Showing papers in "Il Nuovo Cimento B in 1973"

The electronic structure of GaSe

Abstract: The electronic band structure of the layer compound GaSe was calculated with the empirical pseudopotential method. Corrective terms had to be added to the spherical atomic potentials in order to account for the weak van der Waals coupling between layers. It was possible within this approximation to evaluate the effective masses of electrons and holes, both parallel and perpendicular to the layers. The experimentally observed strong dependence of the optical absorption on the polarization of the light is well explained by the present band structure. With the pseudo-wave-functions the charge densities were calculated for several groups of bands. They allow a detailed discussion of the chemical bonding in GaSe.

The band-gap excitons in gallium selenide

Abstract: Absorption, and reflexion spectra of GaSe near the fundamental gap are interpreted in terms of pseudopotential band calculations. Selection rules for the direct optical valence-to-conduction band transitions are derived. Valence band mixing induced by spin-orbit coupling is invoked to explain the low observed probability for transitions in light polarized perpendicular to the crystal c-axis. The spectra of the excitons associated with the direct gap are discussed in the ellipsoidal effectivemass approximation. Corrective terms are added to account for the observed exchange splitting of the exciton ground state. Field-free spectra as well as spectra modified by the presence of magnetic fields parallel and perpendicular to c are considered. The magneto-Stark effect which gives rise to a mixing of the 2s and2py states and thus renders the2py state visible affords determination of the anisotropy parameter. The value of this parameter as well as those of the components parallel and perpendicular to c of the reduced effective masses show that the electronic states in GaSe are nearly isotropic. This is in good agreement with the results of the pseudopotential band calculations which clearly demonstrate the three-dimensional character of valence and conduction bands.

Combinatorics and fermion algebra

Abstract: It is shown that the various types of normal terms arising from the normal ordering of a disordered product of fermion operators can be enumerated with the aid of a well-known combinatorial problem, called the problem of the rooks

Dynamical neutron diffraction by ideally curved crystals@@@Динамическая дифрак ция нейтронов на идеа льно искривленных криста ллах

Abstract: SummaryNeutron diffraction patterns by ideally curved crystals were calculated by extending Taupin’s dynamical theory of X-ray diffraction by deformed crystals. The thickness and the curvature of the crystals were utilized as physical parameters. The results of the neutron diffraction calculations are substantially different from those relative to the X-rays. This is due essentially to the low neutron absorption crosssection. The main part of the neutron results is physically explained with the aid of the concepts of the dynamical theory of diffraction by perfect crystals. This study finds an application in the design of new types of neutron monochromators.RiassuntoSono stati calcolati dei profili di diffrazione neutronica da cristalli curvi ideali estendendo la teoria dinamica della diffrazione dei raggi X da cristalli deformati sviluppata da Taupin. Lo spessore e la curvatura dei oristalli sono stati utilizzati come parametri fisici. I risultati dei calcoli per i neutroni sono sostanzialmente diversi da quelli relatrvi ai raggi X. Ciò è dovuto essenzialmente alla debole sezione d’urto di cattura neutronica. La maggior parte dei risultati nel caso dei neutroni è spiegabile fisicamente con l’aiuto dei concetti della teoria dinamica della diffrazione da cristalli perfetti. Questo studio trova un’applicazione nel progetto di nuovi tipi di monocromatori per neutroni.РезюмеВычисляются картины дифракции нейтронов на идеально искривленн ых кристаллах, с помощ ью обобщения динамич еской теории Таутина для дифракции Х обобщения динамичес кой теории Таутина дл я дифракции Х-лучей на деформированных кри сталлах. Толщина и кри визна кристаллов исп ользуются как физиче ские Х-лучей на деформиров анных кристаллах. Тол щина и кривизна крист аллов используются к ак физические параме тры. Результаты вычис лений дифракции нейт ронов существенно от личаются от результа тов дифракци кривизна кристаллов используются как физ ические параметры. Ре зультаты вычислений дифракции нейтронов существенно отличаю тся от результатов ди фракции Х-лучей. Это об условлено, в основном, малым поперечным сеч ением поглощения ней тронов. Основная ча параметры. Результат ы вычислений дифракц ии нейтронов существ енно отличаются от ре зультатов дифракции Х-лучей. Это обусловле но, в основном, малым по перечным сечением по глощения нейтронов. О сновная часть нейтро нных результатов физ ически объяснятся с п омощью концепции дин амической теории диф ракции в ид существенно отличаю тся от результатов ди фракции Х-лучей. Это об условлено, в основном, малым поперечным сеч ением поглощения ней тронов. Основная част ь нейтронных результ атов физически объяс нятся с помощью конце пции динамической те ории дифракции в идеа льных кристаллах. Про веденное исследован ие находит применени е при конструировани и новых типов нейтр Х-лучей. Это обусловле но, в основном, малым по перечным сечением по глощения нейтронов. О сновная часть нейтро нных результатов физ ически объяснятся с п омощью концепции дин амической теории диф ракции в идеальных кр исталлах. Проведенно е исследование наход ит применение при кон струировании новых т ипов нейтронных моно хроматоров. сечением поглощения нейтронов. Основная ч асть нейтронных резу льтатов физически об ъяснятся с помощью ко нцепции динамическо й теории дифракции в и деальных кристаллах. Проведенное исследо вание находит примен ение при конструиров ании новых типов нейт ронных монохроматор ов. нейтронных результа тов физически объясн ятся с помощью концеп ции динамической тео рии дифракции в идеал ьных кристаллах. Пров еденное исследовани е находит применение при конструировании новых типов нейтронн ых монохроматоров. помощью концепции ди намической теории ди фракции в идеальных к ристаллах. Проведенн ое исследование нахо дит применение при ко нструировании новых типов нейтронных мон охроматоров. идеальных кристалла х. Проведенное исслед ование находит приме нение при конструиро вании новых типов ней тронных монохромато ров. находит применение п ри конструировании н овых типов нейтронны х монохроматоров. нейтронных монохром аторов.

The asynchronous formulation of relativistic statics and thermodynamics

Abstract: An exposition of the covariant asynchronous formulationA of relativistic statics and thermodynamics is given, and this description is compared with the traditional synchronous oneS. The spin equation is given a covariant formulation. Also the equation of motion for extended bodies is given inA. Further the interpretation inS and inA of the elements of the energy-momentum tensor is stated, and the result is employed on an ideal gas. The relativistic concept of heat is discussed. The temperature is introduced as a scalar. Some examples from the statics, the right-angled lever, Trouton and Noble’s experiment and Sears’ relativistic paradox, are discussed. A few topics from the relativistic thermodynamics, the transformation of energy and momentum of an ideal gas and the transformation of thermodynamical work between inertial systems, are treated in some detail. Also the exchange of heat between systems with a relative motion is described and discussed.

A gravitational « Aharonov-Bohm » effect

Abstract: The massless Dirac equation is considered in the presence of weak external gravitational fields. In the presence of fields arising from moving mass currents, solutions are found which are analogous to those giving rise to the Aharonov-Bohm effect in electromagnetic theory. The mass currents play the role of the magnetic fields. Comparison is made with earlier analogous solutions by Plebanski and by Balazs and Bertotti, and an alternative physical interpretation is offered in which simply connected currents can produce an effect which is observable in principle.

Experimental meaning of the concept of identical particles

Abstract: Some of the language used in discussions of identical particles is analyzed and it is found that much of it, along with some of the concepts, is meaningless. The experimental behaviour is studied and shown to be a consequence of quantum meohanics without the need for specific assumptions about the behavior of identical particles, as the special characteristics follow from general principles.

Coherence functions in the far-field diffraction plane

Abstract: Some properties of the angular coherence functions have been considered. These are then used to study the propagation of the mutual coherence function. It is shown that the spectral coherence function in the far-field diffraction plane is directly proportional to the angular coherence function. This approach is applied to several cases of particular interest such as the coherent, the incoherent and the homogeneous sources. The case when the source is a black body having a circular opening is also considered and some polarization properties in the far-field diffraction plane are considered.

Substitution of Fe3+ by Al3+ in the trigonal sites of M-type hexagonal ferrites

Abstract: Mossbauer measurements in Ba1−ySryFe12−xAlxO19 (0 7.2) they rapidly decrease and go down to zero forx- 10. On the contrary, for a givenx, the number of Fe3+ ions in trigonal sites increases with increasingy.

Perspectives on the Schwarzschild singularity

Abstract: A survey and discussion of some of the literature pertaining to the Schwarzschild singularity is presented. Scalar indeterminacies, with particular reference to the metric of Bach and Weyl, are cited as evidence for the reality of the Schwarzschild singularity. An analogy is drawn with the work of Janis, Newman and Winicour.

Measurements of absolute intensities of cosmic-ray muons in the vertical and greatly inclined directions at geomagnetic latitudes 16 °N

Abstract: Absolute integral intensities of vertical cosmic-ray muons with minimum momentum in the range (0.35/2.7) GeV/c and of muons at large zenith angles in the range (75/89)ℴ have been measured by using a very-narrow-angle scintillation counter telescope. In this momentum range the vertical intensities are found to be consistently higher than the standard Eossi integral spectrum at geomagnetic latitude 50 °N, but (4/5)% lower than the best-fit integral intensities up to 1 GeV/c of Allkoferet al., this difference of the present intensities from those of Allkoferet al. being consistent with latitude variation of the muon spectrum. A comparison of the present results with some of the other absolute measurements at lower and higher geomagnetic latitudes is given to show the significant deviation of most of the previous measurements at lower latitudes from the present measurements. The absolute intensities in the inclined directions have been measured in the zenith-angle range (75 /89)ℴ by using the same apparatus. The measured intensities are somewhat lower than the previous measurements, but consistent with the theoretical zenithal distribution according to the calculation of Ashtonet al. The present results in agreement with that of Hickset al. tend to lie between two estimates made assuming kaon-to-pion ratio of 0 and 0.4. The near cosine-square zenithal distribution law up to the zenith angle 73° is found to be changed in the range (75/85)ℴ to a form with an exponent 1.86.

Hooke’s symmetries and nonrelativistic cosmological kinematics. II: Irreducible projective representations

Abstract: The irreducible unitary projective representations of the Hooke groups are constructed by Mackey’s method of induced representations. In this manner, we obtain a classification of the true irreducible representations of the extended and ordinary Hooke group universal covering, and then a classification of the elementary quantum systems which have Hooke symmetries. The eigenvalues of their invariant operators label these irreducible representations, and the corresponding infinitesimal representations define their Lie algebras. When this makes sense, some physical interpretations are given.

Quantum-mechanical analogue of particle creation caused by the expansion of the universe

Abstract: Free spin-1/2 particles in an expanding isotropic and homogeneous universe are treated in the framework of the quantum mechanics of unquantized matter fields. The curved space-time acts thereby as an unquantized external field. The eigenvalues of energy and momentum are time dependent. They are, after a simultaneous energy and momentum measurement, related by the special-relativistic relationE(t) = = ±c √p2(t) +m2c2. A freely moving plane wave (solution of the dynamical equation which is an eigenfunction of the momentum) contains in general cigenfunctions of both signs of the energy, which in special relativity remain decoupled. This is also the case in the universe above for particles with vanishing rest mass (neutrinos) and massive particles with vanishing momentum. For other particles one finds an expansion-induced time-dependent mixing of positive- and negative-energy parts. One can interpret this with regard to the corresponding creation and annihilation operators of quantum field theory as the analogue of particle production. The probability of finding particles of opposite sign of the energy differs with the aget of the universe and is of the order ϱ(t), where ϱ(t) isħ/mc2 times the Hubble parameter at the timet. For electrons ϱ(t) ≈ 10-21t-1 s. While ϱ(t) is today only about 10-39, one can expect considerable particle production for times with ϱ(t) ≥ 1, i.e. during the first 10-21 seconds of the Universe.

Some remarks about dispersion and absorption of sound in monoatomic rarefied gases

Abstract: In the present paper we consider sound propagation in rarefied monoatomic gases from the point of view of a previously proposed modified Navier-Stokes equation. The agreement between theory and experiment is rather good for sound dispersion and absorption in the region where the ratio between the mean free path and the wavelength lies within the limits 0.1 and 1. We also discuss the asymptotic behaviour for high-frequency values of the sound dispersion and absorption and suggest that further measurements in the Knudsen regime of sound dispersion (neglecting absorption) would be useful to test the Validity of sound wave as well as free-molecule propagation theory.

Green’s functions in the study of surface states or excitations in general

Abstract: The method of « surface Green’s functions » introduced by Garcia-Moliner and Rubio to study electronic surface states is expounded in simple terms, showing its wide applicability to different physical problems. Surface elastic (Rayleigh) waves, electrons and plasmons are considered within this context, as well as the dielectric response of a nonlocal semi-infinite medium.

A rotating spheroid as a possible source of the Kerr metric@@@Вращающийся сфероид как возможный источник метрики Керра

Abstract: SummaryThe gravitational field of a sphere rotating steadily about one of its diameters is calculated, inside and outside the sphere, up to the orderk6 using the Florides-Synge method of successive approximations:k∼(m/b)1/2, wherem is the mass andb the radius of the sphere. Under the assumption that the constantsm anda appearing in the Kerr (exterior) metric are of orderk2 andk, respectively, it is shown that the Kerr metric, up to the orderk5, is precisely the (exterior) field of a rotating sphere to the same order. Since in the Florides-Synge method the field is calculated simultaneously inside and outside the sphere, the Kerr exterior metric is automatically extended to an interior metric up to the orderk5.RiassuntoSi calcola il campo gravitazionale di una sfera olie ruota in modo stazionario attorno ad uno dei suoi diametri, all’interno ed all’esterno della sfera, sino all’ordinek5 per mezzo del metodo di approssimazioni successive di Florides-Synge:k∼(m/b)1/2, dovem è la massa eb il raggio della sfera. Supponendo che le costantim eda ehe compaiono nella metrica (esterna) di Kerr siano dell’ordinek2 ek, rispettivamente, si dimostra che la metrica di Kerr, sino all’ordinek5, è precisamente il campo (esterno) di una sfera rotante sino allo stesso ordine. Poiché nel metodo di Florides-Synge si calcola il campo simultaneamente all’interno ed all’esterno della sfera, la metrica esterna di Kerr si estende automaticamente ad una metrica interna sino all’ordinek5.РезюмеИспользуя метод посл едовательных прибли жений Флоридса-Синга, вычис ляется гравитационн ое поле внутри и вне сф еры, равномерно вращающейся вокруг о дного из своих диамет ров, вплоть до порядкаku5,k ∼(т/b)1/2,гдет — масса иb — радиус сферы. Предполагая, чт о постоянныеm иа, поя вляющиеся в (внешней) метрике Керра, имеют с оответственно поряд окk2 иk, показывается, что мет рика Керра, вплоть до п орядкаk5, в точности представляет (внешне е) поле вращающейся сф еры до того же порядка. Так как в методе Флоридса-Синг а поле вычисляется од новременно внутри и в не сферы, то внешняя метрика Керр а автоматически расп ространяется на внут реннюю метрику, вплоть до порядкаk5.

The general form of constitutive equations in relativistic physics

Abstract: In this study we propose a principle of objectivity which is appropriate to the theory of relativity. The transformation equations of kinematic, thermodynamic and electromagnetic quantities as well as their spatial and temporal derivatives are derived and their objectivity examined. Finally the restrictions on the form of constitutive equations of continuum physics imposed by the principle of objectivity are studied.

Trapping levels in anthracene crystals by thermally stimulated currents

Abstract: Thermally stimulated current (T.S.C.) measurements in anthracene crystals indicate the presence of various trapping levels. By regulating the excitation time and the excitation temperature we could isolate a monomolecular T.S.C. signal withE = (0.53 ± 0.03) eV and ϕ = 0.6.108 s-1 and determine the sign of the trapped carriers. The results obtained support the hypothesis that a level is involved which is strictly connected with the crystal lattice and presumably associated with chemical impurities contained in the crystal.

Small-angle scattering from liquid metals and alloys and electronic correlation functions

Abstract: The partial structure factors Sii, Sie and See in pure liquid metals are considered at small wave vectorq. Charge neutrality arguments relate the three functions through the valencyZ atq = 0. It is shown that the partial Ornstein-Zernike functions are proportional toq = 0. It is in the long-wavelength limit, and that they are related, not only throughZ, but through a common characteristic energyE. By setting up a model for the dynamic structure factors, and by assuming well-defined plasmon and phonon modes at smallq, the characteristic energy is shown to be dominated by the zero-point energy of the electronic plasma oscillations. In turn, this same energy is shown to dominate the curvature of See atq = 0, the curvature being pronounced and See therefore rising rapidly away fromq = 0. In contrast, because ion masses enter, the coefficients of q2 in Sie and Sii are shown to be orders of magnitude smaller and these structure factors are therefore quite flat nearq = 0. However, the magnitudes of the coefficients of q2 in Sie and Sii are shown to be influenced by the phonon dispersion, though insensitive to phonon damping. For weak electron-ion interaction, Sie(q) and S(q) can be related through an electronic response function, and the resulting expression satisfies the exact limiting relation between Sie andS atq = 0. Finally, the q2-term in See in an alloy is discussed and is shown to be directly related to the average electronic plasma frequency, involving therefore the valencies of the components and the mean atomic volume. The partial structure factors SAe and SBe can also be related to the (measurable) partial ionic structure factors for weak electron-ion interaction.

Lattice statics of orthorhombic sulphur

Abstract: The structure of orthorhombic sulphur has been fitted using a 6-exp potential function to describe the interactions between nonbonded atom pairs This is done for a series of different potential function parameter values and a means of deciding upon the best set of parameters is considered

Model-potential theory of positron-alkali-atom bound states

Abstract: The model-potential treatment developed in the preceding paper is applied to the study of the annihilation properties of a positron bound to an alkali atom. By using a model wave function for the positron bound state, accounting explicitly for electron-positron correlation, the following quantities are calculated: 1) the electron density at the position of the positron, 2) the spin-averaged two-photon annihilation rate, 3) the angular correlation function of the pair of emitted photons, and 4) the momentum distribution function of the annihilating electronpositron pair. The electronic densities at the positron and the annihilation rates result to be near the corresponding positronium values. This, together with other reported results, allows us to view the positron-alkali-atom bound state as a positronium atom moving in the field of an alkali ion and being very slightly affected by the latter. The presence of a small secondary maximum in the momentum distribution, the previous work on the subject and some limitations of the modelpotential treatment are discussed in detail.

Superheavy elements and nonlinear electrodynamics

Abstract: Maxwell’s equations, which underlie electrodynamics, are linear equations. Nonlinear effects, such as photon-photon scattering, are known to arise in quantum electrodynamics, and one might expect them to become important in the case of strong external fields. We investigate the consequences of a class of nonlinear Lagrangians, which includes that of Born and Infeld and whose common property is that they lead to upper limits for the electric-field strength (somewhat analogous to the upper limit for the velocity of a particle in special relativity). These nonlinear Lagrangians also lead to a finite electromagnetic selfenergy for the electron, unlike the case of Maxwellian electrodynamics. The importance of nonlinear effects of course depends upon the size of the upper limit to the electric-field strength. If this upper limit is determined by requiring that the mass of the electron is of an entirely electromagnetic origin, nonlinear effects become very important in determining the eigenvalues of electrons bound to superheavy nuclei. For example, theIs energy eigenvalue is raised by 270 keV forZ= 164. The Lagrangians considered here do not lead to an absolute gap between bound states and the states of the lower continuum; the Iδ energy eigenvalue becomes equal to —0.511 MeV, where the lower continuum begins, forZ=215. An analogy between nonlinear electrodynamics and higherorder vacuum polarization corrections is studied.

The structure of the sources of weyl-type electrovac fields in general relativity

Abstract: Weyl-type fields are those static electrovac solutions to the Einstein-Maxwell field equations for which the metric component g44 and the electrostatic potential Ψ are related by —g44= 1 — 2cΨ+gY2. In the present paper we investigate the structure of the sources that produce Weyl-type fields. It is found that, if the Weyl relationship holds also inside these sources, then they are structured such that over the extent of the source the ratio of the total mass density to the charge density is equal to the constant c in the Woyl relationship. In our result, the total mass density is that function which, when integrated over the extent of the source, gives the Schwarzschild mass as seen at infinity. It is not equal to the proper mass density — (κ/8π)M44, but is equal to the proper mass density plus the binding energy density.

The cosmic-ray spectral modulation above 2 GV during the descending phase of solar cycle no. 19

Abstract: This is the first of a series of three papers meant to study the short- and long-term spectral modulation of primary cosmic rays above 2 GrV during the time from the IGY to the IQSY, for a large part of solar cycle No. 19, which showed the highest activity recorded so far, and a complex superposition of different kinds of conspicuous solarinduced interplanetary perturbations. In Part I we discuss the information on the modulation as gained by means of neutron monitor data, provided sufficient accuracy is reached; in fact this information covers a fair primary rigidity range and offers a time and rigidity resolution which is not reached by other experimental data. We also present and apply to the 1957–65 data an indirect calibration procedure for practically the whole network of the near-sea-level neutron monitors by means of seven latitude surveys performed by ship or by terrestrial vehicle. This procedure provides a set of daily latitude curves suitable for directly deriving the isotropic variation of the primary differential spectrum.

The Brans-Dicke theory and anisotropic cosmologies

Abstract: The Hamiltonian method developed to study homogeneous, anisotropic cosmological models can be extended to the equivalent models in the Brans-Dicke theory. Universes of Bianchi types I and IX are studied and diagrammatic solutions are obtained in both cases.

Global description of spherical collapsing and expanding dust clouds

Abstract: Co-ordinate systems are derived which are everywhere smooth and globally cover the Oppenheimer-Snyder collapsing dust cloud. A co-ordinate system having these properties in the case of an oscillating dust cloud is also derived. The new co-ordinates enable the behaviour of the clouds to be studied even after the attainment of the critical Schwarzschild radius. In particular the red-shifts of photons emitted from and incident on the surface of the cloud are computed throughout its entire history. The results for clouds which are almost closed (topologically) indicates that they may be of significance in the production of gravitational waves and other energetic cosmogonic processes.

Semi-coherent states of the quantum harmonic oscillator

Abstract: It is shown that there exists for the quantum harmonic oscillator a large class of « semi-coherent » states, which represent harmonically oscillating wave packets whose « spread » or « size » remains constant. These states are different from the coherent states in not having the minimum value 1/2ħ for the uncertainty product Δx·Δp.

Stationary cylindrically symmetric electrovac fields.

Abstract: A particular type of exact solution of the Einstein-Maxwell equations corresponding to stationary cylindrically symmetric electrovac fields is presented here The solutions are linear combinations of static fields with constant coefficients

Null co-ordinate dynamics of linearized gravitation

Abstract: The null dynamics of the first-order linearized theory has different qualitative properties with respect to the well-known dynamical analysis made by Arnowitt and Deser when it is chosen a preferredx0 = const hypersurface. If we focus the study on the hypersurfacesx+ = const, the whole set of new constraints is found and after having been introduced into the action it is seen that the dynamics depend upon 2 dynamical independent variables. These 2 independent variables, which correspond to the fact that the linearized gravitational field is a massless helicity-2 field, are self-conjugate in a Hamiltonian sense,i.e. these variables essentially coincide with their momenta. Thus the Hamiltonian formalism is given without doubling the number of independent field variables, as in any integer-spinx0-formulation happens. The null Hamiltonian is found and it is seen to correspond to the momentumP+ of the field. Thereafter, the Heisenberg commutation relations for the dynamical variables are computed. Null electrodynamics is also studied starting from the first-order action and the so-called null gauge is discussed. In particular it is shown that its choice is not compulsory.