree of linear polarization of x, slightly for Sc¹⁹⁺ but substantially for ²⁰⁵Tl⁷⁹⁺. For individual hyperfine components of x, the increase of the degree of polarization can be much more significant. On the other hand, the effects of E1–M2 interference are found to reduce the anisotropy of the intensity angular distribution of the line x.

We propose a robust scheme for the implementation of two-qubit phase gates with a cavity QED system. After the gate operation the computational basis states are equally damped by the decoherence effect and thus the gate error is suppressed. The scheme is based on resonant atom–cavity interaction and thus the operation speed is high. During the atom–cavity interaction no external laser fields are required and thus the gate errors arising from external sources are suppressed.

Production of positive and negative ions of cytosine molecules (nucleic acid base) has been studied using a crossed electron and molecular beam technique. The method developed by the authors enabled the molecular beam intensity to be measured and the electron dependences and the absolute values of the total cross sections of production of both positive and negative cytosine ions to be determined. It has been shown that the total positive cytosine ion production cross section reaches its maximal value of 7.8 × 10⁻¹⁶ cm² at the 78 eV electron energy. Dissociative ionization cross sections have also been determined. The maximum total negative cytosine ion production cross section was measured to be 4.2 × 10⁻¹⁸ cm² at 1.5 eV.

Both fundamental and second harmonic amplitude squeezed lights were generated from an external cavity-enhanced singly resonant PPKTP frequency doubler. The effect of input coupling and fundamental power on the squeezing was experimentally investigated. It was shown that the optimal conditions (input coupling and fundamental power) are different for the squeezing of the fundamental and second harmonic lights. An agreement between experiment and theoretical prediction was found.

The photoelectron spectrum of krypton was recorded with various photon energies from 60 to 88 eV in the binding energy range of Kr 4s photoelectron line and valence satellite lines. Strong photon energy dependence was found in the experimental cross-sections of the satellite lines. The high experimental resolution of the measured spectra allowed us to really separate close lying states. This, together with the measurement of the angular anisotropy parameter β at hν = 88 eV enabled us to verify the origin of the satellite lines, i.e. whether they are created by shake-up, conjugated shake-up, or by correlation of bound or continuum states during 4s or 4p photoionization.

A new experimental technique has been applied to measure absolute scattering cross sections for electron impact excitation of the n = 2, 3 states of helium at near-threshold energies. The experimental results are compared with predictions from recent state-of-the-art theoretical calculations. The calculations are performed using the R-matrix with pseudostates, B-spline R-matrix, and the convergent close-coupling methods. Generally, very good agreement is found between the experiment and the three theories.

A comprehensive pulsed-laser time-of-flight (TOF) study of H Rydberg matter (RM) fragments is presented. The nature of the fragments released with well-defined kinetic energies of 9–24 eV is investigated: the detected fragments are found to be H* in Rydberg states with principal quantum number n > 28. The only way to produce such states is from Coulomb explosions in a pre-formed easily laser-fragmented molecular entity. Non-symmetric angular distributions of the fragments are measured and Coulombic shockwave phenomena are observed, which prove that the phase of origin is not a gas but an RM phase. The fast particles are concluded to be formed in two-, three- and four-particle Coulomb explosion processes in an H RM cluster. Laser intensity variation measurements indicate that between four and six photons with a total energy of 8.8–13 eV take part in the RM fragmentation. This proves that laser-induced processes in H₂ or H₂⁺ molecules, even in the RM phase, are excluded for energetic reasons. A feasible H RM formation mechanism is deduced from the signal variation with H₂ pressure, with the dissociation of H₂ on the emitter surface as the rate limiting step. The principal quantum number of H Rydberg species H* reaching the detector is estimated to be n > 32 from a comparison of the calculated ionization rate of the H* species in the electric field inside the detector with measurements.

Precisely calculated results of Zeeman g_J factors g_J/g_e − 1 for n³S₁ (n = 2–10) states of all helium isotopes and lithium ions are presented, relativistic and radiative corrections of orders α², α²m/M and α³ are included. All necessary matrix elements are precisely evaluated by the use of variational wavefunctions constructed from double basis sets in Hylleraas coordinates.

We report new measurements of the spectra of argon, krypton and xenon in the autoionization region using a two-step resonant laser excitation and optogalvanic detection technique. By selecting (m)p⁵(m + 1)p'[3/2]₂ as an intermediate state (m = 4, 5 and 6 for Ar, Kr and Xe, respectively), we have been able to single out the (m)p⁵nd[5/2]₃ autoionizing resonances in their spectra. The MQDT parameters have been derived from the analysis of the series perturbations among the (m)p⁵nd[5/2]₃, (m)p⁵nd[7/2]₃ and (m)p⁵nd'[5/2]₃ series in the discrete region using the phase shifted formulation of the three-channel quantum defect theory and from the line profile analysis of the autoionizing resonances above the first ionization threshold. The predicted reduced widths for the autoionizing resonances based on the series perturbation analysis show good agreement with those of the experimentally observed profiles. Accurate values of the resonance energies, quantum defects and reduced widths are reported.

Using time-resolved photoelectron imaging, a time-dependent electron orbital alignment is observed during the recurrences of a Rydberg rotational wave packet in krypton. The time-dependent alignment is created via excitation of two ac-Stark shifted states (5d'[5/2]₃ and 8d[1/2]₁) using a three-photon femtosecond pulse excitation. A straightforward analysis of the measured photoelectron distributions using angular momentum algebra shows that the observed periodic change in the electron orbital alignment is accompanied by a time-dependent change of the associated Bell states. These Bell states describe the entangled system of excited electron and ionic core. Hence, these experiments present a relatively simple excitation scheme for creating a decoherence-free entangled superposition.

We report relativistic multiconfiguration Dirac–Hartree–Fock calculations of transitions between the hyperfine levels of 4s4f ³F_2,3 and 4s4d ³D₂ in Ga II. The capacity of two newly developed programs connected to the graspVU package for generating synthetic spectra is explored. The obtained theoretical spectra are compared to Fourier transform spectra and good agreement is found. The importance of hyperfine induced interference effects for the 4s4d ³D₂–4s4f ³F₂ transitions is pointed out, and the gf values for all the hyperfine transitions are given.

The energies, Auger widths and Auger decay branching ratios of the doubly core-excited 2s2p^{3 5,3}S°, ^3,1P° and ^3,1D° resonances for Be-like oxygen are calculated using a saddle-point complex-rotation method. The relativistic corrections and mass polarization are included using the first-order perturbation theory. The partial Auger widths are obtained for the individual channels and the total Auger widths are obtained by coupling the important open channels and summing over the other channels. The Auger transition energies of these resonances are calculated and compared with the available experimental and other theoretical results in the literature.

New cross sections for the rotational excitation of H⁺₃ by electrons are calculated ab initio at low impact energies. The validity of the adiabatic-nuclei-rotation (ANR) approximation, combined with R-matrix wavefunctions, is assessed by comparison with rovibrational quantum defect theory calculations based on the treatment of Kokoouline and Greene (2003 Phys. Rev. A 68 012703). Pure ANR excitation cross sections are shown to be accurate down to threshold, except in the presence of large oscillating Rydberg resonances. These resonances occur for transitions with ΔJ = 1 and are caused by closed-channel effects. A simple analytic formula is derived for averaging the rotational probabilities over such resonances in a 3-channel problem. In accord with the Wigner law for an attractive Coulomb field, rotational excitation cross sections are shown to be large and finite at threshold, with a significant but moderate contribution from closed-channels.

Radiative atomic processes, in which charged particles moving with velocities much less than the speed of light emit a photon, are normally considered by using the Schrödinger equation. By analysing the transformation properties of the radiative transition amplitudes under the change of a reference frame we establish that the total cross sections and decay rates, calculated with the Schrödinger equation, are Galilean invariant and that this invariance holds irrespective of the accuracy of wavefunctions describing the charged particles. By considering, within the scope of one reference frame, the radiative processes for two identical atomic systems which have different translational (centre-of-mass) velocities we show that the total cross sections and decay rates in general depend on this velocity if approximate wavefunctions are employed and that this is the direct consequence of the problem of gauge dependence. We also present a detailed discussion of the intimate interrelation between Galilean and gauge transformations which, if overlooked, can easily lead to the misinterpretation of the problem of gauge dependence as the 'problem of Galilean non-invariance'.

Absolute total cross section (TCS) for electron–trimethylborane-d₉ (B(CD₃)₃, TMB-d₉) collisions has been measured at energies ranging from 0.4 to 370 eV using the linear electron-transmission technique. The most visible feature of the TCS energy function is a pronounced broad enhancement peaked between 5 and 10 eV. Some weak structures are also perceptible in the TCS curve. At intermediate energies the experimental results are compared with the cross section obtained as a sum of the integral elastic and ionization cross sections calculated in this work for the B(CH₃)₃ molecule. Similarities observed in cross sections for planar, boron-containing BX₃ (X = F, Cl, CD₃) molecules are also pointed out and discussed.

A systematic study of S I levels belonging to 3s²3p⁴, 3s3p⁵, 3s²3p³(⁴S^o, ²D^o, ²P^o)nℓ, where nℓ = 4s, 5s, 6s, 4p, 5p, 6p, 3d, 4d, 5d, 4f and 5f configurations and optically allowed and intersystem transitions among them are presented. A very large set of basis functions are generated using up to three electron promotions from the ground configurations for each of the 24 symmetries considered belonging to two parities. Many of the levels are reported for the first time. Relativistic effects are included through the Breit–Pauli Hamiltonian. The resulting fine-structure levels and oscillator strengths for some astrophysically important transitions are then presented and compared with the available measured and calculated values. Excellent agreement between the present lifetimes and the measurement of Berzinsh et al (1997 Phys. Rev. A 55 1836) and Beideck et al (1994 Astrophys. J.428 393) are achieved for the 3s²3p³(⁴S^o)ns(³S₁^o), 4 ⩽ n ⩽ 6, 3s²3p³(⁴S^o)4p(³P_0,1,2^o) and 3s²3p³(²P^o)4s(³P_0,1,2^o) levels, respectively.

X-ray fluorescence spectra present singular characteristics produced by the different scattering processes. When atoms are irradiated with incident energy lower and close to an absorption edge, scattering peaks appear due to an inelastic process known as resonant Raman scattering. It constitutes an important contribution to the background of the fluorescent line. The resonant Raman scattering must be taken into account in the determination of low concentration contaminants, especially when the elements have proximate atomic numbers. The values of the mass attenuation coefficients experimentally obtained when materials are analysed with monochromatic x-ray beams under resonant conditions differ from the theoretical values (between 5% and 10%). This difference is due, in part, to the resonant Raman scattering. Monochromatic synchrotron radiation was used to study the Raman effect on pure samples of Mn, Fe, Cu and Zn. Energy scans were carried out in different ranges of energy near the absorption edge of the target element. As the Raman peak has a non-symmetric shape, theoretical models for the differential cross section, convoluted with the instrument function, were used to determine the RRS cross section as a function of the incident energy.

The angular distribution parameters α₂ and spin-polarization parameters β₂ of the Auger transitions are presented for transitions in photoexcited Ne*, Ar*, Kr* and Xe* atoms with open shells. Matrix elements are calculated by the multiconfiguration Dirac–Fock method. The wave functions of the initial and final states of the Auger transitions are calculated with allowance for relaxation effects. The one-electron wavefunctions of the continuous spectrum for an Auger electron are obtained using the single-configuration Fock–Dirac method. The matrix elements are calculated by using intermediate coupling. The resulting values of the energy positions, angular distribution parameters are compared with experimental data and other theoretical results.

It was always anomalous that the data of Williams J F 1981 J. Phys. B: At. Mol. Phys.14 1197 for the angular correlation parameters for an electron scattering angle of 100° for 54 eV incident electrons on atomic hydrogen were almost exactly 90° out of phase with the theoretically predicted values. This feature has been traced to a computer programming error of the coordinate system for θ_e ⩾ 90° in a 1977 correlations fitting program which was used only for the 2p correlations studies reported in the above paper.

The authors Brahim Oujia and Florent Xavier Gadea would like to correct an error in the above article published on 4 September 2006.

Due to an oversight one of the authors names was omitted in the final version. The list of authors should be:

Wissem Zrafi, Neji Khelifi, Brahim Oujia and Florent Xavier Gadea.