Rigorous lower bounds to the Weizsäcker energy ${\mathit{T}}_{\mathit{W}}$ of a many-fermion system are derived by means of two and three radial expectation values. Some of them are of variational nature and others are founded on classical integral inequalities and a theorem which allows us to extend universally the validity of the bounds to ${\mathit{T}}_{\mathit{W}}$ obtained for spherically symmetric densities. Also, rigorous and approximate upper bounds, in terms of a radial expectation value and the ionization potential, are encountered in the case of atomic systems by taking into account, at times, the properties of the monotonicity of the electron density. The role of the expectation value 〈${\mathit{r}}^{\mathrm{-}2}$〉 is highly remarkable in the determination of the bounds. The bounds found in this work allow us to correlate rigorously the Weizsäcker energy with numerous fundamental and/or experimentally measurable quantities of the system, such as, e.g., the number of constituents, the diamagnetic susceptibility, the diamagnetic-shielding correction, and the softness kernel in the density-functional theory. Finally, just for checking the quality of both lower and upper bounds, numerical comparisons employing Hartree-Fock atomic densities are done in the whole Periodic Table.

The aim of the present paper is to analyze a realistic model of a quantum chaotic system: the spectrum and the eigenstates of the rare-earth atom of Ce. Using the relativistic configuration-interaction method the spectra and the wave functions of odd and even levels of Ce with J=4 are calculated. It is shown that the structure of the excited states at excitation energies above 1 eV becomes similar to that of the compound states in heavy nuclei. The wave functions of the excited states are chaotic superpositions of the simple basis states (with the number of ‘‘principal’’ components N∼100), built of the 4f, 6s, 5d, and 6p single-electron orbitals. The localization of the eigenstates on the energy scale is characterized by the spread width Γ∼ND, where D is the average level spacing (D∼0.03 eV). The emergence of chaos in the spectrum and the dependence of the N and Γ parameters on the excitation energy are studied. The shape of the localization is shown to be Lorenzian around the maximum (principal components), whereas outside this region the squared components display a faster decrease, in agreement with the perturbation theory treatment of the band random matrix (BRM) model. The structure of the real interaction matrix is compared with that assumed in the BRM models. A formula expressing the mean-squared values of matrix elements between the eigenstates in terms of their parameters and single-particle occupancies is derived, and its applicabilility is checked with the results of numerical calculations. The hypothesis of a Gaussian distribution of the eigenstates’ components and matrix elements between the eigenstates has been checked. The existence of the statistical (dynamical) enhancement of weak perturbations in systems with dense spectra is demonstrated.

The Dirac equation with a scalar potential ${\mathit{U}}_{\mathit{S}}$(r) and the fourth component of a vector potential ${\mathit{U}}_{\mathit{V}}$(r) is considered in the case of rectangular shapes of these potentials with the same radius R; approximate analytic expressions are derived for the single-particle energy of bound states in certain cases. The results obtained with these expressions are compared with the corresponding ‘‘exact’’ results obtained by solving the eigenvalue equation numerically. It is found that very good results are obtained for the ground state and for quite a wide range of values of R with one of the proposed expressions. Even the corresponding nonrelativistic version of this expression has not been derived before, to our knowledge.

The extended cusp condition asserts that h(u)-${\mathit{a}}_0$dh(u)/du≥0, where ${\mathit{a}}_0$ is the Bohr radius, u is the interelectronic spacing, and h(u) is the angle-averaged pair density in the ground state. We prove that this inequality is obeyed by Hooke’s atom for any value of the spring constant. However, we also show that this condition is violated by the uniform electron gas of high density. We explain the qualitative difference between these two systems by subtracting a long-range contribution from h(u), leaving a short-range contribution which is amenable to a local density approximation. Thus the extended cusp condition is not a universal property of the ground state of inhomogeneous electronic systems.

A scheme, analogous to the linear combination of atomic orbitals, is proposed to calculate rates of reactions of nucleon-group transfer between nuclei confined in muonic molecules. It is pointed out that such rates can be rather high if the energy release of a reaction is small. As an example, the rate of the reaction p-μ${\mathrm{-}}^{10}$Be→t-μ${\mathrm{-}}^8$Be is calculated.

Several entropic and uncertaintylike results for three-dimensional many-particle systems are extended to the case of arbitrary dimensionality D. This work deals with (i) upper bounds to information entropies and (ii) radial and logarithmic uncertaintylike relationships. The resulting expressions are given in an analytical compact form for any dimensionality. The first few low-dimensional cases (D=1,2,3,4) are emphasized.

The spectrum of ${\mathrm{D}}_3^{+}$ is analyzed using a spectroscopically determined effective ${\mathrm{H}}_3^{+}$ potential [B. M. Dinelli, S. Miller, and J. Tennyson, J. Molec. Spectrosc. 163, 71 (1994)] and an accurate ab initio potential [G. C. Lie and D. Frye, J. Chem. Phys. 96, 6784 (1992)]. Calculations suggest that the major error in the potential of Lie and Frye is due to the Born-Oppenheimer approximation. ${\mathrm{D}}_3^{+}$ spectroscopic data are used to construct both Born-Oppenheimer and mass-dependent adiabatic surfaces for the ${\mathrm{H}}_3^{+}$ system by fitting only one parameter. These surfaces reproduce the fundamental rovibrational transitions of ${\mathrm{H}}_3^{+}$ and ${\mathrm{D}}_3^{+}$ to within 0.03 ${\mathrm{cm}}^{\mathrm{-}1}$. An accurate adiabatic surface has been determined for a polyatomic molecule.

Fluorescence spectra of a ${\mathrm{C}}_{60}$ polycrystalline film at room temperature, obtained under excitation at 514.5 and 337.1 nm, are presented. The spectra were measured with subnanosecond laser excitation in a 5-ns gate that is synchronous with the excitation. For both excitation wavelengths, the emission spectra show the same band, peaking at 1.68 eV and containing well-resolved structures in the range 1.4 to 1.8 eV. An intense band at energies greater than 1.8 eV emerges for 514.5-nm excitation, while no emission above 1.8 eV could be detected for excitation at 337.1 nm. These spectral features are compared with those of ${\mathrm{C}}_{60}$ dissolved in n-hexane at room temperature.

We describe the coupling of electronic and nuclear motions in slow atomic collisions using a combination of the eikonal and time-dependent Hartree-Fock (TDHF) approximations. Starting with an eikonal representation of the total wave function, a wave function is constructed from classical trajectories in a way suitable for describing atomic collisions with velocities down to a fraction of an atomic unit. The TDHF formulation is developed in terms of its density operator. The differential equations coupling the density operator to the nuclear motions have been solved with a procedure developed to account for the coupling of fast (electronic) and slow (nuclear) degrees of freedom. This is based on a local-interaction picture and on a temporal linearization of the equations, allowing for the integration of the electronic density over large time intervals. Density-matrix equations are derived in a basis of traveling atomic orbitals, and numerical results are presented for ${\mathrm{H}}^{+}$+H and ${\mathrm{He}}^{2+}$+H. Good agreement is found with experimental results for ${\mathrm{H}}^{+}$+H, comparing integral electron transfer cross sections from 2 to 2000 eV. In addition, an analysis of the time dependence of atomic orbital populations provides insight on electronic rearrangement during collisions and shows that even very small contributions from the driving forces of the nuclei on the electrons have a cumulative effect on the density operator that can substantially change final populations.

We have measured coincidences between neutralized projectiles and He recoil ions for 50–175-keV proton-helium collisions. From the data we obtained transfer ionization (TI) cross sections differential in the projectile scattering angle. Laboratory scattering angles range from 0 to 2.0 mrad. The experimental method allowed separation of the postcollision charge states of the target atoms. The ratio of the cross sections for TI to the sum of TI and single capture, F, is presented as a function of projectile scattering angle. Comparison is made to previous measurements of this ratio where data is available. The differential cross sections are compared to dynamical classical trajectory Monte Carlo (dCTMC) calculations. Agreement in the shape of the differential cross sections is good between the theory and measurement over the entire energy range.

Within the context of laser-electron scattering for low intensities of the incoming photon beam, we present a discussion of the leading multiphoton reaction, two-photon absorption by a free electron in a Compton-like process. The two-photon angular distribution is calculated in quantum electrodynamics and compared with existing classical and semiclassical calculations in the Thomson limit. We find that for incident linearly polarized beams all such calculations agree in this limit. Furthermore, the present approach allows us to study the possible effect of the quantum-mechanical correlation of pairs of coincident photons, i.e., the degree of second-order coherence.

We calculated numerically in a relativistic partial-wave formulation the positron energy spectra of pair-production σ(${\mathit{E}}_{+}$) in the field of atoms with atomic number Z=1, 6, 13, and 82 for photons of energies near threshold, k=2.001, 2.01, and 2.10 ${\mathit{m}}_{\mathit{e}}$${\mathit{c}}^2$, where ${\mathit{E}}_{+}$ is the positron energy. Our results indicate that in this low-photon-energy region, the atomic-electron screening effect increases as Z increases, k decreases, and ${\mathit{E}}_{+}$ decreases. The ratio of screened to point-Coulomb cross sections σ(${\mathit{E}}_{+}$) varies from 0.985 to 1.69×${10}^4$. When the screening effect is important, it increases the cross section σ(${\mathit{E}}_{+}$). Our results also indicate that the approximate treatment of screening through energy-shift screening theory becomes inadequate when the screening effect is very important. The approximate treatment of screening through the corrected-effective normalization screening theory works fine in this low-photon-energy region, except for the case with Z=6, k=2.001${\mathit{m}}_{\mathit{e}}$${\mathit{c}}^2$, and ${\mathit{E}}_{+}$=1.0001${\mathit{m}}_{\mathit{e}}$${\mathit{c}}^2$, where the screening effect is not a normalization effect.

The first-order cross section for Compton scattering is expressed in terms of the cross section for scattering by fast charged particles in the plane-wave Born approximation as a function of the momentum, Q, transferred by the projectile to the atomic electron(s). As an example of this relationship, the high-energy photon limit for the ratio of double to single ionization by Compton scattering, ${\mathit{R}}_{\mathit{C}}$(Q), is expressed in terms of the ratio, ${\mathit{R}}_{\mathit{Z}}$(Q), for scattering by charged particles at large Q. Results for ${\mathit{R}}_{\mathit{C}}$(Q) are presented.

An approach to calculate the triple differential cross sections (TDCS) for ionization of hydrogenic ions by electron impact in the intermediate- and high-energy regime and for asymmetric geometry is proposed. The theoretical model is particularly suitable for asymmetric geometry since the two outgoing electrons are treated on unequal footings. The final-state wave function, in the present prescription, involves the electron-electron correlation term and satisfies the asymptotic three-body boundary condition of an ionization process for asymmetric geometry (i.e., for ${\mathit{k}}_1$≫${\mathit{k}}_2$). As is well known, this is one of the most important factors for the prediction of reliable ionization cross sections. The long-range Coulomb interaction occurring in the initial channel has been taken into account properly. TDCS results have been computed for ionization of the ${\mathrm{He}}^{+}$ ion for incident energies of 250, 500, and 1000 eV for fixed values of ejected energy (5 eV) and scattering angle (4°). A large recoil peak is noted in the TDCS structure at lower energies (e.g., 250 eV).

We have applied the finite-element method to electron-molecule collisions. All the calculations are done in the body frame within the fixed-nuclei approximation. A model potential, which is added to the static and polarization potential, has been used to represent the exchange effect. The method is applied to electron-${\mathrm{H}}_2$ scattering and the eigenphase sums and the cross sections obtained are in very good agreement with the corresponding results from the linear-algebraic approach. Finite-element calculations of the R matrix in the region where the static and exchange interactions are strong, however, has about one-half to one-fourth of the memory requirement of the linear-algebraic technique.

Differential cross sections are presented for 15° and 20° electron emission in 100- and 150-keV/u ${\mathrm{C}}^{\mathit{q}+}$-He collisions where the projectile charge states are 0 to 4+. Coincidences between electrons emitted at 20° and projectiles which captured or lost electrons in the collisions were also measured. The coincidence and noncoincidence data are used to demonstrate how partial screening of the projectile nuclear charge and direct interactions between projectile and target electrons influence the electron emission. In addition, the relative importance of multielectron transitions associated with either electron capture or electron loss by the projectile is demonstrated. Finally, the data are used to test whether saddle-point ionization is important in these ionizing collisions, as has recently been suggested. The present data do not support this suggestion and are in disagreement with the measurements which do support it. Furthermore, it is demonstrated that dressed ion impact data are inappropriate for testing for a saddle-point ionization mechanism.

A minimum principle for the nonrelativistic scattering length was derived some years ago under the assumption that only a finite number of discrete states exist below the scattering threshold. The variational bound is applicable even when the bound-state wave functions are imprecisely known–they need only be accurate enough to give binding in a Rayleigh-Ritz calculation. The method is generalized here to apply to potential scattering described by the Dirac equation. An apparent difficulty associated with the existence of a continuum of negative-energy states, that is, the problem of ‘‘variational collapse,’’ is removed through the inclusion of second-order terms in the variational expression involving matrix elements of the square of the Dirac Hamiltonian. In the course of the derivation a relativistic version of the Hylleraas-Undheim theorem is developed. Applications of this theorem are described that provide a sufficient condition for the existence of a given number of bound states, lower bounds on the energy eigenvalues, and a systematic procedure for improving the accuracy of trial bound-state wave functions. A very simple model calculation was performed to illustrate the minimum property and the stability of the numerical procedure.

The structure of a one-dimensional two-electron model atom analogous to helium is examined. Predictions of Hartree-Fock and basis-state diagonalization methods are compared with results of exact numerical techniques. Particular attention is given to the lowest-energy autoionizing resonance and to how the autoionizing state can be defined. The dynamics of the autoionizing decay are examined with regard to the time development of the spatial wave function and various population amplitudes. The photoabsorption line shape of the lowest-lying autoionizing state for dipole excitation from the first excited state is also presented.

We present an analysis, based on the metaplectic group Mp(2), of the recently introduced single-mode inverse creation and annihilation operators and of the associated eigenstates of different two-photon annihilation operators. We motivate and obtain a quantum operator form of the classical Möbius or fractional linear transformation. The subtle relation to the two unitary irreducible representations of Mp(2) is brought out. For problems involving inverse operators the usefulness of the Bargmann analytic function representation of quantum mechanics is demonstrated. Squeezing, bunching, and photon-number distributions of the four families of states that arise in this context are studied both analytically and numerically.

The multiconfiguration relativistic random-phase approximation is applied to the photoionization of magnesium. Autoionization resonances between the 3${\mathit{s}}_{1/2}$ and 3${\mathit{p}}_{1/2}$ ionization thresholds are investigated. The main feature of our results is exhibited by three Rydberg series: the broad 3pns ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ series, the narrow 3pnd ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ series, and the 3pns ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ series caused by the fine-structure splittings. Our predictions of the resonance positions are in excellent agreement with experiment, and are consistent with other calculations. For photon energies above the 3${\mathit{p}}_{3/2}$ threshold, cross sections and spin polarizations of photoelectrons from the ionization channels Mg →${\mathrm{Mg}}^{+}$${(}^2$${\mathit{S}}_{1/2}$)+${\mathit{e}}^{\mathrm{-}}$, Mg →${\mathrm{Mg}}^{+}$${(}^2$${\mathit{P}}_{1/2}^{\mathit{o}}$)+${\mathit{e}}^{\mathrm{-}}$, and Mg →${\mathrm{Mg}}^{+}$${(}^2$${\mathit{P}}_{3/2}^{\mathit{o}}$)+${\mathit{e}}^{\mathrm{-}}$ are obtained and compared with other theoretical results.