Glauber's eikonal approximation for multiple scattering is extended to include inelastic processes. It is found that inelastic contributions to the differential cross section for the reaction ${\pi }^{-}d\to {\pi }^{-}d$ are negligible, while such contributions dominate the double-charge-exchange reaction ${\pi }^{-}{\mathrm{He}}^3\to {\pi }^{+}3n$.

A new method, recently devised by us, is used for the analysis of $K^{+}p$ scattering data below 1.5 GeV/c. This analysis uses, instead of the ordinary partial-wave expansion, a method of expansion with optimally accelerated convergence properties; the method has been devised by the use of analytic approximation theory. Although no experimental information is used which was not available to Lea, Martin, and Oades, somewhat more definite results are obtained by the present method. The results are sensitive to the values assumed for the coupling constants ${g_{\mathrm{KN}\Lambda }}^2$ and ${g_{\mathrm{KN}\Sigma }}^2$; the results appear to be most consistent if values close to the $S{U}_3$ prediction are used for these coupling constants. With the use of the $S{U}_3$ prediction, rather strong $P$-wave scattering is found in the low-energy region.

We show how the reaction $e^{-}{e}^{+}\to {\pi }^{-}{\pi }^{+}\gamma$ can be used to study the dipion system in states of even charge conjugation (and even angular momentum). In particular, its utility for experimentally investigating an $I=0\mathrm{}$, $J=0\mathrm{}$ resonance ($\epsilon$ meson) is discussed in detail.

We find that a coherent-droplet model with long-range pion exchange successfully fits the forward peak structure of the differential cross sections for ${\pi }^{+}p\to {\rho }^0{\Delta }^{++}$, ${\pi }^{+}p\to f^0{\Delta }^{++}$, ${\pi }^{-}p\to {\rho }^{0}n$, ${\pi }^{+}p\to {\rho }^{+}p$, $\mathrm{pp}\to n{\Delta }^{++}$, $K^{-}p\to K^{*0\mathrm{}}\mathrm{}\left(890\right)n$, and $K^{-}p\to K^{*-}\mathrm{}\left(890\right)p$. For $-t^{\prime }<0.02\mathrm{}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$, the measured differential cross sections exhibit anomalous behaviors: spikes and dips and no structure. The different behaviors are explained mainly by the kinematic structure of pion-pole residues. In some of the reactions, the known magnitude of the pion-pole residue leads us to expect structures near $t^{\prime }=0\mathrm{}$ which require data with higher statistical precision for confirmation. In ${\pi }^{+}p\to f^0{\Delta }^{++}$ at 8 GeV/c, our model can explain the absence of an anomaly near $t^{\prime }=0\mathrm{}$ in terms of the large distance from the physical region to the pion pole. However, this distance decreases with increasing energy, and our model predicts structure near $t^{\prime }=0\mathrm{}$ in ${\pi }^{+}p\to f^0{\Delta }^{++}$ at 16 GeV/c.

The process $K^{-}+{\mathrm{He}}^4\to \Lambda +{\pi }^{-}+{\mathrm{He}}^3$ is analyzed in the multiple-impulse approximation for both $1S$ and $2P$ atomic capture at rest. Reaction kinematics and rates, which are free of arbitrary constants, are calculated in both first and second order. The multichannel $\overline{K}n$ amplitudes of Kim are employed to incorporate the ${Y_1}^{*}\mathrm{}\left(1385\right)\mathrm{}$ resonance into the first-order (direct) term, and both the ${Y_1}^{*}\mathrm{}\left(1385\right)\mathrm{}$ and ${Y_0}^{*}\mathrm{}\left(1405\right)\mathrm{}$ resonances into the second-order ($\Sigma -\Lambda$ conversion) term. Agreement with experiment is good, particularly when the conversion term is added.

$\pi \pi$ scattering up to 1.4 GeV of dipion mass is studied from the reactions ${\pi }^{-}p\to {\pi }^{-}{\pi }^{+}n$ and ${\pi }^{-}{\pi }^{\circ }p$ at 7 GeV/c, using the formalism of absorption-modified one-pion exchange (OPE) with dipion in $S$, $P$, and $D$ waves. We limit our analysis to small momentum transfers to the nucleon, including the nucleon-pole terms as background. The ${\rho }^0$, ${\rho }^{-}$, and $f^0$ mesons, and the ${\pi }^{-}{\pi }^{+}$ anomaly in the 1.0-1.2-GeV region are analyzed. The $S$-, $P$-, and $D$-wave $\pi \pi$ phase shifts and inelasticities, of isospin 0, 1, and 2, are obtained.

A study was made of the reaction $\overline{p}p\to \overline{p}p{\pi }^{+}{\pi }^{+}$. The cross section for this reaction is 1.50±0.07 mb at 2.4 GeV/c and 2.57±0.10 mb at 2.9 GeV/c. The data at both momenta are consistent with nearly $100\%{\overline{\Delta }}^{--}{\Delta }^{++}$ double-resonance production. The reaction is peripheral at both momenta, the distribution of the c.m. scattering angle between the incoming $\overline{p}$ and the outgoing $\overline{p}{\pi }^{-}$ system being peaked at small angles. The ${\rho }_{1,1}$ spin-density matrix element has strong dependence on ${\Delta }^2$, the square of the four-momentum transfer from the incoming $\overline{p}$ to the outgoing $\overline{p}{\pi }^{-}$ system. The joint spin-density matrix elements indicate no correlation between the ${\overline{\Delta }}^{--}$ and ${\Delta }^{++}$ production at either momentum. Calculations using the double-isobar one-pion-exchange model with form factors are compared to the data. The reactions $\overline{p}p\to \overline{p}p{\pi }^{+}{\pi }^{-}{\pi }^{\circ }$, $\overline{p}n{\pi }^{+}{\pi }^{+}{\pi }^{-}$, and $\overline{n}p{\pi }^{-}{\pi }^{-}{\pi }^{+}$ have cross sections of 10±5, 14±10, and 17±10 μb, respectively, at 2.4 GeV/c The corresponding values at 2.9 GeV/c are 124±40, 143±70, and 127±70 μb.

A detailed comparison is made of two independent experiments to determine the total cross sections for 3.00-GeV/c protons on protons and deuterons. Part, but not all, of the discrepancy between the two measurements of the $p-d$ cross section is explained. Best values for the two cross sections are given.

In a new measurement of proton total cross sections at 3.00 GeV/c, the $p-d$ total cross section is found to be lower than a previous measurement by 1.17±0.09 mb. This implies a corresponding new value for the total cross section for $I=0\mathrm{}$ which is 2.18±0.27 mb lower than the previous value. Possible sources of systematic error are discussed.

We have measured elastic electron-proton scattering cross sections in the range of four-momentum transfers from 7 ${\mathrm{F}}^{-2\mathrm{}}$[0.27 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$] to 150 ${\mathrm{F}}^{-2\mathrm{}}$ [5.84 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$] and at scattered electron angles of between 20° and 34° in the laboratory. The estimated errors in the cross sections range from ±2.1% at the lowest momentum transfer to ±9.6% at the highest. Both the scattered electron and the recoil proton were detected, resulting in an overdetermination of the kinematics. When the constraint of a coincident proton is removed, there is no significant change in the estimated cross sections.

The reaction $K^{+}p\to K^{+}p{\pi }^{+}{\pi }^{-}$ is studied at incident beam momenta of 2.53, 2.76, and 3.20 GeV/c, using the Argonne 30-in. hydrogen bubble chamber. Cross sections for the production of $K^{*0\mathrm{}}\mathrm{}\left(890\right)\mathrm{}$, $N^{*++}\mathrm{}\left(1236\right)\mathrm{}$, and the double-resonance channel $K^{+}p\to K^{*0\mathrm{}}\mathrm{}\left(890\right)\mathrm{}{N}^{*++}\mathrm{}\left(1236\right)\mathrm{}$ have been determined. We compare the production and decay angular distributions for the double-resonance channel with the predictions of several models which assume pion exchange. The decay angular distributions have also been compared with quark-model predictions. We find that none of the models tested completely accounts for all the features of the data. In addition, a low-mass enhancement in the $K\pi \pi$ system at 1300±10 MeV is observed.

The similarities and differences of a tachyon cloud surrounding a slower-than-light particle compared to that of a meson cloud surrounding a nucleon are given, and a possible elimination of the infrared-divergence catastrophe in terms of renormalization due to the tachyon cloud is pointed out.

It is shown, by an explicit calculation, that the Dhar-Sudarshan theory of tachyons is not unitary.

A previous model of vector mesons is extended to study $\phi -\omega$ mixing in a vector nonet. It is found that a phenomenon which can be interpreted as "spontaneous mixing" does occur in the model, and the well-known equations ${\phi }^2+{\omega }^2=2\mathrm{}{K}^{*2\mathrm{}}$ and $4K^{*2\mathrm{}}-3({cos}^2\theta {\phi }^2+{sin}^2\theta {\omega }^2)-{\rho }^2=0\mathrm{}$ emerge from the calculation. The mixing angle cannot be determined in our model; but it is found that if violations to $\mathrm{SU}\left(3\right)\mathrm{}$ become vanishingly small, we have a 50% mixing.

We investigate the algebraic realization of a pair of sum rules proposed by Weinberg for forward scattering of massless pions, for the case when only $p$-wave pions are taken into account. It is shown that the algebraic structure of the first superconvergence condition is given by the Lie algebra of the group $\mathrm{SU}\left(2\right)\mathrm{}\otimes \mathrm{SU}\left(4\right)\mathrm{}$. A few $p$-wave pion decay widths are calculated and found to agree satisfactorily with experiment. It is further shown that the mass spectra obtained from the second superconvergence conditon are unsatisfactory, as they predict that the hadron masses decrease with increasing isospin (or spin). Various possible reasons for this defect are discussed.

This is the last in a series of four papers devoted to a theoretical study based on canonical field theory of the deep-inelastic lepton processes. In the present paper we present the detailed calculations leading to the limiting behavior—or the "parton model"—for deep-inelastic neutrino scattering, i.e., $\nu +p\to e^{-}+\mathrm{anything},\text{'}\text{'}$ $\overline{\nu }+p\to e^{+}+\mathrm{anything},\text{'}\text{'}$ where "anything" refers to all possible hadrons. In particular, we show that the structure functions depend only on the ratio of energy to momentum transfer $\frac{2M\nu }{q^2}$ as conjectured by Bjorken on general grounds. Experimental implications, including sum rules and the relation of $\nu$ and $\overline{\nu }$ cross sections to each other as well as to deep-inelastic electron scattering cross sections, are derived and discussed.

A set of self-consistency conditions for ratios of hadron-hadron-hadron coupling constants is derived from the Veneziano model for scattering amplitudes and some simple assumptions. This set includes the crossing-matrix condition of the static meson-baryon model and the condition that the absence of resonances in exotic states implies a cancellation from Regge trajectories of opposite signatures. For simplicity, the spins of the external mesons and baryons are neglected. The conditions require that the particles correspond to representations of a Lie group, and that only certain sets of representations are allowed. The relation to previous bootstrap models is discussed. An illustrative solution corresponding to $\mathrm{SU}\left(3\right)\mathrm{}$ is obtained.

We have calculated the three-photon exchange contribution to the sixth-order anomalous magnetic moment of the leptons. Our result for the electron-loop contribution to the muon moment (18.4±1.1) ${\left(\frac{\alpha }{\pi }\right)}^3$ brings the theoretical prediction into agreement with the CERN measurements within the 1-standard-deviation experimental accuracy. The result for the electron-loop contribution to the electron moment is (0.36±0.04) ${\left(\frac{\alpha }{\pi }\right)}^3$. The theoretical errors represent the accuracy of the required seven-dimensional numerical integrations.

A method proposed recently by Lee and Zumino for calculating higher-order corrections to the $S$ matrix in nonpolynomial field theories is investigated. When applied to a perturbed harmonic oscillator, grave difficulties are encountered. The reason is found to lie not in the specific summation method, but in the behavior of the perturbing potential at infinity. In the more realistic field-theoretical case, it is shown that perturbation theory gives anomalous values for the vacuum self-energy and the wave-function renormalization constant under certain circumstances.

We study in detail the implications of the operator formulation of the droplet model. The picture of high-energy scattering that emerges from this model attributes the interaction between two colliding particles at high energies to an instantaneous, multiple exchange between two extended charge distributions. Thus the study of charge correlation functions becomes the most important problem in the droplet model. We find that in order for the elastic cross section to have a finite limit at infinite energy, the charge must be a conserved one. In quantum electrodynamics the charge in question is the electric charge. In hadronic physics, we conjecture, it is the baryonic charge. Various arguments for and implications of this hypothesis are presented. We study formal properties of the charge correlation functions that follow from microcausality, $T$, $C$, $P$ invariances, and charge conservation. Perturbation expansion of the correlation functions is studied, and their cluster properties are deduced. A cluster expansion of the high-energy $T$ matrix is developed, and the exponentiation of the interaction potential in this scheme is noted. The operator droplet model is put to the test of reproducing the high-energy limit of elastic scattering in quantum electrodynamics found by Cheng and Wu in perturbation theory. We find that the droplet model reproduces exactly the results of Cheng and Wu as to the impact factor. Infact, the "impact picture" of Cheng and Wu is completely equivalent to the droplet model in the operator version. An appraisal is made of the possible limitation of the model.