Table of contents

We study the instability of a doubly quantized vortex topologically imprinted on ²³Na condensate, as reported in recent experiment (Shin et al 2004 Phys. Rev. Lett.93 160406). We have performed numerical simulations using three-dimensional Gross–Pitaevskii equation with classical thermal noise. Splitting of a doubly quantized vortex turns out to be a process that is very sensitive to the presence of thermal atoms. We observe that even very small thermal fluctuations, corresponding to 10–15% of thermal atoms, cause the decay of doubly quantized vortex into two singly quantized vortices in tens of milliseconds. As in the experiment, the lifetime of doubly quantized vortex is a monotonic function of the interaction strength.

Based on simple rate equations for the Rydberg excitation process, we are able to model microscopically the dynamics of Rydberg excitation in ensembles of a large number of ultracold atoms, which is beyond the capabilities of fully ab initio approaches. Our results for the distribution of Rydberg atom numbers are in good agreement with recent experimental data, confirming the quenching of the distribution caused by Rydberg–Rydberg interactions.

Hydrogen atoms in a cold supersonic expansion with an average velocity of 700 m s⁻¹ have been excited to Rydberg Stark states with principal quantum number in the range n = 20–25 and subsequently decelerated and accelerated in time-independent inhomogeneous electric fields. Accelerations of up to 2 × 10⁸ m s⁻² have been achieved and the initial kinetic energy of atoms prepared in low (high)-field seeking Stark states could be more than quadrupled (halved) over a flight distance of only 3 mm and in a time of less than 5 µs. The control over the velocity of the Rydberg atoms is such that trapping can be envisaged.

Cross sections have been computed for rotational transitions of H₂, induced by collisions with H atoms, using a recent H–H₂ potential calculated by Mielke et al (2002 J. Chem. Phys.116 4142). These results are compared with those obtained with earlier potentials. Significant discrepancies are found with results deriving from the potential of Boothroyd et al (1996 J. Chem. Phys.104 7139) in the low collision energy regime. We compare also cross sections derived using different levels of approximation to the vibrational motion.

Electron affinities, E_a, E₁ and A₁ are reported for the 12 primary X, A–K (27 spin) states of O₂(−): K_eqT^3/2 = (S_anQ_an)(2πm_ek/h²)^3/2exp(E_a/RT); k₁ = A₁T^−1/2exp(−E₁/RT). These are obtained from pulsed discharge electron capture detector data by rigorously including literature values and uncertainties in a global non-linear least-squares adjustment. Simple molecular orbital theory predicts 27 bonding and 27 anti-bonding low-lying spin states. For the first time, the positive E_a for the 27 bonding states are reported. The partition function ratios of the negative ion and neutral (S_anQ_an), the A₁(X–E) and the spin separations are from fundamental constants. The E_a (in eV) are as follows (with the spin states in brackets): [1.050, 1.070]; [0.915, 0.935]; [0.698, 0.718, 0.746, 0.782]; [0.734, 0.754]; [0.559, 0.587]; 0.518; [0.430, 0.450]; 0.380; 0.354; [0.286, 0.298, 0.318, 0.346]; [0.232, 0.252]; [0.172, 0.184, 0.204, 0.232]. The activation energies (in eV) are as follows: E₁(X–C) 1.0; E₁(D,E) 1.0, 0.8, 0.6; E₁(F–K) 0.12–0.08. The E_a and E₁ are used to calculate bonding Herschbach ionic Morse–Person empirical curves.

When the interactions of the two coupling transitions from an excited level to two nearly degenerate ground levels with the same vacuum occur in a four-level tripod-scheme atomic system, vacuum-induced coherence (VIC) results from the quantum interference between the two spontaneous transitions. We investigate the effects of VIC and the relative phase between the two coupling fields on the probe absorption and dispersion properties as well as the group velocity of the probe field. We find that by adjusting the incoherent pumping field and VIC as well as the relative phase, the central absorption peak in the double transparency spectrum reduces, even develops into a gain dip, and the probe field propagates at a velocity from superluminal to subluminal. It is particularly pointed out that the subluminal light propagation with gain without inversion can be realized in such a system. The physical interpretation of the phenomena has been given.

The spectral width and the energy of the Pt Lβ₁₅(L₃–N₄) emission line have been determined using a Johann-type spectrometer with tunable photon energies around the L₁ threshold. The Pt Lβ₁₅ line has been found to have a FWHM of 9.57(17) eV and a transition energy of 11233.59(29) eV and its values are compared with the ones calculated by the GRASP code.

Energies and transition probabilities of Kβ hypersatellite lines are computed using the Dirac–Fock model for several values of Z throughout the periodic table. The influence of the Breit interaction on the energy shifts from the corresponding diagram lines and on the Kβ^h₁/Kβ^h₃ intensity ratio is evaluated. The widths of the double-K hole levels are calculated for Al and Sc. The results are compared to experiment and to other theoretical calculations.

A numerical simulation of vibrational excitation of molecules was devised and used to excite computational models of common molecules into a prescribed, pure, normal vibration mode in the ground electronic state, with varying, controllable energy content. The redistribution of this energy (either non-chaotic or irreversible IVR) within the isolated, free molecule is then followed in time with a view to determining the coupling strength between modes. This work was triggered by the need to predict the general characters of the infrared spectra to be expected from molecules in interstellar space, after being excited by photon absorption or reaction with a radical. It is found that IVR from a pure normal mode is very 'restricted' indeed at energy contents of one mode quantum or so. However, as this is increased, or when the excitation is localized, our approach allows us to isolate, describe and quantify a number of interesting phenomena, known to chemists and in nonlinear mechanics, but difficult to demonstrate experimentally: frequency dragging, mode locking or quenching or, still, instability near a potential surface crossing, the first step to generalized chaos as the energy content per mode is increased.

The influence of spatial confinement on the structure and spectra of the Rydberg HeH molecule is analysed at the level of the variational full configuration interaction approach. The confining potential is assumed to have cylindrical symmetry, with the symmetry axis of the potential overlapping with the molecular bond. In the direction perpendicular to the axis quadratic dependence of the potential on the electron coordinates is assumed. The influence of the confining potential on the form of the potential energy curves (in particular on the bond lengths), on the electronic spectra and on the ionization due to the confinement is studied in detail.

Direct measurements of the three Stokes parameters (polarization components) P₁, P₂ and P₃ of the VUV Hg transition 6s6p¹P₁ → 6s²¹S₀ (185 nm) have been carried out at electron impact energies of 15 eV, 50 eV and 100 eV. Within the experimental uncertainty, no influence of the electron spin was discovered for scattering angles θ ⩽ 30°. At 15 eV excitation energy and scattering angles θ ⩾ 80°, increasing spin effects become apparent. The experimental data are compared to theoretical predictions from a first-order full-relativistic distorted-wave model, a five-state Breit–Pauli R-matrix (close-coupling) approach, and a convergent close-coupling model, in which relativistic effects are accounted for by adding non-relativistic amplitudes using known intermediate-coupling coefficients. At scattering angles θ ⩽ 15°, all of the theories reproduce the experimental data well, whereas the CCC model exhibits the best overall agreement with experiment at large scattering angles.

The results from an electron momentum spectroscopy (EMS) study of the outer valence electronic region of bicyclo[2.2.1]hepta-2,5-dione (C₇H₈O₂) are reported for the first time. The measured binding energy spectra are presented for the azimuthal angles 0°, 10° and 0° + 10°, respectively, and are compared to new He(I) photoelectron spectroscopy results, which are measured as a part of this work. These experimental data are compared further with results from theoretical computations, using various methods including Hartree–Fock, density functional and an outer valence Green's function theory. Measured orbital momentum distributions are compared on an orbital by orbital basis against those obtained by calculations which employ the plane-wave impulse approximation. These calculations use orbital wavefunctions obtained from Hartree–Fock and density functional theory with a couple of generalized gradient approximation exchange correlation (XC) functionals and the DGauss triple zeta valence polarization basis set. Agreement between the measured and calculated momentum distributions was found to be only fair. Nonetheless, the orbital momentum distributions of the molecule still provide an orbital based assessment of the XC functionals of the density functional theory employed, and an understanding of the chemical bonding mechanisms within the species. Finally, the spectroscopic strengths calculated using outer valence Green's function theory are compared against those derived from our EMS measurements.

Ionization–excitation by electron impact of diatomic species in general and hydrogen molecule in particular presents very interesting mechanisms which can be observed in coincidence (e, 2e) experiments. The dissociative character of the final excited state makes these types of experiments easier to perform than those of atomic targets for which the coincidence measurement of the emitted electron and the photon is necessary. Recently Takahashi et al (2003) Phys. Rev. A 68 042710 have shown large disagreements between their experimental results and theoretical ones obtained by the first-order plane-wave impulse approximation at intermediate impact energies. These authors conclude that a second-order treatment, including the two-step mechanisms (TS1 and TS2), would be necessary to explain these differences. In this paper, we present a second-order Born treatment including the two-step mechanisms and study the simple ionization of H₂ and the ionization–excitation of H₂ to the ²Σ_g(2sσ_g) and ²Σ_u(2pσ_u) levels of H⁺₂ by electron impact.

We have investigated the doubly excited ^1,3P^o resonance states of helium embedded in weakly coupled plasmas. A screened Coulomb potential obtained from the Debye model is used to represent the interaction between the charge particles. A correlated wavefunction consisting of a generalized exponential expansion has been used to represent the correlation effect. A total of 18 resonances (9 each for ¹P^o and ³P^o states) below the n = 2 He⁺ thresholds has been estimated by calculating the density of states using a stabilization method. For each spin state, this includes four members in the 2snp₊(2 ⩽ n ⩽ 5) series, three members in the 2snp₋(3 ⩽ n ⩽ 5) series, and two members from 2pnd(n = 3, 4) series. The resonance energies and widths for various Debye parameters ranging from infinity to a small value for these ^1,3P^o resonance states are reported. In addition, the wavelengths for the photo-absorption of a helium atom from its ground state to such ¹P^o resonance states for different Debye lengths are also reported.

We consider the dynamics of spatial beams in a dual-channel waveguide with competing cubic and quintic (CQ) nonlinearities. Gradually increasing the power in the input channel, we identify four different regimes of the pulse's coupling into the cross channel, which alternate three times between full pass and full stop, thus suggesting three realizations of switching between the channels. As in the case of the Kerr (solely cubic) nonlinearity, the first two regimes are the linear one, and the one dominated by the self-focusing nonlinearity, with the beam which, respectively, periodically couples between the channels, or stays in the input channel. Further increase of the power reveals two novel transmission regimes, one characterized by balance between the competing nonlinearities, which again allows full coupling between the channels, and a final regime dominated by the self-defocusing quintic nonlinearity. In the latter case, the situation resembles that known for a self-repulsive Bose–Einstein condensate trapped in a double-well potential, which is characterized by strong symmetry breaking; accordingly, the beam again abides in the input channel, contrary to an intuitive expectation that the self-defocusing nonlinearity would push it into the cross channel. The numerical results are qualitatively explained by a simple analytical model based on the variational approximation.

We consider rotation of the polarization plane of the laser light when a gas laser is placed in a longitudinal electric field (10 kV cm⁻¹). It is shown that residual anisotropy of the laser cavity 10⁻⁶ and the sensitivity to the angle of polarization plane rotation about 10⁻¹¹–10⁻¹² rad allow one to measure an electron EDM with the sensitivity about 10⁻³⁰e cm.

This paper analyses the capabilities of semi-classical methods in modelling small Na⁺_N clusters. We show that there exist stable semi-classical structures very close to the quantum ground states. We also study the optical response of these semi-classical clusters and compare it to experimental results and quantum results. The semi-classical results turn out to be very close to quantum ones and to experimental spectra. These results show that semi-classical methods provide a fair description of structure and low-energy dynamics of small (even non-spherical) clusters. This then allows one to use these methods consistently and reliably throughout a full simulation of energetic cluster dynamics where the initial stages reside still in the low-energy domain.

A 23-state close-coupling calculation on the slow electron interaction with barium atoms is carried out by using a fully relativistic R-matrix method. The results for the slow electron scattering and photodetachment of the negative atomic barium ions are presented. An apparent relativistic fine-structure split is produced for both the bound states of the negative ion and the shape resonance states of the free electron. The electron affinities for the 6s²6p²P^o_3/2 level and the 6s²6p²P^o_1/2 level are obtained to be 183 meV and 240 meV, respectively. The 57 meV fine-structure split of the 6p orbital is very close to the experimental value. The fine-structure split of the d-wave shape resonance above the elastic threshold is predicted to be 31 meV. The calculated integral scattering cross sections from 0 to 10 eV show that including the relativistic effects cannot eliminate the large discrepancies between theory and the existing experiment.

A scheme is presented for generating entangled states for two atoms in a cavity. In the scheme two atoms simultaneously interact with a cavity mode with a small detuning. The operation time is very short and thus the decoherence can be effectively suppressed. Furthermore, the scheme is valid no matter whether the two atoms have the same coupling strengths or not. The scheme can be used to generate multi-atom W states without the requirement of individual addressing of the atoms, which is also experimentally important. The scheme can also be generalized to produce entangled states in an ion trap without individually addressing the ions.

We compare theoretically the tripartite entanglement available from the use of three concurrent χ⁽²⁾ nonlinearities and three independent squeezed states mixed on beamsplitters, using an appropriate version of the van Loock–Furusawa inequalities. We also define three-mode generalizations of the Einstein–Podolsky–Rosen paradox which are an alternative for demonstrating the inseparability of the density matrix.

We report measurements of the total and absolute differential cross sections for charge transfer of ground- and excited-states O⁺ ions at 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5 and 5 keV in collisions with N₂ at scattering angles −5.2° ⩽ Θ ⩽ +5.2° in the laboratory frame. Total cross sections for ground- and mixed state ions are compared with previous measurements. The behaviour of the absolute differential cross sections display an expected decreasing behaviour with increasing angle. The mixed state ions cross sections are considerably higher than those measured for the ground state ions.

We present in this paper results of a nonlinear optical spectroscopy approach to measurement of excited-state transition matrix elements. Recent advances in the quality of excited-state transition matrix elements have permitted renormalization of earlier measurements of transition amplitudes associated with the 5s ²S_1/2 → 5p ²P_j → 5d ²D_3/2 two-photon transitions in atomic ⁸⁷Rb. Previous measurements were made to high precision, but further improvement of the accuracy was limited by uncertainties in data describing the influence of energetically distant transitions. Availability of more reliable matrix elements, including relativistic all-order calculations of transition matrix elements in alkali atoms, has since significantly improved the situation. In the present paper, we show that theoretical relative transition amplitudes for the excited state 5p ²P_j → 5d ²D_3/2 doublet (ratio = 1.098(9)) are now in excellent agreement with experiment (ratio = 1.090(6)). This result, combined with our recent work on caesium, shows that it is possible to determine relative line strengths, for transitions connecting atomic excited states, with precision previously found only in state-of-the-art measurements of alkali resonance doublets. Detailed discussion of the experimental technique and supporting data, including polarization measurements on the 5s ²S_1/2 → 5p ²P_j → 5d ²D_5/2 transitions, is also presented.

The recombination of D⁺₃ and D⁺₅ ions with electrons in a He–Ar–D₂ flowing afterglow plasma is reported. Low temperature (T = 130–300 K) and high pressure of the He buffer gas (900–1200 Pa) was used to enhance the formation of D⁺₅ ions in the afterglow plasma. The deuterium partial number density was varied over a large range ([D₂] = 1 × 10¹²–3 × 10¹⁵ cm⁻³) to study its influence on plasma decay. At low [D₂], D⁺₃ ions dominate in the afterglow and the plasma decay is controlled by the recombination of D⁺₃ ions (rate coefficient α₃). At high [D₂] and lower temperatures, D⁺₅ ions are effectively formed and the plasma decay is controlled by the recombination of D⁺₅ ions (α₅). In the intermediate region, the rate of recombination is given by the partial densities of both ions, D⁺₃ and D⁺₅. These partial densities are influenced by conditions in the plasma and they are controlled by ion–molecule reactions (D⁺₃ + D₂ ↔ D⁺₅). If the ion–molecule reactions are fast in comparison with the recombination processes the plasma decay can be characterized by the equilibrium constant K_C and by recombination rate coefficients α₃ and α₅. By monitoring of the plasma decay, all three constants α₃ (190 K) = (1.4 ± 0.5) × 10⁻⁷ cm³ s⁻¹, α₅ (190 K) = (3 ± 1) × 10⁻⁶ cm³ s⁻¹ and K_C (190 K) = (3.8 ± 2.0) × 10⁻¹⁶ cm³ are determined.

Absolute total cross section (TCS) for electron scattering from sulfuryl chloride (SO₂Cl₂) molecules was measured in a linear transmission experiment at energies ranging from 0.5 to 150 eV. The most distinct features found in the TCS are the deep minimum located near 1.8 eV and the broad enhancement peaked around 9.5 eV with a shoulder spanned between 3 and 5 eV. At intermediate energies, the present experimental TCS results agree well with our total cross-section estimations, based on calculations of elastic and ionization cross sections. In addition, the calculated total cross section for SO₂F₂ is reported. The results for e⁻–SO₂Cl₂ collisions are compared, for the energy dependence and magnitude, with experimental and computed cross sections for other molecules (SO₂F₂, SO₂ClF) comprising a sulfone group.

Differential cross sections (DCS) for electron-impact excitation of the 3s3p ¹P₁ state in magnesium at incident electron energies E₀ = 10, 15, 20, 40, 60, 80 and 100 eV have been measured and corresponding calculations carried out. Scattered-electron intensities were measured over a wide range of scattering angles (10°–150°) and normalized to the DCSs at 10° experimentally obtained by Filipović et al (2006 Int. J. Mass Spectrom. 251 66). Corresponding calculations have been conducted in the relativistic distorted-wave approximation. Integrated (integral, momentum transfer and viscosity) cross sections are determined by numerical integration of our DCSs. The results are analysed and compared with previous experimental data and theoretical calculations.

Dissociative and non-dissociative charge transfer cross sections in high velocity (v = 2.6 au) collisions between ionic carbon clusters C_n⁺ (n = 2–10) and helium atoms have been measured. The sum of the cross sections has been found to increase significantly with n. Measurements of branching ratios for all fragmentation channels of excited C_n clusters are reported. The summed branching ratios associated with a given number of emitted fragments exhibit odd–even alternations reflecting the higher stability of the species having an odd number of atoms. From an analysis of the summed branching ratios within the statistical microcanonical metropolis Monte Carlo model, and knowing the temperature of the incident clusters, deposited energy distributions due to the charge transfer process are deduced (n = 5–9). These distributions, of similar characteristics whatever n, peak around 4–5 eV and exhibit a large percentage of superexcited states situated above the continuum.

The hydrogen molecular ion in an aligned strong magnetic field is studied in prolate spheroidal coordinates with the Lagrange-mesh method. Different variants of the regularization of singularities are described in detail and tested. The simple resulting equations provide a high accuracy with small computing times. At fixed fields and basis sizes, the accuracy on energies decreases with increasing |m| values. At γ = 1, accuracies from 10⁻¹² for m = 0 to 10⁻⁹ for m = −4 in positive parity and 10⁻⁷ in negative parity are obtained with various bases. Energies at equilibrium for m = 0 can be determined with at least 12 significant digits up to γ = 1000. Equilibrium distances are calculated with at least six significant digits.

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