We improve previously proposed conditions each measure of entanglement has to satisfy. We present a class of entanglement measures that satisfy these conditions and show that the quantum relative entropy and Bures metric generate two measures of this class. We calculate the measures of entanglement for a number of mixed two spin-1/2 systems using the quantum relative entropy, and provide an efficient numerical method to obtain the measures of entanglement in this case. In addition, we prove a number of properties of our entanglement measure that have important physical implications. We briefly explain the statistical basis of our measure of entanglement in the case of the quantum relative entropy. We then argue that our entanglement measure determines an upper bound to the number of singlets that can be obtained by any purification procedure.

We show that the quantum baker’s map, a prototypical map invented for theoretical studies of quantum chaos, has an efficient realization in terms of quantum gates. Chaos in the quantum baker’s map could be investigated experimentally on a quantum computer based on only three quantum bits.

We present a comparison of the calculated resonant $\mathrm{dd}\mu$ formation, $\mathrm{dd}$ fusion, and spin-flip rates with recent precise data from PSI for D${}_2$ gas $(\Phi =0.05\mathrm{}$, $T=50\mathrm{}$–300 K). The calculations are performed beyond the standard dipole approximation, and without multipole expansion of the perturbation potential. The resonance finite width was also taken into account. The ab initio calculations of $\mathrm{dd}$ resonant fusion rates agree with 11$\%$ accuracy with experiment without using any fit parameters. This accuracy is restricted by the 15$\%$ precision of theoretical estimates of the fusion rate ${\Gamma }_f$ for $(dd\mu {)}_{11}.$ If the ${\Gamma }_f$ value is taken from the fit, an excellent 4$\%$ agreement with data can be achieved. The calculations of spin-flip rates are closer to the experiment than the dipole approximation, but they are still 40$\%$ higher. This problem needs a more careful theoretical treatment. New experiments are suggested for investigation of the $\mathrm{dd}\mu$ formation rate density dependence.

Valence and excited dipole-bound states of the ${\mathrm{LiH}}^{\mathrm{-}}$ anion are calculated with the recently developed electron-attachment equation-of-motion coupled-cluster technique. It is found that the first dipole-bound state of ${\mathrm{LiH}}^{\mathrm{-}}$ corresponds to the second dissociation channel ${\mathrm{LiH}}^{\mathrm{-}}{\to \mathrm{Li}}^{\mathrm{-}}{(}^{1}S)+\mathrm{H}{(}^{2}S).\mathrm{}$ The second (excited) dipole-bound state of ${\mathrm{LiH}}^{\mathrm{-}}$ is below the neutral ground-state potential energy curve only for some range of the Li-H internuclear distance. This state appears at bond lengths larger than $\approx 2.0\AA$ and decays at Li-H distances longer than ≈4.2 Å, where the dipole moment of LiH becomes smaller than the critical value of 2.5 D. The adiabatic electron affinity of LiH calculated at the coupled-cluster level with the iterative inclusion of all single, double, and triple excitations and a large atomic natural orbital basis set is 0.327 eV, almost matching the recently obtained experimental value of $0.342\pm 0.012\mathrm{eV}.$

The Hylleraas-type variational method is used to calculate the energies of the lithium ${1s}^{2}2s{}^{2}S$ and ${1s}^{2}2p{}^{2}P$ isoelectronic sequences up to $Z=20\mathrm{}$. The oscillator strengths for the ${1s}^{2}2s{}^2\overrightarrow{S}{1s}^{2}2p{}^{2}P$ transitions are evaluated for $Z$ up to 20, including finite nuclear mass effects, and the corresponding lifetimes are determined. The $1/Z$ expansion method is used to extend the variational results to larger values of $Z$. Relativistic corrections to the dipole transition moment squared are estimated by comparison with the relativistic many-body perturbation theory results of Johnson et al. [At. Data Nucl. Data Tables 64, 279 (1996)]. The final lifetime for the ${1s}^{2}2p{}^{2}P$ state of lithium is in good agreement with recent high-precision measurements.

We present a theoretical calculation of the fine and hyperfine splittings of the energy levels in the metastable states of antiprotonic helium ${}^4{\mathrm{He}}^{+}\overline{p},$ performed with the accuracy of ${10}^{-4}.$ We also discuss the perspectives of obtaining experimental data on the magnetic moment of the antiproton from measurements of the hyperfine structure of antiprotonic helium.

An efficient method for production of cold antihydrogen $\left(\mathrm{H}¯\right)$ is proposed. Alkali-metal atoms laser excited to a Rydberg state are charge exchanged with cold trapped positrons, producing Rydberg states of positronium. In a second Rydberg-state charge exchange, the positronium atoms give up their Rydberg positrons to cold trapped antiprotons, producing Rydberg states of $\mathrm{H}¯$. These $\mathrm{H}¯$ atoms soon decay down to the ground state, and, because they are cold, could be trapped in a magnetic trap. The efficiency of the process results from the extremely large cross sections for Rydberg charge exchange. Classical trajectory Monte Carlo calculations indicate an $\mathrm{H}¯$ instantaneous production rate of 10${}^6/$s.

Kohn-Sham equations are derived for lowest-lying multiplets. A recently proposed method of the author is used to construct exchange potentials of multiplets.

States of positronium hydride having different angular momenta have been studied by means of quantum Monte Carlo techniques. Explicitly correlated wave functions for different states have been obtained using the variational Monte Carlo optimization method. These wave functions have been used in variational Monte Carlo and diffusion Monte Carlo (DMC) simulations to compute energies, annihilation rates, and other observables. Our DMC results compare well with the best published variational ground-state binding energy, and show that positronium hydride has metastable states with angular momentum $L=1\mathrm{}$ and 2 above the ground-state dissociation threshold. The values of the other observables for the ground state are comparable with the best variational calculations. The results for the $L=1\mathrm{}$ and 2 states are used to discuss a proposed model for the annihilation of positrons in alkali hydrides crystals.

Photoexcited Cu $K{\alpha }_{3,4}$ satellite spectra were measured as a function of excitation energy, from threshold at $\sim$10.010 keV to saturation at $\sim$11 keV. A two-regime behavior is found, where in the near-threshold regime (TR) both the shape and the intensity of the spectrum vary. In the higher-energy regime (GR) only the intensity varies but not the shape. The GR spectra are well described by relativistic Dirac-Fock calculations. The analytic Thomas model, applicable in this adiabatic regime, does not agree well with the measured intensity variation with excitation energy. The continuous intensity rise from zero at threshold confirms the shake theory prediction of a pure shake-off process for inner-shell, medium-$Z$ atom satellites. The thresholds for the individual spectral features, the overall shape variation, and the variations of the individual lines in the TR regime are determined, and discussed.

A laser spectroscopic method was developed to directly observe the lifetimes of individual states in metastable antiprotonic helium atoms $\left(\overline{p}{}^4{\mathrm{He}}^{+}\right).\mathrm{}$ Collisional effects with surrounding helium atoms were studied in cryogenic gas targets at pressures between 0.1 and 9.0 bars and at temperatures between 5.5 and 7.0 K. The metastable state $(n,\mathcal{l})=(39,35)\mathrm{}$ showed a lifetime of 1.5 $\mu \mathrm{s}$, regardless of density, whereas the lifetime of the energetically lower-lying state $\mathrm{}(37,34)\mathrm{}$ was found to shorten from 1.3 to 0.1 $\mu$s with increasing density. The lifetimes of the states $\mathrm{}(38,34)\mathrm{}$ and $\mathrm{}(36,33)\mathrm{}$ were determined to be 10 ns and 5 ns, respectively, showing the effects of the internal Auger process. When extrapolated to zero density, the measured lifetimes agreed with the results of calculations for the radiative and Auger widths. Using the fact that the state $\mathrm{}(37,34)\mathrm{}$ becomes short lived at high density, the resonance $\mathrm{}(38,35)\mathrm{}\to \mathrm{}(37,34)\mathrm{}$ at 529.62 nm was detected.

Muon transfer from excited $\mu p^{*}$ and $\mu d^{*}$ atoms to the three gases nitrogen, neon, and argon is studied. Variations of the experimental conditions such as pressure and relative concentrations on the fractions ${\alpha }_{\mathrm{pZ}}$ and ${\alpha }_{\mathrm{dZ}}$ of excited state events in prompt muonic x rays are analyzed. The differences between excited-state transfer from $\mu p^{*}$ and $\mu d^{*}$ to ${\mathrm{N}}_2$, Ne, and Ar are discussed. For these elements, capture ratios $A({\mathrm{H}}_2,Z)$ and $A({\mathrm{D}}_2,Z)$ are given, from which an indirect value $A({\mathrm{H}}_2,{\mathrm{D}}_2)$ is deduced.

Relativistic ab initio pseudopotential and fully relativistic density-functional benchmark calculations have been carried out for the first to fourth ionization potentials as well as the $\mathrm{df}$ charge-transfer energies for the whole series of lanthanide atoms. It was found that the two approaches have essentially the same accuracy compared to the experimental values. In addition, it is shown that the present (nonrelativistic) density functionals work fairly well within an otherwise relativistic framework even for the rather compact $4f$ shells, correcting previous statements to the contrary.

A definition of key quantities of the Kohn-Sham form of density-functional theory such as the exchange-correlation potential $v_{\mathrm{xc}}$ and the energy density ${\varepsilon }_{\mathrm{xc}}$ in terms of wave-function quantities (one- and two-electron density matrices) is given. This allows the construction of $v_{\mathrm{xc}}$ and ${\varepsilon }_{\mathrm{xc}}$ numerically as functions of r from ab initio wave functions. The behavior of the constructed exchange ${\varepsilon }_x$ and correlation ${\varepsilon }_c$ energy densities and the corresponding integrated exchange $E_x$ and correlation $E_c$ energies have been compared with those of the local-density approximation (LDA) and generalized gradient approximations (GGA) of Becke, of Perdew and Wang, and of Lee, Yang, and Parr. The comparison shows significant differences between ${\varepsilon }_c\left(\mathbf{r}\right)$ and the ${\varepsilon }_c^{\mathrm{GGA}}\left(\mathbf{r}\right),$ in spite of some gratifying similarities in shape for particularly ${\varepsilon }_c^{\mathrm{PW}}.$ On the other hand, the local behavior of the GGA exchange energy densities is found to be very similar to the constructed ${\varepsilon }_x\left(\mathbf{r}\right),$ yielding integrated energies to about 1% accuracy. Still the remaining differences are a sizable fraction $(\sim 25\%)$ of the correlation energy, showing up in differences between the constructed and model exchange energy densities that are locally even larger than the typical correlation energy density. It is argued that nondynamical correlation, which is incorporated in ${\varepsilon }_c\left(\mathbf{r}\right),$ is lacking from ${\varepsilon }_c^{\mathrm{GGA}}\left(\mathbf{r}\right),$ while it is included in ${\varepsilon }_x^{\mathrm{LDA}}\left(\mathbf{r}\right)$ and ${\varepsilon }_x^{\mathrm{GGA}}\left(\mathbf{r}\right)$ but not in ${\varepsilon }_x\left(\mathbf{r}\right).\mathrm{}$ This is verified almost quantitatively for the integrated energies. It also appears to hold locally in the sense that the difference ${\varepsilon }_x^{\mathrm{GGA}}\left(\mathbf{r}\right)-{\varepsilon }_x\left(\mathbf{r}\right)$ may be taken to represent ${\varepsilon }_c^{\mathrm{nondyn}}\left(\mathbf{r}\right)$ and can be added to ${\varepsilon }_c^{\mathrm{GGA}}\left(\mathbf{r}\right)$ to bring it much closer to ${\varepsilon }_c\left(\mathbf{r}\right).\mathrm{}$

Theoretical results have been computed to complement recent measurements by Scheer et al. [Bull. Am. Phys. Soc. 42, 1026 (1997)], which yielded electron affinities (EA) of excited states of the ground configuration of ${\mathrm{Sn}}^{\mathrm{-}}$. Our relativistic configuration-interaction values for the position of the excited ${\mathrm{Sn}}^{\mathrm{-}}$ with respect to the negative ion ground state are EA${(}^2{D}_{3/2})$=5903 ${\mathrm{cm}}^{\mathrm{-}1}$ (0.732 eV), and EA${(}^2{D}_{5/2})$=6493 ${\mathrm{cm}}^{\mathrm{-}1}$ (0.805 eV). Triple excitations make a significant contribution. Magnetic dipole hyperfine-structure constants $\mathrm{}\left(A\right)\mathrm{}$ and $M1\mathrm{}$ transition probabilities are also reported.

Based on multichannel quantum-defect theory, a method to calculate and compile radiative transition processes for atoms (including highly ionized high-$Z$ atoms) is proposed. Through defining the renormalized transition matrix elements from initial eigenchannels to final eigenchannels, the transition processes between infinitely many initial states and infinitely many final states can be treated conveniently. As illustrative examples, we study the alkali-metal atoms in detail.

Some properties of atoms defined in terms of two-electron operators are investigated for sodium. Systematic multiconfiguration Hartree-Fock (MCHF) methods are used. Of particular interest are the energy, the isotope shift parameter, and a dipole-dipole parameter defined as the expectation value of the operator $({\sum }_i{\mathbf{r}}_i{)}^2$. Unlike the one-electron dipole operator, where the line strength was predicted accurately from single, double, and triple excitations, these properties require that quadruple excitations also be considered.

Spherically averaged electron-pair relative-motion (intracule) densities $h\left(u\right)\mathrm{}$ in position space and $\overline{h}\mathrm{}\left(v\right)\mathrm{}$ in momentum space represent probability densities of finding interelectronic position and momentum distances, $|{\mathbf{r}}_j-{\mathbf{r}}_k|$ and $|{\mathbf{p}}_j-{\mathbf{p}}_k|,$ of any pair of electrons $j$ and $k$ to be $u$ and $v,$ respectively. Using the numerical Hartree-Fock method, these electron-pair densities $h\left(u\right)\mathrm{}$ and $\overline{h}\mathrm{}\left(v\right)\mathrm{}$ are constructed and examined systematically for the atoms from He to Xe in their ground state. In position space, the intracule density $h\left(u\right)\mathrm{}$ is a monotonically decreasing function for all the atoms. In momentum space, however, the intracule densities $\overline{h}\mathrm{}\left(v\right)\mathrm{}$ are found to be classified into three types according to the number of local maxima and their locations. These different behaviors of the densities $h\left(u\right)\mathrm{}$ and $\overline{h}\mathrm{}\left(v\right)\mathrm{}$ are studied in detail based on the contributions of electrons in a pair of atomic spinorbitals and subshells.

The electronic structure of the hydrogen molecule in a magnetic field is investigated for parallel internuclear and magnetic field axes. The lowest states of the $\Pi$ manifold are studied for spin singlet and triplet ${(M}_s=-1)$ as well as gerade and ungerade parity for a broad range of field strengths $0<~B<~100$ a.u. For both states with gerade parity we observe a monotonic decrease in the dissociation energy with increasing field strength up to $B=0.1\mathrm{}$ a.u. and metastable states with respect to the dissociation into two H atoms occur for a certain range of field strengths. For both states with ungerade parity we observe a strong increase in the dissociation energy with increasing field strength above some critical field strength $B_c.$ As a major result we determine the transition field strengths for the crossings among the lowest ${}^1{\Sigma }_g,$ ${}^3{\Sigma }_u,$ and ${}^3{\Pi }_u$ states. The global ground state for $B\lesssim 0.18$ a.u. is the strongly bound ${}^1{\Sigma }_g$ state. The crossings of the ${}^1{\Sigma }_g$ with the ${}^3{\Sigma }_u$ and ${}^3{\Pi }_u$ state occur at $B\approx 0.18$ and $B\approx 0.39$ a.u., respectively. The transition between the ${}^3{\Sigma }_u$ and the ${}^3{\Pi }_u$ state occurs at $B\approx 12.3$ a.u. Therefore, the global ground state of the hydrogen molecule for the parallel configuration is the unbound ${}^3{\Sigma }_u$ state for $0.18\lesssim B\lesssim 12.3$ a.u. The ground state for $B\gtrsim 12.3$ a.u. is the strongly bound ${}^3{\Pi }_u$ state. This result is of great relevance to the chemistry in the atmospheres of magnetic white dwarfs and neutron stars.

Energy pooling collisions of two cadmium atoms in the state $5s5p{}^3{P}_1$ have been investigated under pulsed laser excitation and cross sections have been measured for the production of atoms in the $5s5d{}^3{D}_J$ states. We have obtained the values $(1.3\mathrm{}\pm 0.6)\times {10}^{-16}$, $(1.1\mathrm{}\pm 0.5)\times {10}^{-16}$, and $(0.7\mathrm{}\pm 0.4)\times {10}^{-16}$ cm${}^2$ for $J=1,2,3\mathrm{}$, respectively. The effects of the radiation trapping phenomenon, important both in the cross-section determination and in the evaluation of the Cd atom density in the sealed cell used in the experiment, have been taken into account through numerical solutions of the radiation diffusion equation in the specific conditions of our experiment.