We note that recent experimental results on the activation energy of electron-hole recombination in bismuth, when combined with recent measurements of the phonon dispersion spectrum, yield the relative separation in momentum space of the valence and conduction band extrema. If we accept the strong experimental and theoretical evidence that the conduction-band minima are at the centers of the pseudohexagonal faces of the Brillouin zone (symmetry points $L$), our results then indicate that the maximum of the valence band is at the center of the hexagonal face of the Brillouin zone (symmetry point $T$).

Boundary scattering in gallium single crystals produces little shift of the superconducting critical temperature $T_c$ consistent with the assumption of specular reflection of quasiparticles at the sample boundary.

We compare an explicit expression for the precession of a gyroscope in the Brans-Dicke scalar-tensor general relativity theory with the result derived by Schiff using Einstein's theory, and suggest that the gyroscope experiment offers the best possibility for testing the Brans-Dicke theory. Further, we conclude that the gyroscope in a satellite offers a more sensitive test than the earth-bound gyroscope.

The measurement of the branching ratio for the direct decay $K^{+}\to {\pi }^{+}+\gamma +\gamma$, where the invariant mass of the two gamma rays is not equal to the ${\pi }^0$ mass, has considerable theoretical importance. We have experimentally established an upper limit of 1.1×${10}^{-4\mathrm{}}$ for this branching ratio. We have used our results to set a limit on the off-the-mass-shell variation of the $K^{+}\to {\pi }^{+}+{\pi }^0$ amplitude.

The total gravitational field energy functional is shown to have only one extremum under variation of the metric field variables. At the extremum the energy vanishes and space is flat; second variation shows that the vacuum state is also a local minimum.

A primary universal vector and axial-vector interaction theory is proposed for strong-interaction phenomena. It is shown that such a hypothesis leads to a definite relation between vector and pseudoscalar coupling constants, which predict the $S$- and $P$-wave pion-nucleon scattering lengths, in good agreement with experiments. The ratio of $\pi$-meson to $\rho$-meson masses is also predicted, which agrees well with the observed value.

The Low theorem is applied to the radiative cross section for unpolarized particles. It is shown that the first two terms of an expansion in the photon energy depend on the unpolarized, nonradiative cross section only.

Phase transitions in solid methane are studied on the basis of the James-Keenan model, in which the intermolecular interaction responsible for the phase transitions is assumed to be electrostatic octupole-octupole interaction between neighboring molecules. The calculations are made in the framework of molecular-field-approximation method in quantum statistical mechanics. Phase diagrams of normal and equilibrium mixtures of nuclear-spin species $A$ and $T$ are presented.

Sum rules are derived which give the distribution of states consisting of an $A$-particle nucleus times a single-particle form factor among all physical states of the ($A+1\mathrm{}$)-particle system. A similar derivation of Butler's new stripping theory clarifies some of its physical content.