Vol. XXI (1962)
Fasc. 1, pages 3–89
Spin Wave Theory for Cubic Ferromagnetics III. Magnetization
Acta Phys. Pol. 21, 3 (1962)
abstract
The spontaneous magnetization of a ferromagnetic is evaluated for three cubic lattice types at low temperatures. The formula for the magnetization is derived by means of the formalism developed in the Part II of this paper. The magnetization is represented as a power series of the absolute temperature and the coefficients of the expansion are identical with those of Dyson’s formula. As to the term containing the fourth power of the temperature, only the part independent of the atomic spin quantum number is computed. A more exact calculation would involve consideration of higher range ladder diagrams.
Dielectric Polarization of Aliphatic Alcohols in Strong Electric Fields
Acta Phys. Pol. 21, 13 (1962)
abstract
In the course of the present investigation, dielectric saturation was measured in solutions of 2-methylpropanol-1, butanol-1, pentanol-1 and hexanol-l in benzene and hexane. Moreover, the dielectric permittivity, density and electric conductivity of these solutions were measured. Because of their considerable conductivity, the pulse method was employed. The results obtained in measuring dielectric saturation in the alcohols and their solutions differ from those of J. Malsch and H. Gundermann. The values of the permittivity variations as measured in solutions of the alcohols point to the presence of a new type of electric saturation effect, which is shared in common by all the systems investigated. The pure alcohols and their concentrated solutions exhibited a decrease of the permittivity in a strong electric field. Solutions of low alcohol concentration were found to exhibit an increase of the permittivity when immersed in the field. At a given concentration, which depends on the choice of alcohol and solvent, 2 maximum in the increase of the dielectric permittivity was found to occur, presenting the same value for all the alcohols investigated. This value, however, was found to be strongly dependent on the choice of the non-dipolar solvent. On expressing the dielectric permittivity variation as a function of the dielectric permittivity of the solution, it became possible to represent the foregoing relationship, for all the alcohols investigated, by means of one single graph for each solvent used. Similar dependences were found in the case of the variations of the molar polarization of solutions in an electric field. The differences in the shape of the saturation curve for solutions in benzene and hexane can be explained on ground of the existence of strong interactions between the molecules of the alcohol and those of the solvent. It would seem that, in addition to association due to hydrogen bonding between molecules of the alcohol, the solutions under consideration present alcohol-solvent molecular assemblies.
On the Relation Between Pressure and Flow in an Elastic Tube
Acta Phys. Pol. 21, 45 (1962)
abstract
The equation for the flow \(\dot {Q}\) (the mass of the fluid flowing in unit time through a cross-section of a tube with elastic walls, e.g. a blood vessel) is given. The solution of this equation yields an expression for \(\dot {Q}(t)\) in terms of \(p(t)\), the radius of the tube and the elasticity modulus and thickness of its walls.
The Fock Representation of the Duffin–Kemmer Algebra
Acta Phys. Pol. 21, 51 (1962)
abstract
A representation of the Duffin–Kemmer algebra is constructed by means of the Fock method. This representation, which corresponds to a new type of quantum statistics, has been considered in papers by H.S. Green and D.V. Volkov. The representation constructed in the present paper is applied for the sake of illustration to a non-relativistic particle system.
Beugungswelle im Falle einer beliebigen einfallenden Lichtwelle
Acta Phys. Pol. 21, 61 (1962)
abstract
Der Integrand im Helmholtz–Huygensschen Prinzip kann als die Normalkomponente eines quellenfreien Vektorfeldes \(V\) angesehen werden, das demgemüss für jede Losung w der Schwingungsgleichung durch ein Vektorpotential \(W\) darstellbar ist. \(W\) ist für die Kirchhoffsche Beugungstheorie von Bedeutung, da es die Abspaltung der Beugungswelle von der durch den Kirchhoffschen Ansatz gegebenen Wellenbewegung ermoglicht. Miyamoto und Wolf haben für das Vektorpotential \(W\) im Falle einer beliebigen Lösung \(u\) der Schwingungsgleichung einen einfachen Ausdruck angegeben, jedoch auf einem längeren und indirekten Wege. Im folgenden werden zwei einfache und zwar direkte Ableitungen dieses Ausdruckes mitgeteilt. Die erste Ableitung ist zwar ganz kurz, jedoch heuristisch. Die zweite Ableitung gelangt zum Vektorpotential \(W\) im wesentlichen auf dem geometrischen Wege, auf dem der Verfasser im Jahre 1917 die Beugungswelle von der Wellenbewegung abgespalten hat, die durch den Kirchhoffschen Ansatz für eine divergierende Kugelwelle gegeben wird. Es werden auch zwei neue Darstellungen für das Vektorpotential \(W\) angegeben. Sie ermöglichen eine einfache Ableitung seiner asymptotischen Entwicklung für Losungen der Schwingungsgleichung von der Gestalt \(u= A\) exp \(ikS\). Unter dieser Voraussetzung kann auch die Lage der singulären Stellen des Vektorpotentials angegeben werden. In erster Näherung kann man schlieBlich annehmen, dass die Beugungswelle im allgemeinen durch Reflexion der einfallenden Lichtwelle am beugenden Rande ensteht, wenn auch nicht immer der Reflexionswinkel gleich dem Einfallswinkel ist.
Correlation of Some Reactivity Criteria of the Resonance Theory and the Simple LCAO MO Method
Acta Phys. Pol. 21, 89 (1962)
abstract
The qualitative resonance theory of substitution and of addition, due to Pauling and Wheland, legitimates itself with much success. However, little reliable theoretical arguments for the validity of this theory are known. In this paper we show that, qualitatively, the reactivity criteria of the resonance theory follow from the simple LCAO MO theory.Fasc. 2, pages 99–193
Localization of Energy and Quantization of the Gravitational Field
Acta Phys. Pol. 21, 99 (1962)
abstract
The concept of families of extremal hypersurfaces enables a definition of quasi-inertial coordinate systems in terms of which covariant, local conservation laws for energy-momentum are formulated. Four supplementary metric tensor components are eliminated and a canonical quantization of the gravitational field is performed.
Differentiale der Schnittweiten eines beliebigen optischen Systems nach seinen Konstruktionselementen: Radien, Krummungen, Linsendicken, Luftabstanden und Brechungszahlen
Acta Phys. Pol. 21, 111 (1962)
abstract
Die Schnittweiten eines beliebigen optischen Systems werden als Funktionen seiner Konstruktionselemente behandelt. Einfache Formeln für die ersten Ableitungen und Differentiale der Schnittweiten nach Abständen zwischen brechenden Flächen, Radien oder Krümmungen und Brechungszahlen sind abgeleitet worden. Zuerst wird der Fall der konstanten Obiektschnittweite betrachtet. In diesem Falle werden einige Formeln für die zweiten Ableitungen und Differentiale abgeleitet. Dann wird angenommen, dass die Vergrösserung konstant ist und in diesem Falle werden auch Formeln für die Ableitungen des Abstandes Gegenstandbild gegeben.
Spin-wave Theory of MeFe2O4 Ferrite. Part I
Acta Phys. Pol. 21, 121 (1962)
abstract
A theory of spin waves in a MeFe2O4 ferrite is presented for the case of arbitrary angle between the magnetization vector and crystallographic axes and of different amplitudes of the spin waves at lattice points belonging to different translational sublattices. Dispersion formulas are derived for two special cases: (1) account being taken of the interactions between nearest \(A\)–\(B\) neighbours; (2) assuming equal amplitudes of the spin waves at \(A\)-sites and another equal amplitudes at \(B\)-sites.
Étude des interactions moléculaires par résonance magneétique nucléaire. Les complexes \(\pi \)
Acta Phys. Pol. 21, 131 (1962)
abstract
L’existence d’un effet 1 des composés aromatiques (benzène, naphtalène) sur différents accepteurs (halogénodérivés du méthane et de l’éthane)’a été prouvé par RMN. Une corrélation entre l’acidité et la structure de l’accepteur a été établie et un nouveau type de liaison hydrogène — liaison \(\pi \) multiple — a été trouvé. D’autre part nous avons constaté l’existence d’un effet r intermoléculaire du cycle des composés hétérocycliques: pyrrole, furane et thiophène. Cet effet est dû à la délocalisation du doublet d’électrons de l’hétéroatome.
Calculation of the Optical Potential with the Nucleon–Nucleon Phase Shifts in the Thomas–Fermi Approximation
Acta Phys. Pol. 21, 145 (1962)
abstract
The radial dependence of the optical potential for nucleon–nucleus scattering is calculated with the help of the empirical nuclear density. The nucleus is approximated locally by the Fermi model. The equation for the scattering in the nuclear medium is solved approximately, and the optical potential is expressed with the help of nucleon–nucleon phase shifts. In the numerical computations the Signell–Marshak phase shifts are used. The effect of the exclusion principle increases the depth of the real part and decreases the depth of the imaginary part of the optical potential in the center of the nucleus. The radius of the real part is practically equal to the radius of the density distribution, whereas the radius of the imaginary part is slightly bigger. The results are compared with the experimental estimates of the optical potential.
Remarks on the “Effective Target Mass”
Acta Phys. Pol. 21, 153 (1962)
abstract
The concept of the so-called target mass, as defined by Birger and Smorodin, is examined first within the general framework of kinematics and secondly by applying the one-pion-exchange model with pole approximation. It is emphasized that this quantity should be regarded as a para- meter measured by experiment, which can give, if properly defined and combined with other quantities, certain information concerning the collision mechanism — such as the magnitude of the invariant energy-momentum transfer. It may possibly lead to some confusion, however, if it is too naively interpreted as the mass of a latent particle or too straightforwardly related to the nucleon structure.
Die magnetische Struktur des anisotropen ferromagnetischen Einkristalls als angenäherter Grundzustand
Acta Phys. Pol. 21, 175 (1962)
abstract
Es wird eine quantentheoretische Methode zur Ableitung der magnetischen Struktur anisotroper ferromagnetischer Einkristalle angegeben. Die Struktur ergibt sich, wenn man in gewisser Näherung die mittlere Energie in einer bestimmten Klasse von Quantenzuständen, entsprechend minimalisiert. Das Verfahren ist einheitlich für alle Kristallgittertypen.
Magnetic Annealing Effect on the Anisotropy of Cobalt Ferrite Single Crystals
Acta Phys. Pol. 21, 185 (1962)
Field Emission Microscope Investigation of Iron Migration
Acta Phys. Pol. 21, 189 (1962)
Absorptions- und Fluoreszenzspektren von Fluorescein in PMAM
Acta Phys. Pol. 21, 193 (1962)
Fasc. 3, pages 199–307
On the End of the Motion of Solids on an Elastic Base
Acta Phys. Pol. 21, 199 (1962)
abstract
Solids moving on an elastic base when passing from the state of motion into that of rest as a result of friction, were found to enter into oscillations before coming to rest. The oscillations were recorded optically; the latter were attributed to elastic deformations of either body due to the forces tangential to the surface of their contact, and the stresses and strain arising in the base owing to compression by the sphere was investigated experimentally for the cases (a) of a sphere rotating about an axis perpendicular to the horizontal of the base and (b) of the sphere having come to rest as a result of friction. An analysis of the phenomenon is proposed on ground of the existing theories of contact between elastic solids.
Spin Wave Theory for Cubic Ferromagnetics. IV. The Coefficient of \(T^4\) in the Magnetization Series
Acta Phys. Pol. 21, 219 (1962)
abstract
The contribution to the magnetization from ladder diagrams obtained within the formalism of the grand partition function and thermodynamical perturbation calculus in an earlier paper are analysed. Therein it has been proved that the first order diagram yields the lowest contribution proportional to \(T^4\). Herein, the second and third order graphs are found to contribute to the coefficients of \(T^4\) corrections identical to those obtained by Dyson.
Remarks on the Order–Disorder Phenomena in Multicomponent Solid Solutions
Acta Phys. Pol. 21, 229 (1962)
abstract
The conditions determining the appearing of the superlattices in the multicomponent solid solutions are given. The exact definitions of the superlattices and their subdivision into sublattices are quoted. The zeroth approximation of phenomena in nonsteichiometric multicomponent solid solutions is discussed and the examples that not even the zeroth-approximation and the nearest neighbour assumption lead to different results for different solutions are given.
A Study of Geodesic Motion in the Field of Schwarzschild’s Solution
Acta Phys. Pol. 21, 239 (1962)
abstract
Geodesic equations are integrated in terms of elliptic functions. A classification of possible types of motion is given. Exact formulae for the perihelion motion, the third Kepler law, etc. are investigated. The problem of the physical validity of the results derived i.e. their independence of the coordinates used, is investigated. A method of studying the physical meaning of the formulae obtained is proposed; this consists in “translating” the data pertaining the motion under consideration into directly observable quantities, when using a telescope at a finite distance. A gravitational equivalent of Rutherford scattering is also investigated.
Contrast Reduction in Mirror Objectives
Acta Phys. Pol. 21, 269 (1962)
abstract
A relative contrast reduction function for aberrations of arbitrary order is derived. The result obtained is discussed for aberrations up to the fifth order inclusively, with the frequency ranging \(0\eqslantless 25\eqslantless 0.5\) and the covering degree \(0\eqslantless n\eqslantless 0.5\). The values of the coefficients given in Tables I–VII make it possible to compute the relative contrast reduction function for each particular aberration. As an example, the changes in contrast in the course of the defocussing process of an ideal mirror objective are considered and it is proved that the central covering of the beam affects but slightly the magnitude of the permissible defocussing.
Quantum Informational Thermodynamics
Acta Phys. Pol. 21, 281 (1962)
abstract
It is shown, that, for every physical quantity \(A\) whose spectrum is discrete and the series \(\sum \limits ^{\infty }_{k=1} e^{c\lambda }k\) (where \(\lambda _, \lambda _2 \dots \) are proper values of \(A\)) is convergent for some constant \(c\), “\(A\)-thermodynamics” can be constructed in which all three laws of the usual thermodynamics hold. It is also proved that such a theory cannot be constructed for any other operator. For certain operators \(A\) such a general approach leads to the new concept of maximal (finite) \(A\)-temperature, i.e. to the finding that the \(A\)-temperature can vary within a finite interval only. In contradistinction to the usual Landau–Bloch–von Neumann quantum statistical mechanics, the notions of “mixed state” and “statistical operator” are not employed. The entire theory is based on the concept of information (Shannon 1918, Ingarden and Urbanik 1961) and the “principle of maximum information” (Jaynes 1957) and may therefore be termed “quantum informational thermodynamics”. The theory is illustrated by simple examples.
The Isotope Shift Effect in the Optical Radiation of Radioactive Nuclide 15263Ey
Acta Phys. Pol. 21, 305 (1962)
Nuclear \(g\)-factor of the 113 keV Rotational Level in 177Hf
Acta Phys. Pol. 21, 307 (1962)
abstract
Nuclear \(g\)-factor of 113 keV state in 177Hf was measured using the method of integral angular correlation in the external magnetic field of 26 300 gauss. The value \(0.245 \pm 0.032\) was obtained.Fasc. 4, pages 313–439
Asymmetry in the Angular Distribution of the Neutrons Emitted in the \(\mu \)-meson Capture Process in Calcium
Acta Phys. Pol. 21, 313 (1962)
abstract
The asymmetry in the angular distribution of the neutrons emitted in negative muon capture in calcium was measured by the method of spin precession in the magnetic field. The value of the asymmetry coefficient was found to be \(A= -(0.066\pm 0.022)\). The value and sign of the asymmetry coefficient indicate that the ratio of the constant of the induced pseudoscalar to that of the axial–vector interaction \(g_p,/g_A\) has a positive sign and a value in excess of that predicted theoretically.
Dynamical Effects of X-ray Interference in Silicon Single Crystals
Acta Phys. Pol. 21, 329 (1962)
abstract
The shapes of the transmission and reflection curves for ideal Si single crystals are computed from the Ewald–Laue dynamical theory of X-ray interference; these show anomalously weak absorption to occur most markedly in the case of crystals 1.6–3.0 mm thick, and anomalously strong absorption — at a thickness of 0.2–1.6 mm. Experiments revealed the presence of a “Strahlenfächer” of anomalous absorption in the silicon single crystal investigated.
Diffraction Scattering of Deuterons on Non-spherical Nuclei
Acta Phys. Pol. 21, 339 (1962)
abstract
The Drozdov–Blair diffraction scattering model is extended to the case of deuteron scattering on nuclei with quadrupole surface deformation. The deuteron diffraction scattering is treated as a superposition of the diffraction scatterings of both the neutron and proton of the deuteron by applying the Achiezer–Sitenko method. The angular distributions obtained are almost identical with those obtained with the simple Drozdov–Blair model (except at larger angles where the cross section calculated in the present work drops down slightly faster), provided one diminishes the \(R_0\), parameter to about its alpha particles scattering value and increases the value of |\(\beta \)|. The results are illustrated in the examples of the 18O, (\(d, d’\)) 18O*, 24Mg(\(d, d’\)) 24Mg*, and 24Mg(\(d, d\)) 24Mg reactions.
Electric Conductivity of Ni Fe2 O4 Ferrite
Acta Phys. Pol. 21, 351 (1962)
abstract
The electric conductivity of single and polycrystalline Ni Fe2 O4 ferrite samples was investigated versus the measuring electric field strength \(E\) and the temperature \(T\). From the experimental results, the conductivity \(\rho \) can be expressed by the formulas \[ \rho = C \exp \left [-\frac {\varepsilon }{2KT}+\alpha \left (E-E_0\right )\right ]\qquad \mathrm {for}\quad E_0\lt E\lt E_k\] \[\rho = C \exp \left [-\frac {\varepsilon }{2KT}\right ] \qquad \mathrm {for}\quad E\lt E_0\,. \] The temperature-independent values of \(E_0\approx 6\) V/cm and 30 V/cm were found for the mono and polycrystalline sample, respectively. On the other hand, both kinds of sample yielded a value of \(E_k\approx 350\) V/cm at room temperature, which decreased towards higher temperatures in accordance with the formula \[E_K = E_{\infty } \exp \left (\frac {\gamma }{kT}\right )\quad \gamma - =0084~\mathrm {eV}.\]
Photoconductivity and Semiconductivity of the Keynon–Banfield Radical
Acta Phys. Pol. 21, 359 (1962)
abstract
The surface conductivity of crystals of the Keynon–Banfield radical in the dark and after UV illumination were measured. Dark conductivity rose exponentially with the temperature, “activation energy’’ ranging from 1.0 to 1.7 eV. After illumination, a slow rise in conductivity was observed, probably related to the formation of an unstable intermediate in the course of photooxidation. The absorption spectrum of the Keynon–Banfield radical in methanol solution is also given.
On the Possibility of Foresight of the Whiskers Growth Conditions from the Metal Vapour Pressure in the for Med Temperature Gradient
Acta Phys. Pol. 21, 365 (1962)
abstract
The slopes of the tangens at the points of optimal temperature for Cd and Zn on the graphs log \(p\) versus \(t\) are equal; the authors have applied this regularity for the subgroup Ag, Au and Cu. The analytic method of the estimation of the optimal temperature is given provided it is known such a temperature at least for one metal in the given subgroup or group in the periodic system and the melting points of metals not differ strikingly. The considerations have been based on the macroscopic thermodynamics and their conclusion supplies an analogy with Sear’s theory of the phase forming a supersaturated metal vapour.
On \(\beta \) Conductivity in Germanium (Conductivity of Germanium Induced by Electron Bombardment)
Acta Phys. Pol. 21, 371 (1962)
abstract
The present investigation deals with the conductivity of homogeneous single germanium crystals, as produced by electron bombardment. The mean effective energy \(\varepsilon \) of electron–hole pair generation was measured. The method of exclusion was applied, making possible the simultaneous determining of \(\tau \) and \(\varepsilon \) for the additional current carriers generated. For energies 1.5 keV < \(E_0\lt 30\) keV of the electrons used in bombardment, a value of \(\varepsilon =3.84\pm 0.4\) eV resulted. For energies \(E_0 \lt 2\) keV, the essential part is played by the non-sensitive layer on the crystal surface. From a comparison of the results obtained in measuring \(\varepsilon \) and the characteristic losses, conclusions are made as to the role of plasmons in the mechanism leading to the appearance of \(\beta \)-conductivity in germanium.
Effective Mass of Holes in InSb
Acta Phys. Pol. 21, 389 (1962)
abstract
An analysis of the state density mass is proposed, basing on Kane’s theory (1957) of the valence band structure in InSb. This mass is shown to depend on the temperature, a result in qualitative agreement with the experimental data. The state density mass of the holes was determined from measurements of the intrinsic concentration. The temperature dependence of the effective mass is due to complex structure of the valence band. The hole mobility is computed, and it is proved that the temperature dependent mass yields good agreement between the theory and experimental data if one assumes a phonon-optical scattering mechanism.
Thermoelectromotive Force and Nernst–Ettingshausen Effect in InSb
Acta Phys. Pol. 21, 399 (1962)
abstract
In Part I, general formulas are proposed for the thermoelectromotive force and Nernst–Ettingshausen (N–E) constant in the case of general non- parabolic structure of the energy band and strong degeneracy of the electron gas. The sign of the N–E effect is shown to depend not only on the mechanism of scattering, but moreover on the shape of the band; hence, conclusions as to the mechanism of scattering from the sign of the N–E effect alone can be erroneous. Part II brings an analysis of the N–E effect and thermoelectromotive force in \(n\)-type InSb. On the assumption of the shape of the conductivity band proposed by Kane, both effects are evaluated as functions of the electron concentration. Agreement between theory and experiment is achieved for scattering on optical phonons in the case of pure samples, and for a joint mechanism involving optical phonons and ionized impurities in the case of doped samples. The experimental change in sign of the N–E effect towards higher electron concentrations results from non-parabolicity of the conductivity band.
Eindeutigkeitsbeweis für das elektromagnetische Sprungwertproblem
Acta Phys. Pol. 21, 415 (1962)
abstract
Es wird ein Beweis des Eindeutigkeitssatzes für das Sprungwertproblem eines zeitlich harmonisch-periodischen elektromagnetischen Feldes mitgeteilt.
Calculation of the Optical Potential with the Nucleon–Nucleon Phase Shifts in the Thomas–Fermi Approximation II
Acta Phys. Pol. 21, 423 (1962)
abstract
The radial dependence of the optical potential for nucleon–nucleus scattering is calculated with the help of the empirical nuclear density. The nucleus is approximated locally by the Fermi model. The equation for the scattering in the nuclear medium is solved approximately, and the optical potential is expressed with the help of nucleon–nucleon phase shifts. In the numerical computations the latest Yale phase shifts are used. In comparison with the analogical calculation based on the Signell–Marshak phase shifts, the radius and the surface thickness of both the real and the imaginary part of the optical potential practically do not change; the depths of the optical potential increase — a little (less than 8%, i.e. less than 2 MeV) for the imaginary part and up to 35%, i.e. up to 15 MeV, for the real part — in the center of the nucleus.
Isotope Shifts in the Cd II Lines \(\lambda \) 3535 Å and \(\lambda \) 3250 Å
Acta Phys. Pol. 21, 429 (1962)
Neue Pulverfiguren auf der Oberflache eines Fe–Si-Einkristalls
Acta Phys. Pol. 21, 433 (1962)
ERRATA
Fasc. 5, pages 445–549
Sur les constantes de force des composés hydrogénées du type H2X de l’oxygène, du soufre et du sélénium
Acta Phys. Pol. 21, 445 (1962)
abstract
Le but de ce travail était d’évaluer les constantes de force et les constantes d’anharmonicité des molécules H2S et H2Se pour les comparer aux constantes des molécules analogues H2O, H2S et H2Se (pour la molécule H2Te il y à trop peu de données (Jarrel et Straley 1949).
Über ein mit einem elektromagnetischen Feld verknüpftes, Quellenfreies Tensorfeld und dessen Tensorpotential
Acta Phys. Pol. 21, 451 (1962)
abstract
Das elektromagnetische Helmholtz-Huygenssche Prinzip kann u.a. in zwei verschiedenen, einander jedoch bei Anwendung auf Lösungen Maxwellscher Gleichungen mathematisch und physikalisch vollständig äquivalenten Fassungen formuliert werden, nämlich einer Larmorschen und einer Kottlerschen. Jede dieser beiden Fassungen kann mit Hilfe zweier Tensorfelder \(\hat {V}_e\) und \(\hat {V}_m\) dargestellt werden, die zur Angabe des elektrischen bzw. magnetischen Feldes dienen und die durch eine gegebene Lösung der Maxwellschen Gleichungen eindeutig definiert sind. Da die Divergenzen dieser Tensorfelder verschwinden, können sie durch Tensorpotentiale dargestellt werden, die eine Umformung des elektromagnetischen Helmholtz-Huygensschen Prinzips in zwei neue Gestalten ermöglichen. Diese sind für die elektromagnetische Kirchhoffsche Beugungstheorie von Bedeutung, da sie mit Hilfe eines zum Stokesschen Satze analogen, für Tensorfelder gültigen Integralsatzes die Beugungswelle abzuspalten gestatten und zwar für beliebige einfallende Lichtwellen. Um auf Grund der Larmorschen und der Kottlerschen Fassung des elektromagner tischen Helmholtz–Huygensschen Prinzips das Tensorpotential beliebiger elektromagnetischeFelder in einer relativ einfachen Gestalt zu erhalten, wird eine geometrische Methode benützt, die vom Verfasser schon früher zur Ableitung des Miyamoto–Wolfschen Vektorpotentials im Falle der skalaren Schwingungsgleichung verwendet wurde.
The Field Method of Obtaining the Conservation Laws and the Lagrangian
Acta Phys. Pol. 21, 469 (1962)
abstract
In this paper we derive the conservation laws straight from the field equations. From them we obtain the Lagrangian, leading to the equations of motion.
Green’s Function for Cubic Ferromagnetics. I. One-particle Green’s Function
Acta Phys. Pol. 21, 481 (1962)
abstract
One-particle Green’s function is introduced. The magnetization for a cubic crystalline ferromagnetic is obtained as the sum of a constant term (saturation magnetization) and the one-particle Green function.
Green’s Function for Cubic Ferromagnetics. II. Two-dimensional Time-dependent Green’s Functions
Acta Phys. Pol. 21, 491 (1962)
abstract
The Bogolyubov and Tiablikov theory of retarded and advanced Green’s functions formulated for one-electron atom ferromagnetics is generalized to many magnetic electron atoms.
Green’s Function for Cubic Ferromagnetics. III. Two-dimensional Time-dependent Green’s Functions. Spontaneous Magnetization
Acta Phys. Pol. 21, 501 (1962)
abstract
The spontaneous magnetization is evaluated with the help of the two-dimensional time-dependent Green function. Two cases are considered: the one concerns low temperatures, whereas the other deals with temperatures near the Curie point. In the last case, the magnetization formula derived provides a degree of agreement with experiment silimat to that predicted by the well-known Weiss theory.
Ferroelectrically Active A-ions in ABO3 Substances
Acta Phys. Pol. 21, 509 (1962)
abstract
The dipole arrangement is discussed that will develop in perovskite-type substances when electric dipoles are formed by displacement of \(A\) ions. It is shown that there are possible only the antiferroelectric arrangements as the crystal transforms from the non-polar to the polar state. The ferroelectric dipole arrays do not appear.
Metallic-dielectric Mirrors with High Reflectivity in the Near Ultra-violet for the Fabry–Perot Interferometer
Acta Phys. Pol. 21, 523 (1962)
abstract
Metallic-dielectric semitransparent mirrors for the Fabry–Perot interferometer in the spectral region of 3000–4000 Å were prepared by evaporation in vacuo, using Al as the metal and MgF2, and Sb2O3 as dielectrics. The coefficients of reflection \(R\) and of transmission \(T\) of the aluminium–dielectric mirrors were measured and compared with the optical parameters of aluminium and of all dielectric mirrors. The aluminium-dielectric mirrors obtained by the present method turned out to possess parameters \(R, T, A\) in the near ultraviolet comparable to the optical parameters of all dielectric mirrors and simultaneously to present a reflection coefficient in the visible region sufficiently large for convenient adjustment of the Fabry–Perot interferometer. Hence these mirrors present greater advantages than all dielectric and than aluminium mirrors, which have a much higher coefficient of absorption.
Scattering of Thermal Neutrons on CH3NH2 Molecules in the Liquid State
Acta Phys. Pol. 21, 529 (1962)
abstract
The total effective cross section of methylamide molecules in the liquid state with respect to thermal neutron scattering was measured in the energy range of 10 meV to 280 meV, at three temperatures of the sample. The effective cross sections were found to be independent of the temperature of the sample, but to depend on non-elastic neutron scattering related to excitation of several close-lying vibrational states of the molecule.
Sur la fonction de potentiel de la molécule d’éthylène
Acta Phys. Pol. 21, 537 (1962)
Electric Properties of Copper-doped Cadmium Arsenide (Cd3As2)
Acta Phys. Pol. 21, 541 (1962)
abstract
The electrical properties (resistivity, Hall coefficient, magneto-resistivity) of copper-doped Cd3As2 in the temperature range between 100° and 700°K are presented. In all samples containing copper, the carrier concentration was found to be of the order of \(1\times 10^{18}\) cm\(^{-2}\), whereas in the pure Cd3As2 it was about twice as large (\(2\times 10^{18}\mathrm {cm}^{-3}\)). The transition into the intrinsic range took place at room temperature (\(\sim 310\)°K). From the temperature dependence of the Hall coefficient and the conductivity, it is plausible that, in the copper-doped Cd3As2, donor \(\Delta E’\) from the equation \(n~n_0 \mathrm {exp} (\Delta E’/kT)\), calculated from the difference between the slopes of the linear sections of the function \(\mathrm {lg}\, R=f \frac {1000}{T}\) for pure and copper-doped Cd3As2 amounts to 0.04 eV. The \(p\)-type material was not obtained even at copper concentration up to 1% weight.
Spinless Interaction of Slow Neutrons with a Particular Type of Rectangular Complex Cavity
Acta Phys. Pol. 21, 549 (1962)
Fasc. 6, pages 557–659
Generalization of the Lorentz–Lorenz Dispersion Formula for Electric Quadrupole Radiation
Acta Phys. Pol. 21, 557 (1962)
abstract
The quantum correspondence theory is proposed for a homogeneous isotropic medium, basing on the Oseen classical molecular theory of light propagation, refraction and reflection. It was assumed that due to the perturbing field the hydrogen-like atoms (neglecting spin) emit electric dipole or electric quadrupole radiation or both kinds of radiation simultaneously. Taking into account Ewald–Oseen’s extinction theorem we obtain, from the above semi-classical theory, the new Lorentz–Lorenz dispersion formulae for the electric quadrupole radiation and for the electric dipole and quadrupole radiation, emitted simultaneously. All formulae mentioned above contain a term relating to J.J. Thomson’s radiation.
Generalization of Fresnel’s Reflection and Refraction Formulae for Electric Quadrupole Radiation
Acta Phys. Pol. 21, 575 (1962)
abstract
Fresnel’s formulae for the reflection and refraction of light are obtained by applying the Ewald–Oseen extinction theorem within the framework of a specially developed quantum correspondence theory in a homogeneous isotropic medium consisting of hydrogen-like atoms (omitting spin). The assumption was made, that the atoms of the medium under influence of a perturbing field emit an electric dipole and quadrupole radiation, joint or separate. Thus, by a semi-classical procedure, generalized Fresnel’s formulae have been derived for all kinds of the above mentioned radiations. The Fresnel formulae for electric quadrupole radiation reveal polarization relations, that differ from those obtained for electric dipole radiation. If for example, Brewster’s angle \(\phi +\psi =\pi /2\) is used, the linear polarization of light does not occur in the case of electric quadrupole radiation.
A Simple Theory of the Photodisintegration of 9Be at Low Energies
Acta Phys. Pol. 21, 583 (1962)
abstract
The cross section for the photodisintegration process of 9Be in the energy range 1.667–5 MeV was calculated on the basis of the molecular model of 9Be. The parameters were chosen so as to obtain the best adjustment to the experimental curve of M.J. Jakobson. The three peaks of this curve result from electric dipole transitions from the ground state of 9Be to: (1) \(S_{1/2}\), neutron state with 8Be left in its ground state (peak at 1.7 MeV), (2) \(D_{3/2}\) neutron state with 8Be left in its ground state (peak at 2.9 MeV), (3) \(S_{1/2}\) neutron state with 8Be left in the excited state of 2.9 MeV (peak at 4.6 MeV). The experimental results of J.H. Carver, E. Kondaiah, B.D. McDaniel were also partly explained.
Reciprocity Theorems and Babinet’s Principle in Kirchhoff’s Theory of the Diffraction of Electromagnetic Waves
Acta Phys. Pol. 21, 597 (1962)
abstract
It is proved that the reciprocity theorems known from classical electrodynamics are fulfilled by Kottler’s formulas if the point of observation is situated in the half-space of shadow. In this case, Babinet’s principle in the form known from the scalar theory is also fulfilled. On the other hand, if the point of observation is in the half-space of light, there is some similarity between the reciprocity theorems and Babinet’s theorem. In spite of the mathematically correct formulation, as Kirchhoff’s solutions devoid of a clear physical meaning can appear.
Homogeneous Variational Principle w Third Order Derivatives in the Special Theory of Relativity
Acta Phys. Pol. 21, 609 (1962)
abstract
The present investigation deals with motion of a free particle in Minkowski space (with velocity both smaller than and equal to that of light) as determined by the homogeneous variational principle \(\delta \int \limits ^{\pi _2}_{\pi _1} L\mathrm {d}\pi =0\), wherein the Lagrangian \(L\) of the particle depends on derivatives with respect to \(\pi \) up to order three inclusively. Such a particle will be referred to as a particle of order three. \(\pi \) is an arbitrary parameter which, in the case of light velocity, will be assumed as being the time \(t\), and in that of velocity lesser than that of light — as being the proper time \(\tau \, t\). The Lagrangian \(L\) is required to be independent of the \(x^{\alpha }\), to assume neither zero nor infinite value for light velocity, and to be a scalar \(\dots \)
Magneto-optical Effects in InSb
Acta Phys. Pol. 21, 637 (1962)
abstract
The absorption coefficient \(\alpha \), Faraday rotation \(\mit \Theta \) and ellipticity \(\mit \Delta \) are computed for the \(n\)-type InSb. The effects computed are related to the free carriers in semi-conductors. The possibility of different kinds of carriers appearing simultaneously is taken into account in the computations, e.g. electrons, heavy holes, and light holes in the intrinsic region.
Laboratory Equipment and Techniques Apparatus for Counting the Number and Integral
Acta Phys. Pol. 21, 645 (1962)
abstract
A simple device used to measure the sum of the lengths of segments viewed under a microscope and to record the number of measured segments is described.
Instrument for Measurements of Multiple Scattering
Acta Phys. Pol. 21, 649 (1962)
abstract
A semi-automatic instrument for calculation and registration of multiple scattering data in nuclear emulsion measurements is described.
Gap Meter
Acta Phys. Pol. 21, 655 (1962)
abstract
A semi-automatic instrument for ionization measurements in nuclear emulsions is described. The apparatus, adapted for a laboratory microscope, consists of an electronics counting system and a stage-feed mechanism.
Microscope Stages for Nuclear Emulsion Measurements
Acta Phys. Pol. 21, 659 (1962)