A new coherent state introduced recently by us is shown to lead to a Wigner distribution function which maximizes the Shannon entropy with given mean, variance, and covariance of position and momentum of a particle. This result is discussed in the light of a recent paper of Senitzky. A more general discussion of entropy based on smoothed Wigner functions is also given.

High-spin metastable atomic beams of high density and extremely small divergence can be produced by electron capture during grazing-angle scattering of ion beams at ferromagnetic surfaces. This can be used to generate a long-lived reservoir of $\mathrm{Li} 1s2s2p {}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^0{}_{}{}^{}$ with enough density of metastables so that after laser-induced transfer to $\mathrm{Li} 1s2p^2{}_{}{}^2{}_{}{}^{}P$ strong lasing at 207 Å should occur. This novel technique can also be used to produce a variety of other metastables known as potential candidates for lasing at shorter wavelengths.

Our previous work on the influence of hydrodynamic effects on the relaxation of concentration fluctuations in liquid mixtures is extended to include the effects of strong diffusion. The fluctuations migrate, as in the diffusionless case, towards the largest scales at a rate dictated by the instantaneous value of the fluctuation strength. Experimental tests of our theory are suggested and discussed.

Intensity-induced frequency shift and precessional frequency of two strong circularly polarized waves are derived in a magnetized plasma. An unexpected feature in the low-frequency limit of a magnetohydrodynamic Alfvén wave is that the ion velocity is comparable to the velocity of light in the presence of a static magnetic field. This process may be useful in the astrophysical energy-transfer studies and in the experiment with ion—laser-induced plasma.

Various expressions for antisymmetrized geminal-power (AGP) states are reviewed. With the use of a simple relationship for creation and annihilation operators of BCS (Bardeen, Cooper, and Schrieffer)-type states, such operators are characterized for AGP and GAGP (generalized AGP) schemes. The effect of degeneracy in the first-order reduced density matrix on these operators is displayed.

For the special case of half-filled subshells, Racah showed in 1943 that his formula relating the coefficients of fractional parentage for a given particle configuration to those for the corresponding hole configuration requires an additional phase factor ${\mathrm{}(-1\mathrm{})\mathrm{}}^{\frac{\mathrm{}(v-1\mathrm{})\mathrm{}}{2}}$, where $v$ is the seniority of the half-filled configuration. This phase factor is incorrectly printed in Racah's 1943 paper as ${\mathrm{}(-1\mathrm{})\mathrm{}}^{\frac{v-1\mathrm{}}{2}}$. Furthermore, this phase factor is omitted in the 1952 paper by Rosenzweig, resulting in sign errors in the table of ($d^5\mathrm{}\left|\right\}\mathrm{}{d}^6$) coefficients. These rather old errors have often been repeated in subsequent publications, including even some recently published monographs and textbooks.

The Coulomb capture of muons has been measured in gaseous Ne, Ar, and Kr mixtures. A concentration dependence of the per atom capture ratio was established for the first time.

Antiparticles are shown to produce inner-shell vacancies in atoms with cross sections that can be orders of magnitude larger than those for particles at the same incident velocity. This phenomenon occurs for projectile velocities which are low compared with the orbital velocity of the electrons. The disparity in vacancy production manifests itself through differences in the characteristic x-ray yields induced by particles and antiparticles. The principle of a self-calibrating detector for antiparticle-induced x-ray emission is given.

The hyperfine structure of the $7S_{\frac{1}{2}}$ state of ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$ has been measured with the use of laser spectroscopy on a cesium atomic beam. We find the magnetic dipole coupling constant $A=545.90\mathrm{}\left(09\right)\mathrm{}$ MHz. From the amplitude of the hyperfine components we find the ratio of the scalar to tensor polarizabilities ($\left|\frac{\alpha }{\beta }\right|$) for the $6S\to 7S$ transition to be 9.80(12).

Laser investigation of the photoionization spectra in the presence of an electric field has been performed in $\pi$ and $\sigma$ polarizations on an ytterbium atomic beam from the particular level $4f^{14}6s7s{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ which was populated by a two-step excitation. Broad modulations (in $\pi$ polarization) and Stark resonances in the vicinity of the zero-field ionization limit are interpreted satisfactorily as in the case of alkali atoms. However, the photoionization spectra are deeply affected by the presence of two perturbing levels belonging to the configuration $4f^{13}5d^{2}6s$. This phenomenon is explained by strong interference effects between the structured Stark continuum and the field-induced autoionizing states corresponding to the doubly excited levels.

Singlet-triplet mixing of $4snd {}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}D_2^{}{}_{}{}^{}$ states of Ca was determined between principal quantum numbers $7<~n<~42$ with the use of Doppler-free two-photon spectroscopy. The hyperfine structure of the $4snd {}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ states was used to probe admixtures of triplet character into the singlet wave functions. It turned out that, in the region of series crossings, an enlarged singlet-triplet mixing was observed.

An amplitude equation is derived for a binary fluid mixture in a porous medium, in the vicinity of the intersection point of the lines of stationary and oscillatory instabilities. This point represents an experimentally realizable example of a codimension-two bifurcation.

This paper makes a contribution towards understanding recent nuclear magnetic resonance measurements of biaxiality in cholesteric liquid crystals. We have made use of a simplified version of Landau theory to obtain the magnetic field dependence of the biaxiality parameter $\eta$. When the magnetic field $H$ is greater than a critical value $H_c$, the parameter $\eta$ vanishes. For $H<\mathrm{}{H}_c$, the ratio $\frac{\eta \mathrm{}\left(H\right)\mathrm{}}{\eta \mathrm{}\left(0\right)\mathrm{}}$ is an almost universal function of $\frac{H}{H_c}$. The predicted magnetic field dependence is free of adjustable parameters, and comparison with experimental results can be made unambiguously.

It is shown that nonlinear mode coupling of magnetic drift modes can excite electrostatic convective cells. Decay and modulational instabilities are examined. The growth rates are obtained analytically. Relevance of our investigation to anomalous particle and heat transport is briefly discussed.

For a driven nonlinear oscillator we report direct evidence for three cases of an interior crisis of the attractor, as conjectured by Grebogi, Ott, and Yorke. These crises are sudden and discontinuous changes in the attractor, observed directly from bifurcation diagrams and attractor diagrams (Poincaré sections) in real time. The crises arise from intersection of an unstable orbit with the chaotic attractor.

Diffusion-controlled cluster formation has been simulated in two-, three-, and four- dimensional space. The radii of gyration ($R_g$) of the resulting clusters have a power-law dependence on the number of particles in the cluster $\mathrm{}\left(N\right)\mathrm{} R_g=N^{\beta }$. The corresponding Hausdorff dimensionality ($D=\frac{1}{\beta }$) is related to the Euclidean dimensionality $d$ by the relationship $D\sim \frac{5}{6}d$ for $d=3\mathrm{}$ and 4. For the two-dimensional case we find that $\frac{D}{d}$ has a value about 2% smaller (0.847 ± 0.01). However, a value of $\frac{5}{6}$ (0.833) is only just outside the 95% confidence limits and cannot be completely ruled out. In the two-dimensional simulations $\beta$ is insensitive to lattice details and in both two- and three-dimensional simulations $\beta$ is insensitive to the sticking coefficient ($S$) over the range $1.0\ge S\ge 0.1$.

We have carried out single-shock experiments with liquid deuterium to 210 kbar ($T\approx 4800$ K) and reflected experiments to 760 kbar ($T\approx 7000$ K) as well as single-shock experiments with liquid hydrogen to 100 kbar ($T\approx 3300$ K). These data enable us to determine a theoretical spherically symmetric, effective intermolecular pair potential. Calculated solid isotherms are compared with recent static measurements.

Floquet theory is applied to systems whose Hamiltonians are periodic in time. Specifically, the application deals with the sinusoidal Hamiltonians for the semiclassical approximation of the radiation — quantum-molecule interaction in an intense field. For these types of Hamiltonians new time symmetries are shown to exist in the Floquet solutions and consequently to yield three useful properties. Three formal approaches to the Floquet solutions are compared. Also the Floquet-state "mean energy" is shown to play the major role in the static part of the molecular-state energy fluctuations. Numerical application to the dynamics of the diatomic HF vibrotor shows multistate participation in both the one- and two-photon excitations, and "resonance interaction" between the one- and two-photon absorption is observed. Also, Magnus approximations to the exact numerical calculations show excellent agreement.

A method based on quantum-mechanical sum rules is presented in which matrix elements of the displacement and the square of the displacement for a general one-dimensional oscillator are expressed directly in terms of the eigenenergies and the potential parameters. Matrix elements of higher powers of the displacement can then be calculated through an exact hypervirial relation. Two important features of the present method, the rapid convergence and the result that successive approximations are alternately upper and lower bounds to the matrix elements, make the method useful in those cases for which accurate eigenenergies are known. Sample calculations for the quartic-anharmonic oscillator are presented and compared with matrix elements obtained by other iterative schemes.