Single crystals of BeO which have been irradiated with neutrons show an EPR spectrum with partially resolved hyperfine structure. An ENDOR study of the hyperfine interaction leads to the conclusion that the spectrum arises from centers which consist of an electron trapped at an oxygen vacancy surrounded by four Be nuclei. The measured hyperfine interaction constants are: $\frac{{\mathrm{A}}_{\ensuremath{\perp}}}{h}=10.3$ MHz, $\frac{{A}_{\ensuremath{\parallel}}}{h}=16.4$ MHz, and $\frac{({e}^{2}qQ)}{h}=1.1$ MHz for the Be nuclei not on the $c$ axis; and $\frac{{A}_{\ensuremath{\perp}}}{h}=4.2$ MHz, $\frac{{A}_{\ensuremath{\parallel}}}{h}=9.2$ MHz, and $\frac{({e}^{2}qQ)}{h}=1.5$ MHz for the nuclei along the $c$ axis. These values lead to ${|\ensuremath{\psi}({r}_{\mathrm{Be}})|}^{2}=0.13\ifmmode\times\else\texttimes\fi{}{10}^{24}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ for the electron wave function at the $c$-axis nuclei, and ${|\ensuremath{\psi}({r}_{\mathrm{Be}})|}^{2}=0.06\ifmmode\times\else\texttimes\fi{}{10}^{24}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ for the nonaxial nuclei. The measured $g$ value for H parallel to the $c$ axis is 2.0030.

The orbital radiation of the Frascati synchrotron has been used to determine the mass absorption coefficients of some heavy elements in the 20 and 130 \AA{} range. Results have been obtained for tantalum, platinum, gold, and bismuth. The photoionization cross sections of the $4d$, $4f$, and $5p$ electron shells have been calculated from a free nonhydrogenic atomic model. A comparison of the experimental and theoretical results shows that the photoionization in the $4f$ and $5d$ shells plays a fundamental role, and that the combined effects of these shells explain the variations of the absorption coefficient in the range examined. Moreover, certain details in the spectra tend to indicate the existence of multiple excitation mechanisms.

Using a previously developed theory, various distribution functions are obtained for the fluctuations in the condensate of a degenerate boson fluid in homogeneous thermodynamic equilibrium. The distribution for the occupation number of the condensate is shown to be Gaussian. The Wigner distribution and the characteristic function for the order parameter are also derived. The nonexistence of Glauber's $P$ representation for this problem is demonstrated for a finite range of temperatures starting at absolute zero.

The paired-phonon analysis operates in the function space generated by product functions compounded from (i) a starting trial function $\ensuremath{\psi}$ of the Bijl-Dingle-Jastrow-type (BDJ) (a product of two-particle correlation factors $\mathrm{exp}[\frac{1}{2}U({r}_{\mathrm{ij}})]$; (ii) paired-phonon factors ${\ensuremath{\rho}}_{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}{\ensuremath{\rho}}_{\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}$ to all powers, (iii) multiple phonon factors ${\ensuremath{\rho}}_{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}\ensuremath{\cdots}{\ensuremath{\rho}}_{\stackrel{\ensuremath{\rightarrow}}{1}}$ to all powers, with neglect of all matrix elements representing processes in which phonons coalesce, split, or scatter. Results in the present study include (i) a simpler and more general derivation of the fundamental relations; (ii) proof that the improved ground-state trial function $\stackrel{^}{\ensuremath{\psi}}$ generated by the analysis is still in the BDJ function space [with $U(r)$ replaced by $U(r)+\ensuremath{\delta}U(r)$]; (iii) a formula expressing $\ensuremath{\delta}U(r)$ in terms of $S(k)$, the starting liquid-structure function, and $w(k)$, the residual interaction function; (iv) a convenient representation of the phonon factor ${\ensuremath{\rho}}_{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}$ as a linear combination of phonon creation and annihilation operators; (v) explicit statement of the relation between the optimization condition $w(k)\ensuremath{\equiv}0$ and the variational extremum property of the expectation value of $H$ in the BDJ-type function space; (vi) usable approximate procedures for evaluating the residual interaction function $w(k)$ based on the hypernetted-chain (HNC) and Percus-Yevick (PY) relations; and (vii) numerical evaluation of $w(k)$, the energy shift $\ensuremath{\delta}E$, and the improved liquid-structure function $\stackrel{^}{S}(k)$ using $\ensuremath{\psi}'\mathrm{s}$ computed by Massey and Woo as starting functions. For $^{4}\mathrm{He}$ at the equilibrium density, $(\frac{1}{N})\ensuremath{\delta}E\ensuremath{\sim}\ensuremath{-}0.7$ \ifmmode^\circ\else\textdegree\fi{}K; for the hypothetical boson-type $^{3}\mathrm{He}$ system at $\ensuremath{\rho}=0.0164$ ${\mathrm{\AA{}}}^{\ensuremath{-}3}$, $(\frac{1}{N})\ensuremath{\delta}E\ensuremath{\sim}\ensuremath{-}0.3\ifmmode^\circ\else\textdegree\fi{}\mathrm{K} (\mathrm{HNC}) or \ensuremath{-}0.5\ifmmode^\circ\else\textdegree\fi{}\mathrm{K} (\mathrm{PY})$. In the discussion, emphasis is placed on the practical possibility of accurate numerical evaluation of the interaction function $\ensuremath{\omega}(k)$ by the method of molecular dynamics applied to systems containing ${10}^{2}$ - ${10}^{3}$ particles.

The following statement is offered as a conjecture. Given two otherwise identically prepared plasmas: If one has $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}\ifmmode\cdot\else\textperiodcentered\fi{}d\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}=0$ at every point of the boundary (except those points that carry essential currents), and the other permits nonessential currents to the plasma boundaries, the former will be more stable and better confined. A general theoretical argument in support of this conjecture (not a rigorous proof) is offered, based on the principle of minimum entropy-production rate. Experimental evidence in support of the conjecture is cited.

Practical techniques are developed for evaluating wave functions and Green's functions using the eikonal approximation. It is assumed that the scattering angle is small. This provides a great simplification in analysis of the trajectory curves, radii of curvature, etc. A sequence of approximations and the use of variational principles are described. Numerical illustrations, particularly for proton-hydrogen-atom scattering, are given for several of the approximations.

The relaxation times of optically oriented metastable atoms of Ne, Ar, and Xe in buffers of noble gases have been measured, and depolarization cross sections obtained. The cross sections range from 0.43 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$ for ${\mathrm{Xe}}^{m}\ensuremath{-}\mathrm{Xe}$ collisions to 190 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$ for ${\mathrm{Ne}}^{m}\ensuremath{-}\mathrm{He}$.

Oscillator strengths have been computed for transitions between a number of low-lying levels in B I and Ne VI. The wave functions were computed by the method of superposition of configurations, utilizing the pseudonatural orbital technique to accelerate convergence. The asymptotic limiting large-$Z$ $f$ values were also computed, using the nuclear charge perturbation expansion. Together with previous theoretical data from C II, these results have been used to make a graphical study of the $f$-value behavior for these transitions along the isoelectronic sequence. Comparisons were made between experiment and the predictions of the Hartree-Fock and charge-expansion methods as well as the present calculations. Finally, these theoretical curves were used to predict individual $f$ values for each member of the sequence through $Z=15$ (P XI).

The method of optical pumping of diamagnetic atoms with zero orbital angular momentum ($^{1}S_{0}$) has been extended to an atom with nonzero orbital angular momentum ($^{3}P_{0}$), yielding ${|{\ensuremath{\mu}}_{I}|}_{\mathrm{uncorrected}}=0.5726(6) {\ensuremath{\mu}}_{N}$. An expression for the signal is found and the complications of branching to the metastables are discussed. The appratus is described.

We have developed and, to some extent, solved a number of kinetic equations for displaced correlation functions in a classical fluid. These functions, of which the Van Hove neutron scattering function is a special example, are one-particle distribution functions obtained from a Gibbs ensemble which is initially, at $t=0$, in equilibrium except for one labeled particle whose distribution $W(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}})$ at $t=0$ differs from its equilibrium value $\ensuremath{\rho}{h}_{0}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}})$, where $\ensuremath{\rho}$ is the average fluid density, and ${h}_{0}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}})$ is the Maxwellian velocity distribution function. We investigate the time evolution of the (self-) distribution function of this labeled particle, ${f}_{s}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}},t)$, as well as the deviation from equilibrium, $\ensuremath{\eta}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}},t)$, of the total one-particle distribution function. The latter represents the density of fluid particles, labeled and unlabeled, at position $\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}$ and velocity $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$. Since both ${f}_{s}$ and $\ensuremath{\eta}$ are linear functionals of $W$, they will satisfy exactly a linear non-Markovian kinetic equation of the form $f=\mathrm{B}f+\ensuremath{\int}{0}^{t}d{t}^{\ensuremath{'}}\mathrm{M}({t}^{\ensuremath{'}})f(t\ensuremath{-}{t}^{\ensuremath{'}})$. B is a time-in-dependent and M a time-dependent (memory) operator (nonsingular in $t$). Our kinetic equations (first- and higher-order) are based on neglecting or approximating M in such a way that the short-time behavior of ${f}_{s}$ and $\ensuremath{\eta}$ is described exactly. The rationale behind this scheme is that our choice of initial ensemble is precisely of the type generally assumed in the "derivation" of kinetic equations. The calculation of B is straightforward and depends in a very important way on whether the interparticle potential in the fluid is smooth or contains a hard core. In the former case, the first-order kinetic equation is of the Vlasov type with an effective potential given by the equilibrium direct correlation function, while in the latter case, B contains, in addition, a linear Enskog-type collision term. We show that this Vlasov equation (also derived previously by many authors) gives a damping linear in the wave number $k$ for small $k$ instead of the hydrodynamic ${k}^{2}$ dependence. The kinetic equation for systems with hard cores does not give correct hydrodynamic behavior. (For a one-dimensional system of hard rods, the first-order kinetic equation is exact.) We also obtain and solve a second-order kinetic equation, which is a generalized Vlasov-Fokker-Planck-type equation, for systems with continuous potentials.