A general perturbation expression is derived for the change, due to a photon mass, in the resonance frequency of a lumped circuit. This expression is shown to imply that the only significant effect of the photon mass is to produce small changes in the inductance and capacitance of the circuit and changes in the radiative half-life of the circuit.

We have observed nine examples of the decay $\Lambda \to p\mu \nu$ in a hydrogen bubble chamber. The branching ratio is (2.4 ± 0.8) × ${10}^{-4\mathrm{}}$.

The backscattering yields for planar channeling as a function of crystal orientation have been calculated using a temperature-dependent average potential. Temperature dependence of minimum yields ${\chi }_m$ and widths ${\psi }_{\frac{1}{2}}$ of the dips are studied and compared with experimental values obtained by different authors. An attempted calculation including nuclear multiple scattering is made.

Interference between ${\rho }^0$ and $\omega$ photoproduced from carbon, aluminum, and lead has been studied in the $2\pi$ decay mode. The branching ratio $\frac{(\omega \to 2\pi )}{(\omega \to 3\pi )}$ is 2.8 ± 0.6%. The phase difference between the decay amplitudes $\omega \to 2\pi$ and ${\rho }^0\to 2\pi$ is 63° ± 16°.

Forward $\omega$ photoproduction from complex nuclei and interference in the ${\pi }^{+}{\pi }^{-}$ decay mode of $\omega$, ${\rho }^0$ photoproduced from complex nuclei are analyzed to determine the $\omega -\gamma$ coupling constant and the magnitude and phase of the $\omega -N$ scattering amplitude. Values obtained are $\frac{\gamma _{\omega }^{}{}_{}{}^2}{4\pi }={7.6}_{-1.1\mathrm{}}^{+1.8\mathrm{}}$; ${\sigma }_{\omega N}=25.3\mathrm{}\pm 7.8$ mb; $invtan{\alpha }_{\omega }=-28\mathrm{}\pm 16°$.

We measured the differential inelastic cross section $\frac{E{d}^3\sigma }{d{P}^3}$ for very high-energy proton-proton collisions at the CERN intersecting storage rings. We studied these inclusive cross sections for reactions of the type $p+p\to {\pi }^{+}+\mathrm{anything}$ and $p+p\to p+\mathrm{anything}$ at energies equivalent to a lab energy of 500-1500 GeV. We found that in our kinematic range $\frac{E{d}^3\sigma }{d{P}^3}$ was equal to its value at accelerator energies, both in shape and normalization. This seems to support a type of scaling.

The $\overline{p}p$ total inelastic cross section has been measured in a hydrogen bubble chamber for $\overline{p}$ momenta from 100 to 550 MeV/c. Below 200 MeV/c the cross section increases rapidly to several barns. From this behavior it is inferred that high partial waves, perhaps to $L=3\mathrm{}$, are important in the annihilation at the lowest momenta studied. An abrupt change in the momentum dependence of the total absorption cross section occurs at about 350 MeV/c in the vicinity of previously observed structure in backward elastic scattering.

We have measured the differential cross section for the reaction ${\pi }^{+}p\to K^{+}{\Sigma }^{+}$ at 3, 5, and 7 GeV/c from 0° to ∼3.5° in the laboratory. The cross section at 5 and 7 GeV/c continues to 0° with an exponential $t$ dependence consistent with data at larger angles. However, the 3-GeV/c data exhibit a change in slope near $\mathrm{}\left|t\right|\mathrm{}\simeq 0.1$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$. We have also measured the differential cross section for ${\pi }^{+}p\to K^{+}{Y}^{*}\mathrm{}\left(1385\right)\mathrm{}$ at 5 GeV/c in the same angular range. These data indicate a dip at 0° as would be expected if the cross section were dominated by the helicity-flip amplitudes.

A straightforward analysis of the time-correlation function of interest in response theory involves the entire complicated solution of the dynamical problem. Using projection techniques we derive a simpler equation obeyed by the time-correlation function. Laplace transforms are used to solve this equation for the case when the driving force is a step function of arbitrary magnitude. The results are independent of the near-origin approximation of the Kubo formalism.

The $2{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ fine-structure interval ${\nu }_{01}$ of helium has been measured by the atomicbeam optical-microwave magnetic-resonance method. The result is ${\nu }_{01}=29\mathrm{}616.864\left(36\right)\mathrm{}$ MHz (1.2 ppm), in which the error is 1 standard deviation. This precision is more than a factor of 10 better than that obtained by any other method. Comparison with the present theoretical value of ${\nu }_{01}$ is given, and the possibility of obtaining a value for the fine-structure constant $\alpha$ accurate to better than 1 ppm from our experimental result is emphasized.

Measurements in a highly ionized plasma of anomalously large absorption and the threshold field required for its onset are presented as a function of plasma density for conditions free of electron inelastic effects. In the weak-field limit the measured absorption is in good agreement with the classical theory for the high-frequency resistivity.

Experimental measurements and numerical simulation show that relativistic electron beams propagating in a drift tube with a net current less than the Alfvén critical current assume an axially dependent equilibrium. The equilibrium of a 40-kA, 3-MeV electron beam propagating in air at 22.5 Torr has been studied analytically, numerically, and experimentally. Reasonable agreement among the results of the three approaches has been found.

We report here a calculation, based on Landau's hydrodynamical equations, of the intensities of the Brillouin spectral components due to density (first-sound) and entropy (second-sound) fluctuations in pure He II under pressure. In the hydrodynamic regime of temperature, the intensities of second-sound Brillouin components are found to be as strong as one tenth of those of the first-sound components under optimum pressure.

The displacement parameter in $\alpha$-quartz consists of a rotation of the Si${\mathrm{O}}_4$ tetrahedra around their two-fold symmetry axis. Its magnitude is given by $x_0(\omega ,T)-x_0(\omega ,T_c)=A\left(\omega \right)\times {(T_c-T)}^{\beta }$, with $\beta =0.34\mathrm{}\pm 0.02$ as determined independently by x rays, ultrasound, and Raman scattering.

The strongly localized model of disordered alloys, where the random perturbations are localized to a single lattice site, is shown not to have much applicability to real systems when the self-consistency requirement on the potential is included.

The susceptibility $\chi \mathrm{}\left(H\right)\mathrm{}$ of a paramagnetic Fermi liquid in a magnetic field is shown to have the logarithmic form $\chi \mathrm{}\left(H\right)=\chi \mathrm{}\left(0\right)(1-b{H}^2\ln H)$, and hence the free energy of the system cannot be expanded in powers of $H$ or in powers of the magnetization. Contrary to the result of the band model, this prediction is consistent with the experimental field dependence observed in Pd.

We propose a new mechanism for the self-focusing of electromagnetic radiation in degenerate semiconductors. The effect is due to the velocity-dependent mass of the conduction electrons. Calculations for InSb and a typical laser intensity give a theoretical focal length of 2.06 mm.

A simple model of heat flow across a metal-insulator interface is used to calculate the spatial variation of the temperature. The characteristic distance for the temperature gradient to reach its bulk value is shown to be of the order of the phonon mean free path in both the metal and the insulator. Explicit expressions are presented for the electron and phonon contributions to the interfacial thermal resistivity.

The latent heats of melting for simple metals at normal pressure are calculated by the pseudopotential method. The Percus-Yevick hard-sphere model is used for the liquid-structure factor, and an uncorrelated harmonic oscillator model is used for the solid-structure factor. Numerical results agree well enough with experiment and are sufficiently stable against changes in the parameters to make further calculations of the latent heat seem worthwhile.

An optical method for detection of electron-nuclear double spin resonance in the relaxed-excited state of $F$ centers is described. It has been successfully applied to KI. The hyperfine splittings inferred from these measurements indicate a relatively compact wave function for the relaxed-excited state.