Showing papers in "Il Nuovo Cimento in 1954"

Über Eigenschaften von Ausbreitungsfunktionen und Renormierungskonstanten quantisierter Felder

Abstract: It is attempted to derive some general properties of the propagation functions for coupled fields (ΔF′,SF′) without the use of power series expansions and to show their connection with the renormalization constants for field operators and masses. Assuming that the coupled functions exist, it appears possible to discuss their behavior near the light-cone (or for large momenta) and to obtain some information about the singularities of these functions when continued analytically. Attempts at the treatment of unrenormalizable theories are criticised on the basis of these results. Formulae are given for the mentioned renormalization constants which contain inequalities for the constantsZ2 andZ3. Finally it is pointed out that the methods introduced are advantageous also for computations by means of power series expansion. As an example the lowest order correction to theSF-function in pseudoscalar meson theory is calculated without the appearance of infinite terms during the calculation.

Optics in terms of observable quantities

Abstract: Space-time correlation functions are defined which express the correlation between components of the electromagnetic field vectors in stationary fields. These functions form sets of 3×3 matrices, the individual elements of which obey the wave equation. Unlike the field vectors which are not measurable at the high frequencies encountered in Optics our correlation functions may be determined with the help of standard optical instruments. The results enable a unified treatment of theories of partial coherence and partial polarization to be obtained, and suggest a formulation of a wide branch of Optics in terms of observable quantities only.

The interaction between equilibrium defects in the alkali halides: The “Ground state” binding energies between divalent impurities and vacancies

Abstract: The binding energies of divalent impurity ions (Cd++, Ca++ and Sr++) and positive-ion vacancies at the distance of next-nearest neighbours have been computed in NaCl and KCl crystals using the Born-Mayer model of ionic solids. The results indicate that the binding energy increases with the ionic radius of the impurity and is somewhat smaller in KCl than in NaCl. They compare favorably with the available experimental estimates of the binding energies for Cd++ in NaCl and for Sr++ in KCl but do not confirm the considerable difference between the binding energies for Cd++ and Ca++ in NaCl that some experiments had indicated.

A study of τ-meson decay

Abstract: The distribution of the π-mesons in the decay of the τ-meson is studied, and approximate expressions for the matrix elements are found. Thus one can justifyDalitz’ results, in which the relativistic corrections are also introduced. The comparison with experiment is done taking into account the charges of the π-mesons; the experimental data, however, are still too poor to give any information about parity and spin of the τ-meson.

Polarization of high energy protons scattered by nuclei

Abstract: The attempt is made to explain the polarization recently observed in protons of several hundred MeV scattered by nuclei in terms of the same spin orbit coupling that is assumed in the nuclear shell model. It is found that the extrapolation to high energy of the spin orbit coupling observed at low energy is adequate to yield the correct order of magnitude of the polarization.

Determination of the mass of slow particles by the constant sagitta method

Abstract: A method is described in which the measurement of scattering of tracks at the end of their range is carried out on sets of cells of varying length, chosen so that the second difference of the sagitta remains constant. This permits the measurements to be made always at the optimum cell length and eliminates the inconveniences and inaccuracies of the methods in which the track is broken into several sections for measurement. The mass values of a series of K and J-particles have been determined, together with those of a group of protons which serves as calibration.

Étude des mésons K chargés, au moyen de deux chambres de Wilson superposées

Abstract: In this paper we present some results on charged heavy mesons. They were obtained with an experimental arrangement consisting essentially of two large cloud-chambers placed one above the other. The top chamber had a magnetic field while the bottom chamber was of the multiplate type. The contents of the different sections of the paper can be summarized as follows: 1. The double cloud-chamber method is compared with other more conventional methods. 2. The apparatus is briefly described. 3. The behaviour in the multiplate chamber of the charged secondaries of V±-decays occurring in the top chamber is disscussed. π-mesons have been identified through their nuclear interactions. The presence of μ-mesons is also strongly suggested by:a) the long mean free path of the secondaries andb) one direct mass measurement. 4. S and slow V±-events observed in the multiplate chamber are discussed. It is shown that one should distinguish between two groups of decays: One with secondaries of range smaller than 20 g cm−2 of Pb, the other with larger range secondaries. Although the first group can be due to τ-mesons, the second group cannot be so explained, at least not phenomenologically. 5. The results of mass measurements—from range and momentum—on the primaries of the second group of events are presented. The measurements agree with a unique value of (914±20) me; which appears to be different from the τ-mass. 6. We show that some, and probably most, of the secondaries of this second group of events are μ-mesons. This conclusion is based on the dynamics of the decay and results from the measured mass of the primary particle and the observed ranges of the secondaries. The observation of one large angle scattering indicates, however, that τ-mesons may also be present among the secondaries.

On the hydrodynamical model of the quantum mechanics

Abstract: A new hydrodynamicla model for the Schrodinger equation is discussed. The new model differs from that ofMadelung by the existence of turbulence. It follows directly from the ordinary interpretation of the quantum mechanics, by the introduction of operators for the charge and current densities and the components of the stress tensor in the one particle formalism. The model is developed for any values of the spin. The Madelung fluid corresponds to the mean motion of the special turbulent medium. The quantum potential appears as a combination of a pressure with terms arising from the turbulence. It is shown that the quantization of the motion of the Madelung fluid introduces the right kind of turbulence. The trajectories of the de Broglie-Bohm theory appear as trajectories of the mean motion of the turbulent medium.

Non perturbation treatment of scattering in quantum field theory

Abstract: A sequence of approximations to theS andK operators is obtained by means of a variational method. The form of the approximations is such that discussions on general questions like convergence and renormalization become possible without any weak coupling assumption. The method is particularly suited for the study of two body collision problems: in this case the difficulties in the treatment of the higher order approximations are reduced to the problem of evaluating the perturbationS-matrix elements.

On quantum field theory. II: Non-perturbative equations and methods

Abstract: The evaluation of an element of theU-matrix between arbitrary initial and final states is reduced to that of a kernel, whose form depends only upon the number of particles involved and is given explicity as a perturbative expansion. Kernels are shown to satisfy systems of «branching equations», which hold independently of perturbation methods and can be taken as the axiomatic foundation of the theory, Lorentz covariance being manifest. Complete systems of such equations are given for the kernels and their derivatives with respect to the interaction strength λ: all other conceivable equations among kernels are necessarily deducible from them. All kernels corresponding to processes involving real bosons can be obtained, with simple integrations, from the kernels for purely fermionic processes; the branching equations for these are also explicity given and suffice to define the theory. A kernel, with its first and second λ-derivatives, satisfies a single integral relation. A variety of approximation methods are immediately deducible from the branching equations; they, while extending and generalizing the known ones, always permit, at least in principle, tests of convergence. Questions of renormalization, existence of solutions, etc., will be studied in the sequel to this paper.

A nuclear inductor for measurements of thermal relaxation times in liquids

Abstract: A device for measurements of nuclear relaxation times in liquids in the range from 10−2 s to the longest observable times is described. Two equivalent methods are used which are based on the record of «in phase» signals due to the total reversal of the nuclear magnetization.

A stable high speed multichannel pulse analyzer

Abstract: A twenty channel pulse analyzer with a resolving power of 3 μs is described. Its chief feature is that pulse selection is accomplished by a single discriminator for each channel whose threshold is set at a height corresponding to the upper boundary of the channel and the channel width is determinated by suitably shaping the incoming pulses.

Progress report on the development of bubble chambers

Abstract: Today I would like to report on the present s tate of development of a new ins t rument fox' the s tudy of high energy nuclear physics. This new device, which has been (.ailed a (( bubble chamber ,), makes it possible to record the paths of charged particles flying through a liquid absorber by photographing the strings of bubbles which mark the tracks when the liquid is highly superheated. Bubble (.hambers have characteristics somewhat intermediate between those of conventional cloud chambers and nuclear enmlsions since the specific gravi ty of the liqmd is about one, the dimensions are of the order of a few centimeters , and counter-(,,ontrolled pictures can be taken.

The coupling constant in field theory

Abstract: The various possible definitions of the coupling constant in quantum electrodynamics and in meson theory are reviewed and their properties are discussed. It is pointed out that the gauge invariance of quantum electrodynamics makes the definition of the renormalized charge unique, at least in a certain sense. This simplification does not occur in meson theory where the definition of the coupling constant is more ambiguous. A recent attempt at comparing different mesic charges is discussed.

Conformal geometry and elementary particles

Abstract: The kinematical consequences of basing (classical or quantum) field theory on the conformal geometry are examined in this paper. The space in question is that of all spheres inR 4 (flat 4-space of signature (+++−)); the fundamental invariant, the angle under which two spheres intersect. In the mathematical preliminaries (§1) a convenient inhomogeneous formalism is developed, permitting the sphere to be treated as a point in a 5-dimensional Riemannian space of constant unit curvature whose length element is the infinitesimal angle between two neighboring spheres. The conformal group (proper Lorentz transformations, translations, uniform dilations, and inversions in spheres) is just the 15-parameter group of motions (metric-preserving transformations) of this space. In §2 the spheres are interpreted as finite (non localized) test particles. Physical fields are thus defined on test particles rather than (e.g. in position space) on the events occupied by these test particles alone. The spheres can be labelled either with the 5-position (test particle’s spacetime position andsize) in aq-frame, or with the 5-momentum (test particle’s 4-momentum and rest mass) in ap-frame. There exists a motion transformingq- intop-space and conversely (in other words,q- andp-observers are physically equivalent), in virtue of which any conformal theory is shown to exhibit an automaticBorn-reciprocity betweenq- andp-space. The 5-position and 5-momentum satisfy an uncertainty-relation type equation; i.e., the non-localizations inq- andp-space are in an inverse relation with Planck’s ħ measuring the intrinsic correlation. All the other motions can be built up from subgroups takingq- andp-space into themselves. These are systematically interpreted as changes of frame. Those involving relative motion representuniform relative accelerations of Lorentz observers (Lorentz group ↔ zero accelerations). Test particle mass and size are invariant under the Lorentz group but non-uniformly renormalized by the accelerative motions. In §3 the geodesics of sphere space (motion equations of (elementary) test particles) are shown to describe uniform motion in the present (force-free) case. Test particles tend to dislocalize inq space with increasing time and inp-space with increasing energy. The time-constancy of the 5-momenta, their inter-dependence as given by special relativity dynamics follow from these motion equations. Free elementary particles are shown to maintain a state of uniform velocity under all motions, in particular the accelerative ones. This contradicts ordinary relativity and suggests an experiment capable in principle of choosing between the conformal and Lorentz geometries for physics.

Angular distributions in cosmic ray stars at 3500 meters

Abstract: Cosmic ray stars have been investigated at 3500 m using an ion chamber surrounded by G.M. counters connected to a 22 channel hodoscope. The events were recorded by a tele-typewriter triggered by the hodoscope, so that a reconstruction of the mutual positions of the stars prongs could be obtained for each event. The analysis reported here refers to about 13 000 stars having eitherat least one secondary branch able to cross 1.2 g/cm2 of brass orno such branch. These «detectable prongs» were protons of energy greater than 25 MeV or mesons of energy greater than 10 MeV. Using photographic emulsion results it is shown that the average energy,\(\bar W\), of the nucleons producing our interactions is about 60 MeV for the stars without detectable prongs and in the neighbourhood of 750 MeV for the stars having at least one prong. The zenith angle distribution of these nucleons is well represented by cosmz andm varies from 2.1±.3 to 2.6±.3 between\(\bar W = 60 MeV\) and\(\bar W = 750 MeV\). It is found, furthermore, that roughly the same distribution holds for both proton and neutron forming stars. The angular distributions of the secondary prongs have been deduced with respect to the vertical and to the direction of the primary. Analytical expressions in terms of power of the cosine of the angle are obtained for the experimental distributions referring to the projections of the tracks on a plane. The distributions in space are derived from these plane distributions through the solution of an integral equation, and they are polynomials of the same type. Comparison of our distributions with those obtained from analysis of stars produced by 300–400 MeV nucleons, suggests that:a) the cross-section for meson production is still very small at energies of 700–800 MeV;b) the cross-section for elastic scattering in nucleon-nucleon interactions remains probably almost constant between 300 and 750 MeV.

The phenomenological treatment of τ-meson decay

Abstract: The decay pa t t e rn of the z-meson is most easily represented on the wellknown tr iangular diagram. This m a y be done as follows: the distances of the point P (Fig. 1) f rom the sides of the tr iangle are proport ional to the kinetic energies of the three ~:-mesons. I n consequence of the m o m e n t u m conservat ion not every point inside the tr iangle corresponds to a possible decay pa t t e rn : the pe rmi t t ed region is defined by the equat ion 1

Self-diffusion in liquid indium

Abstract: The self-diffusion coefficient of liquid indium has been measured in the range from 160 to 480 °C with results which are very close to the ones for liquid mercury. Near the melting point some complication occur, which are discussed in terms of crystallite formation.

On time reversal

Abstract: It is pointed out that a satisfactory definition of time reversibility in quantum theory has not yet been given, so that for example the reasons for the exclusion of a system as irreversible are somewhat obscure. In this paper a definition of reversibility is given, which takes account of the fact that a system may be described by a whole set of equivalent Hamiltonians. Such a definition therefore excludes irreversible systems and not one Hamiltonian which might still be one of a set of Hamiltonians some of which are reversible according to the old set of prescriptions. Our definition is suggested by the correspondence principle and based entirely on the transformation properties of observable quantities. It is found that the new formulation is sufficient to exclude systems whose Hamiltonians had hithertho been labelled as irreversible—though the method of demonstration—owing to the generality of the postulates—is somewhat more complicated than the usual one.

Construction of potentials from phase shift and binding energies of relativistic equations

Abstract: The problem of constructing the potentialV(r) from givenS phase shift and binding energies of the Klein-Gordon equation is treated, and the analogue of the Gel’fand and Levitan integral equation is established.

Time variations of cosmic ray intensity

Abstract: An apparatus for the continuous registration of the total ionization component of cosmic rays at sea level has been set up at Rome. The purpose is to study the correlations between cosmic ray intensity and atmospheric, geomagnetic and solar phenomena. The apparatus consists of telescopes of Geiger-Muller counters in triple coincidence, directed vertically, and inclined at 30° to the vertical in the direction South and North respectively. The difference between the diurnal variations in two inclined directions is considered free from atmospheric effects and is thus able to show up an anisotropy of the primary radiation. There are four independent telescopes in each direction, with a total of about 27 000 coinc./h in North and South directions respectively, and about 48 000 coinc./h in the vertical. The counters are held thermostatically at (30±1)°C. The methods used to reduce the instrumental inequalities and to obtain the maximum operational stability and continuity are described. The preliminary results obtained in the first counting period, from January to March 1954, are presented.

On theL-capture toK-capture ratio in Cd109

Abstract: TheL-capture toK-capture ratio in the orbital electron capture occurring in Cd109 was measured by means of a proportional counter This ratio was deduced from the measured intensities of theLX- andKX-radiations, after correction for the counting geometry, the fluorescence yields of Ag, and the internal conversion of 87 keV γ-rays from the atom produced Thus:PL/Pk=032±004 A test of this result was obtained by measuring the intensities of theKX- and γ-radiations by means of a NaI(Tl) γ-ray spectrometer In this way:PL/PK≊029 Marshak’s formulae were used to calculate the transition energyE0 It was foundE0=67−3+8 keV

Mass determination on steeply dipping tracks in Emulsion Block Detectors

Abstract: In the s tudy of part icle t racks in Emuls ion Block Detectors one can frequent ly observe appreciable length of t r a jec to ry even for those t racks which t raverse individual emulsion sheets with a large dip angle. The cus tomary methods for deducing the mass of such particles f rom mult iple Coulomb scattering and range or f rom mult iple Coulomb scat ter ing and grain densi ty give very unreliable results. The failure of obtaining accurate mass values with these methods is due to the small distortions which are introduced into the emulsions during processing. We will show in this paper tha t the effect of such distortions can be complete ly el iminated if ins tead of deducing the Coulomb scat ter ing f rom second co-ordinate differences one makes use of th i rd or higher order differences. In a small sample of pro ton t racks with dip angles between 32 ~ and 520 good mass determinat ions have been made.