Vol. XXII (1962)
Fasc. 1, pages 3–129
Spin Waves and Phonons in Ferromagnetics I. The Hamiltonian
Acta Phys. Pol. 22, 3 (1962)
abstract
The Hamiltonian of a cubic crystalline ferromagnetic is derived within the framework of the spin wave formalism and on the assumption of longitudinal lattice oscillations. It is assumed that the interaction between spin waves and phonons in a weak external magnetic field is small.
Spin Waves and Phonons in Ferromagnetics II. Spontaneous Magnetization at Low Temperatures
Acta Phys. Pol. 22, 9 (1962)
abstract
The effect of lattice oscillations on the spontaneous magnetization of a cubic ferromagnetic at low temperatures is examined. Interaction of spin waves and lattice waves is proved to produce a small increase in the spontaneous magnetization.
Spin Deviations and Phonons in Ferromagnetics III. Spontaneous Magnetization Close to the Curie Point
Acta Phys. Pol. 22, 21 (1962)
abstract
The influence of the lattice oscillations on the spontaneous magnetization of a cubic ferromagnetic in the temperature range close to the Curie point is investigated. The spontaneous magnetization is proved to diminish owing to interaction between the spin deviations and phonons.
Depolarization of Fluorescence of Dye Solutions by Thermal Motion of the Molecules
Acta Phys. Pol. 22, 29 (1962)
abstract
By means of a high precision polarimeter (Bauer and Rozwadowski), the fluorescence emission anizotropy of uranine in its dependence on the viscosity of the solution for different binary solvents (glycerol + ethanol, glycerol + methanol, glycerol + water) was investigated. In cases of even small water content in the solvent, the well known deviations from the relations resulting from F. Perrin’s theory of depolarization of fluorescence of solutions by thermal rotation of the luminescent molecules were found to occur. Such deviations are explained by the effect of water on the solvation envelope of the luminescent molecule. The volume and constitution of the solvation layer varies with the water percentage of the solvent. Hence, the moment of torsion acting on the luminescent molecule changes, affecting the depolarization by torsional vibrations of the molecules, not considered in Perrin’s theory. The change in volume on the solvation layer affects depolarization by thermal rotation. Such changes in volume were found by one of us (Bauer) in the course experiments to be published shortly.
Über magnetische strukturen im einachsigen ferromagnetischen Einkristall
Acta Phys. Pol. 22, 37 (1962)
abstract
Auf Grund eines neuen quantentheoretischen. Rechnungsverfahrens werden im einachsigen ferromagnetischen Einkristall von der Form eines Quaders die beiden prinzipiellen, bisher einander widersprechenden magnetischen Strukturen nochmals untersucht, und zwar die Struktur von Bloch und diejenige von Landau und Lifschitz. Die sogenannten Randbezirke werden mit- betrachtet, das äußere Magnetfeld dagegen weggelassen. U. a. wird bewiesen, dass beide Strukturen möglich sind je nachdem, ob die Kristalldicke in der magnetisch bevorzugten Richtung größer oder kleiner als ein kritischer Wert ist. Dabei ergibt sich notwendig eine Modifizierung beider Strukturen, die viele Erfahrungstatsachen weit besser zu erklären vermag.
Influence of Intermolecular Forces on the Magnetic Birefringence of Imperfect Gases and Their Mixtures
Acta Phys. Pol. 22, 65 (1962)
abstract
The molecular Cotton–Mouton constant \(C_m\) for imperfect gases and their mixtures is represented in the form of a series: \(C_m = A_C+B_C\rho +\dots \) The first virial coefficient \(A_C\) of this series describes the magnetic birefringence of perfect gases. The second virial coefficient \(B_C\) takes account of the influence of intermolecular two-molecule interactions upon the \(C_m\) constant. It is calculated for some molecular models. In these calculations, besides the usual central forces, also anisotropic dispersion forces and various tensorial intermolecular forces arising from interaction between dipole or quadrupole gas molecules have been taken into consideration. Also, additional contributions to \(B_C\) resulting from the existence of molecular electric or magnetic fields in real gases are computed. Numerical estimations are given, which reveal the rôle of the individual molecular factors in the magnetic birefringence of real gases. Finally, general formulas for the electrostatic interaction energy of two arbitrary charge distributions, and for inductive interaction of such systems are derived.
Some Experiments on the Electric Monopole Transition in 234U
Acta Phys. Pol. 22, 91 (1962)
abstract
The de-exctitation of the 811 keV O+-level in 234U nucleus was investigated by means of coincidences with the beta (—) radiations of \(^{234}\mathrm {Pa}^m\) preceding it. From the measurements performed the ratio of intensities of the 811 keV-EO conversion to the 768 keV-E2 (0—2) gamma transition was obtained as \(1.30\pm 0.30\). The life-time of the first O+ excited state from delayed coincidence experiments was estimated as \(\tau \leq 0.4\times 10^{-10}\)sec., which leads to the monopole strength parameter \(\rho \gt 0.07\). It is pointed out that the 811 keV O+-level in 234U is a \(\beta \)-vibrational one.
Certaines remarques sur l’applicabilité de l’approximation coulombienne au calcul des probabilités de transition dans les atomes et des forces d’oscillateur des raies spectrales
Acta Phys. Pol. 22, 99 (1962)
abstract
L’article donne la comparaison des valeurs expérimentales des forces d’oscillateur des raies spectrales des éléments de la I. II., et la IITième colonne du tableau de Mendéléeff avec les valeurs théoriques calculées dans l’approximation coulombienne et dans les approximations plus exactes. On constate que l’approximation coulombienne donne des bons résultats pour des raies spectrales provenantes des transitions parmi les niveaux peu élevés s’il n’y a pas au voisinage de ces niveaux d’autres niveaux qui peuvent causer des perturbations. Pour ces raies les résultats de la méthode coulombienne sont aussi bons ou parfois même meilleurs que les valeurs calculées dans les approximations plus exactes de la configuration unique. Uniquement calcules dans lesquels l’effet de mélange des configurations est pris en considération donnent des valeurs meilleures que l’approximation coulombienne.
Some Remarks on Retarded and Advanced Green’s Functions for Isotropic Ferromagnetics
Acta Phys. Pol. 22, 125 (1962)
Observation of Thermoelectrons by Means of Geiger–Müller Counters
Acta Phys. Pol. 22, 129 (1962)
Fasc. 2, pages 137–199
Luftspitzenzaähler als Detektor der Exoelektronen
Acta Phys. Pol. 22, 137 (1962)
abstract
Die Konstruktion und die Eigenschaften des offenen Luftspitzenzähler nach Geiger der als Exoelektronendetektor eingesetzt wird, wird diskutiert. Eigene Erfahrungen zu diesen Fragen werden besprochen.
On the Photoconductivity of Polycrystalline Cadmium Sulfide Layers
Acta Phys. Pol. 22, 151 (1962)
abstract
The sensitivity of polycrystalline photoconductor layers was investigated versus the temperature and time of sintering. The presence of oxygen during the activation process was found to be essential in sensitizing the layers.
Measurement of Saturation Magnetostriction in Nickel under Hydrostatic Pressure Up to 10000 Atm
Acta Phys. Pol. 22, 159 (1962)
abstract
Techniques for measuring magnetostriction under conditions of high hydrostatic pressure are described. It is shown that resistance strain gauges can be used with success for pressures up to 10000 atm. A new measuring device based on the principle of a cantilever and optical amplifier with cemented resistance strain gauges as zero pointer of the Wheatstone bridge is also described. Strain sensitivity of \(2 \times 10^8\) per division of the indicating instrument is easily obtained in this way. The accuracy of measurement depends on that of the gauge factor of the strain resistance gauge cemented onto the specimen. The saturation magnetostriction of nickel was found to increase monotonically with pressure at the rate of \((1.1 \pm 0.2) \%\) per 1000 atm.
Two Magnon Relaxation in a Disordered Ferromagnetic
Acta Phys. Pol. 22, 173 (1962)
abstract
A model of a disordered ferromagnetic with two spins, \(S\) and \(S\)’, distributed at random over lattice sites is discussed. The spin–spin relaxation time determined by two-magnon scattering processes in the degenerate spin-wave spectrum is calculated. Anisotropic coupling of spins of a dipolar type is taken into account. The case of cubic lattices is considered. The general formula for the spin–spin relaxation time is given and two special cases are discussed in detail, namely the case of a small paramagnetic impurity and the case of a diamagnetic impurity (dilute ferromagnetic). The result for the last case can be applied to a simplified model of nickel crystal.
Gdańsk C-14 Dating Laboratory Measurements
Acta Phys. Pol. 22, 189 (1962)
abstract
A list of the results obtained at the Laboratory of Absolute Geochronology of the Institute of Nuclear Research, Polish Academy of Sciences. List No 1.
Les surstructures antiferromagnétiques dans les réseaux cubiques simples par la methode du champ moleculaire
Acta Phys. Pol. 22, 195 (1962)
Der Abbildungskontrast (Teil I)
Acta Phys. Pol. 22, 199 (1962)
see erratum: Acta Physica Polonica 23, 853 (1963)
abstract
Es wurde nach Besprechung der Arbeiten über die Theorie des Abbildungskontrasts die Kontrastübertragung durch Objektive von kleinem Sehfeld untersucht. Es wurden analytische Beziehungen für die Kontrast- und Phasenänderung für die einzelnen Aberrationen unter Berücksichtigung der Gauss’schen Näherung für die Amplitudenverteilung in der effektiven Austrittspupille abgeleitet, Es wurde bewiesen dass die durch Hopkins angegebenen Beziehungen nur bei kleinem Sehfeld und nicht großer Helligkeit angewendet werden können. Die Berechnungen wurden unter Berücksichtigung der mit dem Neigungswinkel \(\varphi \) des Büschels verbundenen Änderung der Gestalt und Größe der effektiven Austrittspupille. Der Einfluss der Blendenlagen auf die Kontrastübertragung bei beliebiger Vignettierung wurde diskutiert. Der Fall eines Systems mit zwei wirkenden Blenden wurde ausführlich behandelt und verwiesen wie die Betrachtungen für eine größere Blendenzahl zu verallgemeinern sind. Es wurde bewiesen, dass die angegebene Methode auch für Aberrationen höherer Ordnungen verallgemeinert werden kann. Es wurden unter Berücksichtigung der Vignettierung Beziehungen für die grössten noch hindurchgelassenen Frequenzen (Auflösungsvermögen) abgeleitet, die eine Verallgemeinerung der bekannten Abheschen Formel darstellen. Mit ihrer Hilfe kann die Änderung des Auflösungsvermögens mit der Änderung des Sehfeldes berechnet werden. Es wurde auch die Kontrastübertragung durch abberationslose Systeme berechnet und Bedingungen für die Tolleranzen der optischen Systeme abgeleitet.Fasc. 3, pages 211–293
Intermolecular Energy Migration and Concentrational Depolarization of Photoluminescence in Rigid Solutions
Acta Phys. Pol. 22, 211 (1962)
abstract
A more accurate version of the active sphere model, as appearing in the theory of concentrational depolarization of photoluminescence proposed by A. Jabloński, is given. Assuming with Forster that the probability for the transfer of energy from an excited to a non-excited luminescent molecule is inversely proportional to the sixth power of the distance between them, additionally the fluctuations of the concentration of the luminescent molecules is taken into account. Neglecting quenching by identical and different molecules, an expression for the dependence of the degree of polarization (or emission anisotropy) on the concentration of the dye molecules is derived. The theoretical results are compared with the experimental data of other authors.
Some Problems Relating to the Electrification of Dust from \(\beta \)-irradiated KCl Monocrystals
Acta Phys. Pol. 22, 225 (1962)
abstract
Investigation on \(\beta \)-ray irradiation of KCl monocrystals yielded some information as to the influence of lattice defect concentration in the crystal on the electrification of the dust produced therefrom. The electric charge of the dust from a KCl monocrystal arises as a result of cleavage of the crystal lattice. The presence of lattice defects increases the probability of electrification. The mean surface charge density of the dust particles depends on the concentration of lattice defects in the crystal. Three main factors cause electrification of the dust of KCI monocrystals irradiated with \(\beta \)-rays: the \(F\)-center concentration, absorption of electrons in the crystal, and secondary emission.
Photoconductivity of Polycrystalline Systems of Cadmium Sulphide
Acta Phys. Pol. 22, 241 (1962)
abstract
Photosensitive sintered CdS layers were obtained wherein the photocurrent carriers consisted both of holes and electrons and of holes alone. The semiconductor \(p\)-type system was found to present a spectral distribution of the sensitivity that was shifted towards longer wavelengths as compared with CdS single crystals and sintered layers of mixed conductivity.
Theory of Electric Birefringence for Gases Consisting of Non-rigid Molecules
Acta Phys. Pol. 22, 249 (1962)
abstract
The first part of the present paper contains a general theory of the Kerr constant for gaseous polymeres. It is shown that the Kerr constant can be expressed by means of the electrooptical properties of rigid segments of which the molecules are considered to consist, and some statistical averages depending on the geometrical structure and on the intramolecular interaction. The influence of the change of inertial moment for molecules having one rotational axis as a function of the height of the potential barrier is discussed in section 3. It appears, by the way, that in the case of low potential barriers, the change of inertial moment during rotation can have a dominant influence on the electrooptical properties of the molecule as a whole. Assuming free rotation and a “trans” configuration of the carbon chain, the Kerr constant for some gaseous hydrocarbons (CnH2n+2) is calculated in section 4. A comparison of the results obtained and the experimental results shows clearly, that, for short gaseous hydrocarbons the “trans" configuration yields results that are in better agreement with the experimental values than the assumption of free rotation.
Der Abbildungskontrast Teil II
Acta Phys. Pol. 22, 265 (1962)
Brittleness Anisotropy of an Iron–Silicon Alloy
Acta Phys. Pol. 22, 285 (1962)
Growth of Single Crystals of Nickel–Ferrite
Acta Phys. Pol. 22, 287 (1962)
Zur Spetroskopischen Bestimmung von Dipolmomenten Angeregter Moleküle
Acta Phys. Pol. 22, 289 (1962)
Fermi-energy of Free Electrons and the Size Effect
Acta Phys. Pol. 22, 293 (1962)
Fasc. 4, pages 299–369
A Molecular Theory of Magnetic Birefringence in Diamagnetic Media
Acta Phys. Pol. 22, 299 (1962)
abstract
From classical electrodynamics and statistical mechanics, an equation for the molecular Cotton–Mouton constant \(C_m\) is derived, of such generality as to contain factors of a microscopic nature not taken into account hitherto in theories of the magnetic hirefringence of diamagnetic fluids. This general equation is discussed in detail for gases, non-dipolar liquids and dipolar liquids. Moreover, the fundamentals of a theory of the magnetic birefringence of multi-component systems, with application to gas mixtures and liquids in solution, are proposed. The radial and angular correlations of the molecules of the liquids and their solutions are accounted for by means of molecular functions of the configurational distribution.
Interactions of Nucleons with Heavy Nuclei of Photographic Emulsions at Energies Higher Than 1012 eV
Acta Phys. Pol. 22, 329 (1962)
abstract
The angular distribution of secondary particles of 14 jets with primary energy higher than 1012 eV characterized by high evaporation and very high multiplicity (\(N_h \gt 8, n_\mathrm {s} \gt 40\)) have been analysed. It was found that in central collisions of nucleons with heavy nuclei of photographic emulsion there is a very significant effect of double maximum angular distribution. The double maximum structure becomes more pronounced with increasing anisotropy of angular distribution. In jets with very well separated narrow and diffuse cones, there is an anisotropy in number and shape of both cones. These facts can be explained on the basis of the two centre model taking into account the secondary interactions of particles created in the “slow centre” with the target nucleus.
On Statistics of Particles Which Cannot Exchange Their Places
Acta Phys. Pol. 22, 335 (1962)
abstract
A quantum mechanical definition of a system whose particles cannot exchange their places is given. It is shown that in such a system a kind of Pauli exclusion principle relating to the spatial coordinates only is fulfilled, independently of the statistics of the particles. The energy levels and the density \(\mit {\psi }^*\)\( \mit {\psi }\) are the same as for an antisymmetrical wave function. A simple example is given in which the influence of rare exchanges of places of the ground state energy is small. A special case of perturbation in the boundary conditions is considered.
On the Radiation of a Moving Magnetic Dipole
Acta Phys. Pol. 22, 349 (1962)
abstract
Starting from the formulas for the electromagnetic potentials of a magnetic dipole in motion, the well-known formula for the radiation of a moving charged body is generalized for the case of one possessing a magnetic dipole moment in addition to charge. In deriving the results, retarded potentials were applied. The formulas obtained were applied for computing the radiation in the following three cases: that of a body at rest, of one participating in hyperbolic motion, and of uniform motion along a circular path. In the first case, the result is found to agree with the well-known formulas for magnetic dipole radiation (Rubinowicz–Blaton 1932).
Anisotropic Magnetic Properties of an Iron–Silicon Alloy
Acta Phys. Pol. 22, 363 (1962)
Cryostat for Experiments in the Temperature Range from \(-130\)°C to \(-190\)°C with an Arrangement for the Prevention of Frost Formation
Acta Phys. Pol. 22, 369 (1962)
Fasc. 5, pages 379–441
Some Remarks on the Spin Wave Theory for Cubic Ferromagnetics. I
Acta Phys. Pol. 22, 379 (1962)
abstract
A new form of the proof of Thouless’ theorem concerning the vanishing, on the average, of the normal products of boson operators is given. An easy procedure for computing the ladder diagrams obtained by the present author within the framework of the new spin wave approach developed in earlier papers is proposed.
Some Remarks on the Spin Wave Theory for Cubic Ferromagnetics. II
Acta Phys. Pol. 22, 389 (1962)
abstract
The form of a diagram of arbitrary order is established. Summation of the infinite series of ladder diagrams contributing to the spontaneous magnetization of a cubic ferromagnetic as the fourth power of the absolute temperature is effected. Thereby the entire Dyson’s coefficient of \(T^4\) is obtained.
Inelastic Scattering of Slow Neutrons and the Behaviour of a Single Particle in the Many-particle Scattering System
Acta Phys. Pol. 22, 399 (1962)
abstract
The relations between slow neutron scattering data and the dynamical behaviour of a single particle in the many-particle scatterer were studied. Using no models, the equations describing the momentum and energy relaxation times for single particle in terms of neutron differential cross sections are given. Making use of a model of the behaviour of a particle these equations can serve to determine the potentials of interaction between particles of the scatterer. Also the non-electronic (phonon) part of the heat conduction of liquid metals can be determined in this way.
Proton Spin-lattice Relaxation in Liquid and Gaseous Hydrogen Chloride
Acta Phys. Pol. 22, 409 (1962)
abstract
The proton spin-lattice relaxation time \(T_1\) at 28 Mc/sec was measured for pure hydrogen chloride in liquid state from —48° C to the critical temperature 51.4°C and in gaseous state above this range up to 95°C. The observed \(T_1\) for liquid HCl decreases strongly with increasing temperature especially near the critical point. In the discussion it is shown that such behaviour can be explained by taking into account the spin-rotational interaction.
Urey–Bradley Force Field and Thermodynamic Properties: Planar XYZ2 Type Molecules
Acta Phys. Pol. 22, 417 (1962)
see erratum: Acta Physica Polonica 23, 101 (1963)
abstract
A normal coordinate treatment has been carried out for a few molecules of planar XYZ2 type, using the Urey-Bradley type of potential force field. The thermodynamic properties of NO2F and NO2Cl molecules for different temperatures have also been calculated on the basis of a rigid rotor, harmonic oscillator approximation.
Urey–Bradley Force Field and Thermodynamic Properties of XY3Z Type of Molecules
Acta Phys. Pol. 22, 423 (1962)
see erratum: Acta Physica Polonica 22, 532 (1962)
abstract
Urey–Bradley force constants of XY3Z type of molecules have been evaluated by the normal coordinate treatment. The thermodynamic properties of SiHCl3 and SiHBr3 are calculated for the ideal gaseous state at 1 atmosphere pressure for 11 temperatures from 100° to 1000°K using a rigid rotor, harmonic oscillator approximation.
Two Kinds of Neutrino
Acta Phys. Pol. 22, 429 (1962)
A Note on Quantization and Interpretation of General Theory of Relativity
Acta Phys. Pol. 22, 431 (1962)
\(\gamma \)-Strahlen Absorptionsänderungen in graphitierter Kohle als Auswirkung eines angelegten Druckes
Acta Phys. Pol. 22, 435 (1962)
Structure of Rhombohedral Complicated Modification of Boron
Acta Phys. Pol. 22, 439 (1962)
Effect of the Nuclear Potential Form on the Subbarrier Transfer of a Neutron
Acta Phys. Pol. 22, 441 (1962)
Fasc. 6, pages 445–532
Quantum Statistical Mechanics of Antiferromagnetics, I
Acta Phys. Pol. 22, 445 (1962)
abstract
In this paper the thermodynamical perturbation method for isotropic antiferromagnetics is studied. Average values are computed by the summation of an infinite number of diagrams in the representation of Matsubara, The theory may be applied to lattices divisible into two sublattices such that the nearest neighbours of atoms of the first sublattice lie in the second one.
Second Refractivity Virial Coefficients for Gas Mixtures
Acta Phys. Pol. 22, 477 (1962)
abstract
The present paper brings calculations of the second refractivity virial coefficient \(B_{\mathrm R}=\sum \limits _i\sum \limits _j x_i x_j B_{\mathrm R}^{(ij)}\) for a mixture of quadrupole and dipole gases. In addition to the influence of anisotropy in the polarizability on \(B_{\mathrm R}^{(ij)}\), the effects of hyperpolarizability of the quadrupole or dipole molecules on \(B_{\mathrm R}^{(ij)}\) was taken into account. In carrying out the calculations, the intermolecular central forces, the anisotropic dispersion forces, quadrupole–quadrupole and dipole–dipole interactions, as well as the induction interactions occurring between spherical, quadrupole and dipole molecules of the gas mixture were taken into consideration. Numerical evaluations for the gases CH4, N2, O2, CO2, CHCl3, and CH3F and their mixtures are given. These evaluations establish the importance of the particular contributions to \(B_{\mathrm R}\).
Nucleation Process in Barium Titanate at Cubic–Tetragonal Phase Transitions
Acta Phys. Pol. 22, 489 (1962)
abstract
It is discussed the paraelectric–ferroelectric phase transition in terms of a nucleation process. There is, in the presented mechanism, accounted for the formation of new domains at the phase transition in zero electric field. The activation energy for the formation of an internal domain in a perfect single crystal of barium titanate in zero electric field at the temperatures in the vicinity of the Curie point is found to be of the order of \(kT\).
Equations of Motion of a Rotating Particle with Magnetic Moment
Acta Phys. Pol. 22, 499 (1962)
abstract
The equations of motion for a particle having non-zero rest mass, spin, charge and magnetic moment are derived from Mathisson’s “variational principle” (Mathisson 1940). Methods similar to those applied by Weyssenhoff and Raabe (1947) are used for providing a physical interpretation of the equations derived.
The Total Scattering Cross-section of Slow Neutrons in Gaseous H2S
Acta Phys. Pol. 22, 517 (1962)
abstract
In view of the difference between Heinloth’s measured values for the neutron cross-sections of protons in water vapour and those expected on the Krieger–Nelkin theory, the authors carried out measurements with gaseous H2S. Results for this similar molecule show a smaller divergence from the theoretical values.
Proton Spin-lattice Relaxation in Liquid Benzene
Acta Phys. Pol. 22, 521 (1962)
Surface Migration Measurements on Nickel by the Method of Field Emission
Acta Phys. Pol. 22, 525 (1962)
On the Transfer of Charged Particles in Reactions with Heavy Ions
Acta Phys. Pol. 22, 529 (1962)
ERRATA
Superstructural Anisotropy of the Spin Wave Dispersion in Antiferromagnetics. Part I: Theory
Acta Phys. Pol. 22, 516 (1962)
On the Quantum Theory of Spin-wave Resonance in a Finite Ferromagnetic Linear Chain
Acta Phys. Pol. 22, 516 (1962)
Urey–Bradley Force Field and Thermodynamic Properties of XY3Z Type of Molecules
Acta Phys. Pol. 22, 532 (1962)
Fasc. 7, pages 3–191
Supplementum
Remarks on the Evaluation of Some Integrals in the Relativistic Corrections to the Binding Energy of the H2 Molecule
Acta Phys. Pol. (Supplementum) 22, 3 (1962)
abstract
An expansion in the elliptic coordinates of the inverse powers of the inter-electronic distance \(r_{12}\) in terms of the Gegenbauer polynomials is given. It is shown, that this expansion allows — by means of standard numerical methods — the evaluation of integrals containing in the integrand any inverse power of \(r_{12}\) and a formula convenient for the numerical calculations is presented.
A Theorem on Petrov Types
Acta Phys. Pol. (Supplementum) 22, 13 (1962)
abstract
It is shown that a vacuum metric is algebraically special in the sense of the Petrov classification if and only if it contains a shear-free null geodesic congruence. By noting which field equations are used in the proof of the theorem, the theorem is extended to include an electromagnetic field with geodesic rays as well as a null field. From a theorem of Robinson’s on the existence of a null electromagnetic “test field”, one observes that such a field can be constructed in vacuum if and only if the Riemannian space is algebraically special. From the original theorem, one can easily show that the existence of two independent shear-free null congruences guarantees that the space is Petrov Type I-degenerate.
The Generalized Asymptotic Series
Acta Phys. Pol. (Supplementum) 22, 25 (1962)
abstract
The analysis has been carried out of functions which vanish sufficiently strongly at infinity. It has been shown that such functions, if made to depend in an appropriate way on an additional parameter, may be represented by series formed of the derivatives of Dirac’s \(\delta (x)\) function. Because of their properties they have been called the generalized asymptotic series. They allow, in many cases, to derive the ordinary asymptotic expansions for special functions of physics from their integral transforms. The theory is also intended to serve as the asymptotic theory of source functions. It is supposed that, when extended to many dimensions, it may prove a valuable tool in non-local theories.
Diffraction Scattering of Deuterons on Non-spherical Nuclei II. Deformation of Arbitrary Multipolarity
Acta Phys. Pol. (Supplementum) 22, 35 (1962)
abstract
The Drozdov–Blair diffraction scattering model is extended to the case of deuteron scattering on nuclei with surface deformation of an arbitrary multipole order. The structure of the deuteron is taken into account by applying the Achiezer–Sitenko method. Both the “universal” curve rule and the “phase relation” of Blair remain approximately valid. The differential cross sections obtained are similar to those obtained with the simple Drozdov–Blair model provided one diminishes the black nucleus radius \(R_0\) by approximately one-fourth of the deuteron radius \(R_d\), and increases the deformation parameter \(|\beta _l|\) approximately by the factor (\(1 + 3R_d/8R_0\)).
On the Geodesics in an Expanding Universe
Acta Phys. Pol. (Supplementum) 22, 45 (1962)
abstract
The theory of geodesics in various models of the universe was elaborated by Tolman [1] and later by Schrödinger [2]. The conclusions of these investigations become, however, physically far more meaningful, if we replace the usual system of comoving coordinates by that one in which the field galaxies really recede from the observer situated at the origin of the coordinates.
Universal Fermi Interaction and Rotational Symmetry
Acta Phys. Pol. (Supplementum) 22, 51 (1962)
abstract
In the present paper a particular form of the overall neutral weak current is introduced in such a way that the whole universal Fermi interaction (UFI) displays a rotation and reflection symmetry in a formal three-dimensional space and at the same time the leptonic hyperon decays are considerably damped. This formal space is different from the usual isospace and may be called the “weak isospace”. Due to the proposed UFI there are two modes of \(\mu \) decay, \(\mu ^- \to e^- +\bar {\nu } + \nu '\) and \(\mu ^- \to e^- +\bar {\nu }' + \nu \) with branching ratio 9:1 (\(\nu \) and \(\nu '\) denote two different neutrinos). This “neutrino flip” appears, however, only in processes among leptions alone. In other leptonic processes there is the pairing (\(\bar {\nu }e^-\)) and (\(\bar {\nu }'\mu ^-\)) as a general rule. This UFI is compared with another UFI, having the same rotation and reflection properties in the weak isospace but forbidding the neutrino flip.
Über einige äussere Einflüsse auf die photostimulierte Exoelektronenemission von gedehnten Al-Folien
Acta Phys. Pol. (Supplementum) 22, 59 (1962)
abstract
Es wurde die KEinflussweise einiger äusseren Bedingungen — der Messanordnung, der Wärmevorbehandlung, der Luftfeuchtigkeit und der Oberflächendeckschicht — auf die photostimulierte Exoelektronenemission während und nach einer plastischen Dehnung von Al-Folien technischer Reinheit untersucht. Die Messanordnung gestattete die Durchführung fast punktartiger Messungen des zeitlichen Verlaufes der Exoelektronenemission. Die durch die Art des Bruchvorganges bedingten Schwankungen der angelegten Spannung wirken sich in der Gestalt der Emissionskurven sichtbar aus. Eine Wärmevorbehandlung vergrössert im allgemeinen das Emissionsvermögen, die Abkühlungsart findet sowohl in der Emissionsintensität wie in der Abklinggeschwindigkeit ihren Ausdruck. Mit steigender Luftfeuchtigkeit wird die Abklinggeschwindigkeit der Exoelektronenemission nach dem Dehnungsbruch grösser. Die Dehnung reiner Oberflächendeckschichten (ohne Metallunterlage) führte zu keiner messbaren Exoelektronenemission.
Kerr’s Constant of a “gaseous” Chain Polymer of the (–CR2(1)–CR2(2)–)\(_n\) Type
Acta Phys. Pol. (Supplementum) 22, 71 (1962)
abstract
General expressions derived in earlier papers by the present author for Kerr’s constant of non-rigid molecules are now specialized for the case of a ,,gaseous’’ polymer of the (–CR2(1)–CR2(2)–)\(_n\) type, where \(R^{(1)}\) and \(R^{(2)}\) stand for groups having the axial or almost axial symmetry with respect to the C–R bond. Since the present investigation extends to dipolar polymers, the results derived are of a greater degree of generality than those of Yu.Ya. Gotlib (1956), who computed Kerr’s constant for similar though non-dipolar polymers. The principal simplifying assumptions made here are those of the valence-optical model of the molecule (M.V. Volkenshtayn (1951)) and of interaction only between neighbouring segments of the polymer molecule. The mathematical approach proposed can be applied to isotactic and sinidiotactic polymers.
The Interaction of Baryons with Gravitational and Electromagnetic Field Within Rayski’s Six-dimensional Manifold
Acta Phys. Pol. (Supplementum) 22, 87 (1962)
abstract
Starting from the unitary theory of gravitation and electromagnetic field, given by Rayski, we find the generalized Dirac equations for the family of baryons interacting with gravitational and electromagnetic field. The connection of the charge of proton with the singularity of metric is the same as was found by Rayski in the case of scalar complex field.
On the Complex Effective Mass in the Calculation of the Optical Model Potential
Acta Phys. Pol. (Supplementum) 22, 97 (1962)
Three Pion Wave Functions Method of “Effective Angular Momentum”
Acta Phys. Pol. (Supplementum) 22, 103 (1962)
abstract
A complete orthonormal set of wave functions for three free pions has been worked out (up to \({\mit \Lambda }\leq 4\)), which satisfy the Bose statistics and which possess definite values of the total angular momentum and the parity in the centre of mass system as well as definite total isospin. An essential role in our construction procedure is played by a quantity, \({\mit \Lambda }\), which is defined by (2.15) and is called tentatively “effective angular momentum’’. The states are most conveniently classified by \({\mit \Lambda }\) and the total angular momentum. Similarity of \({\mit \Lambda }\) to the magnitude of relative orbital angular momentum in the two-body problem is found to be far-reaching. This method can be extended to four or more pion system.
Einfluss des äusseren axialen Magnetfeldes auf die Elementarbezirke im einachsigen Ferromagnetikum
Acta Phys. Pol. (Supplementum) 22, 127 (1962)
abstract
Auf Grund des vom Verfasser früher angegebenen quantentheoretischen Rechenverfahrens wird der Einfluss eines äusseren axialen Magnetfeldes auf die magnetische Struktur eines einachsigen ferromagnetischen Einkristalls untersucht. Dabei wird der Einfluss der Randbezirke vernachlässigt. Es wird gezeigt, dass das äussere Magnetfeld vorwiegend eine Verschiebung der Blochwände im Kristallinnern verursacht. Es wird auch die Magnetisierungskurve abgeleitet, die den wohlbekannten Sättigungsvorgang befriedigend wiedergiebt.
Emission of the Heavy Particles in the Interactions at Energies Greater Than 109 eV
Acta Phys. Pol. (Supplementum) 22, 143 (1962)
abstract
The angular distribution and energy spectrum of heavy particles emitted in the interactions of 7 GeV/\(c\) \(\pi ^-\) with C-nuclei in propane bubble chamber have been investigated. The forward-backward asymmetry of emitted protons increases with increasing energy of emitted protons in the energy interval 7–80 MeV. The results have been compared with several emulsion experiments up to the highest cosmic ray energies. It was observed that the emission of heavy particles of energy higher than \(\sim 20\) MeV depends very little on the primary energy. The experimental data are in qualitative agreement with the predictions of the cascade theory.
Multiple Meson Production in 7 GeV \(\pi \)-Carbon Nucleus Collisions
Acta Phys. Pol. (Supplementum) 22, 153 (1962)
abstract
We have investigated 101 stars, representing central collisions of \(\pi ^-\) mesons of the momentum of 7 GeV/\(c\) with carbon nuclei in a propane bubble chamber. By a central collisions we mean the collision with two or more protons engaged. The number of secondary mesons increases with increasing number of engaged protons and is in average greater, than in similar energy \(\pi \)- meson–nucleon collisions. We have compared our results with the tunnel — and the cascade model of collision. The cascade model is in a much better agreement with the experimental results.
Field Induced Nucleation at the Phase Transition in Barium Titanate
Acta Phys. Pol. (Supplementum) 22, 165 (1962)
abstract
A nucleation mechanism of the ferroelectric domains at the cubic-tetragonal phase transition in an externally applied electric field is presented. The macroscopic polarization developed in the crystal during this transformation was determined as a function of the applied field and the temperature. The study of thus developed polarization offers a new method of investigation of the phase transition in ferroelectrics in terms of the nucleation process.
Effective Cross Section for Reaction (\(p, p\pi ^+\))
Acta Phys. Pol. (Supplementum) 22, 173 (1962)
abstract
The cross section for reaction (\(p, p\pi ^+\)) has been calculated which is due to peripheral interactions with the exchange of a charged \(\pi \)-meson. The absorption of the secondary particles in a nucleus has been taken into account. The results calculated for reaction \(\mathrm {Al}^{27}_{13}(p,p\pi ^+)\mathrm {Mg}^{27}_{12}\) are compared with experimental data. In this case the experimental and theoretical cross sections are found to be close.
Application of the Classical Selfcorrelation Function to Determine the Slow Neutron Scattering Cross-section of Free Molecules
Acta Phys. Pol. (Supplementum) 22, 179 (1962)
abstract
The classical selfcorrelation function \(G^{(\nu )}_\mathrm {so}(\vec {r}t)\) is found for an atom in the molecule, considering the translation of the free molecule, its rotation and oscillation. Hence is derived the Krieger–Nelkin formula for the differential cross-section for incoherent scattering of neutron by a molecule.
Equations for the Vector Field in Rayski’s Unitary Theory
Acta Phys. Pol. (Supplementum) 22, 185 (1962)
abstract
The equations for the vector boson field with a rest mass different from zero are derived from the variational principle in the frame of Rayski’s unitary theory. The curvature of the six-dimensional manifold plays a role of the Lagrangian.
Corona Discharge in Air Between Wire and Plate as a Voltage Stabilizer
Acta Phys. Pol. (Supplementum) 22, 191 (1962)