We develop a set of formulas which relate the first two volume derivatives of the temperature-independent Grüneisen parameter $\gamma$ to other more readily measurable quantities. For a quasiharmonic solid in the classical temperature region, these relations are exact and permit accurate calculations of $\gamma$ to second order in compression.

Observations are reported on the appearance of Pendellösung interference fringes within neutron Bragg reflections. These have been used to determine the atomic scattering amplitude of silicon for neutrons as (0.41646±0.00022)×${10}^{-12\mathrm{}}$ cm. Conclusions are drawn concerning the spatial extent of the neutron wave packet from the fringe characteristics.

The Raman spectrum of RbNi${\mathrm{F}}_3$ has been observed over the temperature range 15-300°K, using an argon laser. In addition to vibrational Raman lines, a single strong line of magnetic origin, persisting well above $T_c$, is observed. A proposed ion pairing and scattering mechanism leads to a set of exchange parameters consistent with several other magnetic properties in RbNi${\mathrm{F}}_3$.

We have studied Raman scattering at low temperatures from Mn${\mathrm{F}}_2$ doped with ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Fe}}^{2+}$. Three temperature- and polarization-dependent lines have been observed for each impurity. For each dopant we have identified one line as a two-magon excitation of the impurity and some linear combination of the host spins. When corrections are made for magnon-magnon interactions, the predicted energy is in excellent agreement with the experimental results.

Weak Raman scattering from nickel-doped Mn${\mathrm{F}}_2$ observed below $T_{\mathrm{N}}$ has been identified with the simultaneous excitation of pairs of single-spin-deviation impurity magnon modes. The polarization and scattering frequency are accurately predicted by a simple model allowing for an interaction between the modes.

The reorientation effect in Coulomb excitation with ${\mathrm{S}}^{32}$ ions was used to deduce the static quadrupole moment of the first excited $J^{\pi }=2^{+}$ state in ${\mathrm{Mg}}^{24}$. The value obtained in this experiment is $Q_{2^{+}}=-0.26\mathrm{}\pm 0.08$ b.

If the sun possesses a fast-rotating core, mixing in its interior may be a possibility. We calculate the solar neutrino flux as a function of fractional mass $q_m$ in the mixed zone for "slow," "fast," and "very fast" mixing. Only for "slow" mixing and large $q_m$ could the neutrino flux be decreased appreciably, but such large values of $q_m$ are unlikely.

We have measured differential cross sections for the reactions ${\pi }^{-}p\to {\pi }^{-}p$ and ${\pi }^{-}p\to {\pi }^{\pm }{N}^{*\mp }\mathrm{}\left(1236\right)\mathrm{}$ at an incident pion momentum of 2.15 GeV/c and for center-of-mass scattering angles in the range ${cos\theta }^{*}=-0.999\mathrm{} \mathrm{to} -0.950\mathrm{}$. The elastic differential cross section has a sharp dip in the backward direction, dropping from ∼70 μb/sr at ${cos\theta }^{*}=-0.95\mathrm{} \mathrm{to} \sim 4$ μb/sr at ${cos\theta }^{*}=-1\mathrm{}$; the $N^{*-}\mathrm{}\left(1236\right)\mathrm{}$ differential cross section is, within our errors, consistent with the same size and shape as that for elastic scattering; the average differential cross section for $N^{*+}\mathrm{}\left(1236\right)\mathrm{}$ in our angular region is less than 18 μb/sr with 97% confidence.

A diffractively produced $3\pi$ enhancement is observed with mass ∼1.1 GeV and width ∼0.35 GeV. There is no structure observed in the peak in either the mass or angular distributions. The system is predominantly $s$-wave $\pi \rho$ with a $3\pi$ $0^{-}$ admixture which is essentially constant in percentage and relative phase across the peak.

The cross sections for ${\pi }^{-}{\pi }^0$ and ${\pi }^{-}{\pi }^{+}$ elastic scattering, and the $I=0\mathrm{}$ $s$-wave and $I=1\mathrm{}$ $p$-wave phase shifts, ${{\delta }_0}^0$ and ${\delta }_1$, are calculated for $400<\mathrm{}{M}_{\pi \pi }<900\mathrm{}$ MeV using a Chew-Low extrapolation. The extrapolation information permits resolving a fourfold ambiguity which has been present in other attempts to determine ${{\delta }_0}^0$ from the reaction ${\pi }^{-}p\to {\pi }^{+}{\pi }^{-}n$. The result for ${{\delta }_0}^0$ is consistent with a curve which increases through 90° around $M_{\pi \pi }=720\mathrm{}$. The $\rho$ width obtained from the extrapolated $p$-wave amplitude is 105 ± 15 MeV.

We discuss the requirement of a subtraction constant at infinite energy for the real part of the forward spin-nonflip Compton scattering amplitude from a proton and obtain an upper limit 6.3×${10}^{-4\mathrm{}}$ F/Be${\mathrm{V}}^2$ for such a constant. We show that the model of vector dominance applied to Compton scattering at 3-BeV photon energy is consistent with known photon total cross sections and the application of forward-scattering dispersion relations.

The possibility of a new dynamical effect in muonic lead arising from the excitation of discrete nuclear dipole states just below the neutron separation energy is discussed. The effect although small may be observable in high-resolution work.

The ratio of the differential cross sections at zero-angle scattering for the excitation of the $6{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ and $6{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ states in Cs has been measured for incident-electron energies between 3 and 68 eV. At 68-eV incident-electron energy the ratio is found to be 1.85, as predicted from degeneracy, but decreases significantly below 20-eV incident-electron energy.

It is shown that theoretical calculations which use the exponential model $\overrightarrow{\mu }={\mu }_0\left(\frac{\overrightarrow{\mathrm{r}}}{\mathcal{r}}\right)\times \exp (-\frac{\mathcal{r}}{\rho })$ for the variation of the dipole moment $\overrightarrow{\mu }$ with internuclear separation $\overrightarrow{\mathrm{r}}$ can be forced into agreement with experiment only if one uses dipole parameters ${\mu }_0$, $\rho$ which are in serious disagreement with values computed by the molecular Hartree-Fock approximation. On the basis of a Drude model calculation, it is concluded that the exponential model is an inadequate representation of the true physical situation because of its neglect of electron correlation effects.

A detailed comparison is made between theory and experimental data regarding the evolution of the transverse magnetization for long times (∼180 μsec) in Ca${\mathrm{F}}_2$. There is no doubt that for such times a decaying oscillatory exponential gives the correct behavior of the signal.

It is shown theoretically that nematic liquid crystals in magnetic fields may display alignment inversion walls partially similar to Bloch and Néel walls in ferromagnetics.

A model is presented which explains the observed dependence of the coupling between the primary and secondary vortices on the driving current, or primary vortex velocity, in the dc superconducting transformer. The basic idea is that viscous drag effects lead to a slippage between the vortices in the primary film and those in the secondary film for sufficiently large vortex velocities.

The purpose of this Letter is to report the calculation of the relativistic energy bands and Fermi surfaces of the double hexagonal close-packed light rare-earth elements lanthanum, neodymium, and praseodymium. The relationship of the Fermi surface to the ordering of magnetic moments in Nd and Pr and to the occurrence of the double hexagonal close-packed crystal structure is then discussed.

A self-consistent phonon approximation that includes odd-order anharmonic terms is found to give improvement over the usual lowest-order self-consistent phonon approximation when applied to computation of several properties of crystalline Ne and Ar. At low temperatures the improved theory joins smoothly onto the results of conventional perturbation theory.

Anomalies found in the intensity of $p$-polarized light from concave diffraction gratings have been analyzed in terms of an interaction between the incoming photon and a surface-plasmon resonance in the grating surface. There is clear evidence for zone gaps in the dispersion curves which we have constructed for surface plasmons in Al and Au. The phenomena reported here may be regarded as manifestations of second- and possibly higher-order plasmon-grating interactions.