Showing papers in "Il Nuovo Cimento in 1959"

Introduction to complex orbital momenta

Abstract: In this paper the orbital momentumj, until now considered as an integer discrete parameter in the radial Schrodinger wave equations, is allowed to take complex values. The purpose of such an enlargement is not purely academic but opens new possibilities in discussing the connection between potentials and scattering amplitudes. In particular it is shown that under reasonable assumptions, fulfilled by most field theoretical potentials, the scattering amplitude at some fixed energy determines the potential uniquely, when it exists. Moreover for special classes of potentialsV(x), which are analytically continuable into a functionV(z),z=x+iy, regular and suitable bounded inx > 0, the scattering amplitude has the remarcable property of being continuable for arbitrary negative and large cosine of the scattering angle and therefore for arbitrary large real and positive transmitted momentum. The range of validity of the dispersion relations is therefore much enlarged.

Coherence properties of partially polarized electromagnetic radiation

Abstract: This paper is concerned with the analysis of partial polarization from the standpoint of coherence theory. After observing that the usual analytic definition of the Stokes parameters of a quasi-monochromatic wave are not unique, a simple experiment is analysed, which brings out clearly the observable parameters of a quasi-monochromatic light wave. The analysis leads to a unique coherency matrix and to a unique set of Stokes parameters, the latter being associated with the representation of the coherency matrix in terms of Pauli’s spin matrices. In this analysis the concept of Gabor’s analytic signal proves to be basic. The degree of coherence between the electric vibrations in any two mutually orthogonal directions of propagation of the wave depends in general on the choice of the two orthogonal directions. It is shown that its maximum value is equal to the degree of polarization of the wave. It is also shown that the degree of polarization may be determined in a new way from relatively simple experiments which involve a compensator and a polarizer, and that this determination is analogous to the determination of the degree of coherence from Young’s interference experiment.

Weak and electromagnetic interactions

Abstract: The postulate of a «local connection» in a [3] charge space leads to the introduction of three spin one fields One of these can be identified with the electro-magnetic field and the other two can be shown to mediate all known weak interactions, thus unifying these interactions with electro-magnetism The theory takes account of the fact that weak interactions violate parity and strangeness conservation while electromagnetic interactions do not do so

Quadratic lagrangians and general relativity

Abstract: Two out of the three sets of field equations associated with Lagrangians quadratic in the Riemann-Christoffel tensor, which were recently discussed by Stephenson, are shown to be equivalent to the source-free Einstein equations with an arbitrary «cosmological» term.

On the existence and the unitary property of the scattering operator

Abstract: The mathematical character of the scattering theory is investigated according to the ≪ time-dependent ≫ formulation with special emphasis on the wave and the scattering operators The main contents are: 1) some general properties of these operators are summarized; 2) the existence of the wave operator is proved under rather mild conditions on the potential; and 3) the existence and the unitary property of the scattering operator are proved under certain additional conditions The arguments are mathematically rigorous

Regularization and renormalization

Abstract: The analysis begun in Part I of the conditions under which the regularization, performed by the adoption of the modified integrals introduced there, acts as a renormalization is completed. The «conditions of the second type» announced in I are formulated and discussed; a quantitative analysis may give results different from the standard requirements for renormalizability: as an example, it is shown that the neutral scalar meson theory is not renormalizable, contrary to current belief. The Lie equations of the renormalization group can be derived without difficulty, and their integrability conditions investigated. Finally, it is shown that using our modified integrals amounts to solving the differential branching equations for kernels under the condition that the solutions belong to a certain well-defined mathematical class . In this way, ultraviolet infinities never appear, and the search for the renormalizability conditions becomes a search for the self-consistency of a theory, which need be made once for all and cannot cause inconvenience in computations. The result is a rigorous mathematical formulation of the renormalized theory, which avoids all mentions of «bare particles», is completely rid of ambiguities and is suited both for practical computations and for the study of fundamental questions. The unphysical splitting of processes into Feynman graphs is avoided; the troubles due to overlaps are shown to have a trivial origin and are altogether eliminated; all vertex-part contributions vanish with this method, at least in electrodynamics, since the cancellation of them against electron self-energy contributions occurs prior to actual computation. These criteria will be applied in a forthcoming work to an exhaustive study of electrodynamics; they are expected to play a relevant role in a search for consistent theories of elementary particles.

Muon capture in certain light nuclei

Abstract: The rates of the muon capture reactions: µ+23He→13+v, µ−+36Li→26He+v, µ−+612C→512B+v, with the daughter nuclei formed in their ground states, are calculated assuming ≪ universality ≫ between muon-bare nucleon and electron-bare nucleon coupling constants. The ≪ induced ≫ pseudoscalar interaction and the additional terms arising from the assumption of a ≪ conserved vector current ≫ are included in the muon-nucleon effective Hamiltonian. The ratios of the nuclear matrix elements for the muon captures and for the corresponding s-decays are first estimated in an approximately ≪ model independent ≫ fashion using appropriate nuclear proton density distribution functions and then evaluated in more detail on the basis of variational trial wave functions for23He,13H, and of LS coupling andjj coupling shell model wave functions (with configuration mixing) for36Li,26He, and612C,512B, respectively. The calculated capture rate for µ−+612C →512B+v is in agreement with experiment — experiments however are not yet available in the other two cases.

On the description of unstable particles in quantum field theory

Abstract: The mass and life-time of an unstable particle may be defined by the real and imaginary parts of a complex pole appearing on the Riemann surface in which its propagator can be continued analytically This method, which was originally proposed byPeierls, is studied in detail, first on the basis of a special model, then in a more general field theory The possibility of analytical continuation of the propagator is discussed, using the conditions of causality and unitarity of theS-matrix The appearance of «unphysical» poles in the various sheets of the Riemann surface is also discussed It is inferred that a physical principle must be used in each case, in order to select the particular pole which can be correctly interpreted as describing the properties of an unstable particle

Covariant formalism of a field with indefinite metric

Abstract: The structure of a relativistic field which contains "ghost" (zero norm) states is investigated. Restrictions are made for the case of free fields, which can be thought of as asymptotic parts of a more complicated theory. According to the interpretation the in- or out-going fields may be eliminated from the physical results. If explicit calculations are to be made in any more concrete theory, it is easier to handle dipole ghosts than exponential ghosts. (B.O.G.)

Direct decay π0 → e++e−

Abstract: SummaryThe direct decay π0 → e++e− is discussed and analyzed as a probe of «pion size».RiassuntoSi discute e si analizza il decadimento diretto π0 → e++e− quale mezzo per saggiare la «mole del pione».

Plasma physics on cosmical and laboratory scale

Abstract: The behavior of an ionized gas in cosmical observations and laboratory experiments is examined by means of dimensionless parameters. The deviations of experimental from theoretical calculations on electric neutrality and "creep diffusion" are estimated. The coupling between plasma and neutral gas is investigated by the basic equations for a partially ionized gas, This was found to give a dispersion relation for plane disturbances of small amplitudes. The effective electrical conductivity can be deduced from the corresponding damplng distance. Agreement was obtained with the conclusions of Piddington and Cowling regarding the increased dissipation of magneto-hydrodynamic waves in the solar chromosphere and of magnetic fields in cool interstellar clouds. It was determined that magnetohydrodynamic oscillations with wave lengths comparable to the thickness of the ionospheric F/sub 1/ region and with periods comparable to those of "giant pulsations" are damped moderately only if the ionization degree is about a hundred times greater inside than outside of the auroral zones. As an experimental illustration of the theory, torsional oscillations in a cylindrical "magnetohydrodynamic wave guide" are discussed. It was found that Alfvon waves will exist In an ionized gas in the laboratory only in a high-current discharge of relatively large dimensions. The dlffusion processesmore » which take place in a plasma column situated in a longitudinal magnetic field are discussed, Experimental data on the electric potential drop were found to agree well with the collision diffusion theory in a range of magnetic fields up to a centain critical value. Above this value a marked change occurs which can be interpreted as a sudden and rapid increase in the diffusion coefficient with a simultaneous rise in the noise level, These results support the "drain" diffusion mechanism proposed by Bohm, Burhop, Massey, and Williams-particle dlffusion across the magnetic field is accelerated by the action of transverse electric fields.« less

A new type of particle detector: the «discharge charmber»

Abstract: The possibility of constructing a new type of particle detector based on gaseous discharge is described. This detector secures the precision of the trajectory of the particle and works for groups of particles.

The interaction of K−-mesons with photographic emulsion nuclei

Abstract: The emission of Σ-hyperons from 3 037 K− capture stars at rest in nuclear emulsion has been studied The identification of the hyperons is discussed Charged Σ-hyperons are emitted from (176±10)% of all K−-stars while (96±06)% of them lead to the emission of both Σ-hyperons and π-mesons The Σ−/Σ+ ratio for all stars is 086±012 while for stars in which a π-meson is also emitted it is 045±010 The difference between this latter value and the markedly different value (20) obtained for K−-interactions at rest in a hydrogen bubble chamber is attributed to the Fermi motion of nucleons in the nucleus, and a dependence of the relative K− transition amplitudes on the energy of relative motion of the K−-meson and nucleon The branching ratio,R, of the number of Σ+ decays to π+ and proton respectively is 123±027 The stable prong distribution of the stars in which a hyperon is emitted, as well as the energy distribution of the Σ-hyperons at emission has been studied About 16% of all identified charged Σ-hyperons had an emission energy above 60 MeV, and had to be attributed to multi-nucleon interactions of the K−-meson It is estimated that the proportion of all multi-nucleon primary capture prccesses may be as high as (30÷40)% The interaction of a K−-meson with a pair of neutrons seems to occur rarely, if at all From the fraction of Σ+ emitting stars which also emit a π−-meson it is concluded that only about 10% of the π−-mesons fail to escape from the nucleus in which capture occurs This could be understood if K−-capture occurs predominantly in the peripheral region of the nucleus From a similar study of Σ− emitting stars it is found however that the proportion of π+ or π0-mesons, or both, that are absorbed in the nucleus is much higher Estimates are made of the mean free path in nuclear matter of Σ-hyperons and π0-mesons Most of the one-nucleon interactions leading to Σ-hyperon production take place with protons and the transition amplitudes corresponding to theT=1 state of isotopic spin is smaller than theT=0 transition amplitude

Generalized current conservation and low energy limit of photon interactions

Abstract: If the fields that describe a system are renormalizable their interaction with low energy photons in the first two orders in the frequency is shown to be given by the « static » properties of the system. This is shown to essentially follow from current conservation. Compton scattering, bremsstrahlung and photo-pion production are examined. In the latter case, although our result is gauge invariant in the first two orders in the frequency, we are not certain of obtaining all terms of this order. The missing terms probably arise from Feynman diagrams in which the photon is connected to a part containing no charged links to the rest.

On the analytic properties of partial wave scattering amplitudes obtained from the Schrödinger equation

Abstract: On etudie les proprietes analytiques de l’amplitude de diffusion pour une onde partielle donnee a partir des proprietes de la solution radiale de l’equation de Schrodinger pour une energie complexe. Les resultats connus dans le cas des potentiels a portee finie sont retablis par cette methode. On examine ensuite, en se limitant a l’ondeS, les proprietes analytiques pour des potentiels decroissant exponentiellement. On retrouve ainsi une bande d’analyticite commune a tous ces potentiels. Deux exemples sont traites completement: le cas d’un potentiel produit d’une exponentielle par une fonction sinusoidale, le cas d’une famille assez generale de potentiels comprenant en particulier le potentiel de Yukawa et une somme de potentiels de Yukawa. Le comportement a l’infini de l’amplitude de diffusion est obtenu et il est possible d’ecrire une relation de dispersion pour cette quantite. Sous des conditions plus restrictives, on peut ecrire une relation de dispersion pour une quantite reliee a la fonction d’onde a une distancer de l’origine. La methode employee pour evaluer l’amplitude de diffusion semble etre, en outre, une methode pratique d’approximation valable.

Relaxation of dislocations in copper

Abstract: Frequency and attenuation of standing waves have been measured in polyerystalline-copper in the frequency range between 1.8 kHz and 6.5 MHz as a function of temperature from 60°K to 300°K. Owing to the wide frequency range, the activation energyW and the limiting frequencyω A associated with the attenuation peak due to dislocations have been evaluated with considerable accuracy. The values obtained (W=0.122 eV (molecule)−1,ω A =23.9·1011 s−1) agree satisfactorily with those computed according to the theories given bySeeger, Donth andPfaff. The shape of the attenuationvs. temperature curves shows that the spectrum of relaxation frequencies is a bell-shaped line with its maximum atω=ωm; each frequency of the spectrum is associated with the value ofW given above. The height of the attenuation peaks has been compared with the total relaxation exhibited by the frequencyvs. temperature curves. Below 100 kHz the results agree with the theory of relaxation effects with a continuous spectrum. At higher frequencies the polycrystalline structure gives rise to an attenuation larger than the values that could be expected from the frequency relaxation measurements. The effects of heat treatments have also been investigated, showing that the attenuation and the frequency relaxation are both reduced by treatments whose temperature does not exceed 500 °K, whilstωAis slightly increased. Treatments at higher temperatures give rise to comparatively large changes in attenuation and frequency, which do not seem directly related to the pre-existing dislocations. These changes are reversible and can be cancelled by a suitable amount of cold work.

Possible explanation of the radiation observed by Van Allen at high altitudes in satellites

Abstract: We consider the possibility, suggested byP. Rothwell andT. Gold in conversation with the author, that the radiation observed byVan Allen and co-workers at high altitudes is due to the decay electrons and protons from neutrons produced in the earth’s atmosphere by cosmic rays and stored in the earth’s magnetic field. Order of magnitude estimates for the densities to be expected are presented. Only scattering loss is considered. Using a lifetime of 3 · 109 s for loss through scattering, an upper limit of 10−2 electrons/cm3 near the earth and .05 (RE/r0)3 electrons/cm3 at large distancesr0 in the equatorial plane is obtained. The proton density at large distances is .03(RE/r0)2 cm−3, for a lifetime of 1012 s. If plasma accelerations are not important, then the spectrum of electrons will be that of neutron β-decay. The protons are produced by fast neutrons coming directly from nuclear stars and their spectrum will be approximately that of the protons from stars. The electron density is sufficient to give a counting rate a few times larger than is observed, while the proton density is sufficient to give a counting rate 104 times higher than the observed lower limit. The lifetimes of stored particles are therefore probably much less than those given by scattering. There should be a strong latitude effect which is roughly estimated as proportional to cos6λ. Reasons are given for believing that collective effects will reduce the density below this near the poles.

Heat flush and mobility of electric charges in liquid helium

Abstract: With the aim of a quantitative check of the Landau-Pomerancuk picture of the movement of foreign atoms in liquid helium II, an experiment has been performed in which some elementary charged particles could be dragged perpendicular to their motion in an electric field by a stream of excitations in non-turbulent flow. Using known values for the mobility of charged particles in He II, the drift velocity of the charges parallel to the stream of excitations has been found to be equal to the normal fluid velocity in the temperature range above 1.18 °K. Working under similar conditions, the apparatus has then been used to obtain mobilities at temperatures near 1 °K. The mobility is found to go exponentially with decreasing temperature, and this behaviour is discussed in terms of elastic scattering of the charges by the rotons.

Generalized stokes parameters for waves with arbitrary form

Abstract: The correlation matrix of an arbitrary stationary, quasimonochromatic electromagnetic radiation field is expanded in terms of nine linearly independent matrices and it is shown that the expansion coefficients play a role analogous to the customary Stokes parameters.

On the validity of the exponential law for the decay of an unstable particle

Abstract: The departure from the exponential decay law of an unstable particle is discussed, with the help of the Lee model, starting from an initial state which is a general superposition of eigenstates of the Hamiltonian. It is shown that the asymptotic behaviour and the magnitude of the additional terms are strongly affected by the production mechanism; although they can never vanish exactly, these terms can be made arbitrarily small by an appropriate preparation of the initial state. A possible generalization of this result is discussed.

One particle singularities of green functions in quantum field theory

Abstract: The time ordered Green’s functions are expanded with respect to the singularities arising from intermediate one-particle states.

The field theoretic definition of the nuclear potential — III

Abstract: It is shown that the static limit (µ/M → 0) leads to completely unreliable results in a perturbation theory definition of the potential, even in graphs without elastic scattering intermediate states. However, it is still possible to define a potential which is an energy-independent function ofr alone, which when inserted into a non-relativistic Schrodinger equation reproduces the relativistic field-theoretic scattering matrix at sufficiently low energies. A method is developed whereby such a potential, in which bothμ andM occur as parameters, is defined unambiguously for the case of a proton and a neutron scattering through a neutral meson field. By using dispersion relations for proton-neutron scattering, it is concluded that the potential reproduces the scattering matrix for momenta ≪ √Mµ. Finally, a general method for explicit construction of the potential as a superposition of Yukawa potentials of different masses is proposed, and the one- and two-meson exchange contributions to the potential are evaluated.

The lorentz-covariant approximation method in general relativity. — I

Abstract: The Lorentz-covariant approximation method for the field outside a set of localized particles has been analysed. It is found that as well as the usual equations of motion and energy derived by Eistein, Infeld and Hoffman for the quasi-static approximation, there are three further equations, the equations of spin, which must be satisfied by the structural parameters of each particle. These equations also appear as surface integral conditions in the quasi-static approximation. Furthermore, it is shown that it is not necessary to expand the mass, dipole, or spin parameters, those introduced into the lowest approximation being the physical particle parameters. It is only the differential equations satisfied by these that change in the higher orders.

Momentum spectrum and positive excess of μ-mesons

Abstract: The absolute spectrum and positive excess of cosmic-ray μ-mesons near sea level have been measured in the range 2 to 175 GeV/c. The magnetic spectrometer and the method of data reduction are described in detail. The integral spectrum has been compared with the range distribution in the earth, and the agreement indicates that there is no serious error in the theoretical expression for the rate of energy loss. The π-meson production spectrum has been computed and found to fit a power law with exponent — 2.64. Also the spectrum of the pion positive excess has been obtained, which is related to the pion production by primary protons in their first collisions. It is concluded that at 1012 eV per nucleon, most of the primary cosmic-ray energy is carried by protons, and that the proportion of their energy given to pions in a single interaction is in the neighborhood of 10%.

Introduction of a neutral pseudoscalar field and a possible connection between strangeness and parity

Abstract: A neutral pseudoscalar field with vanishing rest mass is introduced. We first ask for the condition guaranteeing the vanishing rest mass, which turns out to be an invariance requirement under a certain kind of gauge transformation. Then assigning an appropriate transformation to each field one can restrict the possible forms of weak interactions. The main results obtained in this paper are as follows: (1) the change of strangeness necessarily requires the violation of both parity and charge conjugation; (2) the change of the number of electrons or of muons necessarily violates parity and charge conjugation; (3) strangeness can change only by unity in weak interactions.