An energy-minimization principle based on the hydrodynamic formulation of quantum mechanics is used to develop a time-dependent energy-density functional. The external potential considered has a periodic dependence on time and the validity of the functional is restricted to those frequencies which are not so large as to cause a transition to an excited state. The present time-dependent energy-density functional reduces to the time-independent Hohenberg-Kohn-Levy functional in the static limit.

A general coupled-cluster method valid for arbitrary multideterminantal reference states is formulated. The resulting cluster expansion for the wave function is a generalization of that introduced by Silverstone and Sinanoǧlu and applied by Sinanoǧlu and collaborators. The connected nature of the cluster operators and the effective interaction is proven in the case when the reference space is complete, i.e., is invariant under unitary transformations of partly occupied orbitals. For incomplete reference spaces the disconnected terms appearing in the effective interaction are properly generated by the coupled-cluster theory. Approximate schemes for solving coupled-cluster equations are proposed and their relation with perturbation theory is briefly discussed.

A generalization of Hodges's method of obtaining the gradient expansion is derived and then employed to determine the sixth-order term. The formula for it is as follows: $T_6\left[\rho \right]=\frac{{\left(3\mathrm{}{\pi }^2\right)}^{-413\mathrm{}}}{45360\int {\rho }^{\frac{-1\mathrm{}}{3}}[13\mathrm{}{\left(\frac{\nabla {\nabla }^2\rho }{\rho }\right)}^2+\frac{2575}{144{\left(\frac{{\nabla }^2\rho }{\rho }\right)}^3}+\frac{249}{16{\left(\frac{\nabla \rho }{\rho }\right)}^2\left(\frac{{\nabla }^4\rho }{\rho }\right)}+\frac{1499}{18{\left(\frac{\nabla \rho }{\rho }\right)}^2{\left(\frac{{\nabla }^2\rho }{\rho }\right)}^2}-\frac{1307}{36{\left(\frac{\nabla \rho }{\rho }\right)}^2\left(\frac{\overrightarrow{\nabla }\rho ·\overrightarrow{\nabla }{\nabla }^2\rho }{{\rho }^2}\right)}+\frac{343}{18{\left(\frac{\overrightarrow{\nabla }\rho ·\overrightarrow{\nabla }\overrightarrow{\nabla }\rho }{{\rho }^2}\right)}^2+\frac{8341}{72\left(\frac{{\nabla }^2\rho }{\rho }\right){\left(\frac{\nabla \rho }{\rho }\right)}^4}-\frac{1600495}{2592{\left(\frac{\nabla \rho }{\rho }\right)}^6}]d^{3}r}}$. For atomic densities, $T_6\left[\rho \right]$ is divergent near the nucleus and at large distances.

The correlation energy of a relativistic electron gas based on a sum of ring diagrams including the transverse-photon contributions is numerically calculated. From this, a local, relativistic correlation potential is deduced which appears in the density-functional theory of inhomogeneous systems where relativistic effects make important contributions. Comparison with its nonrelativistic counterpart shows that the use of nonrelativistic results is very poor. The correlation contribution to the potential is found to be about 5% of the exchange for $\beta =2.5\mathrm{}$ to about 2.5% for $\beta =1\mathrm{} (\beta =\frac{k_F}{m})$.

In order to rationalize the effects of an external uniform electric field on a perturbed molecule, we introduce the concept of electric shielding as a tensor which determines the effective field at an arbitrary point in the molecular space. The fundamental properties of the nuclear shielding tensor are analyzed in the case of heteronuclear diatomics HF, HCl, and HBr. It is shown that this quantity is essential in accounting for the deformation of the molecular geometry induced by the external field. Uncoupled and coupled Hartree-Fock perturbation theory is applied in order to obtain quantitative estimates of the shieldings and their derivatives with respect to the interatomic distance in HF, HCl, HBr, ${\mathrm{H}}_2$O, N${\mathrm{H}}_3$, and C${\mathrm{H}}_4$ molecules. Accurate linear combination of atomic orbitals wave functions are prepared for the diatomics, and their quality is tested by evaluating a series of first- and second-order electric properties, giving fair agreement with corresponding experimental data. The reliability of the computed shielding is examined to obtain information on the vibrational contribution to the property and the role of the electronic correlation.

The "classical" potential of intermolecular interaction, defining the motion of centers of mass of interacting molecules and taking into account a mutual dependence on internal and external motions of molecules, has been determined on the basis of the quantum theory. A semiclassical representation has been introduced into the quantum theory of interacting molecules and this allows us to obtain the self-consistent semiclassical approximation, to find its applicability limits, and to take into account the quantum and fluctuation corrections to the semiclassical approximations.

The electronic stopping cross sections for 200-840-keV ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ projectiles measured in liquid organic substances are analyzed with respect to the influence of intermolecular interaction. A systematic deviation from the average behavior has been detected. A comparison with the stopping cross sections of gases leads to the conclusion that the deviations are caused by intermolecular interactions. This is confirmed by analyzing other quantities depending upon intermolecular interactions, i.e., the van der Waals coefficients and the velocity of sound.

Energy spectra and angular distributions of quasifree electron bremsstrahlung (QFEB) induced by 20-MeV-proton bombardments of a Be target have been measured with a Si (Li) detector. The Doppler shift of QFEB is clearly observed in the energy spectra and depends on the observation angle. The production cross section calculated from a free-electron approximation is compared with the experimental result and the agreement is quite satisfactory. The spectral shape near the high-energy end point of the QFEB definitely reflects the velocity distribution of the orbital electrons of the target atom. Angular distributions of secondary-electron bremsstrahlung were also measured and are compared with a calculation which includes relativistic retardation effects.

The classical-trajectory Monte Carlo method has been used to determine product-state distributions in $A^{q+}+\mathrm{H}\to A^{\mathrm{}(q-1\mathrm{})+}\mathrm{}\left(\mathrm{nl}\right)+{\mathrm{H}}^{+}$ electron-capture collisions at energies 50 and 100 keV/amu for fully stripped ions in charge states $q=1\mathrm{} \mathrm{to} 20$. In the energy region studied, the electron-capture products are found to populate predominately principal quantum numbers around $n_m\approx q^{\frac{3}{4}}$. Such behavior implies the captured electron tries to preserve both its original orbital energy and dimensions after the electron-capture collision. The orbital-angular-momentum quantum numbers $l$ are more highly peaked than statistical to large $l$ values for $n<\mathrm{}{n}_m$, while they are found to maximize around $l\approx q^{\frac{3}{4}}$ for $n>\mathrm{}{n}_m$.

Angular distributions of electrons elastically scattered from ${\mathrm{H}}_2$ have been measured by a crossed-beam method. Energy and angular range covered were from 2.0 to 200 eV and from -96° to + 156°, respectively. Comparison has been made with the previous measurements and theories. There is a good agreement above 100-eV incident energy between the previous measurements and theories and the present results, but below 100 eV considerable discrepancies exist between the previously reported results and the present measurements in the shape as well as in the magnitude of the angular distribution. The total cross sections of Golden et al. [D. E. Golden, H. W. Bandel, and J. A. Salerno, Phys. Rev. 146, 40 (1966)] above 7 eV are smaller than the present results (pure elastic) by as much as 24%, and the results of Srivastava et al. [S. K. Srivastava, A. Chutjian, and S. Trajmar, J. Chem. Phys. 63, 2659 (1975)] are also smaller than the present results by as much as 15%. The momentum-transfer cross section calculated directly from the present results of angular distribution show good agreement with those results derived from transport coefficients is swarm experiments by Frost and Phelps [L. S. Frost and A. V. Phelps, Phys. Rev. 127, 1621 (1962)] and Crompton et al. [R. W. Crompton, D. K. Gibson, and A. I. McIntosh, Aust. J. Phys. 22, 715 (1969)] below 7 eV, but not for results above 7 eV. The results of Srivastava et al. are in agreement within the experimental uncertainties above 10 eV.

A model is developed to describe the effects of screening by projectile electrons in heavy-ion—atom collisions. The effective nuclear charge of the projectile is estimated as a function of the interaction distance based on the spatial distribution of bound electrons derived from their electronic wave functions. Correlation of the effective interaction distance with collisional energy transfer through the Massey criterion enables comparison of model predictions of effective projectile charge with results obtained from differential-ionization-cross-section measurements. The model is found to provide a reliable estimate of screening for measurements involving fast helium and oxygen ions.

The cross sections for $L$-x-ray production in tantalum following proton-induced inner-shell ionization were measured in 20-keV intervals over the proton energy range of 280-400 keV. The total $L$-x-ray-production cross section was obtained, as well as the cross sections for the $\mathrm{Ll}$, $L{\alpha }_{1,2}$, $L{\gamma }_1$, and $L{\gamma }_{2,3}$ x rays. The experimental results were compared with the predictions of the perturbed-stationary-state theory with relativistic and Coulomb-deflection corrections and were found to be in satisfactory agreement.

Experimental studies of two laser-induced charge-transfer reactions in Ca and Sr are presented. In both reactions, a Ca ion collides with an Sr neutral in the presence of a laser field to produce a Ca neutral and an excited Sr ion. The two reactions differ in the final level of the ${\mathrm{Sr}}^{+}$ species. The collision cross sections associated with these reactions are studied as functions of applied laser frequency and power density. The largest cross section induced is equal to ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$, obtained at a power density of 2×${10}^9$ W/${\mathrm{cm}}^2$. Differences in experimental results associated with the two reactions are explained qualitatively by an examination of the potential curves of the Ca${\mathrm{Sr}}^{+}$ quasimolecule.

The complete density matrix for electron capture into the hydrogenic $n=2\mathrm{}$ projectile level is calculated within a modified Oppenheimer-Brinkmann-Kramers approximation which analytically takes into account the long-range coupling effects between the degenerate states of the projectile. The incorporation of the post-collisional Stark effect removes the shortcoming of the first-order calculations of relative $l$ cross sections and of the alignment. We find reasonable agreement between the calculated $s-p$ coherence and the data of Sellin et al. The experimentally observed shift of the coherent signal can be explained by the transient inhomogeneity of the external electric field.

Electron translation factors (ETF's) appropriate for slow atomic collisions may be constructed using switching functions. In this paper we derive a set of switching functions for the $\mathrm{H}_2^{}{}_{}{}^{+}$ system by an analytical "two-center decomposition" of the exact molecular eigenstates. These switching functions are closely approximated by the simple form $f=tanhb\eta$, where $\eta$ is the "angle variable" of prolate spheroidal coordinates. For given united atom angular momentum quantum numbers ($l,m$), the characteristic parameter $b_{\mathrm{lm}}$ depends only on the quantity $c^2=\frac{-\epsilon R^2}{2}$, where $\epsilon$ is the electronic binding energy and $R$ the internuclear distance in a.u. The resulting parameters are in excellent agreement with those found in our earlier work by a heuristic "optimization" scheme based on a study of coupling matrix-element behavior for a number of $\mathrm{H}_2^{}{}_{}{}^{+}$ states. An approximate extension to asymmetric cases (He${\mathrm{H}}^{2+}$) has also been made. Nonadiabatic couplings based on these switching functions have been used in recent close-coupling calculations for ${\mathrm{H}}^{+}-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions and ${\mathrm{He}}^{2+}-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions at energies 1.0-20 keV.