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The Nuclear Force between a statistical assemblage of nucleon pairs is calculated directly for pseudo-scalar meson exchange. The Nucleon (proton) is treated as a particle with an extended structure. The model of the proton used is the one determined by high energy electron-proton scattering experiments. The self-energy process for such a proton is examined first for the emission and re-absorption of a photon. An appropriate photon propagator is derived for such a system using variational techniques. It is shown that the integrals that occur in the self-energy process converge without any of the difficulties associated with the point charge model. This shows the divergences in Quantum Electrodynamics (for nucleons) do not exist when nucleons are treated as particles with a structure. The pseudo-scalar meson propagator is derived using similar methods and the exchange force is calculated. It is shown that only certain diagrams need be considered when a stable nuclear bond is being calculated. The corrections to the Nuclear Force, which are self-energy processes involving emission and re-absorption of Virtual pseudoscalar mesons, are shown to converge for strong coupling.

In this paper the mathematical methods of quantum field theory are applied to some problems that arise in the statistical description of mechanical systems with very many (in the idealized case, infinitely many) degrees of freedom. This application is based on a graphical representation of the individual terms of the formal perturbation series in powers of the coupling constant in the form of Feynman diagrams. A variety of properties of such diagrams makes it possible to sum partially the perturbation series with a view to obtaining closed integral equations that contain the required quantities as unknowns. The approach is treated in more detail in connection with the statistical hydrodynamics of a developed turbulent flow, which is similar to the theory of a quantum Bose field with strong interaction. The functional formulation of statistical hydrodynamics makes it possible to obtain integral equations of turbulence theory, which can also be derived by means of diagram methods. At the end of the paper, some closed equations of statistical hydrodynamics are considered.

A mathematical model is proposed to examine the interaction between blood perfusion and gas diffusion in the uptake of inert gases in tissue. The standard Haldane perfusion model is contrasted with the Hills radial bulk diffusion model in a variety of homogeneous tissue types used in decompression theory. It is the intention of the present analysis to fix ideas on the role of diffusion, perfusion and axial concentration and quantitative studies are given and seem to show that Haldane's perfusion theory is at best a poor approximation even at asymptotic times. It is shown that a strong interaction exists between diffusion and perfusion in muscle tissue and neither approach adequately describes the actual uptake half-time of an inert gas.

Models for the production of particles at large transverse momentum are reexamined in the light of recent experimental data. A covariant analysis is given of the Berman-Bjorken-Kogut model, with a suitably general form assumed for the parton-parton scattering amplitude. An explicit model of the quark fusion type, developed in a previous paper, is recalculated using new values of a parameter obtained from data for meson production, and agrees well with those data. A model is discussed which could give copious production of protons at large transverse momentum.

A theory of weak interaction of quarks is developed in the framework of SU (2) symmetry. Expressions are obtained for the probability of decay of quarks into leptoquarks, quarks into leptons, and leptoquarks into leptons. A model is also constructed of the interaction of quarks with matter in which strong and electromagnetic interactions of quarks with matter are forbidden. In this model, the weak interaction of quarks is the main form of interaction between quarks and matter. In this connection, it is suggested that quarks should be looked for in nature in the products of their weak decay in accordance with the theory developed here.

The strong decays of meson resonances are treated in a dynamical quark model. The model is formulated in the framework of general field theory and therefore all calculations are fully relativistic covariant. Spectrum and wave functions are derived from a Bethe-Salpeter equation describing the binding of heavy quarks by a smooth, very strong interaction. The mesonic vertices are calculated with help of these BS amplitudes in triangle graph approximation, thereby guaranteeing a symmetric treatment of all mesons involved in the process. A particular spin dependence of the interaction has the consequence that the super-strong quark binding forces lead to mesonic forces of moderate strength only (saturation of quark forces!). The applications refer to the decays of vector mesons, tensor mesons, scalar mesons into pseudoscalars and vectors and are extended to resonances in the R region. In particular, we include the decays into two pions of the radial excited ϱ′(1600). The helicity structure of the decays of the axial vector meson is discussed.

A simple explanation is presented for the observed tendency of the spin-orbit part of the optical potential for a proton scattered by a nonspherical target nucleus to be more deformed than the central part. The explanation is based on the fact that the range of the central two-body force is longer than that of the two-body spin-orbit force.

Particle models for hadron interactions are discussed. The various strong interaction phenomena are considered, and those features of the data which need to be incorporated in a model for it to be successful are discussed. 12 references. (JFP)

The recent discovery that non-Abelian gauge theories of the strong interactions possess an attractive fixed point of the renormalization group at zero coupling constant, which made posslble a field-theoretic explanation of Bjorken scaling, and was previously applied to electroproduction and e/sup +/ + e/ sup -/ annihilation logarithmic corrections is extended to include neutrino production. Attention is focused on the possibility that the strong interaction gauge group is the SU(3) group which acts on the color indices of three triplets of Gell-Mann-Zweig quarks. The moments of the structure functions are found. (JFP)

Energies and intensities of pionic and muonic X-rays in liquid 4 He have been measured with a Si (Li) detector. The energy shift due to strong interaction effects of the pionic 1s level in 4 He was determined to be −75.7±2.0 eV. The natural line width of this level is 45±3 eV. These values are compared with different theoretical predictions. Cascade calculations, including external Auger effect and sliding transitions, have been performed to reproduce the yields of the muonic and pionic transitions. The pionic 2p level width is deduced: Γ 2 p = (1.1 ± 0.5) × 10 12 sec −1 = (7.2±3.3) × 10 −4 eV .

A gauge theory with colour gauge group U( N ) and quarks having a colour index running from one to N is considered in the limit N → ∞, g 2 N fixed. It is shown that only planar diagrams with the quarks at the edges dominate; the topological structure of the perturbation series in 1/ N is identical to that of the dual models, such that the number 1/ N corresponds to the dual coupling constant. For hadrons N is probably equal to three. A mathematical framework is proposed to link these concepts of planar diagrams with the functional integrals of Gervais, Sakita and Mandelstam for the dual string.

We construct a toy gauge model in which the Cabibbo angle is generated by the effects of weak interactions. The model is so arranged that in the absence of the weak and electromagnetic interactions the $\mathfrak{N}$ and $\ensuremath{\lambda}$ quarks are both massless and degenerate with each other. The weak interaction splits this degeneracy and thus generates an angle between the strong and weak interactions. The value of the angle is determined in terms of certain parameters (experimentally measurable but unknown) that appear in the model. More interestingly, we abstract from this model the following statement: In the limit of vanishing Cabibbo angle, chiral symmetry becomes exact. It is argued that this statement holds for a large class of models. We suggest that in the real world this relation is also valid. A certain phenomenon involving $\mathrm{CP}$ violation and various options one may have in constructing a gauge theory including $\mathrm{CP}$ violation are discussed.

Muonic and pionic X-rays of the L- and M-series in C and O have been measured with a Si(Li) detector in the energy range between 7 keV and 60 keV. The target consisted of mylar (C5H4O2). Energies and intensities of 21 transitions have been determined. The strong interaction shift of the pionic 2p level in O was measured and found to be +4.1 ±2.3 eV. The measured width of this level is 11±6 eV. The measured yields have been compared with cascade calculations.

Relative intensities of numerous kaonic X-ray transitions have been measured for the elements C,P,S, and C1, from which level widths due to the strong K-nucleus absorption have been determined. From these and earlier published data, optical potential parameters have been derived and possible consequences on the nuclear matter distribution are discussed.

We have identified X-rays associated with stopped negative kaons in Al, Si, Ni and Cu. We report relative intensities, strong interaction energy shifts and strong interaction line broadenings. The measurements are found to be in good agreement with those predicted on the basis of a simple phenomenological potential except for the Ni (5 → 4) transition width.

Regarding the strong interaction as a manifestation of a strong gravity, the electron and the proton are identified as black holes in the strong gravitational field. The mass and classical radius of the electron are predicted to be $\frac{1}{2}\ensuremath{\alpha}{m}_{\ensuremath{\pi}}=0.51$ MeV and ${r}_{e}=\frac{2{e}^{2}}{2{m}_{p}{c}^{2}}=0.74$ cm, respectively. It is shown that the electron can be strongly interacting at energies above 240 GeV. The strong gravitational constant is predicted to be 3.9\ifmmode\times\else\texttimes\fi{} ${10}^{31}$ dyn ${\mathrm{cm}}^{2}$ ${\mathrm{g}}^{\ensuremath{-}2}$. The neutron-proton mass difference is partly explained. A neutral-pion-electron system bound by strong gravity is interpreted as the muon, and the muon-electron mass ratio is predicted to be $\frac{{m}_{\ensuremath{\mu}}}{{m}_{e}}=\frac{3}{2}(\frac{1}{\ensuremath{\alpha}})+\frac{(\frac{2}{\ensuremath{\alpha}}){m}_{e}}{{m}_{\ensuremath{\pi}}}=206.6$. It is suggested that the weak interaction might also be a manifestation of strong gravity and the intermediate-boson mass is of order 240 GeV.

In the preceding paper, we have made a preliminary study of the short-distance behavior of quantum electrodynamics in the presence of neutral-meson theory with pseudoscalar-pseudoscalar coupling. We have learned in particular, by an elementary summation procedure, that in the single-fermion-loop contribution to the renormalized photon self-energy part, the Adler-Baker-Johnson eigenvalue condition for the fine-structure constant $\ensuremath{\alpha}$, ${F}^{[1]}(x){|}_{x=\ensuremath{\alpha}}=0$, remains unaltered. We extend our results, in the single-fermion-loop context, to the pion self-energy part. As a consequence of the vanishing of the effective strong coupling at high energies, ${\ensuremath{\pi}}^{0}\ensuremath{-}{\ensuremath{\pi}}^{0}$ scattering graphs are finite and no ${\ensuremath{\varphi}}^{4}$ counterterm is required. We finally infer from the above work that the photon self-energy part in the multiloop contribution is asymptotically finite at the eigenvalue [${F}^{[1]}(x){|}_{x=\ensuremath{\alpha}}=0$] independently of the value of the strong coupling. The point $x=\ensuremath{\alpha}$ is the assumed (infinite order) zero of the single-loop electromagnetic-current-correlation functions in mass-zero pure electrodynamics.

In this work we study the possibility of describing inclusive distributions by means of a leading Mueller singularity which is not a factorized pole. According to a «crossed-channel» viewpoint, we first examine a sort of a minimal violation of factorization, namely that the same singularity dominates multiple Mueller exchanges. We study its consistency in inclusive sum rules, paying particular attention to azimuthal correlations and discuss phenomenological consequences. Finally we show with explicit examples that this possibility is not verified in models for exclusive production amplitudes, based on direct-channel considerations.

Properties of the strong nonlinear interaction between solitons have been investigated in detail. In this case, the solitons behave exactly like particles colliding elastically in a potential field: they never pass through each other, but bounce back at a distance. Momentum transfer is considered to be the basic mechanism of interaction. Thus, the velocity of propagation of each soliton is a function of time during collision. Explicit expressions for the minimum distance between solitons, the time when this distance occurs, and the amplitudes of solitons at this time have all been derived. Reversibility and other important properties have also been proved.

It is suggested that strong interactions are described by the renormalizable, asymptotically free gauge field theory of colored quarks and gluons and that the renormalized quark-gluon coupling constant is small, when evaluated at momenta of the order of the proton mass. The true asymptotic predictions of this theory for deep inelastic scattering are shown to be irrelevant for present experiments. Scaling is found to be violated logarithmically according to lowest order perturbation theory. Upper bounds for the strong interaction coupling constant are derived.

A negatively charged strange hadron can be bound by the electromagnetic interaction in the Coulomb field of a nucleus to form an exotic atom. De-excitation of such an atom occurs with the emission of X-rays whose energies, line widths, and intensities have been measured. Deviations from the electromagnetic level scheme are observed for lower-lying states owing to the strong interaction of a hadron with a nucleus. When the wave function of a hadron begins to overlap with the nuclear density distribution, the hadron undergoes nuclear absorption via the strong interaction. The final outcome of such a process is the formation of a Λ hyperon which may be bound in a nucleus by the strong interaction. An exotic nucleus, or a hyper-nucleus, is thus formed making it possible to study the Λ–nucleon interaction. Excited states of hypernuclei decaying via weak, electromagnetic, or strong interaction have been observed and are extensively studied. Investigation of exotic atoms and hypernuclei provides basic i...

NMR investigations of 1H (chemical shifts, line widths) and of 31P (relaxation times, T1) performed on the three-component system of lecithin-benzene-water show that there is an interaction of water with the phosphate group in two regions of different mobility and structure. A fast exchange of the water molecules takes place between both regions. The region of strong interaction involves about 2 and that of the weaker interaction about 5 water molecules per lecithin molecule. When the water concentration is increased a third region is formed which is assigned to the water molecules that are located beyond the two regions of interaction with the phosphate group, but within the micelle. This water has a different structure from that of the second region of interaction with the phosphate group and may also have a different mobility. Addition of water increases the motion of the head groups of the lecithin molecules. This is due to a loosening of the packing of lecithin molecules.

This work evaluates the theory of Coulomb displacement energies of the ground states of 18Ne18O and 42Ti42Ca, with a view to making bounds on the possible violation of charge symmetry in the strong interaction. The theoretical uncertainties are found to be of ∼8%, and the discrepancies between theory and experiment are much larger than the possible charge-violating potential being sought.

The requirement of compatibility of vector-meson dominance and partial conservation of axial-vector current in ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ decay [along with $\mathrm{SU}{(6)}_{W}$ symmetry] determines the absolute value of the $\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}$ coupling constant. The strength of strong interactions results inversely proportional to the number of postulated quarks. In dynamical models of spontaneous symmetry breaking the electromagnetic, weak, and gravitational interactions are found also to have strengths inversely proportional to the corresponding numbers of fundamental fermions.

X-rays from the K α transition (2P → 1S) of the π − d mesic atom have been observed. Their energy, 2592.8 −2.0 +1.6 , has been measured by the critical absorber technique, using the M V absorption edge in bismuth. The strong interaction shift in the 1S state is −4.8 eV, corresponding to a scattering length a ( π d) = −(0.052 −0.017 +0.022 ) m π −1 , in agreement with recent calculations. The intensity ratio K α /K total = 0.548 ± 0.015.

We investigate the high-energy K L → K S regeneration process in nuclei in terms of a coherent production model. The angular distribution of the regenerated K S is calculated for Pb and Cu at an incident momentum of 4 GeV/ c . The experimental data are well reproduced. We have also performed an optical-model calculation which explicitly treats K L as a mixture of K 0 and K 0 particles. We show that it is not necessary to introduce a large neutron skin in the above nuclei to interpret the data, if the finite range of strong interaction is taken into account properly in the density distribution. The coherent production model and the optical model, with seemingly very different physical interpretations, give very similar results. We also show that these models represent two ways of summing the multiple scattering series in the particular case of K L → K S regeneration. In conclusion, we discuss the unique and important feature of using nuclear regeneration scattering to study scattering theories, as compared to other high-energy particle-nucleus scattering.

The directions of breaking of SU(4) ⊗ SU(4) symmetry are examined using the algebraic techniques of Michel and Radicati.

The radiative corrections of order α to the ratio GV/Gμ are estimated in the framework of two simple hadronic extensions of the SU(2) × U(1) gauge model. One involves four quarks with integral charges; the other, three colored quartets. The results are remarkably simple: we recover the corresponding results of the local V-A theory with the mass mZ of the Z vector meson substituted for the cutoff Λ. A phenomenological analysis shows that for a large range of values of mZ, these estimates are of the correct sign and order of magnitude to verify, on the basis of the present data, the universality of the weak interactions in the sense of Cabibbo. The SU(2) × U(1) model has an interesting consequence: by implying a big lower bound for mZ, it gives rise in a natural manner to large corrections of order α. The role of the strong interactions in the treatment of the short distance behavior in these calculations is qualitatively discussed.

We propose a scheme of approximation where strong-interaction processes with a purely longitudinal configuration of external momenta are described by fields which depend on longitudinal spacetime variables only, but retain their full four-dimensional spin structure. The evolution of these fields is governed by an effective Lagrangian, which can be obtained from the four-dimensional Lagrangian using a variational method. We discuss briefly the main features of the effective Lagrangians for one-dimensional and two-dimensional configurations of the external momenta.

The different values obtained for nuclear radii from electromagnetic interactions as compared with specifically nuclear interactions suggest a model of nuclear matter in which the meson field is supposed to condense into an incompressible fluid and the nucleonic sources are confined to its interior by a strong interaction between the sources and the fluid as a whole. The sources are also coupled to spin and charge fluctuations in the fluid, whose exchange leads to further intemucleonic forces. It is necessary to postulate that the fluid have a com ­ paratively low density; as a result rotational levels of the fluid are high, leading to a small probability of exchange of angular momentum (and charge coupled to it) with the sources. The values of the anomalous electrical interactions of nucleons deduced are in rough agreement with the facts. The nuclear structure indicated is a shell model embedded in the mesic fluid whose oscillations, strongly coupled to the nucleons, give rise to the collective features of nuclear structure as in the theory of Bohr & Mottelson. It is suggested that this picture of the mesic field may indicate where to look for solutions of the meson field equations.

A foundation of the Heitler-London approach to electrical conductivity is given, which has been left unproved in the previous paper (J. Phys. Soc. Japan 15 (1960) 802), applying Van Hove's method. The hopping motion of electron is realized under the conditions: large effective mass, strong interaction with lattice and the presence of a potential fluctuation through lattice.

The high-energy pire-leptonic weak interaction is investigated based on the assumption of the existence of a charged vector boson which mediates the weak processes. With the aid of the fixed- t dispersion relation the following relation is obtained: The weak boson mass m W should satisfy m W ⪆ G − 1 2 , with G the Fermi coupling constant, if the asymptotic value of the cross section becomes of the order of the strong interaction in the energy region observable in cosmic rays, etc. The scattering processes e +ν→ e +ν and e + ν → e + ν are examined by the aid of the N / D method. For a large vector-boson mass m W ⪆100 GeV , an S-wave resonance should exist for the process e+ ν →e+ ν while for e + ν → e + ν there should exist a P-wave resonance which corresponds to the intermediate weak boson. The neutral current is then estimated. It is shown that the neutral current produced as a higher-order effect is not inconsistent with the present experiments on the pure-leptonic weak interaction if m W ⪅1 TeV.

A Lorentz field is generated when moving free carriers in semiconductors interact with a crossed magnetic field. A set of computer results show a strong interaction with high‐order transverse modes in a parallelplate wave guide. As a result of this interaction, unstable solutions which lead to the generation of growing waves have been found.

A series of equations is proposed for the description of strong hyperon- meson interactions, in which the global symmetry theory is rejected. (D.L.C.)

A theoretical and experimental investigation has been conducted of the behavior of steady low-density hypersonic flow over a finite-width flat plate. The theoretical analysis, previously hampered by stability problems which dictated small streamwise increments, has been modified within the framework of the original formulation of Rudman and Rubin, in such a manner that larger streamwise increments are now possible without severe stability restrictions. This has been made possible by employing an alternating directional implicit numerical scheme developed by Peace-man and Rachford, such that the Rudman-Rubin analysis is now extendable downstream into the strong interaction region with smaller computational times. Simultaneously, an experimental program was conducted to compare with the theoretical predictions. Measurements of pitot pressure and hot wire output (mass flow and temperature profiles) were obtained at two streamwise locations for several different plate widths. All tests were conducted for a Reynolds number of 300/inch and a temperature ratio ( T w T s ∞ ) of 0.3. Profiles of density, velocity, and temperature ratios in the merged layer were obtained and compared to the theoretical analysis. Good agreement is shown to exist through the merged layer region.

It is shown that an axiomatic formulation of the Gell-Mann model concerning elementary particles is possible. Different kinds of fields are formally introduced (see table II) which are defined by their transformation properties in ordinary (Lorentz) space and isobaric space the latter being three dimensional. The fundamental assumption is that the Lagrangian for strong interactions must be invariant under rotation and reflection in isobaric space. Also postulated are the Lorentz invariance and the conservation of baryons. The most general form of strong interaction Lagrangian that follows from these assumptions is (3.1). From this, the constants of motion I3 and N are deduced as well as a new constant U. Up to this point no assumption has been made concerning the charges of the quanta of the various fields. The constant U allows for a definition of charge and, if the charges of N and Λ° are postulated one has the general relation Q = I 3 + U 2 for all particles. The values of U deduced from the theory turn out to be precisely those postulated in the Gell-Mann model. In fact a complete equivalence with this model is so obtained. Possibilities of introducing other fields are investigated. It is shown that in most cases some difficulties arise for the definition of U (and therefore of Q). Two different approaches are then possible: 1. (i) In the Lagrangian constructed according to the above mentioned rules some interaction terms may be suppressed and new fields can so be introduced. This procedure however cannot be achieved without some degree of arbitrariness. 2. (ii) The following point of view can be adopted: A set of fields is self consistent only when all the true scalars constructed with these fields can, without contradiction, appear in the Lagrangian. This approach is perhaps more satisfactory for, while not being in contradiction with present experimental data, it is at the same time more elegant and may provide a useful means of limiting the number of fields.

The electromagnetic violation of vector current conservation is considered and the strong interaction renormalization of the BETA -decay coupling constant G/sub V/ in the presence of electromagnetism is estimated. It is shown that the existing discrepancy between the G/sub V and the mu -decay coupling constant G/sub mu / may be due to such a renormalization. Use is made of a hypothetical scalar particle with isotopic spin unity. This particle was used as an auxiliary means and the final results do not depend on the parameters of such a panticle. It is shown that this particle has interactions with other particles only if the electromagnetic mass splitting of the isotopic multiplets is not neglected. Other properties of this particle are discussed. (auth)

The adsorption from binary liquid mixtures of n-heptane and n-hexadecane on a graphitized carbon black (Graphon) at 25, 35 and 45°C, and on rutile at 25 and 45°C has been studied. The standard enthalpies of adsorption show good agreement with published heat-of-immersion data. The thermodynamic energy functions indicate a strong interaction between the hydrocarbons and Graphon, which is associated with the graphitic structure of the carbon surface.

It is suggested that the recent fit by Abarbanel et al. of $\frac{d\ensuremath{\sigma}}{\mathrm{dt}}$ for $p\ensuremath{-}p$ elastic scattering at large $s$ and $t$ to a curve of the electromagnetic form factor raised to fourth power, ${[{G}_{{M}_{p}}(t)]}^{4}$, corresponds to the $\mathrm{SU}(3)$-breaking interaction. This is the only non-Regge pole in the strong interaction, which is otherwise entirely described by Regge-trajectory or bootstrap dynamics.

An estimate of the exchange splitting between the up and down spin bands in ferromagnetic Ni is made on the basis of the `strong intra-atomic interaction' model, account being taken of the major electron correlation effects. A splitting of about 0.4 eV at the top of the d band is obtained. It is shown that in the strong interaction model the exchange interaction between electrons in orthogonal orbitals leads to a negligible correction for Ni.

Assuming that the strong interaction ${H}_{\mathrm{st}}$ is invariant under the particle-antiparticle conjugation $C$, it is shown that all possible $C$-noninvariant electromagnetic interactions ${H}_{\ensuremath{\gamma}}$ can be classified according to the anticommutator between $C$ and the charge operator $Q$ into two types: (1) ${C, Q}=0$ and (2) ${C, Q}\ensuremath{\ne}0$. Discussions of the first type $C$-noninvariant minimal electromagnetic interaction have already been given in a previous paper. If ${C, Q}\ensuremath{\ne}0$, then the operator $C$ must be different from what is normally called the "charge-conjugation operator" ${C}_{\ensuremath{\gamma}}$ which, by definition, changes any state of charge $Q$ to that of $\ensuremath{-}Q$. Thus, ${{C}_{\ensuremath{\gamma}}, Q}=0$ and $C\ensuremath{\ne}{C}_{\ensuremath{\gamma}}$. As a consequence, there must exist, at least, a charged particle ${a}^{+}$ which is an eigenstate of $C$; its eigenvalue can always be chosen to be +1. Furthermore, in the framework of a Lorentz-invariant local-field theory, ${H}_{\mathrm{st}}$ and ${H}_{\ensuremath{\gamma}}$ are invariant under ${C}_{\ensuremath{\gamma}}\mathrm{PT}$, but not $\mathrm{CPT}$. The ${C}_{\ensuremath{\gamma}}\mathrm{PT}$ invariance requires the existence of another charged particle ${a}^{\ensuremath{-}}$ which has the same mass as ${a}^{+}$ but the opposite charge. The ${a}^{\ensuremath{-}}$ is also an eigenstate of $C$. The existence of such ${a}^{\ifmmode\pm\else\textpm\fi{}}$ particles necessitates not only the $C$ nonconservation of ${H}_{\ensuremath{\gamma}}$, but also the $T$ noninvariance of ${H}_{\mathrm{st}}$. The general algebraic relations between ${H}_{\mathrm{st}}$, ${H}_{\ensuremath{\gamma}}$, and these symmetry operators are studied, and the properties of the particles ${a}^{\ifmmode\pm\else\textpm\fi{}}$ are discussed. An explicit spin-\textonehalf{} model of ${a}^{\ifmmode\pm\else\textpm\fi{}}$ based on the principle of minimal electromagnetic interaction is given. A possible unifying view connecting the present $C$, $T$ noninvariance with the well-known $C$, $P$ nonconservation of the weak interaction is discussed.

It is proposed that anomalous measurements of cosmic-ray pions and muons above a characteristic energy of ${10}^{12}$ eV can be explained, at least in part, by the presence of the medium-strong contact interaction between protons. That has been suggested by Abarbanel, Drell, and Gilman. The results of a programmed simulation of extensive air showers in a simple model have the correct behavior to explain the pion measurements, and they show a slight tendency in the correct direction for an explanation of the measurements of muons. Some remarks are made on the difficulties associated with theories of direct production of muons.

Beta decay formulae derived in previous papers are re-interpreted on the basis of a quite general V-A interaction which takes into account all effects induced by the strong interaction. As an example of application the induced pseudoscalar interaction is investigated in some detail.

Analytical predissociation linewidths are derived from the scattering solutions to the two-state curve crossing problem. Four cases are considered: ‘inner’ and ‘outer’ crossings in the ‘weak’ or ‘strong’ coupling limits. It is shown that linewidths in each case take the form Γ = Γo cos2 η, where Γ0 is related to the Landau-Zener transition probability and η is a phase integral between one of the classical turning points of the known bound state curve, and the turning point of the continuum potential. Γ0 is a decreasing function of energy in the weak interaction limit, whereas for strong interaction, it is an increasing function of energy. The outer crossing, strong coupling case is shown to provide an interpretation of the characteristic appearance of the visible spectra of ICl and IBr.

Results of threedimensional Monte Carlo Simulations of extensive air shower development are presented and compared with empirical data. The possibility to conclude on various strong interaction parameters is discussed.