Vol. XXVII (1965)
Fasc. 1, pages 3–153
On Kirchhoff Diffraction Theory for Multipole Radiation from Young’s Point of View (Part I — The Dipole)
Acta Phys. Pol. 27, 3 (1965)
abstract
The paper deals with Young’s treatment of diffraction theory for the case of a scalar wave field deriving from a first-order multipole (acoustic dipole) incident on a diaphragm of arbitrary aperture, and stems from earlier papers on Young interpretation of diffraction phenomena in the case of an isotropic spherical wave (Rubinowicz 1917, 1924) providing the foundation of the section of diffraction theory termed geometrical diffraction theory by Keller (1957). The present paper makes use of certain results for the case of an isotropic spherical wave and contains some modifications of the computation method for that case. Because of the restriction to large values of \(k=\lambda /2\pi \) only, in applying the stationary phase method solely the first term of the full expansion in powers of \(k\) is utilized. Formulas are derived for the diffracted waves at arbitrary position of the point of observation, ensuring continuity of the multipole field at an arbitrary point beyond the diaphragm.
Sur les bases de l’electromagnetisme macroscopique
Acta Phys. Pol. 27, 13 (1965)
abstract
L’article comprend deux parties, qui l’une et l’autre se rapportent à des conséquences des équations de Maxwell. Dans la première, l’auteur exprime, sous plusieurs formes, l’énergie électromagnétique, montre que, pour les milieux différents du vide, on ne connaît que son expression différentielle, et que, pour aller plus loin, il faut faire des hypothèses supplémentaires sur les propriétés du milieu; il discute du sens du théorème de Poynting et des tenseurs d’énergie-impulsion de Maxwell et de Minkowski. Dans la seconde partie, on retrouve, par un calcul direct, l’expression des potentiels retardés de Lorentz et de Liénard–Wiechert; on discute de la condition de Lorentz pour des milieux linéaires, dans le cadre de la relativité restreinte.
Überlegungen zur ,,Unbestimmtheitsrelation” in der Matrizenmechanik
Acta Phys. Pol. 27, 25 (1965)
see erratum: Acta Physica Polonica 27, 993 (1965)
abstract
In einer frheren Arbeit [1] hatte Verf. gezeigt, dass eine exakte wellentheoretische Behandlung der Bewegung eines Elektrons zu dem Ergebnis führt, dass die sogenannte “Unbestimmtheitsrelation” nicht gilt, sondern in der Wellenmechanik nur durch die Unvollständigkeit der bisherigen Behandlungsmethode — Zuordnung einer (einzigen) ebenen Welle zu dem bewegten Teilchen — bedingt ist, während die dem Teilchen zuzuordnende Welle in facto wesentlich komplizierter ist und in eine Vielzahl von ebenen Wellen, aber auch in eine Vielzahl von Kopfwellen zerlegt gedacht werden kann. — In vorliegender Arbeit wird gezeigt, dass auch die matrizenmechanische Behandlung bisher unvollständig war und dass auch in der — entsprechend vervollständigten — Matrizenmechanik für die “Unbestimmtheitsrelation” kein Platz ist.
Note on Diffraction by a Circular Aperture
Acta Phys. Pol. 27, 37 (1965)
abstract
Let us consider the diffraction of an acoustic plane wave, \(\exp [i(kz-\omega t)]\), through a circular aperture of radius \(a\) in an infinite rigid plane screen \(z=0\). Let \({\mit \Phi }_2(\varrho ,z)\ \exp (-i\omega t)\) denote the diffracted field at the ‘shadow’ side \(z\gt 0\), where \(\varrho ,z\) are cylindrical coordinates.
Beugungsexperimente mit einem Laser zur optischen Fouriertransformation
Acta Phys. Pol. 27, 41 (1965)
abstract
Es werden Erbegnisse von Beugungsexperimenten zur Durchführung von Fouriertransformationen auf optischem Wege unter Verwendung eines LASERs als Lichtquelle beschrieben. Die bei Benutzung einer LASER-Lichtquelle sich ergebenden Vorteile werden an neuen Methoden zur gleichzeitigen Bestimmung von Amplitudenbetrag und Phase der Transformierten demonstriert.
Inclusion of the Lorentz Effect into Theories of Pressure Broadening of Spectral Lines Based on the Franck–Condon Principle
Acta Phys. Pol. 27, 49 (1965)
abstract
In theories of pressure effects on spectral lines based on the Franck–Condon principle, the absorbing or emitting atom together with the perturbing atoms is treated in a way analogous to the treatment of the intensity distribution in the band system of a molecule. There is, however, an important difference between a stable molecule and atoms in the state of collision (a “quasi-molecule’’). While the lifetime of a stable molecule may be considered as practically indefinite, that of a quasi-molecule is very short. This circumstance leads to an additional broadening of lines (the Lorentz effect) superimposed on that resulting from the application of the Franc–Condon principle. A procedure for achieving such superposition is given. Different tentative assumptions are proposed, from which the lifetime of a quasi-molecule could be determined. They lead for low concentrations of perturbing atoms to results almost identical with those of Weisskopf’s collision damping theory the only difference being that here the broadening of levels is considered as the primary effect of collisions, rather than the direct broadening of the line.
Two-centre Integrals for \(3d\) Electrons in Iron Cobalt and Nickel
Acta Phys. Pol. 27, 57 (1965)
abstract
Nuclear attraction and overlap integrals for \(3d\) electrons in iron, cobalt and nickel have been computed with the atomic wave functions given by analytical expressions with four exponentials.
The Lorentz Principle
Acta Phys. Pol. 27, 61 (1965)
abstract
This article I should like to dedicate to Professor A. Rubinowicz whom I met first in 1947 during the International Conference on Cosmic Rays in Cracow, which conference is a pleasant memory to all of us who participated. In later years I have had the privilege to get closer acquainted with Professor Rubinowicz, and I have had many interesting and stimulating conversations and discussions with him on a wide range of topics. Some of the topics were “non-orthodox” like the subject of the present article and I hope that Professor Rubinowicz will forgive me for the choice of the subject. I wish him good health and that he may continue for many more years in his admirable activity.
Unified Field Theory and Modern Physics
Acta Phys. Pol. 27, 89 (1965)
abstract
Five-dimensional unified field theory with a closed fifth dimension provides us with a geometrical interpretation of the electromagnetic field and of the electric charge. Gauge transformations mean translations and charge conjugation means inversion in the fifth dimension. The gravitational coupling constant is related to the Sommerfeld constant and to the circumference of the world-tube. The unifield theory predicts the existence of giant particles with rest masses of at least \(10^{15}\) times the nucleon rest mass. There are indications that the five (or more)-dimensional approach may become useful for a future understanding of weak and strong interactions.
Action d’une onde électromagnétique plane sur un courant rectiligne indéfini de même fréquence
Acta Phys. Pol. 27, 99 (1965)
Einige Folgerungen aus einer Identität für elektromagnetische Felder
Acta Phys. Pol. 27, 113 (1965)
abstract
Es wird eine beliebige Verteilung von ruhender Materie in einem statischen Magnetfeld \(B\) zugrunde gelegt. Diesem Magnetfeld wird ein elektromagnetisches Feld überlagert, das von einem schwachen eingeprägten elektrischen Feld \(E^e(r,t)\) erzeugt wird, welches einen Einschaltvorgang darstellt. Es werden zunächst die Materialgleichungen besprochen; sie werden als lokal angenommen, enthalten aber Nachwirkung. Aus einer bilinearen Identität für zwei elektromagnetische Felder der angegebenen Art läßt sich dann eine wesentliche Verallgemeinerung des Maxwell’schen Reziprozitätstheorems gewinnen, dessen Wurzel jedoch nicht mehr die Maxwell’schen Gleichungen, sondern die Onsager–Casimir’schen Reziprozitätsrelationen und damit die Thermodynamik irreversibler Prozesse ist. Weiterhin erhält man einen einfachen allgemeinen Beweis für ein bekanntes Theorem über äquivalente elektrische Netzwerke. Wesentliches Hilfsmittel ist die Theorie der linearen passiven Systeme.
Dispersion of Light in Multipole Media
Acta Phys. Pol. 27, 123 (1965)
abstract
On the basis of Oseen’s classical molecular theory of light, a non-relativistic quantum-correspondence theory of light in a homogeneous multipole medium composed of atoms consisting of many electrons with spins is proposed. The atoms interact with the perturbing field by electric dipole and quadrupole radiation and magnetic dipole radiation. From this semi-classical theory a generalized Lorentz–Lorenz formula for electric dipole and quadrupole radiation and for magnetic dipole radiation is derived.
Some Remarks on Diffraction by a Disc
Acta Phys. Pol. 27, 137 (1965)
abstract
An integral equation is obtained for the diffraction by a perfectly conducting circular disc and its solution at low frequencies is indicated.
Multiply-diffracted Boundary Waves
Acta Phys. Pol. 27, 147 (1965)
abstract
One of the great scientific contributions of Professor A. Rubinowicz is his theory of the boundary diffraction wave. It may, therefore, not be inappropriate to present, on the occasion of Professor Rubinowicz’s \(75^{\mathrm {th}}\) birthday, a preliminary account of some of our current researches, which indicate the possibility of a new and useful generalization of Professor Rubinowicz’s results in this field.ERRATA
Light Scattering by an Intense Light Beam
Acta Phys. Pol. 27, 153 (1965)
Theory of Molecular Light Scattering in the Presence of an Intense Light Beam
Acta Phys. Pol. 27, 153 (1965)
Fasc. 2, pages 157–355
Geometrical Wave and Quantum Optics
Acta Phys. Pol. 27, 157 (1965)
abstract
Here we have attempted to show mathematically the connection of geometrical optics on one hand and wave optics and light quanta on the other. The close relationship of the different aspects of light have been established through the intermediary equations, better known as transport equations. These equations are satisfied by the so-called amplitudes of various orders of the full asymptotic solution of the wave equation in terms of the wave parameter (wave length) on one hand and the equations of variations for the rays on the other hand. The transport equations are discussed in detail for a very general partial differential equation of the wave type including their relationship with the equations of variations of different orders which result from the application of perturbation theory to classical dynamical systems or the corresponding ray or geometrical optics equations. This mathematical relationship reveals the asymptotic character of the ray or particles aspect of the wave concept of light or dynamics described by the Schrödinger or Dirac equations. Furthermore, the introduction of light quanta or photon concept in the description of some optical experiments by the usual procedures of quantizing the electromagnetic field, has opened a new field, which for a lack of a better name, we have called quantum optics, that ultimately may give the true, or correct description of many optical phenomena, which at the present time are beyond the scope of classical electrodynamic theory. We have pointed out, that the recent investigations are based on the geometrical wave solution of the equations, that is to say of the wave packet expression for the photons, which correspond to the leading term of the asymptotic solution by neglecting the terms which account for the spreading of packet as it propagates through the medium. Since the transport equations define such a wave packet include also spreading, it is our belief that these equations will play a significant role in the further development of the new field of quantum optics.
The Density Operator and Information Thermodynamics
Acta Phys. Pol. 27, 179 (1965)
abstract
Possibility of performing independent measurements of non-commuting observables on different samples of the same physical system being in an identical state (described by a state vector) is indicated and discussed. By measurement it is meant an infinitely repeated process including at each time a new preparation of the system and giving full statistics of all possible eigenvalues. It is shown that by measuring to two non-commuting observables the state vector can be fixed uniquely (i.e. with accuracy to only one arbitrary phase), while measurement of one observable gives only a density operator. The Von Neumann formula for expectation values in mixed states is obtained by averaging over the unknown phases. It is shown that such an averaging follows from the general variational principle of information thermodynamics (Ingarden 1963) by using Urbanik’s result about entropy increase for operators non-commuting with the Hamiltonian. The complete entropy of the physical system is defined and it is shown how it goes over into entropy in the phase space in the classical limit. A generalized form of Von Neumann’s thermal mixture including higher order temperatures is given.
Electromagnetic Radiation and Diffraction in Anisotropic Regions
Acta Phys. Pol. 27, 197 (1965)
abstract
The thorough understanding of the propagation characteristics of plane wavers in homogeneous and sectionally homogeneous anisotropic regions is of prime importance in the solution and interpretation of radiation and diffraction problems which may be obtained by a synthesis of plane wave results. The nature of plane wave propagation in a homogeneous, lossless anisotropic region may be inferred conveniently from the refractive index plots which highlight in a suitable manner the different orientations of the wave normal (phase propagation) and ray (energy propagation) vectors. These plots may also be employed in the imposition of boundary conditions at a plane interface between two different media, and one frequently used method of ray tracing in a slowly varying medium actually exploits this property. Ray tracing procedures which have been employed successfully in the theory of ionospheric wave propagation may also be applied to the study of radiation from localized current distributions provided that the propagating ray amplitudes excited by the source (either primary as in an antenna, or secondary, as on an obstacle) are known. The latter information is furnished by the asymptotic analysis of the problem of radiation from an arbitrarily oriented electric or magnetic current dipole in an infinite, homogeneous region, the solution for which has recently become available and has been described in Section 3 b of this paper.
Survey of the Theory of Diffraction of Short Waves by Edges
Acta Phys. Pol. 27, 217 (1965)
abstract
A survey is presented of the theory of diffraction of short waves by thin screens and other objects with edges. The hypotheses on which the Geometrical Theory of Diffraction is based are described. The results which have been obtained by other methods are compared with those obtained by means of the geometrical theory. The agreement is interpreted as evidence supporting that theory. Mention is also made of some experimental results which agree with the geometrical theory.
\(S\)-matrix in Terms of Current Operator
Acta Phys. Pol. 27, 235 (1965)
abstract
A functional formulation of the \(S\)-matrix theory is presented in which this matrix is expressed in terms of current operators. The connection with the functional formulation leading to an expression of the \(S\)-matrix in terms of field operators is investigated. A proof of equivalence of the two formulations is given.
Statistical-mechanical Theory of Incoherent Van Hove’S Scattering Function for Thermodynamic Systems
Acta Phys. Pol. 27, 245 (1965)
abstract
Using the so-called second quantization formalism, the incoherent scattering function \(S_{\mathrm {inc}}(Q,\omega )\) is found to be related (in some energy range) in a simple way with the average occupation numbers \(\langle N(p)\rangle \) (being M.-B., F.-D., or B.-E. distributions for non-ideal systems of interacting particles). This gives the possibility of determination of \(\langle N(p)\rangle \) from incoherent scattering experiment, especially, from slow neutron scattering by thermodynamic systems, and, on the other hand, permits to calculate the scattering function using e.g. the (temperature-dependent) perturbation theory. It is found, among others, that the coherent part of scattering tends towards zero for ideal Boltzmann systems. It is, however, no longer valid for ideal quantum systems. The perturbational corrections are given for Boltzmann systems and it is found that the interaction between the particles of the scattering system can cause the decrease of the cross-section. The perturbational corrections depend on the proper form of the potential of interaction between particles of the scatterer.
On Changes in Polarity in Electrets of Certain Organic Materials
Acta Phys. Pol. 27, 259 (1965)
abstract
The influence of the conditions of polarization and preservation of the electrets of bees’ wax, pure resin, their mixtures and polymethacrylate on the time of change of polarization and a dielectric delay effect has been investigated. The results obtained suggest certain new point of view on the mechanism of the electret phenomenon, in particular on the extraction homocharge.
Electroluminescence of ZnS–Cu, ZnS–Cu–Pb and ZnCdS–Cu
Acta Phys. Pol. 27, 267 (1965)
abstract
Basing on results of author and on the concept of electroluminescence mechanism deriving from a Mott–Schottky type potential barrier and electron traps, an explanation is proposed of the effect of the exciting field’s frequency on the electroluminescence intensity distribution in all three groups of luminophors investigated i.e. on the change in colour from green to blue in ZnS–Cu, the slight shift of the green band towards shorter wavelengths in ZnS–Cu–Pb, and the hardly perceptible change from green to blue in ZnCdS–Cu. The phenomenon of ageing of luminophors in the process of light emission is investigated and discussed in detail. A discussion is given of the electroluminescence mechanism and the experimentally measured low energy yield related thereto.
Elektroluminescence of ZnS–Cu–Mn
Acta Phys. Pol. 27, 293 (1965)
abstract
The present investigation brings an explanation of (1) the change in ZnS–Cu–Mn electroluminescence from green to orange with higher voltage applied to the electroluminescence cell and the transition back from orange to green with higher excitation frequencies in luminophors of relatively low manganine content (\(10^{-3}\) g Mn per 1 g ZnS), and (2) the transition from orange to blue at higher excitation frequencies in luminophors containing blue luminescent centres of copper. An interpretation is proposed of energy transfer to the manganine ions and the respective energy transfer yield is proved to depend on the following factors: 1. The manganine ions concentration in the luminophors at constant concentration of the copper ions, 2. The voltage applied to the cell, and 3. The frequency of the exciting field.
The Role of Molecular Multipole Interactions in the Electric Polarization of Multi-component Systems I. Distortion Polarization
Acta Phys. Pol. 27, 305 (1965)
abstract
The theory of the electric polarization of a multi-component system is developed on the basis of the existing statistical theories. It is assumed that a molecule p has in general a \(2^n\)-pole permanent electric moment \(M^{(n)}_p\) and the \(2^n\)-pole moment \(P^{(n)}_p\) induced by the total electric field of order \(n\) (external \(E^{(n)}\) plus molecular \(F^{(n)}_p\)). A general expression for the \(n^{\mathrm {th}}\) order molecular field \(F^{(n)}_p\) at the molecule \(p\) is obtained in terms of the permanent multipole moments \(M^{(n)}_p\), \(2^n\) pole — \(2^m\)-pole interactions tensor \(^{(n)}T^{(m)}_{pq}\) between molecules \(p\) and \(q\) and \(n+m\) rank polarizability tensor \(^{(n)}A^{(m)}_p\) characterizing the polarization of the \(2^n\)-pole moment of a molecule \(p\) due to the electric field of order \(m\). The fundamental equation thus obtained for the dipole distortion polarizability \(P_D\) of the medium is discussed in some orders of approximations. In the zeroth-approximation, when multipole interactions between permanent moments of the molecules are absent in the system, the calculation of \(P_D\) performed to the third power in the dipole polarizability and first power of the field gradient quadrupole polarizability, of the molecule. In this case \(P_D\) is formally expressed as a power series in molar fractions, whose first term represents the additivity rule, while the subsequent terms account for deviations therefrom. By appropriate simplifying assumptions these results reduce to the known formulas. In further approximations the temperature-dependent contributions to \(P_D\) resulting from the non-zero multipole interaction potential energy are calculated in the case of dipolar systems, quadrupolar systems or systems of molecules possessing both dipole and quadrupole moments. The effect of anisotropy in the dipole polarizability of the individual molecules is also taken into account. These calculations are performed for simplicity in the pairs correlation approximation only.
L’Oscillateur harmonique radial
Acta Phys. Pol. 27, 323 (1965)
abstract
On a résolu l’équation de Schrödinger pour la fonction potentielle \(V=\frac {1}{2} k (r-r_e)^2\) avec les conditions aux limites \(\psi = 0\), pour \(r = \infty \) et \(r = 0\). On a constaté que les corrections des valeurs propres résultant du changement des conditions aux limites n’ont aucune importance dans les problèmes moléculaires.
The Production of Light Mesonic Hyperfragments and Li\(^8\) Fragments from the Interactions of \(K^-\) Mesons of 1.3 and 1.5 GeV/\(c\) Momenta with Emulsion Nuclei
Acta Phys. Pol. 27, 329 (1965)
abstract
The production of light mesonic hyperfragments and Li\(^8\) fragments from the interactions of 1.3 and 1.5 GeV/\(c\) \(K^-\) mesons with emulsion nuclei has been investigated. The results are compatible with the assumption that most of the light hyperfragments and Li\(^8\) fragments are emitted from excited heavy residual nuclei moving with an average forward velocity \(\beta = 0.016 \pm 0.005\).
Electric Permittivity of \(AC\) Biased Mono- and Polycrystalline BaTiO\(_3\) Above the Curie Point
Acta Phys. Pol. 27, 335 (1965)
abstract
Electric permittivity \(\varepsilon \) of BaTiO\(_3\) single crystals was measured as a function of an \(AC\) biasing field of 50 Hz in the temperature region above the Curie point. An increase of \(\varepsilon \) with the electric field \(E\) was found, satisfying a parabolic relation, \(\frac {\Delta \varepsilon }{\varepsilon _0}=\alpha E^2\) where \(\alpha \) is a constant. The coefficient \(\xi _{11}\) appearing in the thermodynamical theory of Devonshire was determined as about \(-0.75 \times 10^{12}\) cgs \(E\) near the Curie point. In the case of polycrystalline BaTiO\(_3\), the electric field caused a decrease in \(\varepsilon \).
Recherche d’une structure antiferromagnetique dans l’alliage FeAl
Acta Phys. Pol. 27, 343 (1965)
abstract
Pour résoudre le problème d’antiferromagnétisme de l’alliage FeAl ordonné, on a l’étudié par diffraction de neutrons à 293°K, 4,2°K et à 1,9°K, Aucune raie d’origine magnétique n’apparaît au-dessus de la température 1,9°K.
Density of Solid Methane at \(-196\)°C
Acta Phys. Pol. 27, 347 (1965)
abstract
From the volume of solidified methane and on determining its mass from the pressure, volume and temperature in the gaseous state, the density of solid methande at liquid nitrogen temperature was obtained.
General Rules of Isospin Crossing
Acta Phys. Pol. 27, 351 (1965)
Unitary Symmetry and \(\Delta T = \frac {1}{2} \) Rule
Acta Phys. Pol. 27, 355 (1965)
Fasc. 3, pages 361–521
The “Vectorial” Optics of Fields with Arbitrary Spin, Rest-mass Zero
Acta Phys. Pol. 27, 361 (1965)
abstract
The equations of fields with spin s, rest-mass zero, corresponding to the irreducible representation of the Lorentz group \(D(o, s)\) are studied in the high frequency limit. A formula for the rotation of the planes of polarization-due to curvature — is given. The optical development, i.e. , the development of the field with extracted phase factor into inverse powers of frequency, exhibits in its algebraic structure a characteristic “peeling off” effect.
Excess Free Energy of Multipolar Assemblies
Acta Phys. Pol. 27, 395 (1965)
abstract
Using a classical perturbation method, the contributions to the Helmholtz free energy from tensorial intermolecular forces are calculated up to two-body or three-body interactions. The calculations are carried out with the total tensorial potential energy of an assembly of unlike micro-systems composed of the electrostatic energy of interactions between permanent \(2^n\)-pole and \(2^n\)-pole charge distributions and the induction energy of interactions between permanent \(2^m\)-pole charge distributions and the induced \(2^m\)-pole moments of other charge distributions. The general results thus obtained are discussed for some simpler cases of axially symmetric molecules possessing dipole, quadrupole, octopole etc. moments, for tetrahedral molecules with octopole moment or for octohedral molecules with hexadecapole moment. The tensorial part of the free energy is applied to the case of two-component systems. Application to the equation of state of an imperfect gas mixture is also given.
Ellipsoidal Wavefunctions — Development in Terms of Them
Acta Phys. Pol. 27, 421 (1965)
Über die Anwendung der verschiedenen Formulierungen des elektromagnetischen Huygensschen Prinzips zur Lösung von Sprungwertproblemen
Acta Phys. Pol. 27, 435 (1965)
abstract
Die zuerst von H.A. Lorentz abgeleitete Fassung des elektromagnetischen Huygensschen Prinzips ergibt bei willkürlich auf einer Fläche \(F\) vorgeschriebenen, stetigen oder unstetigen Werten der Tangentialkomponenten der elektrischen und magnetischen Feldstärke die Lösung eines Sprungwertproblems. Diese Losung ist eindeutig festgelegt, sobald noch vorausgesetzt wird, daß sie im Endlichen überall regulär ist und im Unendlichen die elektromagnetische Sommerfeldesche Ausstrahlung- und Endlichkeitsbedingung erfüllt. In der vorliegenden Arbeit werden die aus dem Lorentzschen elektromagnetischen Huygensschen Prinzip ableitbaren Umformungen dieses Prinzips auf ihre Verwendbarkeit zur Lösung von Sprungwertproblemen bei vorgegebenen Werten der Tangentialkomponenten untersucht. Es wird gezeigt, daß die im folgenden als Umformung I oder II oder als Kottlersche Umformung bezeichneten Fassungen alle zur Lösung von Sprungwertproblemen auf der Fläche \(F\) auch bei Vorgabe beliebiger, in gewissen auf \(F\) verlaufenden Kurven unstetiger Werte der Tangentialkomponenten verwendet werden können. Die in ihnen außer den Werten der Tangentialkomponenten sonst auftretenden Randwerte kann man mittels der Maxwellschen Gleichungen direkt aus den Tangentialkomponenten berechnen, ohne das Sprungwertproblem vorerst lösen zu müssen. Mit den vorgegebenen und den berechneten Randwerten erhält man die gleiche Lösung des elektromagnetischen Sprungwertproblems, wie bei der Anwendung der Lorentzschen Fassung des elektromagnetischen Huygensschen Prinzips. Die Arbeit enthält auch eine übersichtliche Ableitung der Kottlerschen Version des elektromagnetischen Huygensschen Prinzips.
Octopole Moment of the Methane Molecule
Acta Phys. Pol. 27, 457 (1965)
abstract
By simple calculations it is shown that available measuring techniques do not allow to determine directly the sign and numerical value of the octopole moment of molecules from the effect of their orientation by the gradient of an external electric field’s gradient. Nevertheless, indirect methods involving contemporaneous results on the second viral coefflcients of the equation of state for gases or dielectric polarization in gases are shown to lead easily, rapidly and with sufficient accuracy to the octopole moment of tetrahedral molecules. These methods as applied by the author led to an octopole moment of 5–\(6 \times 10^{-34}\) e.s.u. cm\(^3\), a value that may well correspond to reality.
Microscopic Foundation of Relativistic Hydrodynamics
Acta Phys. Pol. 27, 465 (1965)
abstract
Relativistic hydrodynamic equations for dissipative processes are derived from the relativistic transport equation obtained by the author earlier. The problem is solved by the method of moments. In order to extend the method of moments to the relativistic case a relativistic generalization of the Hermite–Chebyshev polynomials is introduced. The viscosity and heat conductivity coefficients are expressed in terms of definite integrals of the differential cross-section for the gas particle interaction. The calculation fits in well both the non-relativistic and ultra-relativistic limiting transition.
Determination of the Barrier to Rotation Height of the H\(_3\)O Group in Crystalline Perchloric Acid Monohydrate by Total Neutron Scattering Cross-section Measurement
Acta Phys. Pol. 27, 491 (1965)
abstract
The total cross-section for neutron scattering in the cold neutron region was measured for crystalline H\(_2\)O\(\cdot \)ClO\(_4\) and liquid CH\(_3\)I. From a comparison of the slopes of these cross-sections vs. neutron wavelengths it was deduced that the rotation of the hydronium group in H\(_2\)O\(\cdot \)ClO\(_4\) is hindered. The barrier to rotation was evaluated as being approximately 1.8 kcal/mole.
Электромагнитные свойства элементарных частиц b модели \(G_2\)-симметрии
Acta Phys. Pol. 27, 497 (1965)
abstract
В работе предлагается общий метод исследования электромагнитных свойств элементарных частиц в модели \(G_2\) симетрии. Получснные результаты показывают, что в качестве основной модели высшей симметрии эта модель неприменима.
Sur la période d’oscillation classique de la molécule diatomique
Acta Phys. Pol. 27, 515 (1965)
The Spectrum of Neutrons from a Po+Be Source and the 7.66 MeV Level of C\(^{12}\)
Acta Phys. Pol. 27, 517 (1965)
abstract
The neutron spectrum of a Po+Be source was measured by recording proton recoil tracks in a photographic emulsion. For the reaction channel leading to C\(^{12*}\) (7.66 MeV) an attempt was made to draw some information concerning the neutron angular distribution from the difference between the C.M. and the apparent laboratory spectrum. The angular distribution appears to reach a maximum at an angle \(\varphi \gt 34\)°.
Магнитные весы для определеия абсолютных величин малых магнитных моментов
Acta Phys. Pol. 27, 521 (1965)
abstract
Описывается устройство магнитных весoв, в которых магниный момент образца уравновещивается магнитным момeнтом тока, текущего через катушку. Весы предназначены для работы в вертикальном магнитном поле, в области температур от гелиевых до 300°К. Чувствительность весов \(-3 \times 10^{-6}\) эл. магн. ед. магнитного момента.Fasc. 4, pages 527–609
Molecular Interaction Mechanisms in Fluorescence Quenching Processes
Acta Phys. Pol. 27, 527 (1965)
abstract
It has been found that the charge of interacting molecules has no influence on the shape of the dependence of the fluorescence quenching constant of solutions on the polarizability of the quenchers and their diamagnetic susceptibility. In the case of organic quenchers (iodo-, bromo-, chlorobenzene) we have a similar dependence of the fluorescence quenching constant on the polarizability and diamagnetic susceptibility of the substituents as in the case of the ions J\(^-\), CNS\(^-\), Br\(^-\), Cl\(^-\), suggesting that the primary role in the process of quenching should be attributed to the substituents and not to the molecule as a whole. The presence of a dipole moment in the quenching molecule results in a decrease in its quenching effectiveness
On the Four-particle Correlation Problem in the Superfluid Nuclear Model
Acta Phys. Pol. 27, 537 (1965)
abstract
The problem of the existence of four-particle correlation in a superfluid-type nuclear model is examined. In the first Section, it is shown that approximate methods based on a linear transformation eliminate quadrupling of nucleons. In Section 2, the exact ground-state energy values are found (in the strong-coupling limit), and the existence of four-particle correlation in this model becomes obvious.
Ferromagnetic Domain Structure at Non-zero Temperatures. Molecular Fied Approximation
Acta Phys. Pol. 27, 545 (1965)
abstract
Equations for the magnetization vector in anisotropic ferromagnets at arbitrary temperature are derived. Two independent methods, that of the equation of motion and that of the thermodynamic Green function are used, both in the molecular field approximation. The results are compared with those obtained by Ziętek for zero temperature; it is proved that the approximation used by Ziętek is the zero-temperature limit of the molecular field approximation.
Spin Waves in Screw Magnetic Structures (Magnetization)
Acta Phys. Pol. 27, 557 (1965)
abstract
The temperature-dependent part of the magnetization for a class of magnetic structures is calculated by means of the Holstein–Primakoff spin wave approach. The magnetic sample is considered to be composed of layers of magnetic nodes, the magnetic moments (all of the same magnitude) of each layer being arranged in ferromagnetic order and the magnetization of a single layer being a periodic function of the successive number of the layer. It is assumed that the magnetic nodes form a simple cubic lattice. It is pointed out that certain simplifying assumptions make diagonalization of the Hamiltonian feasible (the determinantal equation which has to be solved is of degree \(\leqslant 4\)). Thus the magnetization, including the term independent of temperature, can be calculated. The structures (aa) “flexible” or (bb) “rigid”, according to how they react to changes in \(H\) and \(T\), are considered. Possible forms of the temperature-dependence of the magnetization, as allowed by spin wave theory, are briefly discussed.
Photostimulated Exoelectron Emission During Freezing of Aqueous NH\(_4\)OH Solutions of Low Concentration
Acta Phys. Pol. 27, 573 (1965)
abstract
Investigation dealt with the electric potentials of liquid and ice in the process of freezing of a low concentration aqueous solutions of NH\(_4\)OH, at various concentrations and rates of freezing. The potential distribution on the ice surface was determined when the potential of the liquid was maximum. Photostimulated exoelectron emission from the ice surface was found to accompany crystallization. The kinetics of emission was measured with an open point, counter containing quenching vapour over the free surface of ethyl alcohol.
Rotational Dynamics of Solid Methane Molecules by Slow Neutron Cross-section Measurements
Acta Phys. Pol. 27, 581 (1965)
abstract
Inelastic scattering of subthermal neutrons by molecules of liquid methane and — in the same neutron energy region — of solid methane, was studied. Comparison of the slopes of the two curves representing the total scattering cross-section as a function of the neutron wave-length leads to the conclusion that in solid methane — at least near the melting-point — molecular rotation is probably free or almost free.
Anomalous Transmittivity in Dynamical X-ray Interference Theory
Acta Phys. Pol. 27, 587 (1965)
abstract
The intensity distribution is found and analyzed on a basic of dynamical X-ray interference theory, for the Laue and Bragg cases when \(\chi _{hr}\) and \(\chi _{hi}\) are of the same order and \(\chi _h \neq \chi _{\bar {h}}\).
The Bethe–Salpeter Equation in Symmetric Meson Theory
Acta Phys. Pol. 27, 595 (1965)
abstract
Some rearrangement of the terms of the perturbation theory is proposed. Three particle vertices appear instead of the initial four particle ones. With.the help of this rearrangement it is shown in any order of perturbation expansion of the kernel of the Bethe–Salpeter equation, that the kernel satisfies the Fredholm condition. The asymptotic behaviour of the leading Regge-pole is found to be \(\alpha (t) \sim (\log t)^{-1}\).
On the Existence of Events with Large Energy Transfer into Neutral Pions in the Investigation of Nuclear Interactions at Mountain Altitudes
Acta Phys. Pol. 27, 609 (1965)
abstract
The experimental data were obtained using apparatus of an area of 10 m\(^2\) installed at 3200 m above sea level. The apparatus contained several layers of emulsion plates and ionization chambers. separated by lead and graphite absorbers. Nuclear interactions in which the neutral pions carry away a large fraction \((k_{\pi ^\circ })\) of the primary energy are discussed. The observed interactions are not in contradiction with the fireball model, but events with \(k_{\pi ^\circ } \geqslant 0.6\) require the additional assumption that the most energetic pions come from an excited baryon decay.Fasc. 5, pages 633–799
ОБ oперaтopе электромагнитонго тoкa b молели унитарной симметрии
Acta Phys. Pol. 27, 633 (1965)
abstract
B работе обслуждаются следствия предположения о скалярносли фотона относительно подгруппы \(SU_3\), так называемой группы \(U\)-спина.
Asymmetric Hysteresis Loop of a Single-domain Ferroelectric
Acta Phys. Pol. 27, 637 (1965)
abstract
Electric charges deposited on a domain boundary are shown to stabilize a single ferroelectric domain against the action of an externally applied electric field. The electric charges compensate the depolarization field and increase the switching field of the polarization when changed in the antinucleation mode. Expressions are obtained for the bias of an anomalous hysteresis loop that are in agreement with the experimental data.
On the Magnetic Properties of the \(^{153}\)Eu Nucleus
Acta Phys. Pol. 27, 649 (1965)
abstract
Experimental data on the magnetic properties of the \(^{153}\)Eu nucleus are analyzed in terms of the effective spin \(g\)-factor. It is shown that spin polarization of the even core by the odd proton explains quite well the observed value of \(g_s^{\mathrm {eff}}\).
A Simplified Procedure for Shell Model Calculations of Alpha Decay Rates of Even–Even Deformed Nuclei
Acta Phys. Pol. 27, 655 (1965)
abstract
A simplified expression of the overlap integral which occurs in the alpha decay theory has been obtained using a harmonic oscillator wave function for the intrinsic alpha particle wave function, the frequency of which being equal to the frequency of the shell model. By means of this simplified expression we firstly calculated, by projecting out from the superfluid model wave function with 24 protonic and 24 neutronic Nilsson levels, an internal alpha particle wave function. Secondly, we calculated the reduced intensity b, for some transuranium elements using the modified Froman’s matrix method for treating the propagation through the anisotropic barrier. The theoretical results describe well the variation with the mass number of the experimental reduced relative intensity \(b_2\), but the values obtained by us are larger than the experimental ones and also than the Mang and Rasmussen results previously obtained, using a superfluid model wave function with 10 protonic and 10 neutronic Nilsson levels.
Stress-induced Variations in the Spectral Distribution of \(\gamma \)-radiation from Cs\(^{137}\) Transmitted by Graphited Carbon
Acta Phys. Pol. 27, 671 (1965)
abstract
Investigation dealt with variations in the spectral energy distribution of gamma (Cs\(^{137}\)) radiation transmitted by graphitized carbon, in their dependence on vertical load, and was aimed at assembling experimental data for clarifying the observed variations in intensity of gamma radiation scattered on carbon, due to the presence of stress therein.
Histograms of the Registration of the Penetrating Component of E.A.S. with Account for Secondary Interactions in the Absorber
Acta Phys. Pol. 27, 681 (1965)
abstract
Secondary interactions of nucleons and muons in a thick absorber caused deformation of the histogram of registration of the penetrating component. Instead of counts having a hypergeometric distribution a tendency is observed for the counts to be in groupings. The paper presents the general method and several special examples of histograms of actual counts being transformed into the form which they would have if there were no secondary multiplications of particles in the absorber. The histograms so corrected represent the undisturbed state of hodoscope registrations and can be used in work where the registrations of the penetrating component are usually affected by quite serious deformations. It seems essential to take these corrections into account in any analysis of experimental results since the registrations are carried out on the surface of the earth and the nucleon component of E.A.S. plays a considerable role (especially close to the axis of the shower: e.g. at an average distance of 15 m these corrections may come to more than 40%).
Изомагнитные взаимодействия поля Янга–Миллса
Acta Phys. Pol. 27, 693 (1965)
abstract
Рассмотрено минимальное взаимодействие спинорных и векторных полей с определённым спином (теории класса \(A\)) в нерелятивистском пределе. Найдено обобщение взаимодействия типа Паули и показано, что изотопическое жиромагнитное отношение является вектором в изопространстве.
Взаимодействия типа магнитного момeнтa поля со спином 1
Acta Phys. Pol. 27, 699 (1965)
abstract
Исследуются взаимодействия скалярных, спинорных и векторных полей с определённым спином (теории класса \(A\)) при включении безразмерных констант связи и констант размерности длины. Получена обобщённая группа изотопических преобразований. Даны примеры, когда включение констант размерности длины не нарушает изотопических свойств теории с безразмерными константами связи.
Theoretical Investigation of Oxygen Hydrides by the United Atom Method
Acta Phys. Pol. 27, 713 (1965)
abstract
The energies and one-centre single determinant wave functions of OH\(_{\mathrm {M}}^{\mathrm {p}}\) oxygen hydrides and of some isoelectronic systems were calculated. Orthonormalized Slater type orbitals were employed. It is shown that they give more accurate energies and bond lengths than the Fock–Petrashen type orbitals. Using semiempirical corrections, OH bond lengths for OH\(^-\), H\(_2\)O\(^+\) and H\(_2\)O\(^-\) were estimated. The possibilities of further applications of the model are also discussed.
Kirchhoff’S Integral for Multipole Radiation and Observation Points Near the Boundary of Shadow
Acta Phys. Pol. 27, 723 (1965)
abstract
The stationary phase method is applied for deriving formulas for wave motion in Kirchhoff’s theory, at points of observation near the boundary of shadow, in the case of the half-plane. Investigation is restricted to multipole fields of orders zero, one and two; the results conform to an interpretation in accordance with Young’s treatment of diffraction phenomena. This completes earlier papers by the same author dealing with the computation of Kirchhoff’s integral by the stationary phase method but considering only observation points distant from the shadow boundary.
Электромагнитные свойства элементарных частиц b модели \(B_2\)-cимметри
Acta Phys. Pol. 27, 737 (1965)
abstract
В работе исследуются электромагнитные свойства элементарных частиц в модели \(B_2\)-симметрии. Полученные результаты не противоречат экспериментальным данным.
O возможности обьединения группы Лоренца с группой унитарной симметрии
Acta Phys. Pol. 27, 749 (1965)
abstract
В работе обслуждается один U3 возможных способов объединения неоднородной группы Лоренца с группой \(SU_3\), в одну 18-параметрическую группу Ли. Предполагая коммутативность генераторов, соответствующих операторам полного изотопического спина \(I\), третьей ero компоненты \(I_z\), полного спина \(S_\varrho \), третьей его компоненты \(S_z\), и четырехмерного импульса \(p_\mu \), получаем, что BCE коммутаторы генераторов группы Лоренца с генераторами группы \(SU_3\) равны нулю.
Overlapping and Splitting of Spectral Lines
Acta Phys. Pol. 27, 753 (1965)
abstract
It is shown that the theory of pressure broadening developed previously by Fano and by the present author is applicable to the problem of line overlapping and line splitting. The connection with Van Hove’s analysis of the persistent effects is stressed. It is proved that the imaginary part of the complex line shift is positively definite provided that the superoperator of “dianogalization” is properly chosen.
Anisotropy of Fluorescence and Phosphorescence Emission of Organic Phosphors
Acta Phys. Pol. 27, 763 (1965)
abstract
Results of measurements of the anisotropy of fluorescence and phosphorescence emission for fluorescein, esculine (\(\beta \)-d-glycopyranoside-6,7-dioxycumarine) and POPOP [1,4 bis 2(5-phenyloxazolyl)-benzene] in vitreous boric acid and in methyl polymethacrylate at 20°C versus the emitted wavelength are presented. For fluorescein, esculine and POPOP in vitrous boric acid a dependence \(r(\lambda _{\mathrm {em}})\) of the emission anisotropy was found both for fluerescence \(r_{\mathrm {Fl}}(\lambda _{\mathrm {em}})\) and phosphorescence \(r_{\mathrm {Ph}}(\lambda _{\mathrm {em}})\). In methyl polymethacrylate solution, fluorescein and esculine yielded no dependence \(r_{\mathrm {Fl}}(\lambda _{\mathrm {em}})\), whereas POPOP showed a decrease of \(r_{\mathrm {Fl}}(\lambda _{\mathrm {em}})\) in the long wavelength region. The emission anisotropy was measured by method who eliminated the influence of the light of phosphorescence (Pohoski 1963). In this paper are also presented the modification of arrangement measuring the emission anisotropy of the phosphorescence.
Asymptotic Properties of the Electromagnetic and Gravitational Fields
Acta Phys. Pol. 27, 775 (1965)
abstract
The Newman–Penrose (N–P) method is applied for investigating the asymptotic properties of the electromagnetic and gravitational fields. A generalization of the Goldberg–Sachs theorem is proved.
Über Remanenzstrukturen, Ummagnetisierungsprozesse und Magnetisierungskurven in grossen Kobalteinkristallen. Teil I: Remanenzstrukturen
Acta Phys. Pol. 27, 783 (1965)
abstract
Es wird eine systematische Untersuchung der magnetischen Remanenzstrukturen und Magnetisierungskurven an Kobalt durchgeführt. Der im Versuch verwendete Korbalteinkristall hat die Form eines Quaders mit den Kantenlängen 12 mm, 8 mm und 7 mm, entsprechend in den Kristallrichtungen [0001], [01\(\bar {1}\)0] und [2\(\bar {1}\bar {1}\)0]. Die Beobachtungen der Remanenzstrukturen wurden mit Hilfe der wohlbekannten Pulverfigurenmethode ausgeführt, die zufolge der Zaponlackschicht-Technik eine bessere Deutung der äusserst komplizierten Figuren auf der hexagonalen Kristalloberfläche ermöglicht. Im Teil I wird gezeigt, dass der Typus der (äussert stabilen) Remanenzstruktur stark von der Richtung des Sättigungsfeldes (Erzeugungsfeldes) bezüglich der Kristallachsen abhängt. Im Teil II wird untersucht, welchen Einfluss ein homogenes äusseres Magnetfeld auf die Remanenzstruktur ausübt und welche minimale Feldstärke benötigt ist um die verschiedenen Remanenzstrukturen ineinander überzuführen. Die Beobachtungen zeigen deutlich, dass die sogenannte “freie” Domänenstruktur, die durch Abkühlung des Kristalls von der Curie-Temperatur erzeugt und üblich als charakteristische Struktur angesehen wird, eigentlich eine mehr oder weniger zufällige Kombination der regulären Remanenzstrukturen ist. Im Teil II wird i eine systematische Untersuchung der Neukurven in den Kristallrichtungen [0001], [01\(\bar {1}\)0] und [2\(\bar {1}\bar {1}\)0] durchfegürt und gezeigt, dass sowohl der Typus der Remanenzstruktur als auch die Richtung des zugehörigen Erzeugungsfeldes einen wesentlichen Einfluss auf die Gestalt der Neukurven ausüben. Es wird bewiesen, dass die Neukurven nur dann symmetrisch bezüglich Feldreversion ist, wenn das Erzeugungsfeld senkrecht zum Messungsfeld ist. Die Arbeit wirft somit ein neues Licht auf die bisherigen, inadäquaten Verstellungen über die Domänenstruktur einachsiger Ferromagnetika.
Differentiale der sphärischen Aberration dritter Ordnung nach Konstruktionselementen in einem Beliebigen optischen System
Acta Phys. Pol. 27, 799 (1965)
abstract
Die sphärische Längsaberration dritter Ordnung betrachtet man als Funktion von Konstruktionselementen, Linsendicken, Luftabständen und Flächenkrümmungen. Es werden Formeln entwickelt, welche Differentiale der sphärischen Aberration darstellen, wobei nur Glieder dritter Ordnung berücksichtigt werden. Es wird der Fall der konstanten Gegenstandlage, der konstanten Vergrösserung und des konstanten Gegenstandbildabstandes betrachtet.Fasc. 6, pages 807–993
Forbidden Lines in the Atomic Spectrum of Si I
Acta Phys. Pol. 27, 807 (1965)
abstract
Two new forbidden lines were obtained experimentally, from Si I: 6526.9 Å (\(M\)1), and 6589.7 Å (\(E\)2). Their existence was predicted from multipole radiation theory and from known values of metastable terms of Si I. Their intensity ratio was also measured and compared with the transition probability ratio known from the \(p^2\) configuration theory. Agreement between the theoretical predictions and experimental results was found to be satisfactory.
Post-Pauli Approximations and the Einstein–Infeld–Hoffmann Approximation Method
Acta Phys. Pol. 27, 815 (1965)
abstract
The non-unitary transformation used by Akhieser and Berestetskii in the second-order approximation in the transition from Dirac’s to Pauli’s formalism is generalized to an arbitrary order of approximation. The related recurrence formulae are obtained in terms of the Einstein–Infeld–Hoffmann approximation method
On a Relativistic Single-point Model of Elementary Particle
Acta Phys. Pol. 27, 821 (1965)
abstract
We consider a free point singularity in Minkowski space whose motion is determined by the variational principle \(\delta \int _{\tau _1}^{\tau _2}Ld\tau =0\), where \(\tau \) is the proper time of the singularity. The Lagrangian \(L\) is chosen so that its four-momentum \(p^\alpha \) shall be non-parallel with regard to its four-velocity \(u^\alpha \). To this aim we put \(L=m_0c(\sqrt {u^\lambda u_\lambda }+{\mit \Lambda }f(w_\lambda w^\lambda ))\), with \(w^\alpha \) denoting the four-acceleration of the singularity, \({\mit \Lambda }\) — a constant compensating dimensionally the first and second terms of the Lagrangian, and \(m_0c\) — a multiplicative constant. The function \(f(w_\alpha w^\alpha )\) is a scalar function of argument \(w\) \(w\) chosen in such a manner that \(L\) shall be of the simplest possible from, shall depend on \(w^\alpha \), and shall be a first integral of the equations of motion. For this, it is sufficient to put \(f(w_\alpha w^\alpha )=w_\alpha w^\alpha \) and \({\mit \Lambda }=-\frac {l^2}{c^3}\) with \(l\) denoting a constant having the dimension of a length and \(c\) — the velocity of light. On introducing two four-momenta …
Gravitational Radiation from a Pulse of Light
Acta Phys. Pol. 27, 831 (1965)
abstract
The gravitational field generated by a pulse of light is calculated in the Einstein weak-field approximation. By properly accounting for energy and momentum conservation at the light source, this gravitational field necessarily satisfies the usual auxiliary conditions, a feature lacking in earlier analyses. The equations of motion for a zero-pressure fluid of uniform density \(\mu _0\) acted upon by this gravitational field are then solved to obtain the total momentum communicated to the fluid. Following Zwicky, the momentum of the fluid is said to be gained at the expense of the momentum of the light pulse; this leads to the conclusion that the momentum of the light pulse decreases with the square of \(l\), the distance traveled by the light pulse. Applied to a single photon, this analysis leads to a red-shift law for which the fractional increase in wave length is: \(\frac {\Delta \lambda }{\lambda }=\frac {2}{3}\pi \mu _0 c^{-2}kl^2\), in which \(k\) is the gravitational constant.
Properties of Linear Hydrocarbons Depending on the Ratio of Neighbouring Resonance Integrals
Acta Phys. Pol. 27, 843 (1965)
abstract
Dealing jointly with olefins and paraffins as \(f\)-electron systems, it is proved that the constant ratio of neighbouring resonance integrals can be usefully assumed at 0.34 for \(\sigma \)-bonds in paraffins and at 0.60 for \(\pi \)-bonds in olefins.
On Sommerfeld’s Diffraction Problem for Multipoles
Acta Phys. Pol. 27, 849 (1965)
abstract
The Sommerfeld method of branched solutions is applied for solving the diffraction problem for the case of a wedge and multipole fields of the first and second orders. The paper brings a generalization of the well-known solution of the problem of diffraction on a wedge in the case of an isotropic spherical wave. By the method of the saddle point, the diffraction wave is computed for observation points distant from and near the boundary of shadow.
SC LCAO MO Treatment of Nonalternant Hydrocarbons and Ions
Acta Phys. Pol. 27, 859 (1965)
abstract
A possible extension of the validity of the SC LCAO MO method (with empirical parameters due to Gołębiewski and Nowakowski (1964)) 1o non-alternant hydrocarbons has been discussed. It is shown that this modification of the Hückel method allows for a more reliable prediction of bond lengths and probably of \(N \to V_1\) transitions, and in some well defined cases of dipole moments and \(N \to T_1\) transitions also. The correlation lines of experimental and calculated \(N \to V_1\) transitions are different for alternants and non-alternants. It is shown that a possible explanation of this fact lies in a different singlet-triplet splitting of the lowest orbital excitation.
Some Aspects of the Multiple Production of Pions by 16 GeV/\(c\) \(\pi ^-\) on Protons
Acta Phys. Pol. 27, 869 (1965)
abstract
170 inelastic interactions of 16 GeV/\(c\) negative pions in hydrogen with four and more charged secondaries have been studied. Angular and momentum distributions of secondary particles in the c.m.s. are given and certain momentum-emission angle correlations shown. A peripheral character of interactions is evident for four-prong events and less apparent for higher multiplicities. An evidence was obtained that the ratio of neutral-to-charged pions decreases with increasing multiplicity of charged prongs.
Dependence of the Volume Recombination Coefficient on the Viscosity and Temperature in a Group of Saturated Hydrocarbons
Acta Phys. Pol. 27, 881 (1965)
abstract
The coefficient of volume recombination of ions was measured in the following group of saturated hydrocarbons: C\(_6\)H\(_{14}\), C\(_7\)H\(+_{16}\), C\(_8\)H\(_{18}\), C\(_9\)H\(_{20}\), C\(_{10}\)H\(_{22}\) in the temperature region 15°C to 50°C. On the basis of Frenkel’s theory of holes formula for the dependence of the volume recombination coefficient of ions on the ion mobility, temperature and distance between neighbouring equilibrium positions of the ions in thermal motion has been derived. The results obtained are discussed on the basis of the existing theories of recombination and compared with an expression derived by this author.
Statistical Theory of Adsorption on Solid Surfaces with Different Adsorption Sites (Application to Adsorption in Conditions of the Müller Microscope)
Acta Phys. Pol. 27, 893 (1965)
abstract
A statistical theory of adsorption on crystallographical planes of a solid possessing various adsorption sites is given. The theory can also be applied in the case when adsorption takes place on different crystallographical planes of the solid. Since the interaction between adsorbed atoms and also the interaction of adsorbed atoms with different adsorption sites of the solid surface is taken into consideration, the state of thermodynamical equilibrium can be attained also in the case when not all adsorption sites with greatest binding energy are occupied. The results are used for the interpretation of experimental data on adsorption of metallic atoms in conditions of the Müller microscope (projector). It is found that the binding energy has a smaller influence on adsorption in the case of repulsional forces acting between adatoms than in the case of attractional forces. It is shown that for a given value of the surface coverage we can obtain different electron patterns of the same crystallographical plane if it once borders upon one group of crystallographical planes and again upon a group of other crystallographical planes. The influence of the different kinds of adsorption sites on the change in work function versus the surface coverage is also taken into account. It is shown that the model given by Crowell and Norberg does not take into account the interaction between adatoms.
On the Track-width Measurements in Nuclear Emulsion
Acta Phys. Pol. 27, 905 (1965)
abstract
A method of charge determination by measuring the width of tracks with small dip angle and short length was elaborated for particles of \(Z \leqslant 5\) coming to rest in nuclear emulsion. The resolving power of the method was investigated for three magnifications: \(\times 4400\), \(\times 11000\) and \(\times 24000\) and for four different residual ranges of length: 50, 100, 150 and 200/\(\mu \)m. Limits and confidence level of the applied method are given for illustration.
On the Multipole Moments Induced in Molecules by the Electric Fields of Several Light Waves
Acta Phys. Pol. 27, 913 (1965)
abstract
A consistent and general tensor formalism is proposed, allowing to compute easily the multipole electric moments induced in atoms or molecules by electric fields that are not only time-variable but are also spatially variable. The dependence of the \(r^{\mathrm {th}}\)-order molecular \(2^n\)-pole moments on the \(r^{\mathrm {th}}\) power of the electric fields of given order inducing them is described by multipole polarizability tensors of appropriate rank. The matrix elements of these tensors for the general case of a transition \(k \to l\) are derived explicitly in the first, second, third and \(r^{\mathrm {th}}\)-order approximations of quantum-mechanical perturbation theory. The formalism proposed can be applied for computing various non-linear effects the investigation of which is liable to provide information on the change undergone directly by the atoms or molecules under the influence of intense oscillating electric fields. The problem is discussed with regard to electric multipole light scattering and non-linear variation of the optical permittivity of a gas, as due to intense light beams from lasers
Effect of Dipolar Interactions on the Spin-wave Spectrum in Spiral Spin Structures
Acta Phys. Pol. 27, 929 (1965)
abstract
The energy of spin waves is calculated for a system of localized spin moments in a hexagonal crystal lattice, assuming a planar spiral configuration of spins in the ground state. Exchange interactions, uniaxial anisotropy energy and magnetic interactions of spins are included in the Hamiltonian of the system. Spin waves are introduced in the standard way as coherent motion of the spins about the ground state configuration. The Hamiltonian is reduced to a form bilinear in the spin-wave amplitudes, higher order terms being neglected. In the presence of dipolar forces this bilinear Hamiltonian cannot be diagonalized by finite number of steps since all spin wave modes whose wave vectors differ by integral multiples of the vector \(\vec {g}\) of the pitch of the spiral are mutually coupled. A perturbation approach is used to calculate the corrections to the spin-wave energy due to dipolar interactions.
Isospin Crossing Matrices for Photoproduction of Many Particles
Acta Phys. Pol. 27, 937 (1965)
abstract
General rules of constructing invariant amplitudes are proposed, even when the symmetry is broken in some way. The crossing matrix is always square and quasi-diagonal — the scalar, vector, and other parts of the amplitude do not mix in crossing. As the application of the formalism the invariant isospin amplitudes for the photoproduction process are chosen and crossing matrices evaluated.
A Unified Description of Space-time and Isospace
Acta Phys. Pol. 27, 947 (1965)
abstract
The assumption of an \(N\)-dimensional manifold with four open dimensions forming the the ordinary space-time and \(N-4\) closed dimensions forming an isospace is investigated. In the case \(N=7\) the properties of the nucleonic iso-dublet and the mesons pi and omega find a very natural explanation. The circumference of the closed dimensions seems to be related to the weak coupling constant.
Über Remanenzstrukturen, Ummagnetisierungsprozesse und Magnetisierungskurven in grossen Kobalteinkristallen. Teil II: Ummagnetisierungsprozesse
Acta Phys. Pol. 27, 955 (1965)
abstract
Es wird der Einfluss eines äusseren homogenen Magnetfeldes auf die im Teil I dieser Arbeit besprochenen regelmässigen Remanenzstrukturen untersucht, wobei das Feld jeweils parallel zu einer der drei Kristallrichtungen [0001], [01\(\bar {1}\)0] und [2\(\bar {1}\bar {1}\)0] und gleichzeitig senkrecht zur Richtung des entsprechenden Erzeugungsfeldes ist. Da die Feldstärke stufenweise bis zu etwa 20 kOe gesteigert werden konnte, war eine systematische Beobachtung der Ummagnetisierungsprozesse möglich, die der Überführung der verschiedenen Remanenzstrukturen ineinander entsprechen. Die diesen Prozessen zugeordneten Magnetisierungskurven werden im Teil III dieser Arbeit veröffentlicht und diskutiert, obwohl einige allgemeinere Folgerungen schon hier gezogen werden, da sie mit dem hier wiedergegebenen Beobachtungsmaterial in enger Verbindung stehen.
Über Remanenzstrukturen, Ummagnetisierungsprozesse und Magnetisierungskurven in grossen Kobalteinkristallen. Teil III: Magnetisierungskurven
Acta Phys. Pol. 27, 969 (1965)
abstract
Von den im Teil I dieser Arbeit untersuchten Remanenzstrukturen ausgehend, werden die Neukurven für die Kristallrichtungen [1000], [01\(\bar {1}\)0] und [2\(\bar {1}\bar {1}\)0] im Kobalteinkristall gemessen und der Einfluss der Domänenstruktur auf die Gestalt der Kurven studiert. An Hand dieser Neukurven werden auch die im Teil II dieser Arbeit analysierten Ummagnetisierungsprozesse erläutert und die dort abgeleiteten allgemeinen Folgerungen begründet. U.a. wird ausführlich bewiesen, dass die Neukurve nur dann symmetrisch bezüglich Feldreversion ist, wenn das der jeweiligen Remanzstruktur zugeordnete Erzeugungsfelds senkrecht zum Messungsfeld ist.
Enforced Electric Dipole Transitions in the Spectra of SnI
Acta Phys. Pol. 27, 987 (1965)
abstract
The arc spectrum of tin has been investigated by Meggers (1940), who tabulated the spectral lines observed and the values of terms for SnI. Four of the lines observed by Meggers coincide exactly with forbidden transitions between energy levels of the configuration \(5p6p\) and levels of the normal configuration \(5p^2\).
High-energy Behaviour of the Real Part of a Charge-exchange Amplitude
Acta Phys. Pol. 27, 989 (1965)