The calculations of a previous paper on Reggeized $U\left(6\right)\mathrm{}\otimes U\left(6\right)\mathrm{}\otimes O\left(3\right)\mathrm{}$ and absorptive corrections are extended to $K^{+}n\to K^{0}p$ at 5.5 GeV/c with the addition of no new parameters. Good agreement with experiment is obtained.

Some recent results of Abarbanel, Drell, and Gilman on high-energy proton-proton scattering are shown to be the consequence of a general property of the Baker-Blankenbecler approximation for the unitarity condition they used. The latter approximation is shown to give results generally consistent with earlier suggestions of Wu and Yang.

A formalism is developed to treat the effects of final-state interactions on the properties of unstable particles produced in high-energy collisions. The formalism is applied to the photoproduction of $\rho$ mesons.

General intermultiplet mass formulas between the decuplet and octet baryons are derived, based on the chiral $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$ charge algebra and the asymptotic $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry imposed only on the charge operator $V_K$ which is the $\mathrm{SU}\left(3\right)\mathrm{}$ raising or lowering operator in the symmetry limit. In the absence of particle mixing, the formulas take on a simple form and are useful as a first guide in deducing baryon mass spectra. Inclusion of particle mixing is possible. The formulas imply that the equal squared-mass spacings of decuplet states ${\left({\delta }_a\right)}^2$ ($a$ specifies the quantum numbers of the $a$ decuplet) are universal [i.e., ${\left({\delta }_a\right)}^2=\mathrm{const}$] and, furthermore, equal to the universal spacings of the $\Xi$ and $\Sigma$ members of any octet baryons. In the case of the usual ${\mathrm{½}}^{+}$ and ${\frac{3}{2}}^{+}$ baryons, the formulas coincide with the well-known $\mathrm{SU}\left(6\right)\mathrm{}$ mass formula. Broken-$\mathrm{SU}\left(3\right)\mathrm{}$ sum rules (in the absence of mixing) for general transitions of the form $\left(\mathrm{octet}\mathrm{baryon}\right)\to \left(\mathrm{octet}\mathrm{baryon}\right)+\pi (or l+\overline{\nu })$ are also obtained. In particular, the strong decays, ${\frac{5}{2}}^{-}\to {\frac{1}{2}}^{+}+\pi$ and ${\frac{5}{2}}^{+}\to {\frac{1}{2}}^{+}+\pi$, are discussed in detail. The sum rules, in general, give rise to significant $\mathrm{SU}\left(3\right)\mathrm{}$-breaking effects. However, for the familiar axial-vector ${\frac{1}{2}}^{+}\to {\frac{1}{2}}^{+}+l+\overline{\nu }$ transitions, our broken-$\mathrm{SU}\left(3\right)\mathrm{}$ sum rules assume the same forms as satisfied by the hypothetical exact $\mathrm{SU}\left(3\right)\mathrm{}$ couplings. This justifies the use of the original Cabibbo analysis [in broken-$\mathrm{SU}\left(3\right)\mathrm{}$ symmetry] in determining the value of the axial-vector Cabibbo angle.

A model for uncorrelated meson production in high-energy nucleon-nucleon collisions is proposed, using the eikonal formalism to extract a specific form for the optical potential from nucleon-nucleon elastic scattering data. This potential is used to form the eikonal wave function of the scattering system, from which is constructed a model source density for radiated pions. The normalization is derived from Adler's formulation of the soft-pion limit. Predictions involving no free parameters are compared with pion spectra from $\mathrm{pp}\to {\pi }^{+}+\mathrm{anything}$ at 12.2, 19.2, and 30 GeV/c. Good to reasonable agreement is obtained for c.m. emission angles less than 20°. The mean multiplicity for charged pions is also found to agree qualitatively with experiment. A covariant formulation of the model, using the Bethe-Salpeter equation, is proposed, but no calculations are presented.

We study the radiative decays of the $D_{13}\mathrm{}\left(1515\right)\mathrm{}$, $S_{11}\mathrm{}\left(1525\right)\mathrm{}$, $F_{15}\mathrm{}\left(1690\right)\mathrm{}$, and ${Y_0}^{*}\mathrm{}\left(1520\right)\mathrm{}$ resonances within the framework of the symmetric quark model with harmonic-oscillator wave functions. We point out that if it is assumed that the quarks have large anomalous magnetic moments, then it becomes necessary to consider the so-called "spin-orbit" term in the nonrelativistic electromagnetic interaction Hamiltonian. Including the effect of this term, we show that it is possible to understand the vanishing contribution of the $D_{13}\mathrm{}\left(1515\right)\mathrm{}$ resonance to backward or forward pion photoproduction in terms of a cancellation between electric and magnetic multipoles. Requiring such a cancellation gives a value of the oscillator range parameter, $\alpha =105\mathrm{}$ MeV. Using this value and assuming that the quark scale magnetic moment $\mu$ is equal to the proton moment, we calculate the multipole amplitudes involved in the decays of interest, and compare the results for the $D_{15}\mathrm{}\left(1515\right)\mathrm{}$ and $S_{11}\mathrm{}\left(1525\right)\mathrm{}$ resonances with the recent phenomenological multipole analysis by Chau, Dombey, and Moorhouse of pion photoproduction in the second resonance region. Agreement is reasonably good. For the ${Y_0}^{*}\mathrm{}\left(1520\right)\mathrm{}$ we obtain a radiative width ${\Gamma }_{\gamma }=0.051\mathrm{}$ MeV to be compared with a recent experimental result ${\Gamma }_{\gamma }=0.15\mathrm{}\pm 0.03$ MeV, and an angular distribution compatible with experimen t. We comment on the contribution of the $F_{15}\mathrm{}\left(1690\right)\mathrm{}$ resonance to pion photoproduction.

We discuss the system of two overlapping resonances along two parallel lines: (A) the general restrictions imposed on the $S$ matrix by unitarity, and (B) the results of the Weisskopf-Wigner approximation. The equivalence between the two is used to get a physical understanding of the formalism applicable to both scattering and decay processes. We show that the connection between the overlap in channel space, ${\chi }_c$, and the overlap of the two resonances, $\chi$, is the unitarity sum rule.

The application of Regge-model ideas to high-energy semileptonic reactions is taken up in some detail for the process $\nu +p\to {\mu }^{-}+p+{\pi }^{+}$ (and its electroproduction analogs), and, qualitatively, for more complicated processes of the sort $\nu +p\to {\mu }^{-}+p+X_1+X_2+\dots$.

The Regge-pole formalism is applied to the calculation of the differential cross section for ${A_1}^{+}$ photo-production in the region $\left|t_{min}\right|<-t<\mathrm{}10\mathrm{}{\mu }^2$. The $\rho$, $A_1$, $A_1$-daughter, $A_2$, and $\pi$ trajectory contributions are considered, and use is made of chiral dynamics to estimate the unknown coupling constants. We find that the $\pi$ and the $A_2$ trajectories provide the dominant contributions.

Direct-reaction reciprocity tests of time-reversal invariance are analyzed on general grounds and specifically with the T-violating force derived in the preceding paper. A simple proof of Robson's theorem that a cut-off distorted wave Born approximation satisfies reciprocity irrespective of $T$ violation is indicated. Numerical calculations are described which show that Robson's theorem is not a severe restriction on direct-reaction reciprocity tests, and that the violation of reciprocity is of the same order of magnitude as the ratio of the $T$-odd to $T$-normal forces. If the $T$-violating term of the nucleon current contains an isovector part, the $T$-odd potential derived in the preceding paper implies roughly 0.2% violation of reciprocity in deuteron stripping. However, if the basic $T$ violation is isoscalar, the violation of reciprocity will be reduced by a factor of 50 in the context of the model considered.

A $T$-violating nucleon-nucleon potential is calculated with a model in which the basic violation is in the electromagnetic interaction. The conditions of Hermiticity and current conservation are applied to choose a $T$-violating matrix element of the nucleon electromagnetic current. Since current conservation requires that the $T$-violating term vanish on the mass shell, the longest-range force comes from diagrams corresponding to the exchange of one photon and one pion. In leading nonrelativistic order, there are three spindependent $T$-violating forces of range roughly equal to the Compton wavelength of the pion and of "strength" about 0.01% of the one-pion-exchange potential.

The low-energy, pion-nucleon scattering is studied by including the $\rho$-meson contribution to the axial-vector amplitude. By using a different treatment for the $\rho$ contribution and the $q^2$ extrapolation, the results for the ${a_{1-}}^{-}$ scattering length and ${b_{0+}}^{-}$ effective range are improved while the results for the ${a_{0+}}^{-}$ and ${a_{1+}}^{-}$ scattering lengths are preserved. An explanation is also given of why there is no double counting of the $\rho$-meson contributions in pion-nucleon interactions when considering current-algebra and $\rho$-exchange models.

By making use of current algebra, $K_{l3\mathrm{}}$ decay amplitudes are deduced from the $K_{l4\mathrm{}}$ decay amplitudes in the generalized Veneziano model. For $K_{l3\mathrm{}}$ decays, we predict that ${\lambda }_{+}=\frac{{m_{\pi }}^2}{{m_{K^{*}}}^2}$ and that $\xi \mathrm{}\left(t\right)=\frac{f^{-}\mathrm{}\left(t\right)\mathrm{}}{f^{+}\mathrm{}\left(t\right)\mathrm{}}=c(t-{m_K}^2)-\frac{0.009t}{{m_K}^2}$, where $c$ is a free parameter.

$\mathrm{CP}$-nonconservation parameters in $K^0$ decay are plotted in a way which directly exhibits the conditions imposed by unitarity and $\mathrm{TCP}$ invariance. A similar construction shows the conditions under which the hypothesis of $T$ invariance can be disproved.

The reactions ${\pi }^{-}p\to p{\pi }^{+}{\pi }^{-}{\pi }^{-}{\pi }^0$ and ${\pi }^{-}p\to n{\pi }^{+}{\pi }^{+}{\pi }^{-}{\pi }^{-}$ have been studied at 8 GeV/c. The measured cross sections are 1.39±0.09 and 0.53±0.04 mb, respectively. Resonance parameters and production cross sections are presented for the following resonances produced in the experiment: ${\rho }^0$, ${\rho }^{-}$, ${\rho }^{+}$, $N^{*++}$, ${\omega }^0$, ${\eta }^0$, and $B^{-}$. The final states $p{\omega }^0{\pi }^{-}$ and $N^{*++}$ ${\rho }^{-}{\pi }^{-}$ are studied and the possibility of their production via a double-peripheral mechanism is described. Evidence for the ${\pi }^{+}{\pi }^{-}{\pi }^{-}$ decay modes of the $R\left(1700\right)\mathrm{}$ and $T\left(2200\right)\mathrm{}$ mesons is presented. An enhancement in the ${\pi }^{+}{\pi }^{-}$ effective-mass distribution at 400 MeV is discussed.

We report on observation of the isospin-½ ${\Xi }^{*}\mathrm{}\left(1530\right)\mathrm{}$ and ${\Xi }^{*}\mathrm{}\left(1830\right)\mathrm{}$ resonances in $K^{-}n$ interactions at 3.6 and 3.9 GeV/c and present results concerning the production and subsequent decay of the ${\Xi }^{*}\mathrm{}\left(1830\right)\mathrm{}$ into $\Xi \pi$, $\Xi \pi \pi$, and $\Lambda \overline{K}$. We have also searched for isospin-$\frac{3}{2}$ ${\Xi }^{*}$ resonances and found no strong evidence for the existence of such states. Upper limits on production cross sections for such a particle are presented.

Prominent features of this reaction include $d^{*}$ production in the $d{\pi }^{+}$ system, ${\rho }^0$ production, and a low-mass enhancement ($A_1$) in the ${\rho }^0{\pi }^{+}$ system. A model for $\pi d$ scattering has been found to provide an adequate description of the properties of the $d^{*}$. A Reggeized pion-exchange model successfully predicts the properties of the ${\rho }^0{\pi }^{+}d$ final state, whether or not $d^{*}$ formation occurs.

A large-area (3.35 ${\mathrm{m}}^2$) scintillation-counter telescope consisting of six scintillation counters and four widegap spark chambers was arranged to detect single particles with charge $\pm \frac{1}{3}e$ or $\pm \frac{2}{3}e$ which might be present in the cosmic radiation near sea level. Upper limits to the vertical intensities of such particles are 9.8×${10}^{-11\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\sec }^{-1\mathrm{}}$ ${\mathrm{sr}}^{-1\mathrm{}}$ for charge $\pm \frac{1}{3}e$ and 1.6×${10}^{-10\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\sec }^{-1\mathrm{}}$ ${\mathrm{sr}}^{-1\mathrm{}}$ for charge $\pm \frac{2}{3}e$ at a 90% confidence level.

We have extended our earlier measurements of the cross section for wide-angle electron bremsstrahlung. Besides the data for symmetric final electron and photon angles already published, we report results for asymmetric angles. The circulating electron beam of the Cornell 10-GeV synchrotron struck a carbon target and was monitored by observing the forward bremsstrahlung beam. Wide-angle photons were counted in coincidence with the corresponding scattered electrons. The recoil momentum of the unobserved nucleus was minimized. The experimental cross sections are compared with the predictions of the Bethe-Heitler formula corrected for elastic and inelastic nuclear form factors and for virtual nuclear Compton scattering. The agreement is excellent, confirming the predictions of quantum electrodynamics for timelike electron four-momenta up to 1.2 GeV. If one assumes a deviation in the experiment/theory ratio proportional to the square of the final electron-photon invariant mass, the 95% confidence upper limit on the corresponding distance parameter is ${{\Lambda }_{\mathrm{}\left(2\right)\mathrm{}}}^{-1\mathrm{}}=5.3\mathrm{}\times {10}^{-15\mathrm{}}$ cm. The upper limit for a fourth-power deviation is ${{\Lambda }_{\mathrm{}\left(4\right)\mathrm{}}}^{-1\mathrm{}}=6.2\mathrm{}\times {10}^{-15\mathrm{}}$ cm.

The elastic muon-electron interactions of 10.1-GeV/c positive and 5.0- and 14.5-GeV/c negative muons produced at the Brookhaven alternating gradient synchrotron have been studied in nuclear emulsions. Energies of knockon electrons calculated from scattering measurements were compared with those obtained from their ejection angles. Integral cross sections were compared with the Bhabha prediction for the scattering of two point fermions. Excellent agreement was found for negative and positive primary muons up to $t=3.3\mathrm{}\times {10}^{-3\mathrm{}}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$ and $t=1.8\mathrm{}\times {10}^{-3\mathrm{}}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$, respectively. Our results are in contradiction to some of the previous cosmic-ray data, which show an anomalously large cross section.