We present a new derivation of the droplet model proposed by Oxtoby and Metiu. The new approach allows a more direct physical interpretation, eliminates some assumptions made in the earlier treatment, and permits extension to the critical isotherm and coexistence curve as well as the critical isochore. Several static scaling laws are derived, and the asymptotic form of certain multipoint correlation functions is studied.

Two infinite families of two-parameter generalized Overhauser orbitals are introduced and shown to satisfy explicitly, for occupied states, the self-consistent Hartree-Fock equations in the thermodynamic limit. For an attractive $\delta$ interaction, they give lower Hartree-Fock energy than the usual plane-wave solutions, even for relatively weak coupling and/or low density. The limiting members (possessing an infinite number of harmonics) of both families appear to tend to a "classical static lattice" state, via a second-order transition for one family and via first order for the other. The related density profiles and energy expressions are calculated as functions of the two new parameters. A direct variation with respect to these parameters was done numerically and results are presented graphically.

It is shown by Monte Carlo calculations that fluid mixtures of classical point ions in an uniform electron-gas background separate into two phases primarily from potential-energy considerations. For protons and $\alpha$ particles the critical temperature over an enormous pressure range is found to be near 1 eV, and only at extremely high pressures (∼${10}^8$ Mbar) does the mixture become stable. Phase separation at lower pressures, as in the interior of Jupiter (∼40 Mbar, 1 eV), is shown to be unlikely on the basis of more realistic models which modify, however crudely, the uniform electron approximation.

The melting characteristics of Ar, Ne, ${\mathrm{H}}_2$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are calculated classically from an effective pair potential, which depends explicitly on the temperature and on the quantum parameter $\frac{{\hslash }^2}{m\epsilon {\sigma }^2}$, by means of simple semiempirical melting equations.

We apply the fully renormalized kinetic-theory formalism of Mazenko to the study of self-diffusion in a dense one-component classical plasma. The memory function associated with the phase-space correlation function for self-diffusion is expressed in terms of an effective two-body problem which allows us to make approximations at a microscopic level in a straightforward manner. We use simple physical arguments to obtain the "effective interaction approximation" for the memory function in which a pair of particles interact via a dynamically screened effective potential. This approximation for the memory function is a nontrivial and natural generalization of the Balescu-Guernsey-Lenard form that includes the exact statics of the system, treats screening at large and small distances consistently, and is valid for all wave numbers and frequencies. The inclusion of the hydrodynamic modes in the memory function leads to an oscillatory long-time tail in the velocity autocorrelation function. We calculate the self-diffusion constant as a function of density using the effective interaction form of the memory function and calculate the memory function associated with the velocity autocorrelation function using an interpolation procedure which incorporates the hydrodynamic modes. Qualitative agreement with recent molecular-dynamics computations of the self-diffusion constant and the memory function is found.

An approximate analytical solution is obtained for the problem of spherical implosion of coalesced weak shocks in an ideal gas. Since the motion is assumed to be self-similar, our expressions are approximations to the exact solution which is valid close to the center of the sphere only. This has been achieved by replacing, in different time regimes, a nonlinear function of the reduced sound velocity and the reduced gas velocity appearing in the self-similar differential equation for these variables, by suitable functions of the reduced gas velocity alone. By considering a fully ionized D-T plasma to be an ideal gas of specific-heat ratio $\gamma =\frac{5}{3}$, it is shown explicitly that coalesced weak spherical shocks are much more efficient than a single strong spherical shock, in generating fusion energy.

A series of lines parallel to the liquid-crystal boundary have been observed using crossed polarizers on a homeotropically aligned nematic liquid-crystal cell excited by ultrasonic bulk waves of about 1 MHz. We propose that the physical mechanism responsible for the rotation of the molecules of the liquid crystal from their perpendicular position is the acoustic streaming which occurs in any viscous liquid. Theoretical analysis of the model shows that the lines should be separated by one quarter of the acoustic wavelength and the intensity of the light reflected from the cell through crossed polarizers should be proportional to ${sin}^2\left(B{V}^4\right)$. where $V$ is the excitation voltage applied to the transducer and $B$ is a constant. Both predictions are supported by our experimental results.

In this paper we show that the fine structure of vertical-horizontal (V-H) light scattering is due to the local order in the liquid. Use is made of the hydrodynamics equations obtained in a previous paper which introduced two tensors to characterize the local order. When one of these tensors is neglected with regard to the other (the one-tensor approximation), the spectrum given previously by different authors is obtained. It is shown in which cases this approximation is valid. The V-H spectrum for the light scattered by a liquid of spherical molecules is also given. The spectrum is computed in the general case when the two tensors are of the same order. In such a case, a spectrum is obtained which gives the broad background observed some years ago, and also the experimental results obtained recently in supercooled liquids which cannot be explained with the one-tensor approximation. The results are compared with previous theories, and it is shown that a generalization of all the previous results is obtained.

The positions $E=\mathcal{E}+\Delta$ of the ${}_{}{}^{1,3}{}_{}{}^{}(S^e, P^o, D^e)$ autoionizing states of ${\mathrm{Li}}^{+}$ below the $n=2\mathrm{}$ threshold of ${\mathrm{Li}}^{++}$ have been calculated using the Feshbach projection-operator technique. The trial wave function is of Hylleraas type. Widths $\Gamma$ and shifts $\Delta$ of these states have been calculated using the exchange approximation for the continuum functions. The calculated positions are generally lower than those obtained in previous calculations. Widths of most of the states have not previously been calculated. The positions are also compared with experimental results of Ziem, Bruch, and Stolterfoht and Bruch et al. Positions of the nonautoionizing (quasibound) ${}_{}{}^3{}_{}{}^{}P_{}^e{}_{}{}^{}$, ${}_{}{}^{1,3}{}_{}{}^{}D_{}^o{}_{}{}^{}$ states have also been calculated. The positions in all cases are lower than those obtained in previous calculations.

The Hartree-Slater (HS) and Green-Sellin-Zachor (GSZ) model atomic potentials are compared. Results of various calculations based upon these potentials show the HS to be decidedly more realistic in diverse physical situations.

We indicate a weakness in the Hartree-Fock-Slater-Latter (HFSL) potential at values of $r$ near the point where the Latter hydrogen-potential addition is made. The GSZ (Green-Sellin-Zachor) potential does not have this weakness and, consequently, can yield energy eigenvalues which are closer to experimental energy levels than are the HFSL energy eigenvalues. We attempt to show that the examples used in Manson and Purcell's Comment fail to demonstrate that the HFSL potential is more accurate than the GSZ potential. We suggest possible avenues along which further development of atomic independent-particle models might proceed.

Recent calculations of oscillator strengths by Armstrong, Fielder, and Lin employing relativistic multiconfiguration Hartree-Fock (MCHF) methods give a disparity between length- and velocity-gauge results. It is shown here that the disparity is due in part to the neglect of certain "exchange overlap" terms in the evaluations of transition-matrix elements in MCHF calculations. Including such exchange overlap terms brings velocity-gauge values into substantial agreement with length-gauge results for high-$Z$ members of the Be isoelectronic sequence. The disparity for lower members of the sequence is increased and the resulting difference between length- and velocity-gauge values reflects the changing reliability of the MCHF calculation as $Z$ increases along the sequence.

When an oscillator with smoothly changing frequency is excited suddenly, its frequency spectrum displays pronounced oscillations. Such oscillations may have been observed recently in x-ray spectra excited by heavy-ion collisions.

We describe two new experiments which demonstrate laser-induced inelastic collisions. Energy was stored in the Sr $5p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ state and selectively transferred both to the Ca $4p^2{}_{}{}^1{}_{}{}^{}S$ and $5d{}_{}{}^1{}_{}{}^{}D$ states. The collision cross sections maximized at the interatomic wavelengths of 4977 and 4711 Å, respectively, and had a half-power width of about 14 ${\mathrm{cm}}^{-1\mathrm{}}$.

In deriving a formula for atomic capture ratios involving negative muons, Daniel postulates a model leading to a muon energy spectrum of a different character from that indicated by a more complete analysis. In this Comment we emphasize the dependence of the energy spectrum on both inelastic and capture processes, and suggest several experiments which may distinguish between different theoretical models.

In the model recently used by me to calculate the Coulomb capture of mesonic particles, the energy spectrum is explicitly shown to be white. Other models, and in particular less appropriate potential shapes, yield other energy spectra. Experiments of the type suggested in the preceding Comment have already been performed.

Positron and orthopositronium ($o$-Ps) decay rates have been obtained in helium gas over the density ranges 72-200 and 80-520 amagat at gas temperatures 300 and 77°K, respectively. The 77°K $o$-Ps results exhibit the onset of bubblelike behavior observed by other investigators. The 300°K $o$-Ps decay rates are in agreement with a linear extrapolation of the high-precision low-density results obtained by Coleman et al. and are in marked disagreement with the density-dependent pickoff annihilation coefficient proposed by Ferrell. The free-positron decay rates are the first to be obtained above 200 amagat at well above saturated vapor temperatures. Above 200 amagat, the free-positron $Z_{\mathrm{eff}}$ is found to exhibit an unambiguous decrease with increasing density. At 520 amagat, for example, $Z_{\mathrm{eff}}=3.71\mathrm{}\pm 0.02$, as opposed to the density-independent value, $Z_{\mathrm{eff}}=3.89\mathrm{}\pm 0.04$ observed in the low-density regime.

The determination procedure for shielded diatomic orbitals which are eigenfunctions of the two-center problem is generalized for any polynomial form of the separated parametric shielding potentials. The matrix technique using a Newton-Raphson scheme for simultaneous resolution of the separated equations, and the matrix elements of the general shielding potential are presented.

The dynamic polarizability of the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ and $2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ states of helium is calculated using a variation-perturbation scheme. The computation includes up to 80 terms for the triplet state and up to 136 terms for the singlet state in the first-order trial function. The radiation frequency ranges from zero up to and beyond the second excitation threshold. The convergence is excellent for the triplet state, it is slightly inferior for the singlet state.

The method used by Cohen and Frishberg to obtain the general hierarchy equation for reduced density matrices is generalized to derive a general hierarchy equation for reduced transition matrices. A general hierarchy equation for reduced Slater-determinant transition matrices is also derived and is then utilized to obtain the orbital equations for multiconfiguration self-consistent field theory without use of the variational principle.