We present calculations of the velocity of second sound $u_2$ below 1 K as a function of pressure. These calculations show that $u_2$ rises above the Landau limit in the presence of positive phonon dispersion. The effect should be experimentally observable in a suitably designed apparatus.

The conditions of validity for the momentum-translation approximation of Reiss are found much more stringent than was thought before: multiphotonic transitions induced by one strong field cannot be described by this method. First-order transitions between bound states dressed by a strong low-frequency field can be calculated, but the method gives nothing but a trivial result; only for the ionization of a dressed atom is the approximation found useful.

Some objections concerning the validity of a method which couples two unitary transformations so different as the Reiss and the Henneberger transformations are presented and discussed. In the present state, it seems that only for weak field or high electron energy the state of an electron hydrogen atom in a field can be obtained.

The experimental data on the solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ magnetic system are reviewed with an eye toward establishing the constraints placed by the data on models of the system. We find that certain of the data are consistent with no conventional-model magnet and that the present models (Heisenberg near-neighbor antiferromagnet and triple exchanged) are inconsistent with the data.

Accurate and coupled Hartree-Fock calculations of the third-harmonic coefficient (THC) of ${\mathrm{Li}}^{+}$ are presented. The zero-frequency THC in the Hartree-Fock case is 0.2190 a.u. and the accurate THC is 0.2411 a.u. The $1s^2\to 1s2p$ transition wavelength is determined to be 196.7 Å from the Hartree- Fock calculation and 199.0 Å from the accurate calculation, whereas the observed value is 199.3 Å.

Line-broadening theory is applied to photons emitted during atomic collisions. The maximum cross section for such collisions has an order of magnitude of ${10}^{-5\mathrm{}}$ $\pi a_0^2$, and is independent of the atomic number $Z$. Excitation of such radiation without the presence of atomic x rays is discussed. The spectrum may show an oscillatory energy dependence. The molecular-orbital x ray may have a linelike emission which is characteristic of the united atom.

The cross sections for the $2{}_{}{}^1{}_{}{}^{}P$ excitation of He by electron impact have been calculated with the distorted-wave Born approximation (by Madison and Shelton) and with the plane-wave Born approximation (by Kim and Inokuti). Although the distorted-wave description of the incident electron results in greatly improved cross sections at large angles compared to the plane-wave method, this paper points out that a substantial part [(35-80)%] of the difference in the two methods for small-angle scattering comes from using different He wave functions in the two computations.

All unitary solutions of the weak-coupling gap equation for $l=1\mathrm{}$ pairing are exhibited, and their rotational degeneracies highlighted. The role of the Zeeman and dipolar energies in resolving these degeneracies is examined. These interactions are used to calculate the NMR frequency, and the assumptions used by Anderson and Leggett in earlier calculations are clarified. In particular, "classical" equations are given which are equivalent to Leggett's quantum-mechanical analysis.

It is shown that when spin currents are included in the neoclassical radiation theory of Jaynes et al., radiative atomic level shifts are obtained which in the case of hydrogen are in strong disagreement with experiment.

The $K$ x-ray transitions of neon produced in single collisions of 40-MeV ${\mathrm{Cl}}^{+7\mathrm{}}$, ${\mathrm{Cl}}^{+11\mathrm{}}$, and ${\mathrm{Cl}}^{+13\mathrm{}}$ beams with neon targets are resolved into eight components. Over half the x-ray production is found to be associated with the two- and three-electron system in all cases. Strongly charge-dependent neon $\mathrm{Ly}-\alpha$ production is also observed. X-ray and vacancy-production cross sections are obtained for each component separately. We show that the vacancy-production cross section rather than the change in fluorescence yield dominates the charge dependence of the x-ray yields.

As their explanation for the relatively precipitous onset of superfluidity in thin helium films which we have reported, Dash and Herb have recently advanced their "connectivity" theory. An analysis of this theory is presented here and some predictions are deduced from it. These predictions appear to be in contradiction to the experimental facts. Hence, the theory seems inapplicable to the onset phenomena reported.

It has been suggested by Laughlin and Dalgarno that transition probabilities derived from beam-foil mean lives are invariably too low as a result of underestimating the importance of cascade repopulation. We show that there is in fact no systematic disagreement between recent beam-foil experiments and recent theoretical calculations. A brief discussion of the factors limiting the accuracy of beam-foil mean lives is also given.

$K$ x-ray and Auger-electron energies in heavy-ion collisions are shifted in energy in an opposite manner as the degree of ionization in the $L$ shell increases. X-rays are shifted to higher energies and Auger electrons to lower energies. We describe a very simple model which accounts for these effects and provide crude estimates of the shifts.

The collisional excitation method is used to excite an autodetaching state of ${\mathrm{F}}^{-}$ and several autoionizing states of neutral F. The ${\mathrm{F}}^{-}$ state lies at 14.85 ± 0.04 eV above the neutral-fluorine ground state and has as its dominant configuration $2p^4\left({}_{}{}^1{}_{}{}^{}D\right)3\mathrm{}{s}^2{}_{}{}^1{}_{}{}^{}D$. The observed autoionizing states of fluorine have configurations $\left({}_{}{}^1{}_{}{}^{}D\right){\mathrm{nl}}^{\prime }$ and $\left({}_{}{}^1{}_{}{}^{}S\right){\mathrm{nl}}^{\prime \prime }$.

The prior (i), post (f), and distorted wave (dw) forms of the first Born approximation, and a one-parameter approximate helium wave function, are used to calculate cross sections for electron capture from $\mathrm{He}\left(1\mathrm{}{s}^2\right)$ by protons. These cross sections are calculated for capture into $\mathrm{H}\left(3\mathrm{}lm\right)$, $l=1, 2$; $-1\mathrm{}\le m\le 1$, for impact energies, $10\le E\le 1000$ keV, leaving the residual ion ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$. The associated polarizations $P$ are calculated for the axis of quantization of H parallel to the direction of incidence, and the apparent cross sections $Q_A=3Q{\mathrm{}(3-P)\mathrm{}}^{-1\mathrm{}}$ are obtained from $P$ and the calculated cross sections $Q=\Sigma {m=-l}^l{Q}_m$. The $Q$ used to determine $Q_A$ are $Q\left(\mathrm{dw}\right)$ and the arithmetic average of $Q\left(\mathrm{i}\right)$ and $Q\left(\mathrm{f}\right)$. Of these two sets, $Q_A\left(\mathrm{dw}\right)$ predicts the measured $Q_A\mathrm{}\left(3p\right)\mathrm{}$ more successfully for $E<\mathrm{}250\mathrm{}$ keV, and the measured $Q_A\mathrm{}\left(3d\right)\mathrm{}$ better for $E<\mathrm{}200\mathrm{}$ keV. For larger values of $E$ both sets predict the measured values equally well. In the range $15\le E\le 60$ keV, the effect of $P\left(\mathrm{dw}\right)$ is more marked for capture into $\mathrm{H}\mathrm{}\left(3p\right)\mathrm{}$ than into $\mathrm{H}\mathrm{}\left(3d\right)\mathrm{}$.

Simple momentum-transfer theory for the composition dependence of ion mobilities and diffusion coefficients in gas mixtures at arbitrary field strengths is corrected and extended, and compared with a similar theory based on momentum and energy transfer, and with results based on direct solution of the Boltzmann equation by Kihara's method. Final equations are recommended for predicting composition dependences, given only results on ion mobilities and diffusion coefficients in the pure component gases.

A direct derivation of the forms of density operator and phase-space distribution functions for unpolarized radiation is given.

An energy-level calculation of the $3d^5$ configuration of Mn III is carried out, including eleven newly observed energy levels. The calculation takes into account the "weak" spin-dependent interactions, namely the spin-other-orbit, the spin-spin, and the effective electrostatic-spin-orbit interactions, which are of special importance in the half-filled $3d$ shell. An excellent fit between the calculated and observed energy levels is obtained, with a mean error of 7 ${\mathrm{cm}}^{-1\mathrm{}}$, and a mean $o-c$ spread" of 3 ${\mathrm{cm}}^{-1\mathrm{}}$ per multiplet. A ratio between effective electrostatic-spin-orbit interaction parameters $Q^2$ and $Q^4$ is established for the first time.