Showing papers in "Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields in 1966"

Gravitation and quantum mechanics of macroscopic objects

Abstract: The problem of the reduction of the wave function in quantum theory is treated from a new standpoint. First, by combining Heisenberg's uncertainty relations with gravitation, quantitative limi tations on the sharpness of the structure of space-time are derived. Second, the resulting uncertainty in space-time structure is incorporated into the equations for the propagation of the quantum-mechanical wave amplitudes. In the resulting theory an initially pure wave function generally develops in time into a mixture. A single pure wave function survives only as long as it corresponds to a sufficiently small spread in the position of any massive part of the system under investigation. Quantitative relations between the mass and the maximum coherent spread in the center-of-mass wave function of a single body are obtained.

Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity-I

Abstract: This paper, the second of a series on the subject, is entirely devoted to the pion-pion scattering amplitude. The main results are: 1) The scattering amplitude can be continued till the border-line of the double-spectral function, except for\(8\mu ^2< s< 32\mu ^2 \). Hence the nearest singularities are really induced by two-particle unitarity. Another consequence is that the only possible static potential describing low-energy pion-pion scattering is a Yukawa superposition. The domain of validity of fixed-transfer dispersion relations is slightly enlarged, as compared to I. 2) A partial analytic completion is carried out by various methods. As a result one finds a very large domain of analyticity for the fixed-angle amplitude and the partial-wave amplitudes; this domain extends from\(s = - 28\mu ^2 \) tos=+∞. However, only in the interval\( - 28\mu ^2< \operatorname{Re} s< 78\mu ^2 \) the extension in Ims is appreciable (\(\left( {\left[ {\operatorname{Im} s} \right.|\max = 70\mu ^2 } \right)\)). 3) The result of Bros, Epstein and Glaser on the validity of fixed, negative-t quasi-dispersion relations is extended to anyt inside the parabola with focust=0 and summit\(t = \mu ^2 \).

Axial-vector coupling constant renormalization and the meson-baryon scattering lenghts

Abstract: Assuming that the current algebra of Gell-Mann and the PCAC (partially conserved axial-vector current) are valid approximations, and that aspecific form of the LSZ reduction formula for pion-nucleon scattering amplitude has a small variation for the change of pion 4-momentumkμ from (0, 0, 0, iμπ) tokμ=0, we derive two simple relations between the axial-vector coupling constant renormalizationgA and the pion-nucleon scattering lengths. (Equations (7) and (8) in the text.) Both are satisfied quite well by the experimental values, and are shown to be intimately related with the Adler-Weisberger relation and the consistency condition of Adler. In a similar way, the scattering lengths of pion-baryon, pion-kaon and kaon-nucleon systems are predicted. The assumption of the generalized form of PCAC in theSU3 context leads to the prediction of the meson-baryon scattering lengths. They are identical to those which are calculated by the model of the vector-meson exchange with the universalF-type coupling.

Equal-time commutators and dispersion relations

Abstract: A new procedure is proposed to transform equal-time commutators of current densities into relativistic dispersion sum rules. The method is illustrated using two physically interesting examples.

On an analogue of the Galilei group

Abstract: The group of space-time transformationsr′=Ar,t′=t−(u·r), which is analogue to the Galilei group with the role of space and time interchanged, has been studied (u is a reciprocal velocity andA represents a space rotation). The relation between this group and the Lorentz groups has been investigated.

Practical theory of three-particle states

Abstract: We obtain covariant equations for the scattering of composite particles. They are coupled linear integral equations in one variable. The solutions satisfy three-particle unitarity, and all observables in three-particle systems can be expressed in terms of them. The equations are derived from field theory, the basic approximation being that each two-particle subsystem is dominated by its bound states and resonances. However, the final equations involve only the wave functions of the composite particles, and not the original Lagrangian. Overlapping resonances are correctly taken into account, and some three-body forces are also included. The « potential » is essentially the Peierls mechanism, and its imaginary part gives the interference effect between overlapping resonances. Our equations are different from and simpler than those of Alessandrini and Omnes, because we eliminate the relative energies in a way compatible with the Landau-Cutkosky rules. The present paper only gives the equations when the elementary particles are spinless (unequal masses).

Ad hoc modifications of quantum electrodynamics

Abstract: Ad hoc modifications of quantum electrodynamics are discussed with special reference to the restrictions imposed by charge conservation. It is shown that modifications in a charged-particle propagator typically require, in addition to the one-photon vertex modification imposed by the Ward identity, the introduction of a possibly infinite number of multiphoton vertices. A procedure, based upon a generalization of the notion of minimal electromagnetic interaction, for constructing the required vertices is given. In the absence of closed loops, it is shown that such propagator modifications have no effect upon the theory. Finally a general procedure is given for characterizing any theory consistent with charge conservation in terms of a modified propagator and intrinsic multiphoton vertices. The actual vertices which appear in the theory are generated by the propagator and intrinsic vertices in accordance with a well-defined procedure. An example is discussed.

Elastic scattering, pion production, and annihilation into pions in antiproton-proton interactions at 5.7 GeV/c

Abstract: An extensive investigation of antiproton-proton interactions at 5.7 GeV/c without strange-particle production was carried out using a hydrogen bubble chamber. Cross-sections for different channels are given and discussed. The reliability of the analysis was checked using artificially generated events. The cross-sections for elastic scattering, for all processes involving annihilation, and for all other inelastic processes are respectively σel=(16.3±0.6)mb,σannlbil=(22.5±2.0)mb, σinel=(24.8±2.0)mb. TheN*1:38 is present both in the single and multiple pion production channels. For the reactionOpen image in new window a cross-section of (1.05±0.21) mb was obtained. Cross-sections forN*1238 production in other channels are also given. Some indication of the presence ofI=1/2 isobars was found in the nucleon-pion and the nucleon-two-pion systems. The inelastic nonannihilation reactions were found to be strongly peripheral. The one-pion exchange model including either a form factor or corrections for absorption was applied to the reactionOpen image in new window. Neither version of the model could correctly account for all features of the reaction. The average number of pions in the annihilation was found to be 7.3±0.6. The presence of an asymmetry in the angular distribution of the charged pions was confirmed at this energy; it is due mostly to high-energy pions. The production of ρ and ω mesons was observed in various annihilation channels. Rates of up to 80% for ρ production and up to 15% for ω production were obtained by fitting phase-space and Breit-Wigner curves to the effective-mass distributions of different channels.

On the shadow effect in high-energy scattering from deuterons

Abstract: Most of the experimental information on high-energy scattering from neutrons has been obtained by comparing cross-sections from protons and deuterons. The extraction of neutron cross-sections from such data is nontrivial; the most widely used model is the semiclassical ray formula of Glauber, which gives, in addition to the impulse approximation terms, a shadow correction due to the mutual «eclipsing» of the nucleons in the deuteron. In this paper we show that, if the nucleon-nucleon scattering amplitudes near the forward direction can be represented as a sum of Regge poles, the shadow term that Glauber includes vanishes rapidly at high energies but that other terms remain which provide a somewhat smaller shadow effect. We first give a diagrammatic derivation of the Glauber formula and show that his shadow term, which comes from the diagram where both nucleons interact with the incident fast particle, does not in fact have the Regge cut necessary for its persistence at high energies. We then show that certain diagrams with inelastic virtual states between the two interactions do have such cuts and we express their contribution in terms of a partial inelastic crosssection and a statistical factor. An experimental clarification can only be achieved by accurate experiments with high-energy neutron beams.

Radio pulses from extensive air showers

Abstract: Radio pulses of short duration (<0.15 μs) have been observed at a frequency of 44 MHz (λ=6.8 m), in coincidence with extensive cosmic-ray air showers having ∼5·106 particles. The energies of these pulses ranged from ∼10−12 erg (receiver noise level) to ∼10−9 erg. The preliminary results reported briefly elsewhere (19,27) were consistent with the hypothesis that the observed pulses arose as a result of enhanced Cerenkov radiation at low frequencies (10). However, following the treatment of Kahn and Lerche (16), it is evident that the observed energy of the radiation is also consistent with charge separation effects in the earth's magnetic field. Experiments at a higher frequency (150 MHz, λ=2m), and a tentative analysis of the pulse-height spectrum, suggest that the radiation observed is enhanced by effects of mutual coherence among the particles in the shower. The paper concludes with a discussion of other alternative radiation mechanisms.

The de Sitter groupL 4,1 and the bound states of hydrogen atom

Abstract: Assuming that bound states of the nonrelativistic hydrogen atom are basis vectors of a unitary irreducible representation of the 4 + 1 de Sitter group, the generators of this group are builtclassically in terms ofr andp using Poisson brackets.

Singular hypersurfaces and thin shells in general relativity

Abstract: An approach to shock waves, boundary surfaces and thin shells in general relativity is developed in which their histories are characterized in a purely geometrical way by the extrinsic curvatures of their imbeddings in space-time. There is some gain in simplicity and ease of application over previous treatments in that no mention of « admissible » or, indeed, any space-time co-ordinates is needed. The formalism is applied to a study of the dynamics of thin shells of dust.

Embedding properties of general relativistic manifolds

Abstract: Integrability conditions for embedding a Riemannian manifold in a pseudo-Euclidean space of higher dimensions are derived. They are used to show that essentially the only physically significant solutions of the Einstein field equations which can be embedded in five dimensions are the Friedmann universes. The relation between symmetry properties and embedding properties of a manifold is discussed, setting upper bounds to the embedding class in certain cases.

A one-paramenter fit to the electromagnetic form factors of the nucleon

Abstract: A new fit to the world data on (ep) and (en) elastic scattering, and on (\(\bar p\)p) annihilation into lepton pairs, has been obtained by using a model for the isovector and isoscalar nucleon form factors, which is suggested by the use of unitary symmetry and of its breaking. The fit allows for a nonpointlike behaviour of one out of the two couplings which enter in the expression for nucleon electromagnetic form factors. The fit is a one-parameter fit and the corresponding values ofχ2 for the proton and neutron data are discussed. The contributions coming from the possible existence of « core-terms » and of «q2-dependent background » in the expression of the nucleon electromagnetic form factors are found to be lower than a few per cent. Theq2 dependence of the vector-meson-nucleon couplings is also discussed.

Elastic n-p charge-exchange scattering at 8 GeV/c

Abstract: The differential cross-section for elastic charge-exchange scattering of neutrons on protons has been measured at 8 GeV/c over forward laboratory scattering angles (0÷90) mrad (square of four-momentum transfer 0 0.1 however, energy dependence is apparent. The results also suggest that the interaction is spin-dependent and/or that the real parts of the scattering amplitudes in the isospin states 0 and 1 are different. Comparisons with the theoretical predictions show good agreement with the value of forward cross-section given by the Regge pole approach ofAhmadzadeh (3). The model ofRingland andPhillips (4) for single-pion exchange with absorption agrees with our results for −t<0.01 but a predicted secondary peak at −t∼0.08 is not observed.

Inconsistency of canonical commutation relations among current densities

Abstract: Ordinary commutation relations among current densities have been shown to lead to inconsistency without assuming the conservation law of currents. Also it is demonstrated that the ordinary PS-PV meson theory and also the σ-model will give rise to similar inconsistencies in general.

Nucleon magnetic moments and photoproduction sum rules

Abstract: We derive, in the framework of the vector-axial vector current algebra, dispersion sum rules for the nucleon anomalous magnetic moments. So, the magnetic moments are obtained through dispersive integrals over photoproduction amplitudes. Explicit evaluation of the sum rules shows good agreement with experimental data.

Flux and energy spectrum of secondary electrons in the upper atmosphere

Abstract: Detailed calculations have been made on the vertical flux and energy spectra of the secondary γ-rays and electrons in the upper atmosphere. The results given refer to the atmospheric depth of 1 g/cm2 for γ-rays and of 2, 4, 6 g/cm2 for electrons, at the geomagnetic vertical cut-off rigidity of 0.5, 2, 4.5, 10, 16 GV at solar minimum. The processes taken in consideration are the π0→λ+λ decay, the chain π±→μ±→e± and the γ→e++e− conversion. The calculations have been based on a pion-source spectrum obtained using accelerator data on the basic nuclear interaction, from the production threshold up to 30 GeV energy for incident protons. The precision on the numerical values obtained is estimated at better than 2%, for γ-ray and electron energies up to few GeV; the indetermination derives from the errors in the data on the nuclear interactions and from the approximation introduced on the angular spread of the secondary particles. The data obtained are used for estimating the contribution of secondary electrons and γ-rays to the total flux observed in the upper atmosphere with balloon experiments.

Antiproton-proton elastic and inelastic total cross-sections between 57 and 178 MeV

Abstract: About 25 000 interactions of antiprotons of kinetic energy between 57 and 178 MeV have been measured in a hydrogen bubble chamber. Elastic and inelastic total cross-sections have been determined at 15 values of the antiproton energy. The results are compared with theoretical predictions.

K+p elastic scattering at 3.5 and 5.0 GeV/c

Abstract: The elastic scattering of K+ mesons on protons is studied at 3.5 and 5 GeV/c. The total elastic cross-sections are found to be (4.36±0.36) mb and (3.82±0.41) mb respectively. The differential elastic cross-sections, which exhibit characteristic diffraction peaks, are fitted by dσ/dt=(dσ/dt)0eαt, giving α=(3.85±0.12) and (4.70±0.21) (GeV/c)−2 for the two momenta respectively, with |t|⪝0.65 (GeV/c)2. The results are compared to those at neighbouring energies, giving some support to the presence of a real part of the forward scattering amplitude. The diffraction peak shows definite shrinking with increasing momenta. The data are examined in the light of models for high-energy scattering.

A determination of the $$B_\Lambda $$ values of light hypernucleivalues of light hypernuclei

Abstract: Results are presented on the\(B_\Lambda \) values of hypernuclei in the mass rangeA=3 toA=12 obtained from a sample of 595 uniquely identified π−-mesonic decays. The problems of what constitute adequate selection criteria for the unique identification of an event are discussed. The disagreement between the\(B_\Lambda \) values obtained from different decay modes of\({}^4B_\Lambda \) indicates a possible error in the range-energy relationship.

Asymptotic behaviour of a Dirac particle in a Coulomb field

Abstract: The asymptotic form for the wave-function of a spin-1/2 particle scattered by a Coulomb potential is discussed. A convergence theorem is proved establishing the existence of a generalized Moller wave-matrix. Problems remaining in the theory are mentioned.