Physical Review

A Bethe-Salpeter model is proposed which sums graphs that are very similar to those summed in the work of Chew, Goldberger, and Low. This model yields considerably simpler equations and allows the analytic continuation of the amplitude into the angular momentum plane. This model is used to perform the bootstrap calculation for several input trajectories, including the $\ensuremath{\rho}$ and the …

A model for interacting single-mode electromagnetic radiation and matter consisting of $N$ two-level particles is solved exactly using a representation in which the creation and destruction operators for the field act by multiplication and differentiation, respectively. The model includes off-resonant interactions. Closed-form expressions can be given for some special cases. The solutions are tra…

A multiperipheral model, based on one-pion-exchange dominance of low-momentum-transfer processes, is used to study the dynamical origin of the leading Regge trajectories which are coupled to the two-pion system. A Bethe-Salpeter technique is used to calculate the leading singularities in the angular-momentum plane from an input interaction that is determined by the observed low-energy pion-pion s…

We illustrate in detail the summation of multiphoton exchange diagrams for $\mathrm{ee}$, $\ensuremath{\gamma}e$, and $\ensuremath{\gamma}\ensuremath{\gamma}$ elastic scattering amplitudes at the high-energy limit using the infinite-momentum technique reported earlier. These diagrams are shown to give rise to amplitudes proportional to $s$, the center-of-mass energy squared, multiplied by simple …

A hypothesis of limiting fragmentation of the target and of the projectile in a high-energy lepton-hadron or hadron-hadron collision is defined. Arguments are given for the hypothesis. Comparisons with various models and concepts are made. Further speculations are made, including the absence of pionization processes in high-energy collisions and the dependence of multiplicity on the momentum tran…

We present a comprehensive phenomenological examination of the Veneziano ansatz for pion-nucleon and kaon-nucleon processes. Using invariant amplitudes constructed as sums of beta-function terms, we attempt to fit simultaneously all the relevant high- and low-energy scattering data as well as the elastic widths of baryon resonances. We discuss a useful technique for ensuring that the theoretical …

Assuming a picture of the strong interactions in which the Hamiltonian is the sum of an $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$-symmetric piece ${H}_{0}$ plus a small symmetry-breaking term $\ensuremath{\epsilon}{H}_{1}$, we show how to calculate relations among the corrections of order $\ensuremath{\epsilon}$ to the symmetry limit. Our techniques are purely group-theoretic and invo…

By means of a mathematical transformation, we introduce a set of reference frames, called superluminal inertial frames, relative to which tachyons in one spatial dimension behave as ordinary particles. One-dimensional processes involving tachyons and photons can be analyzed in the new frames, and the results transformed to the subluminal frames. The mathematical symmetry or duality between sublum…

Values for the electro-optic and second-harmonic-generation coefficients ${r}_{41}$ and ${d}_{14}(\mathrm{SHG})$ can be calculated from absolute spontaneous-Raman-scattering data alone. The ratio of electronic and lattice contributions to ${r}_{41}$, and the stimulated Raman gain coefficients for the LO and TO modes, may also be obtained. The technique is applied to GaAs and the value for ${r}_{4…

Multiphonon Raman scattering from LO phonons has previously been observed in CdS in the case where the laser frequency lies near the energy gap. The combined effects of finite wave vector and resonant energy denominators are offered as the explanation for certain features of the scattering. These features include the unusual polarization properties of the single-phonon scattering and the unexpect…

The electron contribution to the phonon spectrum is formulated in terms of the microscopic response function. The long-wavelength behavior of the lattice vibration is then investigated, with due attention to the long-range Coulomb interaction. An important quantity which emerges is the effective charge of the vibrating nuclei, which is shown to obey a sum rule. From this follows the existence of …

The diffusion coefficient $D={D}^{0}{e}^{\ensuremath{-}\frac{{Q}^{0}}{\mathrm{RT}}}$ and isotope effect for ${\mathrm{Kr}}^{78}$ and ${\mathrm{Kr}}^{86}$ in solid Ar have been measured using a tracer technique. The activation energy $Q_{\mathrm{Kr}}^{}{}_{}{}^{0}$ depends on the interchange parameter $w$, but is estimated to lie in the range 3500-3900 cal ${\mathrm{mole}}^{\ensuremath{-}1}$, with…

The diffusion of Sn, Pb, Sb, and Bi tracers in Li metal has been investigated, using a thin-film evaporating-sectioning technique. The results can be expressed by the Arrhenius relations ${D}_{\mathrm{Sn}}=0.62{e}^{\ensuremath{-}\frac{(15.0\ifmmode\pm\else\textpm\fi{}1.2)}{\mathrm{RT}}}$, ${\mathrm{D}}_{\mathrm{Pb}}=1.6\ifmmode\times\else\texttimes\fi{}{10}^{2}{e}^{\ensuremath{-}\frac{(25.2\ifmmo…

The energy-band structures of ${\mathrm{Cd}}_{3}$${\mathrm{As}}_{2}$, ${\mathrm{Zn}}_{3}$${\mathrm{As}}_{2}$, and ${\mathrm{Cd}}_{1.2}$${\mathrm{Zn}}_{1.8}$${\mathrm{As}}_{2}$ in a hypothetical fluorite structure have been determined, employing the pseudopotential method. From these results a qualitative picture of the band-edge structure in real crystals is deduced. It is shown that many optical…

A hydrodynamic theory of spin waves is developed for certain magnetic systems in analogy with the derivation of two-fluid hydrodynamics for liquid helium. The systems considered are "isotropic" and "planar" ferromagnets and antiferromagnets. In each system, low-frequency spin waves are predicted to exist at long wavelengths for any temperature below the transition to the paramagnetic phase. The r…

The fine structure of the optical fluorescence spectrum arising from the fourth-nearest-neighbor chromium ion pair system in ruby is studied using high-resolution optical spectroscopy, ordinary electron-spin resonance, and optically detected electron-spin resonance. The ground-state energy levels of this system are found to be describable by a simple spin Hamiltonian of the form $\mathcal{H}=g\en…

The inelastic scattering of light arising from the time-dependent polarizability induced by intermolecular interactions has been observed in the simple classical liquid, argon. The spectrum at 90 \ifmmode^\circ\else\textdegree\fi{}K and 1.5 atm is centered at zero frequency shift, and is exponential in shape, with a characteristic width of 21 ${\mathrm{cm}}^{\ensuremath{-}1}$. The depolarization …

Several earlier computer studies of nonlinear oscillator systems have revealed an amplitude instability marking a sharp transition from conditionally periodic to ergodic-type motion, and several authors have explained the observed instabilities in terms of a mathematical theorem due to Kolmogorov, Arnol'd, and Moser. In view of the significance of these results to several diverse fields, especial…

A simulation of the longitudinal nuclear-electromagnetic cascade development in an ionization spectrometer has been carried out using a Monte Carlo method. Details of the cascade model and the technique used for the calculations are presented. Calculations have been performed to correspond to an actual spectrometer which was exposed to 10-, 20.5-, and 28-GeV/c incident protons at the Brookhaven A…

An analysis of high-energy $\ensuremath{\pi}N$ scattering is made, through the range $0\ensuremath{\le}\ensuremath{-}t\ensuremath{\le}2$ (${\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$, in terms of $P$, ${P}^{\ensuremath{'}}$, ${P}^{\ensuremath{'}\ensuremath{'}}$, $\ensuremath{\rho}$, and ${\ensuremath{\rho}}^{\ensuremath{'}}$ Regge poles. High-energy data are supplemented by continuous-momen…