The amplitude of adiabatic perturbations that might have existed in the early universe is limited by the nonlinear transfer of energy to high frequencies. For flat cosmological models, this limit, together with the effect of linear dissipation, yields a residual perturbation in the matter distribution comparable with the semiempirical estimate of what is needed to produce massive galaxies.

Long-range weak-interaction forces arising from multiple neutrino exchange do not significantly affect the evolution of a homogeneous, isotropic universe. Inhomogeneities can induce an effective local $\frac{1}{r^2}$ force between electrons but the magnitude of this force is much smaller than gravity for our universe.

The energy per particle in a many-particle system, both for bosons and fermions, is discussed using a perturbation method and some results on reduced density matrices obtained previously. The theory is tested for hard-sphere, Lennard-Jones, and nonsingular potentials; it exhibits clearly the difficulties in going to higher-order approximations and gives results which correspond to those obtained by other methods.

Beginning with the definition of a duplicated experiment and the fact that the resulting data are summarized as a set of configurations of some observables, together with frequencies of occurrence of each configuration, we derive the formal structure of conventional quantum theory using only the statistical properties of such data, and show that certain elements of the theory have heretofore been overlooked. This derivation yields a rather broad generalization of the theory which suggests new methods for describing phase transitions and possibly fundamental particles as well.

The propagation of electromagnetic waves in a Fermi sea of neutrinos is investigated on the basis of the photon-neutrino weak-coupling theory and is compared with the result obtained by Royer on the basis of the $\left(e\nu \right)\left(e\nu \right)$ coupling. It is shown that a photon propagating through the neutrino sea satisfies a dispersion relation of the form ${\omega }^2={{\omega }_0}^2+k^2{c}^2$, where ${\left(\hslash {\omega }_0\right)}^2\approx 6.2\times {10}^{-23\mathrm{}}$ ${E_F}^2$, $E_F$ being the Fermi energy of the sea. Finally, some remarks are made as to the possibility of the destruction of a photon when propagating through the sea due to the process $\gamma +\nu \to \nu +\nu +\overline{\nu }$. It is found that the mean free path corresponding to this process is ≈ ${10}^{69}$ cm, much larger than the radius of the universe.

The orbital angular momentum of the $A_1$ meson produced from ${\pi }^{-}p\to {\pi }^{-}{\pi }^{-}{\pi }^{+}p$ at 16 GeV/c was studied by analyzing the decay angular distributions in the ${\rho }^0{\pi }^{-}$ state. A completely Bose-symmetrized formalism was used to measure the ratio $\frac{g_1}{g_0}$ of the helicity states of the $\rho$ from the $A_1$ decay. The value obtained, $\left|\frac{g_1}{g_0}\right|=0.48\mathrm{}\pm 0.13$, indicates a substantial $d$-wave contribution in the $A_1$ decay.

We show that the Veneziano-Lovelace one-term formula for pion-pion scattering, although a good first approximation, has some undesirable features. With the help of a few secondary terms, a model amplitude, which is consistent with the known properties of the pion-pion system up to the $f^0$ mass region and the high-energy phenomenology, is constructed.

The radiative decays of the $X^0$ meson are analyzed in the framework of an effective Lagrangian with vector-meson dominance, using vector gauge fields with current mixing and assuming $X^0$ to be a unitary singlet. The underlying $\mathrm{VVP}$ strong interaction obeys octet-broken $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry. The model is shown to predict branching ratios different from those obtained in the $\eta -X^0$ mixing model. An analysis of the experimental situation is presented, and the relevance of the $X^0\to 2\gamma$, $X^0\to \omega \gamma$ partial decay modes for distinguishing between different theoretical models is pointed out.

We present the decay characteristics of the low-mass $Q^{+}$ enhancement in the ${\left(K\pi \pi \right)}^{+}$ system which is produced in the reaction $K^{+}p\to {\left(K\pi \pi \right)}^{+}p$ at 12.7 GeV/c. When treated as a single resonance, this enhancement has the properties expected for the strange member of an $\mathrm{SU}\left(3\right)\mathrm{}$ meson octet with $J^{\mathrm{PC}}=1^{++}$. The resonance position and width of the $Q$ are, respectively, 1260±20 and 180±20 MeV.

The properties of the hypernucleus ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ were measured in an analysis of helium-bubble-chamber pictures taken at the Argonne ZGS. Some 90 examples of the production reaction $K^{-}+{\mathrm{He}}^4\to {}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}+p+{\pi }^{-}$ were found in which the $K^{-}$ stopped and the ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ decayed via ${\pi }^{-}$ emission. Twenty-seven events were observed to decay via the two-body mode ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}\to {\pi }^{-}{\mathrm{He}}^3$, with the remaining events decaying to ${\pi }^{-}\mathrm{pd}$ or ${\pi }^{-}\mathrm{ppn}$. The production rate was measured to be (${1.8}_{-0.6\mathrm{}}^{+0.7\mathrm{}}$)×${10}^{-3\mathrm{}}$ per stopping $K^{-}$. The mean life of the hyper-fragment was measured from the two-body decay mode as (${2.64}_{-0.52\mathrm{}}^{+0.84\mathrm{}}$)×${10}^{-10\mathrm{}}$ sec. The lifetime obtained from the three-body decays was consistent with this value, after the elimination of a serious source of background. The binding energy of ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ was measured to be 0.25±0.31 MeV. The decay ratio $R_3=\frac{\Gamma ({}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}\to {\pi }^{-}{\mathrm{He}}^3)}{\Gamma ({}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}\to \mathrm{all} {\pi }^{-})}$ was measured to be ${0.36}_{-0.06\mathrm{}}^{+0.08\mathrm{}}$, in agreement with values from previous experiments and with the value calculated for spin ½ for the ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ hypernucleus.

Results are presented from a study of 1983 six-prong ${\pi }^{-}p$ interactions observed in the ANL 30-in. hydrogen bubble chamber. The incident ${\pi }^{-}$ momentum was 5.97 BeV/c. The measured cross sections for the $3{\pi }^{-}2{\pi }^{+}p$, $3{\pi }^{-}2{\pi }^{+}p{\pi }^0$, and $3{\pi }^{-}3{\pi }^{+}n$ final states are 0.25±0.02, 0.35±0.04, and 0.14±0.03 mb, respectively. The general features of the data, e.g., the angular and momentum distributions of the individual particles in each final state, are presented, and agree with the results of experiments at other energies. Resonances are produced in more than half the events. The ${\Delta }^{++}\mathrm{}\left(1236\right)\mathrm{}$ isobar and the ${\rho }^0$ and ${\omega }^0$ mesons dominate the resonance production. Associated production of the ${\Delta }^{++}$ isobar and the ${\rho }^0$ meson is observed in the $3{\pi }^{-}2{\pi }^{+}p$ final state. In the $3{\pi }^{-}2{\pi }^{+}p{\pi }^0$ final state, the ${\Delta }^{++}$ isobar and ${\omega }^0$ meson are produced simultaneously. The ${A_1}^{-}$ meson is observed in the $3{\pi }^{-}2{\pi }^{+}p$ final state. Evidence consistent with the production of higher resonances is also presented.

The reaction $\overline{p}p\to \overline{p}p{\pi }^{+}{\pi }^{-}$ has been studied for $p{\pi }^{+}{\pi }^{-}$ and $\overline{p}{\pi }^{+}{\pi }^{-}$ enhancements using 719 events at 2.7 GeV/c and 1015 events at 2.9 GeV/c. We find that the $p{\pi }^{+}{\pi }^{-}$ and $\overline{p}{\pi }^{+}{\pi }^{-}$ mass spectra can be adequately explained by assuming that the reaction proceeds 100% through the ${\overline{\Delta }}^{--}\mathrm{}\left(1236\right)\mathrm{}{\Delta }^{++}\mathrm{}\left(1236\right)\mathrm{}$ channel, and that it is not necessary to assume the production of $p{\pi }^{+}{\pi }^{-}$ or $\overline{p}{\pi }^{+}{\pi }^{-}$ resonances in this reaction at these energies.

Evidence is presented from a proton-proton bubble-chamber experiment at 6.6-GeV/c beam momentum that the cross-section ratio $\frac{\sigma (pp\to {\pi }^{+}p{\pi }^{+}{\pi }^{-}n)}{\sigma (pp\to {\pi }^{+}pn)}$ for low momentum transfer to the neutron ($t<\mathrm{}0.2\mathrm{}$ Ge${\mathrm{V}}^2$) is approximately the same as the cross-section ratio $\frac{\sigma ({\pi }^{+}p\to {\pi }^{+}p{\pi }^{+}{\pi }^{-})}{\sigma ({\pi }^{+}p\to {\pi }^{+}p)}$ when compared as a function of invariant mass of the non-neutron system in the $\mathrm{pp}$ reactions. These results imply that (a) pion exchange dominates $\mathrm{pp}\to \left({\pi }^{+}p{\pi }^{+}{\pi }^{-}\right)n$ for low momentum transfer to the neutron, in view of the recent results of Ma et al. on $\mathrm{pp}\to \left({\pi }^{+}p\right)n$, and (b) the off-shell corrections to the pion pole equation for $\mathrm{pp}\to \left({\pi }^{+}p{\pi }^{+}{\pi }^{-}\right)n$ are similar to those for $\mathrm{pp}\to \left({\pi }^{+}p\right)n$; the results presented here complement those presented earlier by Colton et al. for the reactions $\mathrm{pp}\to \left(p{\pi }^{-}\right){\Delta }^{++}$, $\left(p{\pi }^{-}{\pi }^0\right){\Delta }^{++}$, and $\left(n{\pi }^{-}{\pi }^{+}\right){\Delta }^{++}$.

The present data for the reaction $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ are analyzed with the aid of a general effective-range resonance formula for the $\rho$ meson. It is concluded that (a) $m_{\rho }=769\mathrm{}\pm 5$ MeV and ${\Gamma }_{\rho }=109\mathrm{}\pm 10$ MeV provide a reasonable explanation of the present experimental points; (b) the full width at half-maximum regardless of the peak height should give an excellent estimate of the $\rho$ width; (c) it is hard to escape ${\left|F_{\pi }\right({m_{\rho }}^2|}^2=\frac{{m_{\rho }}^2}{{{\Gamma }_{\rho }}^2}$; (d) the effects of final-state interactions on resonance shape ought to be investigated.

By using a previously developed dispersion technique, we investigate the Chew-Frautschi and the $\mathrm{Im}\alpha$-versus-$s$ plots for the cascade resonances. The eight resonances are found to lie on three nearly linear plots on both graphs as was found to be the case previously for the baryon $N_{\gamma }$ and ${\Delta }_{\delta }$ sequences. Of the two types of resonances, probable and doubtful, all of the former are fitted (with no gaps on the trajectories) and none of the latter is needed. Severe self-consistency requirements are well satisfied by the two plots.