We present a Q function of a state of a quantum-mechanical system in a finite-dimensional Hilbert space. This discrete Q function is defined with the help of the Wódkiewicz concept of propensities, i.e., we define the Q function as a discrete convolution of two Wigner functions based on Wootter’s formalism, one of the state itself and one of the filter state. The discrete Q function takes nonnegative values in all ‘‘points’’ of the discrete phase space and is normalized and it is possible to reconstruct from it the density operator of the state under consideration. We analyze Q-function graphs for several states of interest.

We use the distorted-wave approach in the eikonal approximation to show that polarization effects play a significant role in the direct excitation process of atomic hydrogen by electron impact.

We show how losses in photodetection and in quantum-state measurements can be numerically compensated after the measurements have been performed. When the overall efficiency exceeds 1/2, our recipe works for all quantum states. For smaller efficiencies, however, the convergence of the compensation procedure depends on the quantum state under investigation.

Using relativistic configuration-interaction wave functions, we have obtained length and velocity f values for all lower J=2,3,4 (4d+5s${)}^4$ levels connected to the z ${4\mathrm{d}}^3$5p ${}_{}{}^5{}_{}{}^{}\mathrm{G}_3^{\mathrm{o}}{}_{}{}^{}$, and ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_3^{\mathit{o}}$ levels. Our lifetime results for length and velocity operators are τ${(}^5$${\mathit{G}}_3^{\mathit{o}}$)=5.16 and 6.53 ns, respectively, and τ${(}^3$${\mathit{D}}_3^{\mathit{o}}$)=4.67 and 5.60 ns, respectively. These are in good agreement with the experimental values of 5.8–6.2 and 5.0 ns. As we find for hyperfine structure, the 4${\mathit{d}}^4$, 4${\mathit{d}}^3$5s interactions are important in generating accurate lifetime and f-value results.

We present predictions for the scalar and tensor components of the linear, α, and nonlinear, γ, polarizabilities of the excited valence states of Be, 1${\mathit{s}}^2$2s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^0$, ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^0$, 1${\mathit{s}}^2$2${\mathit{p}}^2$ ${}_{}{}^3{}_{}{}^{}$P, and 1${\mathit{s}}^2$2${\mathit{p}}^2$ ${}_{}{}^1{}_{}{}^{}$D. Also reported are results on the previously extensively studied ground state 1${\mathit{s}}^2$2${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$S. The all-order variational calculations solved state-specific complex eigenvalue matrix equations and accounted for valence electron correlation and field-induced mixing effects. The results demonstrate the importance of valence-Rydberg mixing on these properties, even when the valence states are the lowest of their symmetry. For example, whereas for Be 1${\mathit{s}}^2$2s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^0$, where such mixing is very small, ${\mathrm{\alpha }}_0$=39.33 and ${\gamma }_0$=9.49×${10}^4$ a.u. for 1${\mathit{s}}^2$2${\mathit{p}}^2$ ${}_{}{}^1{}_{}{}^{}$D, which mixes heavily with the 1${\mathit{s}}^2$2snd Rydberg series (especially with 1${\mathit{s}}^2$2s3d), ${\mathrm{\alpha }}_0$=42.73 a.u. and ${\gamma }_0$=0.48×${10}^7$ a.u.

We have calculated all O(${\mathrm{\alpha }}^2$) corrections to the orthopositronium and parapositronium decay rates due to vacuum polarization graphs. These contributions are independent of gauge and bound state formalism. Our results are +0.964 960(4) (α/π${)}^2$ for orthopositronium and +0.447 343 0(6) (α/π${)}^2$ for parapositronium relative to the lowest order rates. We also have an improved result for the one-loop one-photon-annihilation orthopositronium decay graph of -0.814 057 4(10) (α/π) times the lowest order rate.

In our previous studies with the evaluation of traces of p-order replacement operators calculated in finite-dimensional, antisymmetric, and spin-adapted N-electron spaces (p≤N), we described a technique for the calculation of those expressions based on the reduction of the opertor order [A. Torre, L. Lain, and J. Millan, Phys. Rev. A 47, 923 (1993)]. Now, we report a general formula which, condensing all the reduction steps, leads to the direct evaluation of those traces. Some examples for illuminating the usefulness of that formula are reported.

Probabilities of intercombination transitions 2${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$–2s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$, 2s3p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ for Be-like ions are calculated along the isoelectronic sequence for a large range of Z with the 1/Z expansion method. Results agree well with experimental data, including the recent ones. A comparison is also made with other theoretical calculations.

We have measured the relative shape of the bremsstrahlung-photon energy spectrum from 7.0-keV electrons incident on Ag and Au targets; the targets are thick enough to stop the incident electrons, yet thin enough to transmit a substantial fraction of the radiated photons. Our results for the ratio of double differential cross sections for the bremsstrahlung-photon emission from Ag and Au at 90° to the incident electron beam direction are found to yield excellent agreement with Pratt’s theoretical prediction [Comments At. Mol. Phys. 10, 121 (1981); .ul2 Electron Bremsstrahlung ×80: Theory and Recent Developments, Proceedings of the International Conference on X-ray Processes and Inner Shell Ionization, Stirling, Scotland, 1980, edited by D. J. Fabian, H. Kleinpoppen, and L. M. Watson (Plenum, New York, 1981)] on the relative shape of the spectrum; however, the thick-target effect introduces a discrepancy between experiment and theory of about 20%. Also, the calculated absolute efficiency of the detector employed using the theoretical bremsstrahlung cross sections is found to agree with the normalization to the radioactive source within the uncertainty of about 20% in the target thickness.

As shown recently by Zawisky, Rauch, and Hasegawa in neutron interferometry [Phys. Rev. A 50, 5000 (1994)], the interference pattern obtained with a low-intensity particle beam is deeply modified when a selection is made of the time intervals between successive detected events. Experiments of the same type performed with a Stern-Gerlach interferometer using a metastable hydrogen atom beam are described. Results very similar to those of the neutron experiment are obtained, in particular a strong enhancement of the contrast when large time intervals are selected.

We confirm numerically the presence of shape invariant wave packets of highly excited electrons in the hydrogen atom in a strong circularly polarized electromagnetic field. In this case, the electron’s motion in the vicinity of the saddle point created by the Coulomb and the constant electric field is stabilized by the action of Coriolis and centrifugal forces in the rotating frame.

A diagnostic method for detecting ordering in one-dimensional ion beams is presented. The ions are excited by a pulsed laser at two different positions along the beam, and fluorescence is observed by a group of four photomultipliers. Correlation in fluorescence signals is a firm indication that the ion beam has an ordered structure.

We present an interpretation of recently measured single- and double-ionization yields by strong laser pulses in He in terms of the independent-electron model. We show that the single-electron ionization probability may be extracted simply in terms of the ratio of doubly to singly charged ion yields. The data lie in the strong-field intensity range where tunneling ionization is the predominant mechanism, and we discuss its extension to the low-intensity limit of multiphoton ionization and to the ultrahigh intensity region of over-the-barrier ionization.

We show, in contrast to what has hitherto been believed, that the linewidth of the side peaks in the resonance fluorescence spectrum of an atom interacting with broadband squeezed fields and driven by a strong pump can be reduced below the normal vacuum value. In particular, for squeezing parameter N in the range 0<N<0.125 and relative phase θ=0 we observe narrowing of the linewidth, and for N=0.125 the linewidth is identical to that of the normal vacuum case. For N>0.125, side peaks always broaden.

We present the effects of time-dependent parameters, such as frequency and nonlinearity, on the dynamics of a mode propagating throughout a Kerr medium described as an anharmonic oscillator. The time-dependent frequency only gives a rotation of physical observables in the phase space, while the time modulation of the nonlinearity allows one to obtain the macroscopic superposition of quantum states at every crystal length larger than the canonical ones.

The dynamics of copropagating femtosecond pulses with different carrier frequencies is modeled for a semiconductor amplifier. The propagation induced four-wave mixing signal is studied as a function of the pulse intensity and the spectral detuning between the pulses.

The completeness relation of the eigenstates of the higher powers ${\mathit{a}}^{\mathit{k}}$ (k≥3) of the annihilation operator a, proposed by several authors including Sun et al. [Phys. Rev. A 44, 3369 (1991)], is modified. Thus this relation holds true when its expectation value in the vacuum state ‖0〉 is calculated.