Following the Golden-Kalman one-component-plasma nonlinear response-function approach, the authors formulate an approximation scheme for the calculation of dynamical ionic polarizabilities in binary-mixture plasmas. Preliminary collective-mode calculations are presented in the weak- and very-strong-coupling regimes.

WKB-type connection formulas, established by Miller and Good and based on the quadratic mapping of a section of a potential containing a local minimum, are used to obtain ‘‘modified-well’’ quantization conditions for general double minimum potentials. Significant improvements in the usual WKB eigenvalues may be achieved by combining these with the corresponding ‘‘modified-barrier’’ rules. This is shown to be true in the context of the anharmonic oscillator potentials V(x)=-${\mathrm{kx}}^2$+λ$x^4$ (k,λ>0) for a wide range of λ. The characteristic features of the different modified formalisms are also discussed.

The Green’s-function Monte Carlo method is used to calculate the ground-state wave function of the muonic-molecular ion composed of a negative muon bound to a deuteron and a triton. Using the sudden approximation, the probability that the muon will remain bound to the escaping alpha particle after fusion occurs is found to be 0.90%, about 25% smaller than previous estimates based on the Born-Oppenheimer approximation. The numerical method for determining the wave function is discussed in detail.

It is generally accepted that with suitable boundary conditions the Lippmann-Schwinger (LS) integral equation is equivalent to the Schrödinger equation, even in systems of more than two particles. It also is generally accepted that although in two-particle systems the scattering solutions to the LS equation are uniquely defined by that equation without need for boundary conditions, the same cannot be said of systems containing more than two particles; in such many-particle systems, it is generally agreed, unique scattering solutions to the LS equation are not obtained unless boundary conditions are imposed. However, these assertions have not been verified heretofore in any system of three or more particles, because exact closed-form solutions of the Schrödinger or LS equation for such systems are so difficult to achieve. We have examined these questions in a one-dimensional three-body model first discussed by McGuire, wherein three equal-mass particles interact via equal and finite strength attractive δ-function potentials. With this model, the scattering solutions to the Schrödinger equation can be written exactly, in closed form. Thereby we are able to demonstrate explicitly that in this model the scattering solutions to the Schrödinger equation do satisfy the LS equation; we also demonstrate explicitly that the LS equation’s scattering solutions really are nonunique unless boundary conditions are imposed. This latter result strongly suggests that, in three-particle systems at any rate, recent criticisms of the aforementioned generally accepted nonuniqueness thesis are not well taken.

We study the strong-coupling limit of some relativistic wave equations describing bound states of oppositely charged fermions or bosons 1 and 2, of arbitrary mass. Using both numerical and analytic momentum-space methods we find the value ${\gamma }_{\max }$ of γ=-$e_1$$e_2$/4π for which the lowest-lying bound state disappears from the spectrum, as well as the smaller value ${\gamma }_{\mathrm{dec}}$ for which 2 becomes unstable to the decay into the composite (1,2) system and the antiparticle 1¯. We also consider the limit $m_2$→∞ and discuss the connection of our results with the so-called breakdown of the vacuum in quantum electrodynamics for a sufficiently strong external field.

If the time dependence of a Hamiltonian can be eliminated by an appropriate symmetry transformation, the corresponding quantum-mechanical problem can be reduced to an effectively stationary one. With this result we investigate the behavior of nonrelativistic particles in a spherical radiation field produced by a rotating source—then the symmetry transformation corresponds to a rotation. We calculate the transition probabilities in the Born approximation. The extension to problems involving an additional Coulomb potential is briefly discussed.

Results of relativistic multiconfiguration Dirac-Fock calculations with an extended nucleus are used to analyze the volume isotope shifts of the resonance transitions in the group-IIa and -IIb elements as well as in Yb. This is done together with a review of the isotope shift theory, including a critical evaluation and comparison of the semiempirical calculation of volume isotope shifts commonly used today. Electronic factors $F_i$, proportional to differences of electronic densities over the nuclear volume, are discussed within various approximations and compared with experimental results.

A special coordinate realization of the Lie algebra so(4,2) is used to reformulate the perturbation problem of a hydrogen atom in a linear radial potential over a complete and discrete Sturmian basis. In this way, the Rayleigh-Schrödinger coefficients $E_{\mathrm{NLM}}^{\left(n\right)}$ may be calculated to arbitrarily high order for any state. The large-order behavior of these coefficients is determined by Bender-Wu WKB theory. A general formula for the large-order behavior of the coefficients $c_n^{\mathrm{NLM}}$ of the Stieltjes continued-fraction representations of these perturbation expansions is given and related to that of the $E_{\mathrm{NLM}}^{\left(n\right)}$.

The relativistic eigenvalue equation involving the Liouville operator [H, ] applied to the general relativistic transition operator represented symbolically by t, [H,t]=λt, is solved for many-electron atomic systems. We derive the governing equations for Liouville Dirac-Fock theory in the restricted case where we limit the states used inside the commutator to those contained in the model space defined by multiconfiguration initial and final wave functions, and in the unrestricted case where we do not. The unrestricted theory is applied to calculations of transition energies and oscillator strengths for test cases in both closed- and open-shell systems.

A new form of the time-energy uncertainty principle is presented. It has the form τ ΔE≥3π$5^{1/2}$/25, where τ is the average lifetime of a decaying state, and ΔE is the energy spread of the state computed from Δ$E^2$=〈$E^2$〉-〈E${〉}^2$. The particular state for which the above relationship becomes an equality is identified, and it is proved that all other states give a greater τ ΔE product. This general result should have a wide range of applications.

The vacuum fluctuations of the electric field will shift the energy levels of an atom between two neutral, conducting planes. We have calculated these shifts in hydrogen atoms, and numerical values for the shifts of the lowest levels are given.

Components of the magnetizability of the B’ ${}^1$${\Sigma }_u^{+}$ state of the hydrogen molecule have been calculated for a wide range of bond lengths. Explicitly correlated, ‘‘generalized James-Coolidge-type wave functions’’ were used. It is found that in the B’ ${}^1$${\Sigma }_u^{+}$ state the molecular magnetizability is a positive quantity for bond lengths near equilibrium due to the mixing in of the nearby $D^1$${\Pi }_u$ state by the magnetic field. As a result ‘‘van Vleck paramagnetism’’ exists in the lowest vibrational level of the B’ state. At larger bond lengths this mixing is reduced by increasing influence of the $C^1$${\Pi }_u$ state. The crossing of the potential curves of B’ and C states produces the singularity point on the ${\chi }_{\perp }^p$ curve. As a result the paramagnetism disappears for higher vibrational states. The long-range parts of the components of the magnetizability of the a ${}^3$${\Sigma }_g^{+}$ and B${}^1$${\Sigma }_u^{+}$ states of ${\mathrm{H}}_2$ also have been calculated in order to study the asymptotic behavior of the magnetizability at large bond length.

Truncated diatomic orbitals (TDO) that we define in retaining only one term in the expansions of diatomic orbitals (DO) which are exact Born-Oppenheimer solutions of the one-electron two-center problem are proposed as basis functions for describing electronic molecular states of diatomic systems. Test calculations are performed and compared to the exact values for the electronic energy as well as for values of the wave function for some states of ${\mathrm{H}}_2$${\mathrm{}}^{+}$ and ${\mathrm{HeH}}^{2+}$ in order to check the efficiency of the TDO’s as a basis set. TDO’s are then used as basis functions to describe 38 electronic states of ${\mathrm{Li}}_2$${\mathrm{}}^{+}$ in the framework of a model-potential method, in the range 2≤R≤20 a.u.

The central practical problem which has impeded the development of the valence-bond theory of molecular electronic structure for the past fifty years has been the so-called nonorthogonality problem. In this article we develop a new method for calculating electronic energy matrix elements between Slater determinants constructed from a set of nonorthogonal orbitals. The method should lead to a reduction in the time needed for the evaluation of the crucially important Hamiltonian and overlap matrix elements needed in valence-bond theory by about 2 orders of magnitude for typical (small) molecular problems. The time required by previously available methods for the evaluation of these matrix elements increases as $N^6$, where N is the number of electrons. We show that the time required by our new method increases only as $N^4$. .AE

The spin-adapted pth-order reduced Hamiltonians (SRH) are obtained for an m-electron system, within the formalism of second quantization. This transformation is applied to the usual many-body Hamiltonian and involves an augmenting mapping, a spin projection, and a reducing mapping into the p-body reduced space. These three operations are combined into a single algorithm, allowing the work to be carried out within the two-body space. The SRH matrices thus obtained (1) have the same trace as that of the corresponding full configuration-interaction (CI) matrix, and (2) can be written as expansions involving the p eigenvalues and the corresponding pth-order reduced density matrices (RDM) of the m-body system in the chosen spin symmetry. Both of these properties guarantee that all and only the relevant information about our system is contained in the SRH matrices (and the SRH operators). The excitations of the eigenstates of the 1-SRH and the 2-SRH can be interpreted as the normal modes (or elementary excitations) of our electronic system in a given symmetry. A preliminary calculation on the Be atom yields encouraging results when compared with experiment. In the following paper (paper II of this series) the theory is applied to obtain the total energy and the reduced density matrices.

In the preceding paper (paper I of this series) the spin-adapted reduced Hamiltonian theory was developed and applied to the study of the elementary excitations of a test example; the Be atom. Here this theory is extended in order to obtain other observables: the total energy and the reduced density matrices for an m-electron system, always working within the two-body space. Preliminary applications of this formalism produce very satisfactory results.

Energy and transformed-velocity spectra of electrons emitted in the forward direction have been experimentally determined for 20–120-keV ${\mathrm{H}}^{\mathrm{-}}$ projectiles traversing thin Ar targets. The spectra from ${\mathrm{H}}^{\mathrm{-}}$ are surprisingly cusplike in shape even though single-electron loss is known to dominate. In contrast to the findings of Menendez and Duncan, who performed similar measurements at higher projectile velocities, target-induced structures in the electron loss to the continuum spectra are not pronounced in this velocity regime.

The pseudopotential molecular-structure method has been used to calculate the $X^1$Σ and $a^3$Σ interaction potentials for the alkali-metal-atom–hydrogen-atom systems. These potentials were then used in a quantum-mechanical calculation to determine the spin-exchange cross sections in the energy range from 2.5×${10}^{\mathrm{-}4}$ eV to 2.5 eV. The cross sections follow the general form $Q^{1/2}$=a-b lnv. However, abundant structure on the cross sections is present due to orbiting resonances induced by the deeply bound well of the $X^1$Σ molecular state. The spin-exchange cross sections range from 17×${10}^{\mathrm{-}16}$ to 25×${10}^{\mathrm{-}16}$ ${\mathrm{cm}}^2$ at room temperature for H(F=1) transferring to H(F=0) in collision with unpolarized lithium and cesium, respectively.

The Magnus expansion, to second order, has been used to solve the coupled-channel, symmetrized impact-parameter equations for electron-atom scattering. Collision integrals are evaluated in the dipole approximation, allowing both first- and second-order terms to be written in closed, analytic form. The numerical work is therefore essentially reduced to a matrix exponentiation for each value of the impact parameter, which can be efficiently carried out by the well-known diagonalization procedure. It thus becomes computationally feasible to handle problems involving a large number of closely coupled states. As a test case, the theory has been applied to electron-impact excitation of the resonance transitions of Li, Na, and K. The calculated cross sections were found to be in good agreement with experimental data over most of the intermediate-energy range. Thus far, the present method appears to be competitive with more sophisticated approaches and is readily applicable to complex processes, such as electron collisions with atoms in excited states.

An experimental and theoretical study of ${\mathrm{He}}^0$ on ${\mathrm{D}}_2$ collisions at energies 1.0, 1.5, and 2.0 keV has been carried out to probe and to understand the energy surface of the ground electronic state of the ${\mathrm{HeH}}_2$ triatomic molecule and of the intersections of this surface with those of low-lying electronically excited states. At each collision energy, doubly differential energy-loss spectra have been obtained and the results have been analyzed in terms of a parametric fit to an ab initio calculated ground-state energy surface. The scaled energy loss for quasielastic collisions (electronically elastic collisions with vibrational-rotational excitation) are shown to constitute a sensitive probe of the region of the ground-state energy surface in which the proximity of the He projectile breaks the ${\mathrm{H}}_2$ (or ${\mathrm{D}}_2$) bond. Sigmund scaling has been experimentally demonstrated to hold for the quasielastic channel in He on ${\mathrm{D}}_2$ collisions despite the strong presence of electronically inelastic processes, a finding of particular significance, since the scaling law was derived under the assumption that there are no accessible electronically inelastic channels in the collision system. The theoretical study confirms this behavior for collisions in which electronic excitation is velocity independent and occurs in well-defined surface intersection regions. Cross sections differential in angle but integrated over all vibrotational-rotational inelastic energy losses have been both calculated and experimentally measured for the quasielastic channel, and the two are found to be in good agreement.