We consider the problem of quantum ‘‘reflection above the barrier,’’ introducing a distorted-wave Born approximation based on the primitive semiclassical Wentzel-Kramers-Brillouin wave function. The idea generalizes to the concept of an unperturbed Hamiltonian defined as the exact Hamiltonian plus small parts which ‘‘turn off’’ nonclassical processes such as barrier reflection and barrier tunneling. © 1996 The American Physical Society.

Garrison and Wright showed that upon undergoing cyclic quantum evolution a metastable state acquires both a geometric phase and a geometric decay probability. This is described by a complex geometric phase associated with the cyclic evolution of two states and is closely related to the two-state formalism developed by Aharonov et al. Applications of the complex geometric phase to the Born-Oppenheimer approximation and the Aharonov-Bohm effect are considered. A simple experiment based on the optical properties of absorbing birefringent crystals is proposed. © 1996 The American Physical Society.

Two types of relativistic corrections in molecular electronic structure calculations that are based on the Kohn-Sham approach to density-functional theory have been studied: (1) relativistic corrections to the exchange-correlation functional, both in the local density and in the generalized gradient approximation; (2) a description of the nuclear charge distribution that avoids the Coulomb singularity. The diatomics AuH, AuCl, ${\mathrm{Au}}_2$, ${\mathrm{Ag}}_2$, and ${\mathrm{Cu}}_2$ were chosen as examples. Although significant effects on the total energy and on core-level energies are found, only the relativistic correction to local-density approximation has a noticeable impact on molecular observables: it induces changes of bond lengths by up to 0.005 Å, of vibrational frequencies by up to 10 ${\mathrm{cm}}^{\mathrm{-}1}$, and of binding energies by up to 0.05 eV. Thus, taken together, the relativistic corrections discussed here are much smaller than those obtained with density-gradient corrections to the exchange-correlation functional. Therefore, the common practice to neglect these relativistic corrections in molecular density-functional calculations is justified, at least for compounds without superheavy elements. © 1996 The American Physical Society.

A sophisticated theoretical description of the electronic states of americium has been hindered by the need to treat the half-filled 5f shell. We present here ab initio calculations for americium on a multiconfiguration Dirac-Fock level. The calculations were possible because only the dominant configuration state functions were used. The results give a reasonable description of the energy of the electronic ground states for the various total angular momenta and parity of americium. The results indicate some corrections for the spectroscopic assignments. © 1996 The American Physical Society.

High Rydberg states about a dipolar molecular core can exhibit special features due to the exceptionally long range of the electrical anisotropy of the core. Unlike all other, more localized, couplings of the Rydberg electron to the ion, here the interaction is not shielded by the centrifugal barrier. The influence of the core even on states of the electron with higher angular momentum l and the significant matrix elements between states that differ considerably in the principal quantum number n make this problem worthy of separate considerations. Using specialized computational techniques (both analytical and numerical) for the exact evaluation of the relevant matrix elements, the role of both inter- and intra-Rydberg series coupling is discussed. The importance of the latter (i.e., the coupling of the Rydberg electron to the rotation of the core) is emphasized. Special attention is given to the role of an external dc electrical field that is different in the present problem in that it does not significantly dilute the strength of the electron-core interaction. A positively charged core can have a dipole moment (defined with respect to its center of mass) larger than that of neutral polar molecules, particularly if the charge is localized. Hence the interseries and intraseries dynamics discussed in this paper can give rise to experimentally measurable special effects. © 1996 The American Physical Society.

A general method is presented for ab initio dynamical simulation of tunneling processes in solids and molecules, including both nuclear and spin degrees of freedom. This technique accounts for the adiabatic evolution of the potential associated with the nuclear and spin degrees of freedom in tunneling processes, in contradistinction to semiempirical approaches. To illustrate the method, inversion splitting in ${\mathrm{NH}}_3$, ${\mathrm{ND}}_3$, and ${\mathrm{PH}}_3$ is calculated within the local-density approximation. © 1996 The American Physical Society.

Most approximate exchange-correlation functionals used within density-functional theory are constructed as the sum of two distinct contributions for exchange and correlation. Separating the exchange component from the entire functional is useful since, for exchange, exact relations exist under uniform density scaling and spin scaling. In the past, accurate exchange-correlation potentials have been generated from essentially exact densities but they have not been correctly decomposed into their separate exchange and correlation components (except for two-electron systems). Using a recently proposed method, equivalent to the solution of an optimized effective potential problem with the corresponding orbitals replaced by the exact Kohn-Sham orbitals, we obtain the separation according to the density functional theory definition. We compare the results for the Ne and Be atoms with those obtained by the previously used approximate separation scheme. © 1996 The American Physical Society.

A theoretical study of the muon spin relaxation of the gaseous muonated ethyl radical ${\mathrm{C}}_2$${\mathrm{H}}_4$Mu is expanded in this paper to include both longitudinal and transverse signals. This study is based upon an operator expansion of the spin-density operator for the radical with its time dependence described by the linearized quantum Boltzmann equation. Relaxation is due to collisions which reorient the radical’s rotational angular momentum while effects on the muon’s spin are due to couplings between the muon’s spin, the radical’s free-electron spin, and the radical’s rotational angular momentum. The coefficients of the radical’s spin Hamiltonian and the collisional lifetimes (cross sections) are used as fitting parameters to describe the transverse signals. A fit to the transverse data by itself and a global fit to both the transverse and longitudinal data are obtained with good accuracy. © 1996 The American Physical Society.

In this paper, we investigate the dielectric screening process in the Thomas-Fermi model with several variations such as the thermal effects, relativistic effects, motion of the test charge, and the effect of a very strong magnetic field. Comparisons are made with the corresponding results in a classical plasma. Some apparently anomalous results are pointed out and explained. © 1996 The American Physical Society.

Analyses based on the theories of Kennard and of Stepanov (KS) often claim to support an assumption that emitting manifolds associated with excited electronic states are in thermal equilibrium. KS predict a certain linear F(ν) with slope -h/${\mathit{k}}_{\mathit{BT}}$, where T is ambient temperature. Variation in T*(ν)=-(h/${\mathit{k}}_{\mathit{B}}$)/(dF/dν) reveals the likelihood of extensive excited-state nonequilibration. T*(ν), not necessarily an actual temperature, reduces to T under fast relaxation. Its observed variation in certain systems can be modeled with coupled submanifolds far from the equilibrium envisaged by KS. © 1996 The American Physical Society.

Ramsey patterns for radio-frequency multiquantum transitions among Zeeman levels of the ground state of thallium, cesium, and francium have been calculated. The narrowing of these patterns observed earlier by Gould is predicted to occur only when both static electric and magnetic fields are present. © 1996 The American Physical Society.

We present accurate ground-state energies for the positronium atom in a Coulomb field of point charge Z (${\mathit{X}}^{\mathit{Z}}$Ps), for the positronium hydrogen (HPs) and positronium lithium (LiPs) atoms. Calculations are done using the diffusion quantum Monte Carlo (DQMC) method. For ${\mathit{X}}^{\mathit{Z}}$Ps, the critical value of Z for binding is examined. While HPs is stable, the results show that LiPs is unstable against dissociation to a lithium atom and a positronium. © 1996 The American Physical Society.

Rabi oscillations reflect the existence of a coherent superposition of two molecular eigenstates during the interaction of molecules with a strong, resonant electromagnetic field. This phenomenon is not restricted to two-level systems. We demonstrate its occurrence in a three-level system where the radiation induces a two-photon absorption. The intermediate level is (slightly) detuned from resonance. For a theoretical description the dressed-state picture is adopted. The two-photon excitation is performed either by using one laser, yielding a one-color two-photon process, or by using two counterpropagating, spatially overlapping laser beams, yielding a two-color two-photon process. Rabi oscillations are produced by varying the fluence, i.e., by changing either the laser power or the molecule-laser interaction time. For the one-color case the two-photon transition dipole moment for an ${\mathrm{SF}}_6$ transition has been determined from the relation between laser fluence and number of Rabi oscillations. For the two-color cases the detuning with the intermediate level is varied by tuning the respective laser frequencies while keeping the sum frequency constant. A dramatic change in the degree of excitation as a function of the intermediate detuning has been observed. © 1996 The American Physical Society.

It has been shown previously that under certain circumstances the correlation energy density functional ${\mathit{E}}_{\mathit{c}}$[ρ] and its kinetic ${\mathit{T}}_{\mathit{c}}$[ρ] and potential ${\mathit{V}}_{\mathit{c}}$[ρ] components can be expanded in terms of homogeneous functionals ${\mathit{A}}_{\mathit{n}}$[ρ], with n=1,2,3,..., and where ${\mathit{A}}_{\mathit{n}}$[ρ] is homogeneous of degree (1-n) with respect to coordinate scaling. In this paper, we extend the analysis to expand similarly the pair distribution function ${\mathit{g}}_{\mathrm{xc}}$([ρ];${\mathbf{r}}_1$,${\mathbf{r}}_2$) and the second-order density matrix ${\mathrm{\rho }}_2$(${\mathbf{r}}_1$,${\mathbf{r}}_2$). It is found that both of them can be expanded under certain circumstances in terms of functionals ${\mathit{a}}_{\mathit{n}}$([ρ];${\mathbf{r}}_1$,${\mathbf{r}}_2$), with n=1,2,3,..., that are homogeneous of degree -n in coordinate scaling. The ${\mathit{A}}_{\mathit{n}}$[ρ] are explicitly obtained in terms of the ${\mathit{a}}_{\mathit{n}}$([ρ];${\mathbf{r}}_1$,${\mathbf{r}}_2$). © 1996 The American Physical Society.

We investigate classical dynamics and properties of highly excited charged two-body systems in a magnetic field. We hereby focus on the regular regime which can be described by perturbation theoretical methods. After introducing the exact constants of motion as canonical momenta we apply a perturbation theoretical series expansion with respect to the parameter σ:=${\mathit{B}}^{1/2}$ and use a time-averaging method to obtain the long-time dynamical behavior of the system. This procedure allows us to identify approximate constants of motion and enables us to derive effective Hamiltonians which describe the averaged dynamics on different time scales. The doubly averaged equations of motion are in fourth-order perturbation theory integrable. The solutions of these equations in terms of rotators and librators are given analytically and phase space is classified completely. Finally we arrive at a thorough understanding of the recently found self-stabilization effect of the center-of-mass motion of the ion in the context of our perturbation theoretical investigation. © 1996 The American Physical Society.

The times-order external-potential Bethe-Salpeter formalism is reformulated in a Schrödinger-like equation and in a form suitable for calculation of contributions arising from the relativistic momentum region. O(${\mathrm{\alpha }}^7$${\mathit{mc}}^2$) corrections to the fine structure of helium arising from the relativistic momentum region due to exchange diagrams are derived and presented. They are expressed in the form of expectation values of nonrelativistic operators. These off-leading-order contributions arising from the relativistic momentum region are not sensitive to any experiment in hydrogen, positronium, or muonium but they are larger than experimental errors in the measurements of fine structure in helium. Therefore, they provide a test of corrections of this kind, which has not been carried out in any other bound-state system. © 1996 The American Physical Society.

We study theoretically the formation of positronium atoms through electron capture in collisions of positrons impacting on hydrogenlike targets such as ${\mathrm{He}}^{+}$, ${\mathrm{Li}}^{2+}$, and ${\mathrm{Be}}^{3+}$. We obtain the scattering amplitude of the charge-exchange process by using a distorted-wave model derived from the first order of a Dodd and Greider’s expansion. We compute differential and total cross sections by using a partial-wave technique. © 1996 The American Physical Society.

Transitions of one or two electrons in ${\mathrm{C}}^{5+}$-He collisions are studied within the semiclassical close-coupling description of atomic collisions, at impact energies of 1–35 keV/u. Angle-integrated cross sections are determined for single-transfer, double-transfer, and transfer-excitation channels. For single capture to 3p states and for two final states in the two-electron transfer channel, angle-differential cross sections are derived and a number of coherence parameters that depend on the quantum-mechanical phases are calculated. The results are compared with recent data on angle-differential two-electron transfer and with results from an earlier theoretical study. © 1996 The American Physical Society.

We solve the SU(N)-invariant Yang-Baxter equations imposing only the unitarity condition. The usual S matrices should satisfy the crossing symmetry which originates from the CPT invariance of relativistic quantum-field theory. In this paper, we consider nonrelativistic SU(N)-invariant factorizable S matrices by relaxing the crossing symmetry and making the amplitudes for creating and annihilating new particles vanish and find that these S matrices are exactly the same as those of the multicomponent Calogero-Sutherland model, the quantum-mechanical model with the hyperbolic potential between particles and antiparticles. This particular solution is of interest since it cannot be obtained as a nonrelativistic limit of any known relativistic solutions of the SU(N)-invariant Yang-Baxter equations. © 1996 The American Physical Society.

Coherent scattering cross sections of 59.54-keV photons on target foils of ${}_{}{}^{64}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{66}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{68}{}_{}{}^{}\mathrm{Er}$, ${}_{}{}^{70}{}_{}{}^{}\mathrm{Yb}$, ${}_{}{}^{72}{}_{}{}^{}\mathrm{Hf}$, and ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ta}$ at 60°, 90°, and 120° have been measured to provide information on the region of K anomalous elastic scattering. The results are compared with the values calculated by the second perturbative order S matrix and by two procedures based on the form-factor approximation corrected by the anomalous scattering factors. Agreement of the S matrix values is very satisfactory, on the whole, and that of the values given by the form-factor approximations is fairly good. © 1996 The American Physical Society.