The Gaussian-distributed random-bond Ashkin-Teller model on a Cayley tree is studied in the limit of infinite coordination number. This study is based on the relationship between the properties of the system defined on the usual Cayley tree and those of the system defined on a related hierarchical tree, the so-called closed asymmetric tree (CAT). With exploration of the hierarchical nature of the CAT a real-space renormalization-group procedure is implemented to obtain the generalized Sherrington-Kirkpatrick (SK) equations. The phase diagrams in three particular cases are obtained by numerical analysis of the SK equations.

Ion formation in sodium vapor (∼${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}3}$) containing Rydberg atoms (18≤n≤35) was investigated. Both atomic ions and diatomic molecular ions resulting from collisions between highly excited sodium, ${\mathrm{Na}}^{\mathrm{*}\mathrm{*}}$, and Na(3s) were observed. However, the predominant production mechanism was found to be photoionization of ${\mathrm{Na}}^{\mathrm{*}\mathrm{*}}$ by blackbody radiation, the rate of which was measured at 500 K and found to be ≃5.7×${10}^3$ ${\sec }^{\mathrm{-}1}$ for n=18, in good agreement with theory. The ${\mathrm{Na}}^{+}$ signal from blackbody photoionization is observed to be independent of n, which we interpret as implying rapid and nearly complete self-l-mixing, mixing by collisions with Na(3s) atoms, for both s and d states. It is probable, however, that the s states are mixed to the adjacent, n-1, manifold of l states. It was also found that the heavy-body collision cross sections for ${\mathrm{Na}}^{+}$ and ${\mathrm{Na}}_2$${\mathrm{}}^{+}$ formation, while roughly three orders of magnitude lower than our estimate of the self-l-mixing cross section, are appreciable, of order 100 A${̊}^2$.

Relativistic plane-wave Born-approximation calculations of cross sections for N-shell ionization of ${}_{83}{}^{}{}_{}{}^{}\mathrm{Bi}$ and ${}_{92}{}^{}{}_{}{}^{}\mathrm{U}$ by protons with incident energies from 0.02 to 5 MeV are reported. The calculations were carried out by using Dirac-Hartree-Slater wave functions. Binding-energy change and Coulomb deflection were taken into account. The relativistic cross sections are compared with values from nonrelativistic Hartree-Slater wave functions to study the effects of relativity. A test calculation with hydrogenic wave functions yields very different results. The only available measurements (for ${}_{74}{}^{}{}_{}{}^{}\mathrm{W}$), revised with a corrected 4d fluorescence yield, agree with present theoretical predictions for $E_1$≤0.1 MeV but fall below theory by a factor of 6 above $E_1$=0.4 MeV. This glaring discrepancy invites further investigation.

Electron-photon coherence and correlation parameters for electron-impact excitation of the n ${}_{}{}^1{}_{}{}^{}P$ (n=2–8) states of helium at 80 eV are predicted to be essentially independent of the principal quantum number (n), and the available experimental data for n=2 and 3 show (semiquantitatively) the same behavior. The n independence of these parameters predicted by first-order many-body theory can be explained using basic concepts associated with quantum-defect theory and, if verified by further experimental results, has important consequences for understanding the physics of the electron-atom scattering process.

Absolute electron-impact ionization cross sections were measured as a function of collision energy for the multicharged metallic ions ${\mathrm{Ni}}^{3+}$, ${\mathrm{Cu}}^{2+}$, ${\mathrm{Cu}}^{3+}$, and ${\mathrm{Sb}}^{3+}$. The measurements cover an energy range from below threshold to 1000 eV (1500 eV for ${\mathrm{Cu}}^{2+}$). Recent distorted-wave direct ionization calculations agree with the measurements for ${\mathrm{Ni}}^{3+}$, ${\mathrm{Cu}}^{2+}$, and ${\mathrm{Cu}}^{3+}$ within 20%. Inner-shell excitation followed by autoionization produces up to a factor-of-2 enhancement in the ${\mathrm{Sb}}^{3+}$ cross section, and a rapid decrease in this indirect contribution at higher energies indicates the dominance of dipole-forbidden excitations.

A trap for charged particles is an important tool in many important experiments in atomic physics. The electrodes in many such traps are truncated hyperboloids. Data given here allow evaluation of the effects on trap performance of some of the details of the truncation. It is shown that if the truncation of the ring and endcap electrodes is done in a ‘‘balanced’’ way the performance degradation can be small. Some specific designs are suggested and some appropriate data reported.

By using the Fourier-transform technique, the explicit expressions for the one-electronndashtwo-center overlap integrals of Slater-type atomic orbitals up to 3d are derived. The final expressions are analytic, simple, and independent of local coordinates. Furthermore, they do not contain the non-closed-form of exponential integrals which were presented in expressions given in earlier work. It is shown that the two-electron–two-center Coulomb integrals, as well as the hybrid integrals, can simply be expressed in terms of these integrals. The numerical instability arising from the situation in which the exponents of the two orbitals are almost equal is discussed, and a solution for this problem based on a Taylor-series expansion of the integral is suggested.

We have measured the wavelength of the 1s2s ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$–1s2p ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ transition in heliumlike Ti xxi using fast-ion spectroscopy of 216-MeV titanium ions. Our wavelength value of 389.49±0.07 Å is in agreement with the most recent calculated value of 389.57±0.04 Å, which includes both relativistic and quantum electrodynamic corrections for the two-electron system. We compare our result with earlier calculations and with measurements for this transition in other heliumlike ions.

Using an integral representation involving the radial Coulomb Green’s function an analytic closed-form expression is derived for the dynamic multipole polarizability of atomic hydrogen in an arbitrary state. The application of the general expression to practical problems is discussed. Comparison is also made with other theoretical models.

A LCAO-MO (linear combination of atomic orbitals–molecular orbitals) relativistic Dirac-Fock-Slater program is presented, which allows one to calculate accurate total energies for diatomic molecules. Numerical atomic Dirac-Fock-Slater wave functions are used as basis functions. All integrations as well as the solution of the Poisson equation are done fully numerical, with a relative accuracy of ${10}^{\mathrm{-}5}$–${10}^{\mathrm{-}6}$. The details of the method as well as first results are presented here.

In this paper a unified analytical treatment of overlap, two-center nuclear attraction, and Coulomb integrals of B functions [E. Filter and E. O. Steinborn, Phys. Rev. A 18, 1 (1978)] via the Fourier-transform method is presented. B functions, which are a special class of exponentially decreasing functions (for large arguments), have a relatively complicated analytical structure. However, the Fourier transform of a B function is of exceptional simplicity. Consequently, it is relatively easy to express the Fourier integral representations of the two-center integrals mentioned above as finite sums or infinite series of Fourier integral representations for B functions and irregular solid harmonics which may be considered to be limiting cases of special B functions. The only advanced mathematical concepts which we need are the connection between B functions, classically divergent Fourier integrals, and derivatives of the three-dimensional δ functions. The other mathematical tools—partial-fraction decompositions and Taylor expansions of rational functions—are fairly elementary. Our approach leads not only to a considerable simplification of the derivation of the previously known analytical representations for the two-center integrals but also to a large number of hitherto unknown representations.

The analytical representations for overlap, two-center nuclear attraction, and Coulomb integrals of B functions [E. Filter and E. O. Steinborn, Phys. Rev. A 18, 1 (1978)] can be divided into two categories: representations containing only a finite number of terms which, however, may contain canceling singularities for small internuclear distances and nearly equal scaling parameters, and infinite-series representations which do not contain canceling singularities but where enormous convergence problems may occur. In this paper we analyze the numerical properties of the infinite-series representations for the two-center integrals mentioned above. In our approach, we first analyze the convergence type of an infinite series by deriving asymptotic approximations for the terms of the series with large summation indices. The information which is gained by this asymptotic analysis can be used to choose the convergence accelerator which has optimal properties for the series under consideration. In this paper we only use two nonlinear convergence accelerators, the Shanks transformation, and Levin’s u transformation. The Shanks transformation, which essentially produces Padé approximants, is our choice in the case of linearly convergent monotonic series, whereas Levin’s u transformation leads to spectacular acceleration effects in the case of alternating series and in the case of logarithmically convergent series. According to our experience the use of nonlinear convergence accelerators greatly enhances the applicability of these infinite-series representations.

We introduce a series of new linear-response tensors which enable one to estimate the actual electric and magnetic fields at the nuclei of a molecule immersed in an external, spatially uniform, periodical electromagnetic field. The analysis is extended to the case of an electric field gradient. These tensors may be called electromagnetic nuclear shieldings. They possess interesting properties and fulfill a series of general sum rules and equations, showing the deep relations among the electromagnetic properties of molecules. An accurate numerical test has been performed on the water molecule, with use of the random-phase approximation to decouple the polarization propagator equations.

A no-pair formalism employing external-field projection operators correct to second order in the potential is used to calculate the 1s energies of one-electron atoms and ground-state properties of the bromine and silver atoms in the framework of the multireference double-excitation configuration-interaction (MRD-CI) method. It is found that the relativistic two-component method that has been used reproduces the one-particle energies of the Dirac equation to order (Zα${)}^3$. The operator is bounded from below and can be used variationally in relativistic electron-structure calculations of many-electron atoms and molecules. The relativistic correction to the total energy recovers 97% of the relativistic correction of the Dirac-Hartree-Fock (DHF) result in the case of the bromine atom and more than 99% in the case of the silver atom. The relativistic correction of the ionization potential of silver has been calculated to be 0.47 eV at the CI level, in good agreement with DHF results, the correlation contribution in the relativistic case being 0.42 eV. The remaining discrepancy of the absolute value of 6.85 eV (DHF 6.34 eV) to experiment (7.57 eV) is attributed to basis-set deficiencies. The corresponding CI value of the electron affinity (relativistic CI value 1.05 eV, nonrelativistic 0.90 eV) is in much better agreement with experiment (1.30 eV). It is found that correlation contribution and relativistic effects are nonadditive.

The low-energy two-body scattering S- and P-wave parameters, together with a shape-dependent S-wave quantity, which appear in the well-known low-density expansions for the ground-state energy of many-boson and many-fermion systems, are accurately calculated for several central pair potentials for spin-polarized atoms, helium atoms, and nucleons. An integral-equation method allowing accurate determination of the coefficients of the above-mentioned parameters expanded in powers of the attraction strength of the pair potential is presented and applied. The results are needed for perturbation studies of ground-state energies of various quantum many-body systems.

We report the ratio of rate coefficients for the excitation-transfer reaction Na(3PJ)+Na(3PJ′)→Na(nLJ″)+Na(3S1/2), which has sometimes been labeled energy pooling, measured in a cell at T=640 K. Rate-coefficient ratios are given for nLJ″=4D3/2, 4D5/2, 4F5/2, 4F7/2, and 5S1/2, each for J=J′=1/2 and 3/2. We also report the nLJ″ ratios when the 3P states are populated in nearly statistical ratios; these are related to the rate coefficients when J=1/2 and J′=3/2.

A comparison is given between an exact numerical calculation and two approximate analytic expressions for the Mott correction to energy loss of heavy ions. A complete tabulation of the Mott correction is given for use when the approximate expressions are not valid. The validity of possible relativistic corrections to the Bloch correction is discussed. A comparison of the calculations to some recent experiments is given.

A quantum-mechanical inverse scattering method is used to find local exchange potentials which are exact within the context of the static-exchange approximation for e-He scattering at energies between 19 and 200 eV. These local exchange potentials are also successful in the presence of other potentials, such as polarization and absorptive potentials. The present exchange potentials are compared with the semiclassical exchange potentials in common use in the energy range under consideration.

Absolute electron-impact ionization cross sections were measured as a function of collision energy for ions in the Mg-isoelectronic sequence ${\mathrm{S}}^{4+}$, ${\mathrm{Cl}}^{5+}$, and ${\mathrm{Ar}}^{6+}$. The measurements cover the energy range from threshold to 1500 eV and show onsets due to the indirect ionization process of inner-shell excitation followed by autoionization. The relative magnitude of the indirect ionization process increases dramatically in comparison with the direct process along the sequence, a feature which is also emphasized by earlier data for ${\mathrm{Al}}^{+}$.

Excitation-autoionization contributions to the electron-impact ionization of the Mg-like ions ${\mathrm{S}}^{4+}$, ${\mathrm{Cl}}^{5+}$, and ${\mathrm{Ar}}^{6+}$ are calculated in the distorted-wave approximation. The calculations indicate that the largest contributions are due to the 2p→3p monopole and 2p→3d dipole excitations from either the 2$p^6$3$s^2$ ground-state configuration or the 2$p^6$3s3p excited-state configuration. Excellent agreement with the experimental crossed-beam measurements of Howald et al. is obtained when one assumes that a substantial fraction of the ions coming from the electron cyclotron resonance ion source are in metastable states of the 2$p^6$3s3p excited-state configuration.