Detailed calculations are presented for the energy splittings of the states 2$s_{1/2}$-2$p_{1/2}$ and 2$s_{1/2}$-2$p_{3/2}$ for the muonic ions ${\mu }^{\mathrm{-}}$-Li, ${\mu }^{\mathrm{-}}$-Be, and ${\mu }^{\mathrm{-}}$-B obtained by numerical integration of the Dirac equation. It is shown that there is severe cancellation between the vacuum polarization and finite nuclear size contributions to the energy differences, leading to transition frequencies which lie in the visible region of the spectrum. As a consequence of the cancellation, a measurement of the transition frequency would provide a sensitive probe of nuclear size and structure. The system ${\mu }^{\mathrm{-}}$${\mathrm{-}}^7$Li appears to offer particularly good possibilities for performing such an experiment.

Slater’s transition-state equations, which are used for calculating electronic properties of excited states of atoms, molecules, and solids, are similar to the Kohn-Sham (KS) equations, apart from the fact that the former involve fractional occupation numbers. The subspace density functional theory (SDFT) was introduced by one of us [A. K. Theophilou, J. Phys. C 12, 5419 (1979)] for the development of an excited-state DFT. The lowest-order approximation of SDFT coincides with Slater’s transition-state theory. However SDFT shares the mathematical deficiencies of the initial Kohn-Sham DFT for the ground state. In this paper a rigorous derivation of SDFT equations is presented, which lacks these mathematical deficiencies and, in particular, bypasses the v-representability problem. The present formalism makes use of density functionals for subspaces similar to those defined by Levy and Lieb. The procedure followed is along the same lines as the recent developments in the rigorous derivation of the KS theory [N. Hadjisavvas and A. K. Theophilou, Phys. Rev. A 30, 2138 (1984); M. Levy and J. P. Perdiew, in Density Functional Methods in Physics, edited by R. M. Dreizler and X. da Providencia (Plenum, New York, 1985)].

The problem of finding the spectrum of the Fock-space Hamiltonian Ĥ for a system of many fermions is analyzed. The quasiparticle formalism is employed, with ‘‘holes’’ and ‘‘particles’’ defined with respect to some N-particle determinantal wave function (the model vacuum). The basic idea behind the proposed approach is to perform a similarity transformation of Hamiltonian Ĥ, such that the resulting effective Hamiltonian Ĝ is, unlike Ĥ, a quasiparticle-number–conserving operator. It is shown that eigenvalues of Ĝ, corresponding to small numbers of quasiparticles (0,1,2) can be easily calculated. This is equivalent to finding eigenvalues of Ĥ for certain states of N, N±1, and N±2 particles. The construction of the operator transforming Ĥ into Ĝ (the wave operator) stems from an analysis of the structure of the algebra of linear operators acting in a (finite-dimensional) Fock space. The exponential Ansatz for the wave operator is used, resulting in a generalization of the coupled-cluster (CC) method of Coester [Nucl. Phys. 7, 421 (1958)]. The generalized CC equations determining the wave operator, and equations determining the effective Hamiltonian Ĝ, are presented in a diagrammatic form. An effort has been made to obtain a concise notation for expressing these equations in an algebraic form. Approximation schemes, necessary for practical applications of the proposed method, are also studied.

The generalized coupled-cluster (CC) method of the preceding paper is cast into the form of the Brueckner-Hartree-Fock (BHF) method. In this approach the model vacuum Φ is optimized to become the maximum-overlap configuration for the reference eigenfunction Ψ. One of the approximation schemes of the preceding paper is applied to derive explicit algebraic equations which can be used for practical calculations of (approximate) energies of several states of a many-fermion system. These include the N-particle ground-state energy, energies of some (N-1)- and (N+1)-particle states, as well as energies of certain N-particle excited states. It is indicated that the numerical effort required in the present approach is comparable to that of the coupled-cluster singles and doubles (CCSD) method of Purvis and Bartlett [J. Chem. Phys. 76, 1910 (1982)].

A zeroth-order wave function is constructed as an antisymmetrized product of two-electron group wave functions (geminals) expanded in disjunct but overlapping subspaces of basis orbitals. The geminals are obtained as exact solutions of the two-electron Schrödinger equations within the corresponding local basis sets, and thus give a fully correlated description of the two-electron chemical bonds coupled by inductive (Coulomb and exchange) effects, the latter being taken into account by an appropriate effective core operator. A second-quantized formulation [P. R. Surján, Phys. Rev. A 30, 43 (1984), Part I] is applied where the wave functions of the individual bonds are represented by appropriate composite particle creation operators. Individual chemical bonds thus correspond to Bose quasiparticles composed of two electrons. Second-order perturbation theory is used for calculating interbond delocalization and dispersion effects. The treatment is based on a biorthogonal formulation [I. Mayer, Int. J. Quant. Chem. 23, 341 (1983); Ph. W. Payne, J. Chem. Phys. 77, 5630 (1982)] which makes the handling of interbond overlap very effective, and represents essentially a method of moments in the perturbation theory.

The no-pair equation with free-particle projection operators proposed by Sucher is employed for linear combination of atomic orbital calculations on one-electron atoms and a self-consistent-field configuration-interaction calculation of the ground-state energy and the spin-orbit splitting of the bromine atom. A matrix technique used for the representation of the required operators is discussed. Comparison of the results with Dirac-Hartree-Fock calculations shows that no-pair Hamiltonians furnish a convenient approximation for introducing relativistic effects in atomic and molecular structure calculations.

The hypothesis of an internal symmetry of quantum systems, presented in previous papers and recapitulated here, implies a modified geometrical interpretation of the nonrelativistic internal wave functions of loosely bound systems. This reinterpretation modifies the vertices of loosely bound composite particles and can be tested in elastic, inelastic, and dissociation processes. Three effects which follow from this hypothesis are analyzed.

Cross sections for elastic scattering and excitation of the n=2 states of atomic hydrogen by electrons are computed for incident energies in the range from 12 to 54 eV. The calculations are based primarily on an 11-state expansion including seven pseudostates. Pseudothresholds and pseudoresonances are suppressed by appropriate averaging.

Total charge-neutralization cross sections have been measured with use of an attenuation method for ${\mathrm{Li}}^{+}$ ions in the energy range from 1 to 10 keV incident on thin targets of Mg, Ca, Sr, and Ba vapors. These cross sections exhibit an energy dependence characteristic of asymmetric charge exchange, increasing with collision energy up to a broad maximum, then decreasing at higher energies. The ${\mathrm{Li}}^{+}$+Ba cross section reaches a maximum value (${\sigma }_m$) of 4.0×${10}^{\mathrm{-}14}$ ${\mathrm{cm}}^2$ at ∼3.5 keV impact energy. The corresponding values of ${\sigma }_m$ for Sr and Ca are 2.85×${10}^{\mathrm{-}14}$ ${\mathrm{cm}}^2$ at 6.0 keV, and 3.3×${10}^{\mathrm{-}15}$ ${\mathrm{cm}}^2$ at 10 keV. The ${\mathrm{Li}}^{+}$+Mg cross section only attains a value of 1.1×${10}^{\mathrm{-}15}$ ${\mathrm{cm}}^2$ at the highest energy measured (10 keV), thus, ${\sigma }_m$ clearly occurs at even higher energies for this system. The energies at which these cross-section maxima occur increase monotonically through the series from Mg to Ba, while the magnitude of ${\sigma }_m$ decreases in that order. This ordering is consistent with the inverse ordering of the asymptotic energy defects for the process: ${\mathrm{Li}}^{+}$(1${\mathrm{s}}^2$)+M(${\mathrm{ns}}^2$)→Li(2s) +$M^{+}$(ns), where M is an alkaline-earth element.

Differential cross sections for coherent or Rayleigh scattering of photons on atoms were measured using a 59.54-keV ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$ source. Scattering angles ranging from 20° to 107° were studied, corresponding to a momentum transfer of 0.8 to 4.0 A${̊}^{\mathrm{-}1}$. At angles greater than 60° the results are compared with values of other authors. The measurements are in agreement with calculations of second-order perturbation theory within the experimental error of 4–10 %.

The influence of the ionic core in Rydberg-atom–neutral collisions is evaluated within the framework of the impulse approach. It is shown that this contribution exhibits the same n behavior as that due to the Rydberg-electron–perturber interaction, though its magnitude is usually smaller. The general features of the core-perturber contribution are investigated. It is shown that there exists some situations for which effects ascribable to the core-perturber interaction are expected to be noticeable.

Charge transfer in ${\mathrm{H}}^{+}$+${\mathrm{H}}_2$(${\mathrm{X}}^1$${\mathrm{\Sigma }}_{\mathrm{g}}$; v=0) collisions has been studied theoretically at energies from 0.2 to 20 keV with use of a molecular-state–expansion method incorporating electron translation factors. Two-state semiclassical close-coupling calculations have been performed to investigate the ion-molecule collision dynamics. The molecular states, used as the expansion basis, have been obtained by using the diatoms-in-molecules (DIM) method as functions of the internuclear distance R and two molecular orientation angles θ and φ. The effect of orientation of the target molecule on the charge-transfer mechanism has been examined and the charge-transfer cross section is found to be very sensitive to the molecular orientation at energies below 0.5 keV or above 10 keV. Between these energies, however, the orientation effect was small (due to accidental near-degeneracy of the probability from different θ). Our results are in good agreement with experimental measurements in the energy range where they are available.

This article describes a measurement of charge- and energy-transfer reactions in ion-atom collisions involving a doubly charged projectile ion. The reactions studied, ${\mathrm{Ar}}^{2+}$${(}^1$S, ${}^1$D, ${}^3$P)+Ar, are important in nonreactive plasmas and in chemical plasma processes like those used to deposit metal oxides and in plasma etching. This study reports the measurement of the transfer of charge and electronic energy from the metastable ${}_{}{}^1{}_{}{}^{}\mathrm{S}$ and ${}_{}{}^1{}_{}{}^{}\mathrm{D}$ states of ${\mathrm{Ar}}^{2+}$ to the parent atom. The experiment uses a novel technique in which the angular deflection and energy of a near-thermal target atom produced by expansion from a supersonic jet is measured. The metastable reactions ${(}^1$S,${}^1$D→${}^3$P) result from collisions in which the particles penetrate to a small distance of closest approach and undergo a relatively large angle of deflection. The symmetric charge transfer which occurs in the ground ${(}^3$P→${\mathrm{}}^3$P) state of the doubly charged system yields a large number of oscillations in scattering cross section whose peaks are separated by 104 eV deg for collisions of 260 eV primary impact energy. These oscillations are caused by the ungerade-gerade character of the interaction, that is, they result from interference resulting from the symmetric and antisymmetric interaction potentials. This study enables the measurement of both the endothermic and exothermic energy-transfer reactions in which electronic and ion kinetic energy is interchanged.

The strong-potential Born (SPB) approximation is examined by comparing various SPB calculations of high-velocity 1s-1s electron capture cross sections with one another and with experimental data. Above about 1 MeV, calculations using the SPB method of McGuire and Sil (SPMS) [Phys. Rev. A 28, 3679 (1983)] are in good agreement with total-cross-section observations for protons on H, He, C, Ne, and Ar as expected. For p+H and p+He, the SPB full-peaking (SPB-FP) approximation of Macek and Alston [Phys. Rev. A 26, 250 (1982)] and the SPB transverse-peaking (SPB-TP) approximation of Alston [Phys. Rev. A 27, 2342 (1982)] differ from our SPMS total cross sections by typically a factor of 2, as expected from general validity criteria. However, the differential cross sections at very forward angles (well within the Thomas angle) are the same in SPMS, SPB-FP, and SPB-TP methods in all cases. Below 1 MeV, cross sections obtained with use of various SPB methods differ considerably from one another, placing a limit of validity for these SPB calculations. We also suggest that in the gap between those energies where continuum intermediate states simply dominate, and above those energies where bound intermediate states simply dominate, detailed conceptual understanding of electron capture is incomplete.

In analogy with recent work on dielectronic recombination, an average-configuration distorted-wave method is developed to calculate resonance structures in the electron excitation of ions. Confirming previous results, large resonance contributions are found for the 2s→3s and 2p→3s excitations of ${\mathrm{O}}^{5+}$. Large resonance contributions are also found for the 2$p^6$→2$p^5$3s excitation of ${\mathrm{Ti}}^{12+}$. Radiative-coupling and electric-field-mixing effects are discussed.

Cross sections for production of positive and negative charge for 10–2000-keV ${\mathrm{He}}^{+}$ ions on He, Ne, Ar, Kr, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, CO, ${\mathrm{O}}_2$, ${\mathrm{CH}}_4$, and ${\mathrm{CO}}_2$ were measured by the transverse-field method. Electron-capture and -loss cross sections for 5–350-keV ${\mathrm{He}}^{+}$ ions on the same targets were measured by the method of beam deflection of various charge states after passing through a known length of target gas. Secondary-emission detectors were used to detect neutral, singly charged, and doubly charged beam components. The equation ${\sigma }_{+}$-${\sigma }_{\mathrm{-}}$=${\sigma }_{10}$-${\sigma }_{12}$ relating the four measured cross sections was utilized to make a least-squares adjustment of the data.

The polarization of $L_{\alpha }$ radiation is measured in coincidence with the scattered ${\mathrm{H}}_2$${\mathrm{}}^{+}$ resulting from the collision process: ${\mathrm{H}}_3$${\mathrm{}}^{+}$+He→(${\mathrm{H}}_3$${\mathrm{}}^{+}$) *+He →${\mathrm{H}}_2$${\mathrm{}}^{+}$+H(n=2)+He for specific laboratory angles. Our results are interpreted within the quasidiatomic approximation, which provides a reasonable picture of the changing nodal structure of the wave function during the collision. Within this description, the excitation is dependent upon the orientation of the molecule relative to the beam direction.

We present the results of an experiment designed to probe the collision-induced relaxation of excited-state Yb Zeeman coherences. Our experiment is sensitive not only to the depolarization-type relaxation mechanisms often observed in optical-pumping experiments, but also to the effects of collisionally induced velocity changes. Our measurements were performed in the 6s6p ${\mathrm{}}^3$$P_1$ excited state of the even (I=0) isotopes of gas-phase atomic Yb by means of a trilevel photon-echo technique. Depolarization rates, velocity-change spectra, and total scattering cross sections of Yb-He (Yb-Ar) collisions were measured (deduced). Both rank-1 and rank-2 spherical tensor components of the ${}_{}{}^3{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$ state play a role in our experiment, and our results represent averages of potentially different relaxation rates attributable to these quantities. Comparison of our results with rank-0 results obtained elsewhere reveals interesting similarities as well as differences.

An improved version of the Glauber-eikonal amplitude for electron-molecule scattering, originally developed by Bhattacharyya and Ghosh, that includes the effects of nonspherical potential terms up to ν=6 is presented. Application is made to e-${\mathrm{H}}_2$ scattering at intermediate energies to test a recently proposed, parameter-free, correlation-polarization potential. This potential is based, as suggested by O’Connell and Lane, on the hybridization of local-electron-gas theory and the long-range polarization. Results obtained are found to be very encouraging.

We analyze the structure of time-delay and transition probabilities in a collinear classical inelastic collision. It is shown that the classical time delay for a given transition is not restricted to one single value and that the appropriate transition probability varies with time delay.