Entanglement is the fundamental quantum property behind the now popular field of quantum transport of information. This quantum property is incompatible with the separation of a single system into two uncorrelated subsystems. Consequently, it does not require the use of an additive form of entropy. We discuss the problem of the choice of the most convenient entropy indicator, focusing our attention on a system of two qubits, and on a special set, denoted by $\mathfrak{I}.$ This set contains both the maximally and partially entangled states that are described by density matrices diagonal in the Bell basis set. We select this set for the main purpose of making our work of analysis more straightforward. As a matter of fact, we find that in general the conventional von Neumann entropy is not a monotonic function of the entanglement strength. This means that the von Neumann entropy is not a reliable indicator of the departure from the condition of maximum entanglement. We study the behavior of a form of nonadditive entropy, made popular by the 1988 work by Tsallis [J. Stat. Phys. 52, 479 (1988)]. We show that in the set $\mathfrak{I},$ implying the key condition of nonvanishing entanglement, this nonadditive entropy indicator turns out to be a strictly monotonic function of the strength of the entanglement, if entropy indexes q larger than a critical value Q are adopted. We argue that this might be a consequence of the nonadditive nature of the Tsallis entropy, implying that the world is quantum and that uncorrelated subsystems do not exist.

The hyperfine splitting of the $1s$ ground state of hydrogenlike Tl has been measured for the two stable isotopes using emission spectroscopy in the SuperEBIT electron-beam ion trap, giving $3858.22\pm 0.30\hspace{0.5em}\AA$ for ${}^{203}{\mathrm{Tl}}^{80+}$ and $3821.84\pm 0.34\hspace{0.5em}\AA$ for ${}^{205}{\mathrm{Tl}}^{80+}$ with a wavelength difference $\Delta \lambda =36.38\mathrm{}\pm 0.35\hspace{0.5em}\AA .$ This difference is consistent with estimates based on hyperfine anomaly data for neutral Tl only if finite size effects are included in the calculation. By using previously determined nuclear magnetic moments, and applying appropriate corrections for the nuclear charge distribution and radiative effects, the experimental splittings can be interpreted in terms of nuclear magnetization radii $〈r_m^2{〉}^{1/2}=5.83\mathrm{}\left(14\right)\mathrm{}\hspace{0.5em}\mathrm{fm}$ for ${}^{203}\mathrm{Tl}$ and $〈r_m^2{〉}^{1/2}=5.89\mathrm{}\left(14\right)\mathrm{}\hspace{0.5em}\mathrm{fm}$ for ${}^{205}\mathrm{Tl}.$ These values are 10% larger than derived from single-particle nuclear magnetization models, and are slightly larger than the corresponding charge distributions.

The low-energy amplitude of Compton scattering on the bound state of two charged particles of arbitrary masses, charges, and spins is obtained. A case in which the bound state exists due to electromagnetic interaction is considered. The term, proportional to ${\omega }^2,$ is obtained taking into account the first relativistic correction. It is shown that the complete result for this correction differs essentially from the commonly used term $\Delta \alpha ,$ proportional to the rms charge radius of the system. We propose that the same situation can take place in the more complicated case of hadrons.

Two methods to scale plane-wave Born cross sections for electron-impact excitations of neutral atoms are shown to produce excitation cross sections comparable in accuracy to those obtained by more sophisticated collision theories such as the convergent close-coupling method. These scaling methods are applicable to integrated cross sections for electric dipole-allowed transitions. Scaled cross sections are in excellent agreement with available theoretical and experimental data for excitations in H, He, Li, Be, Na, Mg, K, Ca, Rb, Sr, Cs, Ba, Hg, and Tl, indicating the possibility of rapid and reliable calculations of excitation cross sections for many other neutral atoms.

We discuss the usefulness of the independent-particle model to describe charge-transfer processes. We consider, as a benchmark case, avoided crossing transitions in two-electron systems, described by means of the Landau-Zener-Stueckelberg model. It is shown that the independent-particle model, with an equivalent-electron interpretation of the one-electron transition probabilities, reproduces single-electron transition probabilities for a wide range of physical situations. Significant deviations with respect to a two-electron calculation are related to Stueckelberg oscillations of the transition probabilities.

The rates of positron annihilation in molecular gases are known to depend on the nanoscopic structural features of the ambient molecules. The aim of the present study is to explore the possible relationships that exist between some of the most salient molecular structural features and the ensuing positron annihilation rates at room temperature. Quantum dynamical calculations are applied to a broad variety of polyatomic targets using a parameter-free model interaction with the impinging positrons. The $Z_{\mathrm{eff}}$ values, as well as the integral elastic cross sections, are computed for such systems over the relevant range of collision energies. The dynamical treatment is shown to yield realistic values for the cross sections and to produce $Z_{\mathrm{eff}}$ values whose agreement with the few existing measured data varies greatly from one system to another.

We have studied the $4d$ photoabsorption process of ${\mathrm{Eu}}^{+}$ ions by the linear-density-response theory with the density-functional theory and an optimized effective potential and self-interaction correction. Different from the recent experimental observation, which found that the $4d$ photoabsorption spectrum of ${\mathrm{Eu}}^{+}$ ions is almost the same as that of neutral Eu atoms, our calculated $4d$ photoabsorption spectrum of ${\mathrm{Eu}}^{+}$ ions shows many sharp and window resonances, which do not appear in case of neutral Eu atoms. The discrepancies between the experimental observation and our calculation are due to the experimental energy resolution. The convoluted spectrum with the experimental energy resolution is in good agreement with the experimental observation. Moreover, we predict the $4d$ photoabsorption spectra with several given energy resolutions, which call for a further higher-resolution experiment.

Electron capture resulting from collisions of ${\mathrm{Al}}^{2+}$ ions with He atoms from 0.15 to 1000 keV/u is investigated using a molecular-orbital representation within a semiclassical frame. Molecular electronic states and corresponding couplings are determined by the ALCHEMY program. Sixteen molecular states all connecting to single-electron-capture processes are included, and hence radial and rotational couplings among these channels are fully considered. The trajectory effect arising from the straight-line, Coulomb, and ground-state potential trajectories for electron-capture and excitation processes is carefully assessed. The electron-capture cross section by ground-state ${\mathrm{Al}}^{2+}{(}^2\mathrm{S})$ ions slowly increases before it reaches a maximum of $1.3\times {10}^{-16}{\mathrm{cm}}^2$ at 100 keV/u. Those for metastable ${\mathrm{Al}}^{2+}{(}^2\mathrm{P})$ ions sharply increase with increasing energy, and reach a peak at 1 keV/u with a value of $1.5\times {10}^{-16}{\mathrm{cm}}^2.$ The earlier experimental data are found to be larger by an order of magnitude although their energy dependence is in good accord with the present result. Excitation cross sections for both the ground and metastable states are found to be much larger by a factor of 2–3 than corresponding capture cross sections above 1 keV/u although they become comparable below this energy.

The results of R-matrix with pseudostates (RMPS) and time-dependent close-coupling (TDCC) calculations of electron-impact excitation in Li are presented. We included 55 terms in the RMPS close-coupling expansion, of which nine are spectroscopic and 46 are pseudostates. The two-electron radial wave functions generated from earlier TDCC calculations for ionization from the ground state of Li by Colgan et al. [Phys. Rev. A 63, 062709 (2001)] are employed to determine the TDCC excitation cross sections. The RMPS and TDCC cross sections for transitions from ${1s}^{2}2s$ to ${1s}^{2}2p,$ ${1s}^{2}3l,$ and ${1s}^{2}4l$ are compared to each other and to cross sections determined from our R-matrix calculation without pseudostates, the convergent close-coupling calculations presented by Schweinzer et al. [At. Data Nucl. Data Tables 72, 239 (1999)], the coupled-channel optical calculations of Bray et al. [Phys. Rev. A 47, 1101 (1993)], and experimental measurements. These results indicate that coupling to the target continuum has a significant effect on electron-impact excitation in this atom; this increases with the principal quantum number of the excited term, and is large for transitions to ${1s}^{2}4l.$

Relativistic and channel coupling effects in photoionization and unified electronic recombination of $\mathrm{Fe}\mathrm{XVII}$ are demonstrated with an extensive 60-level close-coupling calculation using the Breit-Pauli R-matrix method. A multiconfiguration eigenfunction expansion up to the $n=3\mathrm{}$ levels of the core ion $\mathrm{Fe}\mathrm{XVIII}$ is employed with five spectroscopic configurations ${2s}^2{2p}^5{,2s2p}^6{,2s}^2{2p}^{4}3s,3p,3d,$ and a number of correlation configurations. The unified $e+\mathrm{ion}$ recombination calculations for $e+$$\mathrm{Fe}\mathrm{XVIII}\to \mathrm{Fe}\mathrm{XVII}$ include both the nonresonant and resonant recombination (“radiative” and “dielectronic recombination”—RR and DR). Photoionization and $e+\mathrm{ion}$ recombination calculations are carried out for the total and the level-specific cross sections, including the ground and several hundred excited bound levels of $\mathrm{Fe}\mathrm{XVII}$ (up to fine-structure levels with $n=10).\mathrm{}$ The low-energy and the high-energy cross sections are compared from (i) a three-level calculation including only the ${2s}^2{p}^5\hspace{0.5em}{(}^2{P}_{1/2,3/2}^o)$ and ${2s2p}^6\hspace{0.5em}{(}^2{S}_{1/2})$ levels of $\mathrm{Fe}\mathrm{XVIII},$ and (ii) the first 60-level calculation with $\Delta n>\mathrm{}0\mathrm{}$ coupled channels. Strong channel coupling effects are demonstrated throughout the energy ranges considered, in particular via giant photoexcitation-of-core (PEC) resonances due to $L-M$ shell dipole transition arrays ${2p}^5\to {2p}^{4}3s,3d$ in $\mathrm{Fe}\mathrm{XIII}$ that enhance effective cross sections by orders of magnitude. Comparison is made with previous theoretical and experimental works on photoionization and recombination that considered the relatively small low-energy region (i), and the weaker $\Delta n=0\mathrm{}$ couplings. While the simpler three-level results describe the near-threshold photoionization and recombination, they are inadequate for practical applications that also require the higher-energy cross sections for modeling ionization balance of $\mathrm{Fe}\mathrm{XVII}$ in laboratory and astrophysical plasmas. The present 60-level results should provide reasonably complete and accurate datasets for both photoionization and $e+\mathrm{ion}$ recombination of $\mathrm{Fe}\mathrm{XVII}.$

The conditions satisfied by saddle points of the analytical potential-energy surfaces of the triatomic molecule are derived from the algebraic approach. The conditions cause the potential parameter $\alpha ,$ introduced in a previous paper [J. Chem. Phys. $111,$ 4466 (1999)], to be imaginary. The criterion is applied to the triatomic molecules ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{O}}_3.$

We study numerically the interaction between an intense circularly polarized laser field and an electron moving in a potential that has a discrete cylindrical symmetry with respect to the laser-pulse propagation direction. This setup serves as a simple model, e.g., for benzene and other aromatic compounds. From general symmetry considerations, within a Floquet approach, selection rules for the harmonic generation [O. Alon et al., Phys. Rev. Lett. 80, 3743 (1998)] have been derived recently. Instead, the results we present in this paper have been obtained solving the time-dependent Schrödinger equation ab initio for realistic pulse shapes. We find a rich structure that is not always dominated by the laser harmonics.

On the basis of a simple exactly solvable model we discuss the possibilities for state preparation and state control of atoms in a periodic optical potential. In addition to the periodic potential a uniform force with an arbitrary time dependence is applied. The method is based on a formal expression for the full evolution operator in the tight-binding limit. This allows us to describe the dynamics in terms of operator algebra, rather than in analytical expansions.

We calculate the light-induced collisional loss of laser-cooled and trapped magnesium atoms for detunings up to 50 atomic linewidths to the red of the ${}^1{S}_0{-}^1{P}_1$ cooling transition. We evaluate loss rate coefficients due to both radiative and nonradiative state-changing mechanisms for temperatures at and below the Doppler-cooling temperature. We solve the Schrödinger equation with a complex potential to represent spontaneous decay, but also give analytic models for various limits. Vibrational structure due to molecular photoassociation is present in the trap loss spectrum. Relatively broad structure due to absorption to the ${\mathrm{Mg}}_2{\hspace{0.5em}}^1{\Sigma }_u$ state occurs for detunings larger than about ten atomic linewidths. A much sharper structure, especially evident at low temperature, occurs even at smaller detunings due to ${\mathrm{Mg}}_2{\hspace{0.5em}}^1{\Pi }_g$ absorption, which is weakly allowed due to relativistic retardation corrections to the forbidden dipole transition strength. We also perform model studies for the other alkaline-earth-metal species Ca, Sr, and Ba, and for Yb, and we find similar qualitative behavior as for Mg.

By solving the Maxwell equations, an effective plasma dielectric constant is obtained to replace the quasistatic plasma dielectric constant derived from the Drude model. In the vicinity of resonance absorption, the electron density and temperature undergo such a rapid change that the quasistatic dielectric constant is no longer appropriate to describe the behavior of resonance absorption. Using this effective dielectric constant to modify the hydrodynamic model developed by Ditmire and co-workers, we studied the interaction between different-sized atomic clusters and high-intensity laser pulses of different wavelengths. Reasonable agreement between the calculated results and published experimental results was found.

We propose a strategy to eliminate coherent Raman scattering from a two-component quantum gas. This occurs when the two Raman coupling laser fields are far detuned from intermediate states and when an equal number of atoms are initially maintained in the two ground states, a situation reminiscent of the dark state in stimulated Raman adiabatic passage. The total scattered light then becomes completely incoherent and depends on second order atom number correlation functions. We study this Hanbury-Brown–Twiss type interferometry and present atomic bunching/antibunching effects readily observable from the angular distribution of the total scattered light.

We have used an ultralow threshold continuous-wave optical parametric oscillator (OPO) to reduce the quantum fluctuations of the reflected pump beam below the shot noise limit. The OPO consisted of a triply resonant cavity containing a periodically poled lithium niobate crystal pumped by a Nd:YAG (yttrium aluminum garnets) laser and giving signal and idler wavelengths close to $2.12\mu \mathrm{m}$ and a threshold as low as $300\mu \mathrm{W}.$ We detected the quantum fluctuations of the pump beam reflected by the OPO using a slightly modified homodyne detection technique. The measured noise reduction was $30\%$ (inferred noise reduction at the output of the OPO $38\%).$

The complete solutions of the Schrödinger equation for a particle with time-dependent mass moving in a time-dependent linear potential are presented. One solution is based on the wave function of the plane wave, and the other is in the form of the Airy function. A comparison is made between the present solution and former ones to show the completeness of the present solution.

Transition probabilities of three magnetic dipole $\mathrm{}\left(M1\mathrm{}\right)\mathrm{}$ transitions in multiply charged ions of potassium have been measured using the Livermore electron beam ion trap EBIT-2. Our results for the atomic level lifetimes are $4.44\pm 0.10\hspace{0.5em}\mathrm{ms}$ for K XI (F-like) ${2s}^2{2p}^5{}^2{P}_{1/2}^o,$ $4.47\pm 0.10\hspace{0.5em}\mathrm{ms}$ for K XV (B-like) ${2s}^{2}2p{}^2{P}_{3/2}^o,$ and $7.6\pm 0.5\hspace{0.5em}\mathrm{ms}$ for K XVI (Be-like) $2s2p{}^3{\mathrm{P}}_2^o.$ The results confirm the accuracy of most predictions to within 3% of ground-state and 7% of excited-state transitions.

In this work we present an improvement over the over-barrier model (OBM) described in a recent paper [F. Sattin, Phys. Rev. A 62, 042711 (2000)]. We show that (i) one of the two free parameters introduced there actually comes out consistently from the starting assumptions underlying the model; (ii) the modified model thus obtained is as much accurate as the former one. Furthermore, we show that OBMs are able to accurately predict some recent results of state-selective electron capture, at odds with what was previously supposed.