Using a differential-equation formulation, we have found the exact solutions to the fixed-point functions of the renormalization-group equations for intermittency based on a class of two-dimensional area-preserving maps.

We study smectic-$A$ defect structures which preserve layer thickness. We deduce that the interstitial regions between the well-known focal conic domains are filled with concentric spheres.

We describe a very new topology for a nematic—smectic-$A$—smectic-$C$ polycritical point which results from the insertion of a reentrant-nematic phase in an isobaric binary phase diagram. For the first time the nematic—to—smectic-$C$ transitions around this point are seen as a line of second order. Thus the $N_{\mathrm{re}}\mathrm{AC}$ point is basically different from the other $\mathrm{NAC}$ multicritical points reported so far, in the sense that the three coexisting branches are of second-order type. A short phenomenological interpretation with the use of a mean-field approach is given which agrees fairly well with the experimental results.

Using geometric focusing technique with a magnetically insulated diode, we have studied the focusing properties of an intense pulsed proton beam. Local divergence is found to have less effect on the focusing than deviation of ion trajectories from the ideal ones (aberration), which strongly affects the focusing. An annular distribution of the ion current density is found by ion-trajectory calculations to be a space-charge effect. The space-charge neutralization factor is estimated to be more than 99.9%.

Energies of the bound states of the hydrogen atom in a uniform magnetic field are calculated for field strengths greater or equal to $B_0\approx 2.35\times {10}^9$ G. The convergent behavior of the quantum excesses (negative quantum defects) makes it possible to determine completely the bound-state spectrum for given values of the field strength $B$ and the azimuthal quantum number $m$. For $\mathrm{}\left|m\right|=0,1, \mathrm{and} 2$ results are presented which determine to a uniform relative accuracy of at least 0.1% the energies of all bound states for arbitrary field strengths from $\frac{B}{B_0}=1\mathrm{}$ to $\frac{B}{B_0}=500\mathrm{}$ or higher, beyond which the adiabatic approximation is of comparable accuracy.

Electron affinities are calculated with a procedure in which the change in the total correlation energy associated with the added electron is modeled by the interaction of the attached electron in a polarization potential of the atom. The single-configuration relativistic Hartree-Fock method, which by itself yields completely unsatisfactory affinities, is modified here by the addition of a single polarization potential with two parameters, the static dipole polarizability $\alpha$ and the size of the core $r_0$, which are determined independently of the affinity data. Results for halogen atoms are in excellent agreement with experimental data and with results of much more involved computations, where these have been successfully implemented.

For noninteracting fermions, some explicit examples using first-order density matrices built from orthonormal orbitals like those of Harriman are first summarized, and the relation to the Thomas-Fermi statistical theory is emphasized. The relation of Harriman's work for interacting fermions to some exact properties of the first-order density matrix for atoms and molecules is considered.

Collision strengths are calculated in a five-state close-coupling approximation for excitation of ${\mathrm{C}}^{3+}$, ${\mathrm{O}}^{5+}$, ${\mathrm{Ne}}^{7+}$, and ${\mathrm{Ar}}^{15+}$ by electron impact for energies less than the $3d$ threshold. Resonance contributions enhance the allowed $2p-3s$ collision strength by larger factors than the enhancement of the forbidden $2s-3s$ collision strength. The resonance enhancement is approximately independent of nuclear charge $Z$ for $2s-3s$, $2s-3p$, and $2p-3p$, and increases nearly linearly with $Z$ for $2p-3s$. The average effect of resonance contributions to $\Omega \mathrm{}(2s,2p)\mathrm{}$ is only 4%.

We have calculated the excitation cross sections of ${\mathrm{H}}_2$ ($X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\to b{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$) by combining the advantageous features of the close-coupling and $R$-matrix methods. In this work approximate close-coupling solutions are used as basis functions to calculate the $R$ matrix inside a sphere of radius $a$. The $R$-matrix boundary condition then provides the starting solutions at $r=a$ with which the coupled differential equations are integrated outward by the Numerov method into the asymptotic region with the electron-exchange terms neglected. Comparison with the standard close-coupling calculation shows an agreement typically within 5%, while the computing time is reduced by a factor of about 5. The basis set employed in constructing the $R$ matrix consists of two or three functions per channel, which is a markedly smaller set than usually included in $R$-matrix calculations for similar processes.

The generalized oscillator-strength formulation of the Born approximation was used to generate a large sample of subshell excitation and ionization generalized oscillator strengths across the periodic table. These were used to calculate the excitation and ionization contributions to the proton stopping power by individual subshells. The subshell ionization stopping powers are expressed in scaled form, depending on the subshell ionization energy. Detailed comparison of the calculated total proton stopping power is in good agreement with experiment across the periodic table. Detailed calculations show the importance of outer-shell ionization and excitation to the total stopping power for protons with energy less than 10 MeV.

Calculations are presented for the stopping power of ${\mathrm{Au}}^{n+} \left(0\mathrm{}\le n\le 11\right)$ for protons with energy between 0.1 and 10 MeV. Over this range the proton stopping power changes by at least a factor of 2 between neutral and 11 times ionized gold. Explicit Born-approximation calculations are done for both excitation (for all ions considered) and ionization (for selected ions). For inner shells ($\mathrm{nl}\le 4d$) the explicit calculations are in excellent agreement with results obtained from scaling laws. For outer shells ($\mathrm{nl}\ge 4f$) there are differences of as much as a factor of 2 between the explicit calculations and the scaling laws for some subshells of some ions. A correction to the scaling laws using an integral over optical oscillator strength is developed which removes some of the disagreement between the explicit calculations and scaled values. The residual difference between the explicit calculations and the scaled values appears to arise from the spatial expansion of an ion subshell orbital compared to an atom subshell orbital even when the subshells have the same ionization energy.

$M$-shell x-ray-production cross sections are reported for ${}_1{}^1{}_{}{}^{}\mathrm{H}_{}^{+}{}_{}{}^{}$ and ${}_2{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ ions incident on thin targets of ${}_{79}{}^{}{}_{}{}^{}\mathrm{Au}$, ${}_{82}{}^{}{}_{}{}^{}\mathrm{Pb}$, ${}_{83}{}^{}{}_{}{}^{}\mathrm{Bi}$, and ${}_{92}{}^{}{}_{}{}^{}\mathrm{U}$. The energy of the ions ranged from 0.3 to 2.6 MeV in increments of 0.1 MeV. The first Born calculations overpredict the data at all energies studied. The perturbed-stationary-state calculations with energy loss, Coulomb deflection, and relativistic effects agree with the present data for both ${}_1{}^1{}_{}{}^{}\mathrm{H}_{}^{+}{}_{}{}^{}$ and ${}_2{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ ions at ∼0.35 MeV/u, overpredict the data at higher $\frac{E_1}{A_1}$, and underpredict the data at lower $\frac{E_1}{A_1}$. The electron-capture contribution to the target ionization is calculated to be less than 3.4% for the targets, projectiles, and energies reported in this work.

Total electron-capture cross-section measurements are reported for ${\mathrm{C}}^{q+} \left(3\mathrm{}\le q\le 6\right)$ and ${\mathrm{O}}^{q+} \left(2\mathrm{}\le q\le 6\right)$ ions colliding with hydrogen atoms and molecules in the energy range ($0.01\le E\le 10$) keV/amu. The cross sections range from (0.5-7)×${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$, and neither obey simple charge-scaling rules, nor exhibit uniform dependences on collision velocity in this energy range. For a given charge $q$, cross sections for the less-highly-stripped oxygen ions exceed those for carbon ions at energies below a few-hundred eV/amu. Comparison is made between these measurements and theoretical calculations which have heretofore remained untested at low collision energies. In general, the agreement is good for those systems where detailed perturbed-stationary-state theory is available, but is best with those calculations in which the collision dynamics as well as the molecular couplings are treated quantum mechanically. Generalized theories which work well for collision systems containing many bound electrons, do not give accurate representations of these few-electron systems at low energies.

The differential cross section for electron-impact ionization of atoms has been derived for the general case and the dipole ($E1$) limit of the Born approximation. Emphasis was placed on the theoretical description of the ($e$,$2e$) angular correlation between fast electrons scattered in the forward direction and electrons ejected by the ionization process. The general angular-momentum treatment of this work results in a more complete description of the dipole ($e$,$2e$) angular distribution than previous purely kinematic analyses.

${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ ions having a specific energy of 1.4 MeV/u were implanted into stacks of self-supporting C, Al, Ti, Ni, Nb, Pd, and Sn foils that were produced by evaporation. The number of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ atoms stuck in the individual foils was determined by thermal neutron activation analysis. The mean ranges and range-straggling results are given for the energy region (0.15-10) MeV/u with the use of measured stopping-power values of uranium ions in the solids. The results are compared to the theoretical predictions and to semiempirical range tables.

Single-configuration Hartree-Fock calculations are reported on the He${\mathrm{H}}_2$ triatomicmolecular system in the range of small He-${\mathrm{H}}_2$ separation, $R$, to complement earlier studies, so that the entire energy surface of interest to He on ${\mathrm{H}}_2$ collisions in the low-keV collision-energy regime has now been determined. It is found that strong repulsive three-body polarization forces exist which dominate the physics of this collision-energy regime. Because a Legendre-polynomial expansion in the angular variable is found to be useless in this region of the energy surface, a new parametrization is introduced which includes both binary and three-body terms. The three-body terms are needed because the electron distribution in ${\mathrm{H}}_2$ is different from the sum of the distributions of two individual H atoms.

Cross sections differential in energy loss and scattering angle and most-probable reciprocal-mass functions are calculated for several rare gas on ${\mathrm{H}}_2$ collisions in the low-keV collision-energy range. Specifically, the collision systems He +${\mathrm{H}}_2$, Ne +${\mathrm{H}}_2$, and ${\mathrm{Ne}}^{+}$ +${\mathrm{H}}_2$ have been considered. The classical-trajectory calculations are based on a triatomic-molecular potential-functional form suggested by ab initio calculations of the He-${\mathrm{H}}_2$ energy surface, which serves as a prototype for all rare-gas-${\mathrm{H}}_2$ systems. The parameters in that functional form have been fitted from the experimental differential energy-loss measurements for Ne on ${\mathrm{H}}_2$ collisions to yield the Ne-${\mathrm{H}}_2$ energy surface, and from the ${\mathrm{Ne}}^{+}$ on ${\mathrm{H}}_2$ differential energy-loss measurements to yield the Ne-${\mathrm{H}}_2^{+}$ energy surface. With the energy surfaces thus parametrized, the calculated differential energy-loss cross sections agree well with the experimental data. They explain the anomalously large range of scattering angle in which the collision is elastic, with no vibrational-rotational excitation.

Cross sections for exciting KrI and XeI resonance radiation in ${\mathrm{Kr}}^{+}$+Xe collisions are reported for ion energies below 100 eV (lab). Excitation of the lowest-energy resonance line in KrI and XeI is found to be significantly different for the two $J$ states of the ${\mathrm{Kr}}^{+}$ beam. Reaction cross sections and kinetic-energy thresholds are reported for reaction of each $J$ level. Results are discussed in terms of the transfer of translational energy into internal energy by the mechanism of potential-energy curve crossing.

In the now popular version of the eikonal theory of charge transfer, the eikonal wave function does not satisfy the proper boundary conditions and the charge-transfer amplitude is uncertain by an undefined phase factor. The inclusion of the internuclear potential, in a consistent way, in the eikonal theory overcomes these difficulties. However, it also changes the high-energy asymptotic form of proton-hydrogen charge-transfer cross section from ${\sigma }_{\mathrm{eik}}\sim \left(\frac{23}{48}\right){\sigma }_{\mathrm{BK}}$ by a small amount to ${\sigma }_G\sim \left(\frac{20.109}{48}\right){\sigma }_{\mathrm{BK}}$ where ${\sigma }_{\mathrm{BK}}$ is the Brinkman-Kramers cross section.

Experimental studies of the ionization of helium by fast, light ions have been carried out to investigate deviations from a $q^2$ scaling of the ionization cross section by ions of charge $q$. Systematic studies were performed for equivelocity H, He, Li, B, C, and O ions, carrying up to a maximum of three to four electrons, at reduced energies of 0.64, 1.44, and 2.31 MeV/amu. For ions of low charge, the results show good agreement with the theoretical work of Gillespie and Inokuti, who treat the deviations arising from ionic structure within the framework of the Bethe theory. In contrast, fully stripped ions of sufficiently high nuclear charge show deviations from a $q^2$ scaling, due to the failure of the first Born approximation. Such deviations from the first-order perturbative results were found to be well described by the qualitative approach of Bohr as well as by the three-state, close-coupling approach of Janev and Presnyakov.