The high-temperature behavior of the lattice version of the Widom-Rowlinson "$A-B$" model is studied, under the assumption of a finite repulsion $W$ between neighboring $A$ and $B$ molecules. Application of the extended Yang-Lee theorem shows the grand partition function (for the square lattice) to be analytic on the positive real axis for sufficiently high temperature ($\beta W<\mathrm{}\ln \left[2\right(2-\surd 2\left)\right]\simeq 0.158$).

The nonlinear response of an atom to a near-resonant light pulse is studied using a novel approximation scheme. In first order, the approximate solution reduces to the well-known rate equations. The second-order approximation contains Grischkowsky's adiabatic-following approximation. In each order, the approximate solution of the Bloch equations is presented with a closed-form expression for the error that can be used to investigate its range of validity.

Calculations of the frequency spectrum of lattice vibrations of a finite two-dimensional electron crystal show a soundlike shear mode and a longitudinal mode that has an anomalous dispersion relation. At long wavelengths the frequency of the longitudinal mode varies as the square root of the wave vector. This arises because of the long-range nature of the Coulomb force between the electrons and is analogous to the longitudinal plasma vibration in a three-dimensional Wigner lattice.

Several experiments are described in which the structure factor $S\left(k\right)\mathrm{}$ was determined for gaseous ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at temperatures near 5 K. In the momentum-transfer range $0.15<k$ <2.09 ${\mathrm{\AA }}^{-1\mathrm{}}$ $S\left(k\right)\mathrm{}$ was obtained for both ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ gas at densities of 1.95 × ${10}^{-3\mathrm{}}$, 2.66 × ${10}^{-3\mathrm{}}$, and 3.5 × ${10}^{-3\mathrm{}}$ mole/${\mathrm{cm}}^3$. In the momentum-transfer range 0.133 ${\mathrm{\AA }}^{-1\mathrm{}}$ < $k$ < 1.125 ${\mathrm{\AA }}^{-1\mathrm{}}$ $S\left(k\right)\mathrm{}$ was obtained for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ gas at densities of 1.348 × ${10}^{-3\mathrm{}}$, 2.598 × ${10}^{-3\mathrm{}}$, 3.599 × ${10}^{-3\mathrm{}}$, and 5.557 × ${10}^{-3\mathrm{}}$ mole/${\mathrm{cm}}^3$. For the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ temperature was 5.23 K while for the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ the temperature was 4.99 and 5.08 K. The first moment of the pair-correlation function was obtained by even-power-series fits to the structure-factor data at each density. Other power-series expansions have also been examined. The present experimental results are compared with $S\left(k\right)\mathrm{}$ values obtained from modifications of the pair correlation function as calculated by Jordan and Fosdick for a temperature of 5 K.

The object of the present paper is the elaboration of a model formalism for solid ${\mathrm{He}}^3$. This is based on postulating isotropic first-neighbor antiferromagnetic — $J_1$ and second-neighbor ferromagnetic $J_2$ exchange interactions between pairs of atoms. Using some of the averaged pressure data along isochores of the unmagnetized and magnetized solid, due to Kirk and Adams, and assuming the exchange-strength functions to have constant logarithmic volume derivatives ${\gamma }_1$ and ${\gamma }_2$, we derive $-J_1\mathrm{}\left(V\right)\mathrm{}$, $J_2\mathrm{}\left(V\right)\mathrm{}$, ${\gamma }_1$, and ${\gamma }_2$; a satisfactory theoretical representation of all the isochore data, restricted to the asymptotic high-temperature range, is thereby achieved. The complete verification of the model formalism, however, can only be performed once data become available on various thermal properties of the solid, in absence and presence of external uniform and constant magnetic fields of moderate strength, at low enough temperatures $T<\mathrm{}10\mathrm{}$ mK. Earlier high-temperature nuclear-paramagnetic-susceptibility data of low precision can be accounted for by the model and its parameters at small-volume isochores, but numerical discrepancies develop at the larger volumes. Accurate susceptibility measurements are required for a detailed comparison of theoretical and experimental values of the asymptotic Curie temperatures of the solid along a series of isochores.

Phenomena in "ordinary" fluid mixtures (such as C${\mathrm{H}}_3$OH-${\mathrm{H}}_2$O-C${\mathrm{O}}_2$) which are analogous to tricritical points in ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures, metamagnets, etc. have been reported for some years in the Soviet physical-chemistry journals. References to these papers are given, together with a brief explanation of why the two types of phase transition are analogous, and reasons why further experiments on the "ordinary" mixtures would be of interest.

The correction to the order-parameter decay rates near the critical point of fluids arising from the frequency dependence of shear viscosity was calculated, and was found to be generally small ranging from 0.6% at $q\xi =0.1\mathrm{}$ to 6% at $q\xi =30\mathrm{}$, where $q$ and $\xi$ are the wave number and the range of correlations of order-parameter fluctuations, respectively.

The dynamic form factor for high frequencies and short wavelengths is calculated for a specific model in the nematic phase as well as in the isotropic liquid phase. The zero-sound feature is revealed.

The elastic constants of a hard-rod liquid crystal are calculated using the Onsager theory, with results similar to those given by Priest.

Reliable calculations of the shift ($\Delta$) and width ($\Gamma$) are combined with precision calculations of the unshifted energy ($\mathcal{E}$) to obtain the position and width of the lowest ${}_{}{}^1{}_{}{}^{}S$ resonance in $e-\mathrm{H}$ scattering. These values together with our previous results for the two higher, ${}_{}{}^3{}_{}{}^{}P$ and ${}_{}{}^1{}_{}{}^{}D$, resonances are compared with the previous most-accurate calculations and some differences are noted. Comparison with experiment is also made.

A crystal spectrometer is used to study 6.5-MeV, foil-excited oxygen-beam x rays. The transitions from $\mathrm{}\left(1s\right)\mathrm{} \mathrm{}\left(2p\right)\mathrm{} 2 {}_{}{}^3{}_{}{}^{}P$ to ${\mathrm{}\left(1s\right)\mathrm{}}^{2}1 {}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ He-like and from $\mathrm{}\left(1s\right)\mathrm{} \mathrm{}\left(2s\right)\mathrm{} {}_{}{}^4{}_{}{}^{}P_{}^{\circ }{}_{}{}^{}$ to ${\mathrm{}\left(1s\right)\mathrm{}}^2{\mathrm{}\left(2s\right)\mathrm{}}^2{S}_{\frac{1}{2}}$ Li-like oxygen states are observed to have lifetimes of 1.47 ± 0.02 and 1.87 ± 0.1 nsec, respectively. Both decays are observed to have long-lived components. These results are compared to previous lifetime measurements of x-ray emitting and electron-emitting oxygen states.

The recently proposed analytic methods, which reduce the Glauber amplitude for charged-particle—neutral-atom collisions to a one-dimensional integral representation involving modified Lommel functions, are used to evaluate the cross sections for the direct excitation of the $2 {}_{}{}^1{}_{}{}^{}S$ state of helium by electron and positron impact. Comparison is made with the Coulomb-projected Born approximation of Hidalgo and Geltman and the truncated eigenfunction-expansion method of Berrington, Bransden, and Coleman.

Linked-cluster many-body perturbation theory is applied to the contact hyperfine interaction at the proton in the ${}_{}{}^2{}_{}{}^{}\Sigma$ state of the OH radical. Using a molecular-orbital basis set, the first-order result for the isotropic hyperfine constant $A$ in $A\overrightarrow{\mathrm{I}}·\overrightarrow{\mathrm{S}}$ is found to be 750 MHz, in very good agreement with the recently measured value of 760.5 MHz.

This paper reports the observation of the two-photon ionization of molecular cesium as a continuous function of laser wavelength in the 6200-6600-Å region with a tunable dye laser having a 0.18-${\mathrm{Cm}}^{-1\mathrm{}}$ linewidth. To the author's knowledge, it serves to illustrate the first extension to neutral molecular species of the important techniques of resonant multiphoton photodetachment spectroscopy. The resulting two-photon photoionization spectrum is intepreted in terms of the vibrational structure of the resonant intermediate molecular state.

A careful discussion of the no-retardation (instantaneous) limit of the Bethe-Salpeter (BS) equation is carried out, as illustrated by one-photon exchange in the radiation gauge for positronium. Comparison is made with equations obtained by other authors, using the effective potential to order $m{\alpha }^4$ as a test. Detailed analysis, using a new approach to the BS equation, recently proposed by the authors, indicates that the equations do not give equivalent results to order $m{\alpha }^4$ and that the arguments leading to the experimentally well verified $m{\alpha }^4$ potentials are sometimes defective.

Using energetically reliable configuration-interaction and Hartree-Fock wave functions for $\mathrm{He}\left({}_{}{}^1{}_{}{}^{}S \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{e}\right)-$, $\mathrm{Li}\left({}_{}{}^2{}_{}{}^{}S \mathrm{and} {}_{}{}^2{}_{}{}^{}P \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}\right)-$, and $\mathrm{Be}\left({}_{}{}^1{}_{}{}^{}S \mathrm{state}\right)$-like ions, we applied the method of successive partial orthogonalizations to determine orbital correction $f$ functions (introduced by Sinanoğlu in his many-electron theory) which arise from electron-correlation effects. The addition of an $f$ function to an appropriate Hartree-Fock orbital gives an improved orbital representation as far as the one-particle density is concerned. Hence, changes in the corresponding radial density distributions were obtained and their characteristics and $Z$-dependent trends were rationalized in terms of the fluctuation potential proposed by Sinanoğlu. For He-like ions, changes in the $K$-shell density showed strong split-shell characteristics. This also held for the $K$ shell of the Be-like ions; however, as $Z$ increased, the perturbative influence of the $L$ shell became more apparent. In the $L$ shells for the Be-like systems, because of the $2s-2p$ near degeneracy, angular correlation is relatively high and, consequently, the fluctuation potential gave rise to an $f$ effect which produced an over-all density contraction towards the nucleus. These density changes for the $2s$ electrons are considerably larger than the changes associated with the $K$ shells. At a low-$Z$ value for $\mathrm{Li}\left({}_{}{}^2{}_{}{}^{}S\right)$-like ions, spin polarization of the $K$ shell owing to the unpaired $L$-shell electron is small, the changes in density being predominantly intrashell effects. For high $Z$, spin-polarization effects are greatly increased. The $L$-shell electron in the ${}_{}{}^2{}_{}{}^{}S$ state experiences only an intershell fluctuation potential—which is purely attractive. For this state, the density changes for the outer electron are about 25% of the $L$-shell effect in the $\mathrm{Be}\left({}_{}{}^1{}_{}{}^{}S\right)$-like ion and they are almost four times larger than the corresponding $K$-shell effect. In the $\mathrm{Li}\left({}_{}{}^2{}_{}{}^{}P\right)$ series of ions, the $K$-shell density shifts due to the $f$ functions are dominated by intrashell effects for $Z=3\mathrm{}$ whereas, at higher-$Z$ values, an exchange effect becomes the major influence. Our results for the $L$ shell appear less satisfactory and suggest that a further such study of the excited state of these ions would be of interest.

The $g_J$ factor for the excited $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state of helium has been calculated from a generalized Breit equation which includes radiative corrections. The result is $g_J$ $(\mathrm{He},2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{})=g_e(1-40.91640\mathrm{}\times {10}^{-6\mathrm{}})=-2.002237379\mathrm{}$. This result is in good agreement with the previous theoretical value calculated by Perl and Hughes to order ${\alpha }^2$. Higher-order corrections (${\alpha }^3 \mathrm{and} {\alpha }^2\frac{m}{M}$) contribute -0.151 ppm. Combining this result with the calculated value for the atomic hydrogen $g_J$ factor gives the ratio $\frac{g_J(\mathrm{He},2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{})}{g_J(\mathrm{H},1\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{})}=1-23.212\mathrm{}\times {10}^{-6\mathrm{}}$ with an estimated uncertainty of 3 × ${10}^{-9\mathrm{}}$. This value is in agreement with the old experimental and theoretical values of Hughes et al., and improves upon the accuracy of the latter, but disagrees with a recent experimental value obtained by Leduc, Laloë, and Brossel.

The Sternheimer shielding-antishielding parameters are reported for 77 ions in $3d$, $4d$, $5d$, and $5f$ groups, as well as for gold and lithium atoms. The parameters $\lambda$ and $R$, which take into account, respectively, the effect of the core electrons on the quadrupole perturbing potential outside the ion and within the ion (owing to unfilled valence-shell electrons), have been calculated for varying ionic charge and varying atomic number in each group. The electronic wave functions used throughout the work are of the nonrelativistic Hartree-Fock-Slater type. Interesting differences of the results in each group are seen to be the values of Sternheimer parameters and ${\alpha }_q$ for ions with and without the closed-shell configurations. Also, for the lithium atom with $1s^{2}2p^1$ configuration we obtained $1-{\lambda }_0=3.46\mathrm{}$, assuming $2p^1$-shell perturbation to be one-sixth that of the closed $p$ shell. This value, incidentally, is the same as that measured recently by Anderson and Karra for the lithium ion (${\mathrm{Li}}^{+}$) in LiF. For gold atoms the configurations $5d^{10}6p^1$ and $5d^{10}6s^1$ were considered and we obtained the ratios of atomic core $5p_{\frac{3}{2}} \mathrm{to} 4p_{\frac{3}{2}}$ energy-level splittings as 1.6 and 1.7, respectively, against approximately 2 determined experimentally by Novakov and Hollander for Au in gold-cyanide compounds. The significance of these calculations is emphasized by the possibility of experimentally determining the quadrupole splittings of the atomic core by high-resolution electron spectroscopy.