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A parametrization of Regge residue for \(\mit \Delta \) exchange which incorporates MacDowell symmetry, sense–nonsense zeros, constraints and cancellation of kinematic singularities is proposed. Absence of the parity partner of the (3,3) resonance is included through a zero in the residue. Explicit results are given for the cases of \(\pi ^-\)p \(\to \) \(\pi ^-\)p, \(\varrho ^-\)p, A\(_1^-\)p, and A\(_2^-\)p using the Gell–Mann choosing nonsense mechanism. Other sense–nonsense behaviours are discussed.

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We evaluate the energy spectrum of the photons emitted in the reaction \(e^+e^- \to \mu ^+\mu ^-\gamma \) and the hard photon correction to the total cross-section of the reaction \(e^+e^- \to \mu ^+\mu ^-\). We develop a simple technique based on the analytical QED formulae, in particular, on the current conservation.

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Considered are properties of the form factor \(F(t)\) which follow from the assumptions that \(F(t)\) satisfies an unsubtracted dispersion relation and its imaginary part is non-negative for \(t \geq T_0\).

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The semi-relativistic approach, widely applied to the two-body problem, is generalized onto the three-body disintegration process of deuteron by a high energyelectron. The proposed way of description of fast moving, Lorentz contracted, composite systems leads us to small anisotropy of the angular distribution of the “spectator” nucleon in the lab-system. This effect increases with energy, but it saturates for electron energy of the order of 20 GeV.

abstract

An effective potential is computed for 2-body elastic scattering with the experimental on-shell \(t\)-matrices as an input. Nonrelativistic eikonal approximation and locality, together with spherical symmetry of potential, are assumed. The explicit form of potential for pp, \(\pi ^+\)p and \(\pi ^-\)p in the energy range from 5 to 20 GeV is investigated. The half off-shell scattering amplitude is calculated in the potential model. In the position representation this amplitude is found to be asymmetric along the eikonal direction, and an interesting absorption interpretation of this fact is given.

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The mass dependence of the slopes in hadronic production processes is analysed. Different parametrizations of the data are compared. A parametrization is found which describes very well the data for processes of different kinds (exclusive: diffractive and non-diffractive, and inclusive) and which exhibits some interesting regularities in the data. In particular the slopes in production processes at large invariant masses of the produced system of particles are related to the slopes in two-body and quasi-two body reactions. The slopes for meson resonances produced in non-diffractive processes are found to deviate from a smooth slope-versus-mass dependence of the background in a way depending on the \(Q\)-value of the resonance.

abstract

The experimental facts on two-particle correlations and charge transfer in high energy proton–proton collisions suggest that the secondaries in the central rapidity region are produced in clusters of dominantly neutral charge and low multiplicity, these central clusters being independently emitted. Since fragmentation of either incident hadron is in effect formation of a leading cluster, one is led to a unified picture of independent cluster production (ICP) for all common inelastic collisions. The paper first reviews the evidence for ICP and gives an estimate of the mass and multiplicity distributions for central clusters. Following Stodolsky, it then uses the bremsstrahlung analogy to express the leading particle spectrum \(d\sigma /dx\) in terms of the density \(\varrho \) of central clusters. On the basis of ISR data, we find agreement between the approximate constancy of \(d\sigma /dx\) for \(0.2 \lesssim x \lesssim 0.8\) and our estimate of \(\varrho \simeq 0.9\)–1.2. We also discuss the \(p_T\) properties of clusters by using the condition that the overlap function should agree with elastic data. The paper ends with a possible interpretation of ICP in terms of the present view on hadron structure based on deep inelastic lepton–nucleon scattering experiments, which suggests that a hadron is mainly composed of its “valence quarks” arid of neutral “glue” (there is in addition a probably infinite number of quark–antiquark pairs, but the total amount of four-momentum they carry is very small). High energy hadron collisions can then be pictured as follows. The valence quarks fly through and give rise to the leading particles or clusters, while some glue can be radiated away in bremsstrahlung-like fashion and gives rise to the central clusters.

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The problem of fission fragment deexcitation through the charged particle evaporation channel was investigated using the statistical angular momentum dependent model. The anticipated intensities of emission and the energy spectra of p, d, t, \(^3\)He, \(^4\)He, and \(^6\)He, evaporated from the \(^{236}\)U fission fragments were calculated. The results regarding \(\alpha \)-particles explain to some extent the “polar emission” phenomenon. Assuming that the “polar” \(\alpha \)-particles are evaporated in flight from the excited fragments the mean experimental mass of the \(\alpha \)-emitting light fragments can be reproduced theoretically. Similarly, the \(\alpha \)-particle energy spectrum and the intensity of emission from the heavy fragments are explained quantitatively without parameter fitting. The energy spectrum of alphas going along the light fragment trajectory can be explained if the fragment deformation is taken into account. The intensity of the last mentioned alphas and the large anisotropy of the polar alphas angular distribution can be explained only by assuming a very low value of the moment of inertia or a high angular momentum of the fragments. Suggestions are given as to carrying out further experiments as well as making use of this phenomenon in the study of fission fragment properties and in testing the statistical model of reactions.

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The theoretical quadrupole and hexadecapole ground state equilibrium deformations and deformation energies are calculated by the method of summation of the single-particle energy levels, for even tungsten, osmium and platinum isotopes. They are in a good agreement with the known experimental data. The reduced transition probability \(B(E2)\), and Rasmussen parameter for the one-phonon vibrational \(0^+\) and \(2^+\) states are calculated for the same elements, in the framework of the “quasiboson” approximation. The results show that with the use of proper quadrupole and hexadecapole equilibrium deformations of the nucleus one is able to fit the experimental data for tungsten and osmium quite satisfactorily, while for platinum isotopes this method fails.

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It is shown that the relativistic contraction of the wave function of deuteron results in a small positive forward–backward asymmetry of the spectator nucleon from the disintegration of deuteron. This effect is compared with the Dubna experiment of dp \(\to \) ppn process at 3.3 GeV/\(c\) deuteron momenta.

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Angular distributions of particles produced in collisions of protons with the nuclei of photographic emulsion are investigated in function of the excitation of the target nucleus. The data favour the models of elementary collisions in which particles are generated through an intermediate state.

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Gottfried’s theory of multiple production of particles in hadron–nucleus collisions is compared and found consistent with experimental data. The theory and the data are used to predict the inclusive distribution in \(- \ln \tan {\mit \Theta }_{\rm lab}/2\) for particles produced in proton-arbitrary nuclear target collisions at 67 and 200 GeV/\(c\) incident momentum.

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This note contains an analysis of the motion of some special observers moving in the Schwarzschild gravitational field.