Vol. XXX (1966)
Fasc. 1, pages 3–165
Influence of Thermal Motions on Depolarization of Fluorescence of Dye Molecules in Solutions
Acta Phys. Pol. 30, 3 (1966)
abstract
Polarization and mean duration of fluorescence components of acriflavine and acridine yellow in cyclohexanol and glycerol have been measured at various temperatures of solutions. On the basis of a simplified version of the theory of depolarization of fluorescence by the simultaneous action of torsional vibrations and Brownian rotations of luminescent molecules and the results of these measurements the following data are obtained: the limiting values \(r_0\) of the emission anisotropy, the mean values of frequencies of torsional vibrations and the angular dispersion due to these vibrations, the mean square value of angles of rotation due to Brownian rotations, the volume \(v\) of luminescent molecules together with their solvation shells, and the activation energy for Brownian rotations. It appears that \(r_0\) and \(v\) depend on the nature of the solvent and the temperature of the solution.
On an Approximate Solution to Field Equations of Two Relativistic Models of Spin Particles
Acta Phys. Pol. 30, 21 (1966)
abstract
The paper considers field equations obtained by a method usually applied in the general theory of relativity for the single-point and two-point models of a spin particle. In the single-point model the particle is represented by point singularity of a Lagrangian \(L_1\) containing higher derivatives \(L = -m_0 c \left (\sqrt {g_{\mu \nu }u^{\mu }u^{\nu }}- \frac {l^2}{c^3}g_{\mu \nu }\omega ^{\mu }\omega ^{\nu }\right )\) where \(m_0\) is the rest mass of the particle, \(c\) is the velocity of light, \(u^{\nu }\) is the four-velocity and \(\omega ^{nu}\) is the four-acceleration of the particle, \(g_{\mu \nu }\) are the gravitational potentials of the field in which the particle is found, \(l\) is a constant of length dimensions which represents the particle’s diffluence and spin, of the order of the Compton Wavelength of that particle. In the two-point model the particle is represented by a set of point singularities with four-velocity \(u^{\lambda }\) and a space-like four-vector \(r^{\lambda }\) such that \(r_{\lambda }r^{\lambda }= -l^2=\) constant…
On the Electric Conductance of Benzene Purified by Means of Multiple Crystallization
Acta Phys. Pol. 30, 39 (1966)
abstract
While comparing benzene with other liquid hydrocarbons it was noticed by Forster that there are the following differences in the electric properties of this compound: 1. high natural conductance, 2. time independence of conductance, 3. independence of the activation energy of this process from the degree of purity of the particular sample. These were the premises on the basis of which the hypothesis of non-ionic conduction of benzene was suggested. In the present work the authors have tried to decrease the conductance of benzene by intensive purification and to study its time and temperature characteristics. The purification of benzene consisted in: removing thiophene by acting with concentrated sulphuric acid, drying by means of metallic sodium, fractional distillation from sodium and crystallization repeated nine times. The conductance of benzene purified in this way became lower than \(10^{-16}\) \(\Omega ^{-1}\)cm\(^{-1}\). The values of activation energy determined from the temperature characteristics of samples with conductances of \(10^{-13}\) \(\Omega ^{-1}\)cm\(^{-1}\) and \(10^{-16}\) \(\Omega ^{-1}\)cm\(^{-1}\) amounted 0.42 eV\(\pm 10\%\) and 0.29 eV\(\pm 10\%\) respectively. The results obtained seem to be in contradiction with the hypothesis of Forster.
On the Deposition of Thin Tin Oxide Films by Reactive Bias Sputtering
Acta Phys. Pol. 30, 45 (1966)
abstract
Thin tin oxide films have been obtained from a cathode covered with tin. The degree of purity of tin was \(99.999\%\). Some antimony and indium admixtures were also present. Owing to the application of a biased substrate a good reproducibility of results has been obtained, as well as the possibility of controlling the degree of oxidation of the oxide film. The introduction of Sb and In admixtures to the cathode permitted to vary the conduction of oxide films in the range from \(10^2\) to \(10^{-6}\Omega ^{-1}\)cm\(^{-1}\).
On the Photostimulated Emission of (Exo)electrons to Air Atmosphere During the Recrystallization of Metals and Alloys
Acta Phys. Pol. 30, 51 (1966)
abstract
The emission of exoelectrons to air atmosphere during the recrystallization of bismuth, cadmium and their alloys has been studied. The compositions of the alloys were: Cd — \(10\%\), Bi — \(90\%\); Cd — \(50\%\), Bi — \(50\%\); Cd — \(90\%\), Bi — \(10\%\). The exoelectrons were detected by means of an air-point counter with quenching vapour above the free surface of the liquid. From the investigations carried out follows that (a) the condition necessary for the observation of exoelectrons emission during the phase transformation of the investigated metals and their alloys in atmospheric air is a stimulation by the UV-light; (b) the emission of exoelectrons associated with the phase transformation is probably connected with the change of the volume of the specimen and here with the disruption of the covering oxide layer.
Zur Ableitung der Kottlerschen Fassung des Elektromagnetischen Huygensschen Prinzips
Acta Phys. Pol. 30, 59 (1966)
abstract
Es wird eine direkt aus der Lorentz–Larmorschen Formel folgende, einfache Ableitung der Kottlerschen Version des elektromagnetischen Huygensschen Prinzips für den Fall angegeben, wo die Normalenrichtung auf der im Huygensschen Prinzip auftretenden Fläche nicht konstant ist. Es ergibt sich, dass der im betrachteten Falle erhaltene Ausdruck, ganz genau der früher durch Kottler angegebenen Formel für \(n =\) const, entspricht.
Einfluss der Gitterdeformation auf die Elementarbezirke einachsiger Ferromagnetika
Acta Phys. Pol. 30, 65 (1966)
abstract
Mit Hilfe der von Ziętek aufgestellten Methode wird eine Theorie der Struktur der Elementarbezirke einachsiger ferromagnetischer Kristalle entwickelt. Es wird die Möglichkeit der Umkehrung der Richtung der leichtesten Magnetisierbarkeit durch homogene Deformationen gezeigt. Die Rechnungen wurden praktisch für willkürliche Kristallstrukturen durchgeführt unter Berücksichtigung der weiteren, Nachbarn. Die Arbeit zeigt, dass der Effekt der Richtungsveranderung der leichtesten Magnetisierbarkeit und was damit verbunden ist, der Drehung der Magnetisierbarkeitsrichtung der Elementarbezirke um den Winkel \(\pi /2\) bei ihrer gleichzeitigen Verschiebung bei genügend grosser und in entsprechender Richtung durchgeführter Deformation des Kristalgitters immer auftreten dürfte. In der Arbeit wird eine genügend allgemeine Abhängigkeit der Pseudodipolwechselwirkungskonstante von den Entfernungen zwischen den wechselwirkenden Atomen angenommen, mit Hinweis auf die Möglichkeit ihrer genaueren Bestimmung durch Aufnahme von systematischen experimentellen Untersuchungen.
Central Collisions of Nucleons with Heavy Nuclei for Energy Higher than 10 eV
Acta Phys. Pol. 30, 73 (1966)
abstract
220 interactions originated by singly charged or neutral particles of the energy above \(10^{12}\) eV have been analysed. The analysis has been performed in six groups of events defined by multiplicity \(n_s\) and number of evaporation tracks \(N_h\). Angular distributions of secondaries, distributions of anisotropy parameter \(\sigma \), distributions of bimodality parameter \(D\), \(\sigma \)–\(D\) correlation and distributions of inelasticity coefficient \(K\) have been studied. For central collisions between nucleons and heavy nuclei (these collisions were selected by criteria of \(N_h \gt 8\) and \(n_s \geqslant 30\)) a model has been proposed. In the model these collisions are treated as a superposition of the elementary nucleon–nucleon collisions.
“Oscillator-like” Representations of the \(U(N, N)\) Algebras
Acta Phys. Pol. 30, 93 (1966)
abstract
In this paper we consider a certain class of very special infinite-dimensional, unitary, irreducible representations of non-compact \(U(N, N)\) groups and their algebras, which we call “oscillator-like” representations, and which are explicitly constructed out of boson creation and annihilation operators. They contain infinite “towers” of multiplets of the maximal compact subalgebra \(U(N)\otimes U(N)\) of \(U(N, N)\), which, in the case of \(N = 6\), leads to the “ladder representations” recently discussed by Dothan, Gell-Mann and Ne’eman, and others. The possibility of obtaining mass formulae from such representations according to the ideas of Barut, is mentioned and will be considered in the next paper, as well as the possibility of their “boosting” (relativistic completion).
The Explicit Construction of the “Oscillator-like” Representations of the U\((2,2)\) Algebra in a “Spin Basis”
Acta Phys. Pol. 30, 105 (1966)
abstract
We begin the explicit construction of the “oscillator-like” representations of \(U(N, N)\) algebras (introduced in our previous work) in a “spin basis” with the simplest non-trivial case of the \(U(2, 2)\) algebra. In this case we can apply the standard angular momentum algebra to reduce the \(SU(2)_I\) “spin” subalgebra out from the maximal compact \(U(2)\otimes U(2)\) subalgebra of \(U(2, 2)\) and to take all generators (compact and non-compact) of \(U(2, 2)\) as irreducible, spherical, tensors of rank 0 and 1, in the sense of Racah. The procedure of computing all their non-zero matrix elements, in a “spin basis”, is thus limited to their reduced matrix elements, which can be easily obtained. We introduce also the “Dirac” basis of generators of \(SU(2, 2)\) algebra, which is also a suitable basis for the isomorphic \(SO(4,2)\) algebra. Finally, we calculate the Casimir operators of some subgroups of \(SO(4, 2)\) and discuss the possibility of obtaining various forms for the ‘‘mass operators”, and their corresponding mass formulae.
Étude du systeme Ga2O3FeO — Fe2O3FeO par diffraction de neutrons
Acta Phys. Pol. 30, 125 (1966)
abstract
Par diffraction de neutrons on a pu préciser la structure nucléaire des spinelles \(\mathrm {Fe}_{3-\alpha }\mathrm {Ga}_{\alpha }\mathrm {O}_4\) (degré d’inversion et position des atomes d’oxygéne) ainsi que la structure magnétique. Les sites tétraédriques sont occupés pour la plupart par les ions Ga3+. Les spinelles avec \(\alpha \lt 2\) ce sont des ferrimagnétiques normaux dont les valeurs des moments magnétiques des atomes en sites tétraédriques et octaédriques ont pu étre précisées. A neutron diffraction study of the cubic spinels \(\mathrm {Fe}_{3-\alpha }\mathrm {Ga}_{\alpha }\mathrm {O}_4\) gives both the ions positions and magnetic structure. The tetrahedral sites are occupied mostly by the Ga3+ ions. The spinels with \(\alpha \lt 2\) are the ferrimagnetics normal. The values of the atomic magnetic moments in the sites tetrahedral and octahedral are determined.
Зарядовые распределения частиц в одномезонной теории неупругих взаимодействий при высоких энергиях
Acta Phys. Pol. 30, 135 (1966)
abstract
Обсуждается простой метод расчета зарядовых распределений частиц, образующихся при неупругих столкновениях в области высоких энергий. На примере \(\pi ^- -р\) столкновений при 7 Гэв показано, что результаты одномезонных полюсных расчетов хорошо согласуются с опытом и сравнительно мало чувствительны к предположениям о величине плохо известных нам сейчас сечений нестабильных частиц \(\pi +\pi , \pi +K\) и т.д.
Über die Selbstdepolarisation Des Fluoreszenzlichtes von Trypaflavin und Eosin in Polymethylmethakrylat
Acta Phys. Pol. 30, 141 (1966)
abstract
Es wurden die Untersuchungen der Konzentrationsdepolarisation des Fluoreszenzlichtes von Trypaflavin und Eosin in festen Lösungen von Polymethylmethakrylat mit \(15\%\) Methanol durchgeführt. Insbesondere wurde der Einfluss der Erregungswellenlänge auf die Wawilovsche und Jabłońskische aktiven Sphären, die für die Wahrscheinlichkeit der Energiewanderung charakteristisch sind, untersucht.
Generation of the High Energy Nucleon–Electron Cascade by Means of the Program Written for the Small Computer
Acta Phys. Pol. 30, 149 (1966)
abstract
Using the Monte Carlo method program for the generation of the nucleon–electron cascade along whole depth of the absorbent in the apparatus installed on the Mount Aragac has been written. This work has been undertaken with the aim to find the proper set of the parameters describing the nuclear interaction (for example inelasticity coefficients for C and Pb) by comparing the ionization in the trays of ionization chambers calculated by means of the program with the actually observed one in the apparatus. The above mentioned program can be run on a such small computer as \(UMC 1\).
Program for the Interpolation of the Cascade Curves with the Aid of a Small Electronic Computer
Acta Phys. Pol. 30, 159 (1966)
abstract
In the generation of the nuclear-electron process with the help of the program for the computer \(UMC 1\) there was necessary to estimate simultaneously the number of the electrons for the four values of the absorbent thickness and for the optional value of the photon energy, which initiates a given cascade. The requirements of the short time and good accuracy of the computation have been achieved when one uses the table of the cascade curves and the total number of electrons is estimated by the interpolation method. The total number of electrons as a function of two variables (the photon energy and the depth of the absorbent) can be represented by the Taylor’s expansion and the acceptance of the first two terms only appears to ensure good accuracy.ERRATA
Quasilinear Structure of Luminescence Spectra of Triphenylene in Frozen Crystalline Solutions
Acta Phys. Pol. 30, 165 (1966)
Fasc. 2, pages 169–341
Resonance Quenching of Solid Solution Luminescence
Acta Phys. Pol. 30, 169 (1966)
abstract
The theory of quenching of luminescence by foreign absorbing substances in the case of solid solutions and dipole–dipole interaction between the molecules of the sensitizer \(S\) and those of the acceptor has been generalized, using the multilayer model of the luminescence centre. Fluctuations of the molecule concentration of the quencher, as well as the dependence of the probability of the resonance excitation energy transfer \(P_{SA}(dd)\) on mutual orientation of the transition moments of the interacting molecules have been taken into account. A previous simplifying assumption about the independence of \(P_{SA}(dd)\) on the distance for quenchers from a given layer of the luminescence centre (Bojarski 1960) has also been weakened. Furthermore the quantitative relation between the critical distance \(R_1\) appearing in the theory of Förster and the constant \(r^{(1)}\) introduced into the present quenching theory has been established. An analytical expression for quantum yield of the sensitizer has been obtained and compared with the experimental results of other authors.
Optical Absorption Anisotropy of \(p\)-Nitroaniline Single Crystals in the Near Infra-Red Region
Acta Phys. Pol. 30, 187 (1966)
abstract
The absolute intensities of the –NH2 and –C–H overtone and combination bands have been measured in polarized light for a number of \(p\)-nitroaniline crystal plates. The observed polarization directions of the bands are in agreement with the directions of the corresponding transition moments deduced from the symmetry type of the normal vibrations. The splitting of the –NH, combination band can be explained by assuming that the intermolecular dipole–dipole interactions cause the molecules to associate into molecular pairs.
Introduction to the Photoelectric Model of Cone–Rod Colour Determination
Acta Phys. Pol. 30, 199 (1966)
abstract
A discussion was carried out on known basic phenomena in the process of colour determination. Upon the basis of the discussion a new theory of colour determination was worked out which assumes participation of rods as well as cones in colour determination and photoelectric perception of light energy. A theoretical model of light energy perception was given on the basis of protein treated as a specific organic semiconductor. The said model was used to explain some phenomena of colour discrimination.
On a New, Integral Method of Thermal Conductivity Measurement of Cylindrical Semiconductor Specimens Immersed in Helium Bath
Acta Phys. Pol. 30, 205 (1966)
abstract
A formula for the thermal conductivity coefficient of semiconducting cylindrical specimens immersed directly in liquid helium and superheated by Joule’s effect heat generated in the whole volume of the specimen has been derived. It has been shown that with the increase of power the value of the effective temperature determined by means of effective resistance measurement of the superheated specimen approaches the numerical value of the temperature at the axis of the specimen. The temperature of the surface was determined knowing the temperature of the helium bath and the temperature jump at the surface corresponding to the power released in the specimen. The results were compared with those from the differential method and with the data from literature.
On the Huygens Principle for Elastic Media
Acta Phys. Pol. 30, 223 (1966)
abstract
A comparison of the Huygens principle groups given by Kupradze (1963) for elastic media with the forms of this principle contained in the papers of Knopoft (1956) and Boillet (1956) has been done. It has been shown that in the case when there are no discontinuities of the field on the integration surface the Huygens principles in the formulation made by Kupradze are identical with the results of Knopoff and Boillet for the monochromatic case. It was proved that in the case of an integration surface, where discontinuities are present, as it is the case for diffraction, one can only use Huygens’ principles in the formulation of Kupradze. It has also been shown that the results of the considerations of Knopoll concerning the application of the Huygens principle to the diffraction problem are a particular case of the general conclusions obtained from the application of the Huygens principles of the formulation of Kupradze to the diffraction on screens of the Kirchhoff type. The paper also gives a proof that in the elastic case a Kirchhoff’s type of screen is defined by the conditions: \(\vec {v} = 0\) and \(\frac {\partial \vec {v}}{\partial n}= 0\) for all cases considered by Kupradze.
A Method for Solving the Nucleon–Phonon Interaction Problem
Acta Phys. Pol. 30, 237 (1966)
abstract
A method to solve the Schrödinger equation for fermions interacting with phonons for the case of a sufficiently small number of different fermion states is suggested. The method is described by an example of a problem with one type of a scalar phonon coupling the orbitals of two energy levels in a spherical nucleus. The method consists in an introduction of the generating functions of a complex variable \(z\). The Tailor coefficients of the functions arc simply related to the probability amplitudes of the n-phonon excitation in an eigenstate of the system. The solution of the Schrödinger equation is achieved by finding the integrals of a system of first order differential equations which are given by entire functions. Such solution are found in the limits of a weak and strong coupling and in the special case of a resonance between the phonon and nucleon excitation energies.
The Influence of Force Constants on the Energy Levels of Dimers
Acta Phys. Pol. 30, 251 (1966)
abstract
The influence of force constants on the energy levels of dimers is discussed. The strong and weak coupling limit is investigated. It is shown that in this limits the change of the energy levels depends mainly on the linear part of the potential for small vibration quantum numbers when for higher quantum numbers the energy levels are dependent on the difference in force constants. The main feature of the strong limit of the vibronic coupling by the difference in force constants is the appearing in the electronicly-forbidden spectrum of simultaneous transitions with \(\Delta m = \pm 1\) in symmetric and nontotally-symmetric vibrations.
The Two-Center Acceptor States in Germanium and Silicon. I. The General Theory
Acta Phys. Pol. 30, 267 (1966)
abstract
The energy levels and the wave functions of a hole in the field of the two acceptor ions and the nearest ionized donor are considered in \(p\)-type Ge and Si in range of separations between the acceptor ions for which the hopping model is valid. The wave functions for these states are obtained in the form of linear combinations of the wave functions of an acceptor ground states given by Schechter in the approximation of infinite spin–orbit splitting. We get four energy levels instead of two. This splitting follows from anisotropy of the one-center acceptor functions. The simplified expressions for the energy and the wave functions obtained by averaging over directions of the quantities determining the energy and the wave functions are also given.
The Two-Center Acceptor States in Germanium and Silicon. II. The Two-Center Integrals
Acta Phys. Pol. 30, 277 (1966)
abstract
The matrix elements of the Coulomb potential between the Schechter’s functions and the overlap integrals that are necessary to find the two-center acceptor states in Germanium and Silicon are calculated.
The Two-Center Acceptor States in Germanium and Silicon. III. The Numerical Results
Acta Phys. Pol. 30, 283 (1966)
abstract
The energy levels of holes in two-center acceptor states are calculated for germanium and silicon.
The Nature of the Lorentz-Invariants
Acta Phys. Pol. 30, 293 (1966)
abstract
An attempt is made to show that any theory based on the directly observable continuum of events, as is the Theory of Relativity, is to scanty to account for the physical nature of all Lorentz-invariant quantities. In particular the rest-masses of isolated systems (particles) are in our picture among the invariants whose nature cannot be understood within the Lorentz geometry. The geometrical framework proposed here is thus based on the directly unobservable variables, and as they are canonical variables, we call the corresponding geometry the Phase geometry. The continuum of events (\(t, x\)) ceases to be an ultimate physical continuum, and it becomes analyzable in terms of the Phase geometry variables. The relationship between the “directly observable” events and the Phase geometry coordinates is established by means of the Lorentz momentum-invariants only.
On the Scattering of Slow Neutrons by Ortho- and Parahydrogen
Acta Phys. Pol. 30, 323 (1966)
abstract
The scattering of slow neutrons by ortho- and parahydrogen is treated on the basis of Fadeev’ Equations (4). In cases when the Fermi’s potential is used, the problem is reduced to the solution of a system of 16 integral equations.
Some Depolarizing Factors of Photoluminescence in Thermodynamic Approach
Acta Phys. Pol. 30, 331 (1966)
Pair Correlations in C Atom
Acta Phys. Pol. 30, 335 (1966)
The Reaction \(\mit {\pi }^+ p\to \omega N^{*++}\) at High Energies and the Regge-pole Exchange Model
Acta Phys. Pol. 30, 339 (1966)
Equal Time Commutators and Scalar Mesons Decays
Acta Phys. Pol. 30, 341 (1966)
Fasc. 3, pages 347–481
Investigation of Double Layers in Alternating Electric Field
Acta Phys. Pol. 30, 347 (1966)
abstract
The aim of this paper is an explanation of the reason for the differences between acoustical spectra of various electrolytes in electrolyte-mercury systems, excited to mechanical vibration by means of alternating voltages. In the first part of investigations the capacitance of the double layer electrolyte-mercury was measured. The measurements were carried out for various electrolytes and with different polarizing voltages by means of the resonance method in a mechanically non-vibrating system. In the second part of the investigations, the occurrence of an electric resonance was found in the case of an electrolyte-mercury system supplied with a.c. after exciting the mercury electrode to mechanical vibration. The experimental evidence for an electric resonance in the case of a vibrating mercury surface indicates that there is a possibility of attaching both capacitance and inductance to the vibrating double layer electrolyte-mercury. An analysis of results based on the analogy between a piezoelectric oscillator and the electrolyte-mercury system, playing the role of an electrolytic oscillator enabled the authors to make an attempt of interpretation in which the capacitance and inductance of the vibrating double layer are defined by quantities connected with mechanical parameters.
On the Temperature Jump Between the Surface of a Superheated Thermometric Carbon Resistor and Helium II Bath
Acta Phys. Pol. 30, 357 (1966)
abstract
With the use of relationships derived earlier, studies had been conducted on the temperature jump between the surface of a carbon resistor, superheated by released Joule heat, and a helium II bath. The dependence received are qualitatively similar to results given by other authors for superheated metal specimens. This conformity, it appears, speaks for the correctness of the proposed new method of investigating the temperature jump between the surface of superheated semiconductor specimens and helium baths.
On the Properties of Point Counter with Quenching Vapour Above Free Liquid Surface (Exoelectron Detector)
Acta Phys. Pol. 30, 365 (1966)
abstract
A new type of an open counter with quenching vapour has been designed. This constructional solution is characterized by stable operation. Properties of the counter were investigated. It has been shown that an important parameter of the counter is the radius of the cathode.
Temperature Dependence of Spectral Lines Intensity Emitted by Thermal Plasma
Acta Phys. Pol. 30, 375 (1966)
abstract
The paper presents expressions which make it possible to find the temperature dependence of atom, ion and electron concentrations, and graphical method of determining the temperature \(T_m\) at which the intensity of a spectral line reaches maximum value under condition when the sum of atom and ion concentrations is constant (independent of temperature). This method can be applied to the lines emitted by atoms and ions of any multiplicitys of ionization.
Effects of Heat Treatment and Neutron Irradiation on the Magnetization Curve of Cobalt
Acta Phys. Pol. 30, 381 (1966)
abstract
The elementary magnetization processes defining the reversible susceptibility of polycrystalline cobalt are discussed on the basis of temperature-dependence measurements. In the unannealed specimen there is no first maximum of susceptibility which appears at a temperature of +290°C in cobalt annealed in a hydrogen atmosphere. The isotherms \(\kappa ^{-1}_\mathrm {rev} = f(H)\) are a linear dependence within a broad range of fields. It was found that temperature affects the Gans curves. Irradiation with a \(0.8 \times 10^{18}\) cm\(^{-2}\) dose of fast neutrons brings about permanent radiation defects which cause a drop in the initial susceptibility of cobalt by 2.5 per cent and an increase in coercive force by 15 per cent.
Theory of Multiphoton Transition Probabilities
Acta Phys. Pol. 30, 393 (1966)
abstract
The formal quantal theory of first-, second-, and higher-order radiation processes inherent in electric and magnetic multipole transitions is developed. The calculated probabilities of two- or more-photon processes consist not only of indirect multipole transitions from initial to final states via one or more successive virtual states, but also of a direct multipole transition related to the second- or higher-order time-dependent interaction Hamiltonian. The general results are discussed in some special cases of electric or magnetic dipolar, quadrupolar, etc. transitions. Tensors of electric and magnetic multipole polarization are derived in the \(r\)-th-order approximation of quantal perturbation theory and expressed in terms of \(r\)-th-order multipole susceptibility tensors and electromagnetic field strengths in the \(r\)-th power. The multipole and nonlinear formalism is given in a compact tensorial notation and can be applied for computing various multiple-photon processes, the investigation of which is liable to provide information on the change undergone by atoms or molecules under the influence of intense electromagnetic fields, e.g. from lasers.
Some Remarks on the Theory of Spin Waves in Ferrimagnetics
Acta Phys. Pol. 30, 415 (1966)
abstract
As model of a ferrimagnetic, a body-centered cubic lattice with two identical simple cubic sublattices is taken with two different spins of the same direction, namely \(S\) for the first and \(s\) for the second sublattice. The calculations are based on Dyson’s spin-wave theory. The Hamiltonian in the ideal model consists of the first and second neighbours approximation, of the quasi-diagonal and interaction parts. By diagonalization the diagonal part determining the energy of free waves and the nondiagonal part representing dynamical spin-wave interaction is obtained. For calculating the magnetization, the method due to Szaniecki is used. The discussion is limited to the first order of Feynman’s graphs only. The higher-order graphs contribute very small corrections. A formula for the magnetization depending on temperature powers (including the 4th) is derived. The coefficients of the magnetization series are functions of the spins and exchange integrals.
Sign of Difference of the Real Parts of the Elastic Pion–Proton Scattering Amplitudes in the Very High Energy Region
Acta Phys. Pol. 30, 427 (1966)
Vibronic Coupling in Molecular Crystals
Acta Phys. Pol. 30, 431 (1966)
abstract
Coupling of excitons with molecular phonons results from a change of molecular potential energy in excited molecular electronic state. Exciton-phonon Hamiltonian when written in the second quantization language contains terms linear in the phonon variables. Separation of excitons (treated as bosons) from the phonon variables by a suitable unitary transformation is shown to lead to exciton–exciton interaction term. Some possible consequences of this new interaction type are outlined.
On the Problem of Diffraction of Elastic Waves in the Formulation of Young
Acta Phys. Pol. 30, 437 (1966)
abstract
It was found that similarly as in the case of acoustic waves, there is also a possibility of interpretation of diffraction phenomena for elastic waves according to the idea of T. Young (Rubinowicz 1957). The paper also contains the form of tensor potential for longitudinal waves.
“Oscillator-like” Representations and Mass Formulae of U(3,3)
Acta Phys. Pol. 30, 445 (1966)
abstract
In this paper we continue the investigation of \(U(N, N)\) algebras by explicitly constructing the “oscillator-like” representations, defined in our first paper, of the \(U(3, 3)\) algebra in a base in which the “unitary spin” \(SU(3)\) subalgebra is diagonal (as well as the isospin and hypercharge operators). This is the second simple case of \(U(N,N)\) algebras (the first one of \(U(2, 2)\) has been treated in our second paper) in which such a construction was possible in a completely general form owing to the existence of analytical expressions for \(SU(3)\) Clebsch–Gordan coefficients for the product \((\lambda ,\mu )\otimes (1,1)\), published by Kuriyan, Lurić and Macfarlane in Journal of Mathematical Physics. In the first part of this paper we recapitulate the main results of our first paper, applied to the \(N = 3\) case, analyse some subgroups of \(U(3, 3)\) and obtain the diagram of \(SU(3)\) multiplets contained in a special irreducible representation of \(U(3, 3)\). In the second part we represent all generators of \(U(3, 3)\) as irreducible (singlet and octet) tensors with respect to the \(SU(3)\) subgroup which reduces the calculation of their matrix elements to a small number of [reduced matrix elements according to the Eckart–Wigner theorem. After getting some reduction formulae the calculation of some special matrix elements of some components of generators is straightforward and leads to the reduced matrix elements when the corresponding \(SU(3)\) Clebsch–Gordan coefficients are taken into account. In the third part we discuss certain possible mass formulae obtained easily when the mass operator is constructed out of the generators of \(U(3, 3)\) in a definite manner. These mass formulae are some generalizations of the well-known Gell-Mann–Okubo formula. Their possible application to mesons is discussed.
Sur des valeurs propres d’énergie des oscillateurs ayants la même dépendence de la période et de l’énergie
Acta Phys. Pol. 30, 477 (1966)
A Note on the Lagrangian Density for Fluid Systems in General Relativity
Acta Phys. Pol. 30, 481 (1966)
Fasc. 4, pages 487–683
The Space of States of Relativistic Double Pole Field
Acta Phys. Pol. 30, 487 (1966)
abstract
The space of states for the simplest case of relativistic multipole, double pole field, is investigated. The analogy with free quantum electrodynamics in three (two space, one time) dimensions is pointed out. The positive metric and indefinite metric formalisms are presented. It is shown that the conventional positive metric formalism does not allow the construction of vacuum state vector with finite norm. The only admissible space of states has indefinite metric. The vacuum state has finite length and is degenerated. It is also shown that the modification of dual space by introducing a metric tensor in a way which leads to positive norms of state vectors (so-called \(\hat {\eta }\)-formalism in quantum electrodynamics) breaks the translational invariance of two-point Greens functions.
Method of Determination of Dielectric Constant by Direct Measurements of Frequency
Acta Phys. Pol. 30, 519 (1966)
abstract
A measuring device has been constructed which enables determination of the dielectric constant \(\varepsilon \) of liquids in the range between 2 and 3 by direct measurement of frequency with a digital frequency meter. The means to diminish the dead capacity of a measuring condenser have been discussed. The method gives an accuracy of a single measurement of \(\Delta \varepsilon /\varepsilon \cong 2\times 10^{-4}\).
Electronic Structure and Spectra of Organic Molecules. Part II. SCF MO Calculations for Aniline and Some of Its \(N\)-derivatives
Acta Phys. Pol. 30, 529 (1966)
abstract
A theoretical study with the use of the Pariser–Parr–Pople method (SCF MO CI) is made for some anilines (aniline, \(N\)-methylaniline, \(N,N\)-dimethylaniline, \(N\)-ethylaniline, \(N,N\)-diethylaniline and \(N\)-\(n\)-butylaniline). A satisfactory interpretation is given for the iransition energies from the ground state to the singlet excited states and for the oscillator strengths. The theoretical interpretation of the electronic spectra of some other monosubstituted benzenes, fluorobenzene and phenol, is also given.
On the Radioelectret Effect in Paraffin Wax
Acta Phys. Pol. 30, 549 (1966)
abstract
The paper contains a description and results of experiments on the influence of temperature and \(UV\)-light on the charge of radiolectrets from paraffin wax. It was found that the radioelectret charge decreases with the increase of temperature at which the samples are subjected to ionizing radiation and stored before forming. Illumination \(UV\)-light before forming of irradiated samples results in an increase of electret charge, whereas illumination after forming leads to a considerable decay of the charge. The spacial distribution of free charge and internal polarization in radioelectrets formed from paraffin wax has also been determined.
On the Electroluminescence of Zirconium Oxide Films Obtained by Anodic Oxidation
Acta Phys. Pol. 30, 559 (1966)
abstract
The paper concerns the electroluminescence properties of zirconium oxide layers obtained by anodic oxidation on metallic substrate in the systems Zr–ZrO2–Al. A stationary luminescence of Zr–ZrO2–Al cells in a constant and in a sinusoidally alternating electric field was found. A distinct influence of \(D.C.\) and \(A.C.\) voltage and current intensity as well as of frequency changes of the latter on the integral intensity of electroluminescence has been observed.
Hydrodynamic Equations and the Elementary Excitations in Fluids
Acta Phys. Pol. 30, 567 (1966)
abstract
The hydrodynamic equations with ‘‘density sources” are obtained for the Bose and Fermi systems. After solving the linearized hydrodynamic equations the expressions for the retarded, thermodynamical Green’s functions are obtained in the long-wavelength low-frequency domain. Damping phenomena are taken into account.
On Asymptotic Solutions for Domain Structures in Untaxial Ferromagnets
Acta Phys. Pol. 30, 577 (1966)
abstract
In the framework of Ziętek’s microscopic formalism, the variational principles for 180-domain structures in uniaxial ferromagnetic crystals are derived and solved under asymptotic boundary conditions. Hexagonal and \(fcc\) crystal lattices are examined, and the influence of uniform lattice deformations respectively in the crystallographic directions [0001] and [111] on the rotation of the magnetically preferred direction is studied, in the absence of an external magnetic field. The Hamiltonian is expressed in terms of second-order interactions between the lattice spins, the interaction being restricted to the nearest neighbourhood. Anisotropic interactions are assumed to be of pseudo-dipolar form, and the behaviour of the corresponding coupling function under lattice deformation is analysed, in a certain class of functions. It is found that, in this approximation, a sufficiently large linear deformation in the direction [0001] or [111], for the respective lattices, causes a rotation of the direction of easiest magnetization by angle \(\pi /2\). Further, the thickness and the energy of Bloch walls are calculated, either quantity shown to be a function of the lattice deformation parameter.
On the Thermodynamic Fluctuations of Magnetization in Ferromagnets
Acta Phys. Pol. 30, 591 (1966)
abstract
We have discussed the influence of crystal lattice vibrations on the building up and decay of thermodynamic fluctuations of magnetic moment in ferromagnets. The crystal lattice vibrations have been described by the temperature of the lattice. We have arrived at the conclusion, that a thermodynamic fluctuation of magnetic moment is conditioned by fluctuation of temperature in the corresponding region of the crystal lattice. Decay in time of this fluctuation of temperature is determined by the Fourier equation and owing to the spin-crystal lattice coupling is transmitted on the fluctuation of magnetic moment. This effect, together with that of spin diffusion investigated earlier, determine the decay of thermodynamic fluctuations of magnetic moment. The relation between the range of correlation between spins and the dimension of the fluctuation of magnetic moment has been discussed. The dimension of this fluctuation depends on the dimension of the fluctuation of temperature in the lattice. For the previously calculated distribution of magnetic moment determined by the function \(|\sin k_2r|/r\) the dimension of the corresponding fluctuation of temperature has been evaluated and expressed as a function of the temperature \(T\) of the fluctuation and temperature \(T_0\), of the total sample (reservoir). With spherical symmetry assumed, the radius of the latter fluctuation determines the range of correlation between spins. This range of correlation serves in determining with help of the correlation \(|\sin k_2r|/r\) a new cross section for critical magnetic scattering of neutrons, for temperatures above or at the Curie point. We have discussed the physical picture of critical magnetic scattering of neutrons, in particular its analogy to that of critical opalescence. In view of the discussion performed for the ferromagnetic case, the Ornstein and Zernike theory of critical opalescence is treated as a better approximation than the Smoluchowski theory but not as refutation of the latter; the Smoluchowski assumption, that a fluctuation can be treated as subsystem in reservoir remains valid even at the critical point. We have also discussed physical aspects of our earlier calculation of the distribution of magnetic moment in the fluctuation.
On Marx’s Variational Principle
Acta Phys. Pol. 30, 617 (1966)
abstract
The matter tensor of a generally relativistic perfect fluid is derived from an invariant integral by a method of Marx and a condition on the Ricci scalar \(R\) gives Einstein’s material equations. A reasonable physical interpretation can be given to the form of the matter tensor which is found.
Application of Transversity Amplitudes to the Kinematical Analysis of Two-Body Processes at High Energies
Acta Phys. Pol. 30, 629 (1966)
abstract
The transversity amplitudes (in which the normal to the scattering plane is chosen as the spin quantization axis) are applied to the analysis of the two-body processes at high energies. This leads to the following simplifications: (a) the crossing relations are simple (the crossing matrix has only one non-zero element in each row and in each column-; thus there is no summation in the crossing relations), (b) parity conservation implies vanishing of some transversity amplitudes what is especially convenient in evaluation of spin density matrices of produced resonances in terms of scattering amplitudes, (c) Lorentz transformations in the scattering plane can change at most a phase of the amplitude (and, consequently, of the spin density matrix of a produced resonance). The angular distributions of the decay products referred to the normal to the scattering plane are explicitly evaluated for several most frequent types of decays. The transversity amplitudes can be expressed in terms of helicity amplitudes; a simple algorithm is given.
On the (109°120°) Bloch Wall in the Face-Centred Cubic Ferromagnetic Lattice
Acta Phys. Pol. 30, 647 (1966)
abstract
The (109°|120°) Bloch wall in the face-centred cubic ferromagnetic lattice is examined, on the basis of a theory developed by Ziętek. This includes the derivation and solution of the variational principle as well as the calculation of the thickness and energy of the (109°|120°) Bloch wall. Quantitative results for Ni are given and found to be in exact agreement with those obtained by phenomenological methods.
One-Electronic Eigenfunctions of Atoms
Acta Phys. Pol. 30, 657 (1966)
abstract
Simple, analytic eigenfunctions in the one-electronic approximate theory of atoms are given. The behaviour of these eigenfunctions agrees with experiment for arbitrary energy states of every element. Solution of this problem from the relativistic viewpoint is also given. An application of the results obtained to the solid state theory is shown to be possible.
One-particle Pauli Master Equation for Indirect Interactions
Acta Phys. Pol. 30, 671 (1966)
abstract
The interactions between a system, of particles (bosons or fermions) and a boson field, described by the (non-relativistic) Hamiltonian of the Fréhlich type are discussed. The Markovian Master Equation of the Pauli type for these interactions is not fulfilled by the diagonal elements \(N(p, t)= a^+(p, t) \alpha (p, t)\) of the one-particle density matrix operator (\(a^+a\)), as is the case for direct interactions between the considered particles, and it is found that such an equation describes the time evolution of another operator, \(N’(p, f)\), which contains also the nondiagonal elements of (\(a^+a\)), and the two- and more-particle correlations. For this purpose the unitary transformation is applied, which transforms the Hamiltonian into the form where the indirect interactions between the considered particles via boson field appear explicitly. These results seem to deny the popular opinions that (i) the one-particle density matrix is sufficient for description of a system of non-interacting with each other particles in interaction with another system, when the behaviour of the first system is of only interest, and (ii) that the correlations between such particles cannot be created.
Optically Induced Birefringence
Acta Phys. Pol. 30, 683 (1966)
abstract
From considerations of classical electrodynamics and statistical mechanics, a general theory of birefringence induced in nondispersive isotropic dense media by a light beam of very high intensity is developed. By a semi-macroscopic method a general equation for the light intensity-dependent refractive index is derived, and the optical birefringence constant \(B\) is obtained therefrom. This constant \(B\) is proved to consist of two terms, one of which results from the third-order optical polarization due to the strong oscillating electric field, whereas the second term arises from the optical molecular orientation effect which depends directly on the temperature. The birefringence constant \(B\) is then discussed in detail for the case of systems consisting of mutually interacting molecules, the latter being isotropically polarizable, or optically anisotropic with a centre of symmetry, or possessing no centre of inversion. Both the radial and angular interactions of the molecules are accounted for by means of binary and ternary correlation functions. The immediate effect on \(B\) of the electric fields of the induced and permanent molecular dipoles is also taken into account. Finally, the fundamentals of a statistical theory of the optical birefringence of multi-component systems, with applications to compressed gas mixtures, are proposed.Fasc. 5, pages 711–901
Some Remarks on Weinstein’s Method of the Solution of the Wave Equation for an Optical Electron
Acta Phys. Pol. 30, 711 (1966)
abstract
The semi-empirical method of the determination of wave functions for an optical electron and of the potential of the field in which this electron exists given by Weinstein have been generalized. In the original method of Weinstein the expression for the potential appearing in the wave equation for an optical electron is applied only in the case of atoms or ions having closed electron shells with the principal quantum number \(n\leqslant 3\) and with a single electron in the external shell. The present paper contains an expression for the potential in the case of more complex atoms or ions with a single optical electron in the outer shell.
On the Electric Conductivity of Hexamethylbenzene
Acta Phys. Pol. 30, 715 (1966)
abstract
Measurements of the electric conductivity of hexamethylbenzene (in the form of pellets) were carried out in the temperature range 85—135°C. The change of conductivity occurring at the transition point (\(\sim \) 110°C) amounts to about a factor of 2. The effect observed can be explained in terms of molecular interaction by means of hydrogen atoms of methyl groups.
The Interaction Potential Between Mercury and Helium Atoms
Acta Phys. Pol. 30, 721 (1966)
abstract
The potential curves for the interaction of a mercury atom in the \(6^1S_0\), and \(6^3P_1\) states with a helium atom in the \(1^1S_0\) state have been determined by means of the Lennard–Jones (12–6) potential. The potential curve for the interaction in the ground states has been determined on the basis of experimental studies of the thermodynamical properties of the two gases. For the interaction between helium and a mercury atom in the \(6^3P_1\) state the attraction energies, corresponding to the quantum numbers \(Q = 0\) and \(Q = \pm 1\), have been calculated in dipole–dipole approximation. The repulsion branches of the potential curves for both values of \(Q\) have been determined by means of spectroscopic analyses of the effect of helium on the mercury resonance line. The determined potential curves gives a qualitatively correct description of the phenomena of pressure broadening and shift of the mercury resonance line by helium.
On the Preparation of Thin Antiferroelectric PbZrO3 Layers by Means of the Electrophoresis Method
Acta Phys. Pol. 30, 731 (1966)
abstract
Thin PbZrO3 layers having antiferroelectric properties can be obtained by means of the electrophoresis method. The stock material is powder obtained from polycrystallic PbZrO3-sample. The mechanical and electrical properties of the thin layer thus obtained depend on conditions in which electrophoretic deposition on metallic substrate occurs, as well as on thermal treatment of the deposited antiferroelectric material. The dielectric constant of PbZrO3 layers is a dozen or so times smaller than that of polyerystallic samples, and the Curie point is shifted by several degrees towards higher temperature. The loss factor tg \(\sigma \) for thin layers becomes smaller in the vicinity of the Curie point, however high porosity is presumably the reason for the fact the tg \(\sigma \) is still several times greater than in the case of solid sample.
Mean Amplitudes of Vibration, Thermodynamic Functions Molecular Polarizability and Absolute Raman Intensities of \(\Sigma ^+_g\) Modes in Diacetylene
Acta Phys. Pol. 30, 743 (1966)
abstract
A detailed account of the vibrational and structural data for diacetylene possessing a linear symmetrical structure with the symmetry point group \(D_{\infty h}\) has been given. Mean amplitudes of vibration at the room temperature have been computed by the Cyvin method utilizing the symmetry coordinates. Molar thermodynamic functions have been calculated on the basis of a rigid rotator, harmonic oscillator model for the ideal gaseous at one atmospheric pressure. Bond polarizabilities, molecular polarizability and polarizability derivatives corresponding to absolute Raman intensities of \(\Sigma ^+_g\) modes in the ground electronic state have been calculated by the Lippincott–Stutman. method employing the delta-function model of chemical binding. Results are briefly discussed.
Meson–Baryon Forward Scattering in Relativistic Theory of Spin and Unitary Symmetry
Acta Phys. Pol. 30, 753 (1966)
see erratum: Acta Physica Polonica 31, 1082 (1967)
abstract
In the present paper in the scheme of \(SU(6)\) symmetry all possible relations among meson baryon forward scattering amplitudes are systematically studied. In the frame of \(U (6,6)\) the most general expression including 30 regular and irregular amplitudes is obtained for the forward meson baryon scattering matrix element, the last being invariant under \(SU(6)_W\). The method applied in the present paper differs from that developed in [28]. (J.C. Carter, et al. , Phys. Rev. Letters, 15, 373, (1965).) We show that many relations which have been obtained in [28] for forward meson baryon scattering cross sections are not the consequences of \(SU(6)_W\) as they hold only in the non-relativistic limit, provided only regular amplitudes are taken into account.
On the Dependence of Mobility of Ions on the Viscosity of Dielectric Liquids in the Range from 5P to \(2.10^{-5}\)P
Acta Phys. Pol. 30, 767 (1966)
abstract
A summary of the mobility values of ions ranging from \(10^{-7}\) to \(10^{-2}\) cm\(^2 V^{-1}\) sec\(^{-1}\) depending on the viscosity of fluids, the latter within the interval from \(2\cdot 10^{-2}\)P to 5 P has been presented (from liquefied noble gases to most viscous paraffin oil). The possibility of interpretation of experimental results from the viewpoint of ion structure has been discussed. From the data complied follows that the mobility of ions systematically decreases with increasing viscosity satisfying in a very wide range of investigated liquids the law \(u = A \cdot \eta ^{-\kappa }\) which in some cases may become the form of Stokes–Walden law: \(u = A\cdot \eta ^{-1}\). The constant \(A\) amounts to \(A = 3\cdot 10^{-6}\) (cm\(^2 V^{-1}\)sec\(^{-1}\)P) for negative ions and \(A_+ = 1.5\cdot 10^{-6}\) (cm\(^2 V^{-1}\) sec\(^{-1}\)P) for positive ions. On the other hand, the power index \(\kappa \) may vary within 1-2, depending on the type of liquid and ion.
On the Equations of Motion for Two Relativistic Models of Spin Particles in Weak External Gravitational Field
Acta Phys. Pol. 30, 777 (1966)
abstract
A spin particle represented by relativistic one and bi-point model in a weak external electric field is considered. The equations of motion of these particles contain a characteristic constant \(l\) having the dimension of a length which generates their spin as well as the diffluence. (These equations go into normal equations of geodesics — if we put \(l = 0\)). The equations of motion of spin particles are linearized with respect to gravitational potentials and their partial derivatives. Then all terms containing the products of this potentials (or their derivatives) with \(l^2\) are omitted (\(l\) being a measure of the difference of the particle is of the order of \(10^{-11}\)–\(10^{-13}\) cm). Assuming that the external gravitational field is so weak that the equations obtained in this approximation are already linear with respect to the particle coordinates, they are solved once basing on the metric of a plane wave and another time on diagonal metric. It is shown that although (in our approximation) there is no perceptible influence of the field on the motion of the particle as a whole, however, if the particle is described in terms of the one point model there occurs an increase of its acceleration energy i.e. a specific energy generated by spin due to the presence of a gravitational field. In the case of the bi-point model there is no such behaviour.
On the Energy-momentum Tensor of Spin 1/2 Particles
Acta Phys. Pol. 30, 791 (1966)
abstract
The present paper is concerned with the structure of the matrix elements of the symmetrical energy-momentum tensor between one-particle spin 1/2 states. For definiteness the case of the one-electron system is examined. Two different methods have been applied to the problem of computing the matrix elements to the lowest order in the fine-structure constant \(\alpha =\frac {e^2}{4\pi }(a)\) Using the perturbation approach we relate the matrix elements to the corresponding transition amplitudes in an external gravitational field. The actual form of the mechanical form factors of the system is established. (b) The imaginary part of the form factors is calculated by relating the matrix elements to the negaton–positon scattering processes. There is a complete agreement between the two methods. In the course of our work there appeared a paper by H.R. Pagels (Mechanical Form Factors, preprint) in which the imaginary part of the form factors has been calculated. Our results, obtained independently, will therefore be but briefly mentioned without going into details.
Generalised Mean Amplitudes and Coriolis Constants in Dichloroborane, Dibromoborane and Chlorine Trifluoride
Acta Phys. Pol. 30, 801 (1966)
abstract
The generalised mean amplitudes of the molecules B11Cl2H, B11Br2H and ClF3 belonging to the planar \(XYZ_2\), type have been estimated at 300°K. The Coriolis coupling coefficients of these molecular are also evaluated.
Generalised Mean Square Amplitudes and Coriolis Constants of Some Pyramidal \(XY_3\) Type Molecules and Ions
Acta Phys. Pol. 30, 807 (1966)
abstract
The Coriolis constants for the pyramidal \(XY_3\) model have been evaluated using force constants and Coriolis matrices, \(C^{\alpha }\). Morino and Hirota’s method has been applied to obtain the generalised mean Square amplitudes at 300°K. Values are reported for three halides and four oxide-ions.
Some Notes on the Coulson–Neilson Relation
Acta Phys. Pol. 30, 813 (1966)
abstract
A sufficient criterion for a trial function to satisfy the relation of Coulson and Neilson stating the existence of a linear relation between the error in the approximate energy and the mean value of the inverse interelectronic distance \(r^{-1}_{12}\), is presented. As an illustration, numerical results for several functions hitherto not discussed are given.
Interaction Between Diffusion and Viscous Flow in the Mixtures of Rarified Gases with Maxwellian Intermolecular Forces
Acta Phys. Pol. 30, 821 (1966)
abstract
The collisional terms of the first and second moment equations derived from Grad’s treatment of Boltzmann equations for rarified gas mixtures have been evaluated in the case of Maxwellian intermolecular forces. The results obtained have been applied to a discussion of the diffusion — viscosity coupling phenomena in the stationary flow a N2O–CO2 mixture.
Infinite Dimensional Solutions of the Generalized Feynman–Gell-Mann Equation
Acta Phys. Pol. 30, 827 (1966)
abstract
Some obstacles connected with the problem of the geometrical binding of the Poincaré group and the internal symmetry group \(SL(2, C)\) are discussed. The infinite dimensional nonunitary solutions of the generalized Feynman–Gell-Mann equation are obtained in the spinor space.
The Reaction \(\pi (K)+p\to \pi (K)+ N^*\) and the One-Particle Exchange Models
Acta Phys. Pol. 30, 833 (1966)
abstract
The polarization of the nucleon (3,3) resonance produced in the reaction \(\pi (K)+p\to \pi (K)+ N^*\) is investigated. It is shown that the measurement of the angular distribution of the \(N^*\) decay can provide an information on the relative phases of the helicity amplitudes in that process. This information can therefore be used as a general test for the applicability of the one-particle and/or Regge-pole exchange models which predict equal phases of all helicity amplitudes. The test is independent of any details of the considered model (like e.g. the values of coupling constants or the shape of formfactors, absorption factors or vertex functions).
On the Mapping of Spin Hamiltonians
Acta Phys. Pol. 30, 839 (1966)
abstract
By using a general method developed by Blatt and Matsubara, the problem of mapping of operators from the Hilbert space of angular momentum operators onto the Hilbert space of harmonic oscillators is re-examined, from the viewpoint of its applicability to Dyson’s spin wave formalism. An alternative proof is given of the respective formulae obtained by different authors and varying by both degree of generality and correctness of derivation, according to which the mapping operation can be reduced to a simple substitution.
Sur les propriétés tensorielles des molécules dans les champs électromagnétiques statiques intenses
Acta Phys. Pol. 30, 851 (1966)
abstract
En utilisant un formalisme tensoriel général et compact, on a calculé les éléments matriciels diagonaux du moment électrique ou magnétique 2”-polaire d’une molécule soumise à l’effet des champs électromagnétiques statiques intenses. Les calculs furent effectués dans les approximations du premier, deuxième et troisième ordre du calcul des perturbations de la mécanique quantique. De pareils calculs de l’énergie de la molécule perturbée furent effectués dans l’approximation jusqu’au quatrième ordre, et on a trouvé une relation générale entre l’énergie d’ordre \((p+1)\) et le moment d’ordre \(p\) de l’approximation. En outre, on a obtenu des expressions quantiques-mécaniques pour les éléments matriciels diagonaux des polarisabilités multipolaires de premier, deuxième et troisième ordre des molécules multipolaires. Le formalisme proposé sert pour le calcul de différents effets non-linéaires dont l’étude permet d’obtenir des informations directes sur les multipôles moléculaires permanents et induits qui déterminent les propriétés tensorielles des molécules dans des champs électromagnétiques intenses. On donne une discussion basée sur le cas des variations du tenseur de la perméabilité électrique d’un gaz dues à un champ électrique intense homogène, au gradient d’un champ électrique, ou au gradient d’un gradient de champ électrique. En outre, on a considéré les variations non-linéaires du tenseur de la perméabilité électrique produites par des champs magnétiques intenses. Ces effets, bien que de faibles valeurs, pourront être mesurés, au moins en partie, dans des conditions expérimentales appropriées, ce qui rendra directement accessibles des données sur les variations des propriétés électriques et magnétiques des molécules, dues à un champ électrique ou magnétique du degré respectif.
Propagation of an Intense Laser Beam in Liquids
Acta Phys. Pol. 30, 877 (1966)
abstract
A giant pulse ruby laser beam was focused in various liquids. Normal propagation of the light, selftrapping of the beam in its own wavequide, and breakdown of the liquid were observed as a function of the flux density.
Surface States of a Deformed One-Dimensional Crystal II
Acta Phys. Pol. 30, 883 (1966)
abstract
The energies of surface states as functions of four parameters: \(\alpha , \beta , \gamma \), \(p\) and \(q\), which measure the deformation of the lattice constant at the surface, the change of dimensions of the first barrier, the change of the potential of the bulk atoms and the change of the potential step at the surface, respectively, are calculated for a one-dimensional semi-infinite crystal. It is shown that two, one or zero surface levels exist owing to the value of the various parameters.
Plasma Generation at Solid Surfaces in a Giant Pulse Ruby Laser Beam
Acta Phys. Pol. 30, 891 (1966)
abstract
Experiments on plasma generation on solid targets with the use of a giant pulse ruby laser beam are described. The laser beam was fairly or not focused at all at different solid surfaces, including very hard materials like ruby or tungsten. The generated plasma was photographed perpendicularly to the beam, i.e. , almost parallely to the solid target. The most striking effect was obtained with silver film on a glass substrate.
Relative Strengths of Spectral Lines for ZnII and CdII Doublets
Acta Phys. Pol. 30, 897 (1966)
Rainich Problem for Complex Scalar-Electromagnetic Field
Acta Phys. Pol. 30, 901 (1966)
abstract
Under which conditions a symmetric tensor may be considered as an energy-momentum tensor of a combined electro-magnetic and complex scalar field have been ascertained.Fasc. 6, pages 913–1057
Mean Amplitudes of Vibration, Shrinkage Effects and Coriolis Coupling Coefficients of C3O2
Acta Phys. Pol. 30, 913 (1966)
abstract
The theory of mean-square amplitude matrices is applied to the carbon suboxide molecule. The parallel and perpendicular mean-square amplitudes for the interatomic distances are calculated. The perpendicular amplitudes have been used for calculating the “shrinkage effects”. The Coriolis coupling coefficients are also evaluated using \(C\)-matrix method.
Transition Heat and the Phenomenological Theory of Ferroelectricity
Acta Phys. Pol. 30, 921 (1966)
abstract
Formulae for the transition heat or, respectively, the specific heat anomaly are derived in ferroelectrics with a first or second order transition. The temperature-dependence of the coefficients in the expansion of the Gibbs function is taken into account. Devonshire’s equation is a special case of these formulae.
Ionization Currents Induced by Alpha Radiation in Liquid Hexane and Heptane
Acta Phys. Pol. 30, 927 (1966)
abstract
The paper present the results of measurements of the intensity of ionization currents induced by alpha particles from 239Pu in hexane and heptane. The effect of simultaneous ionization by alpha particles and gamma radiation from 137Cs has been investigated. The dependence of the ionization current on activity of the source of alpha radiation was found to be linear.
Negative Photoconductivity and Optical Quenching in CdSe Crystals
Acta Phys. Pol. 30, 933 (1966)
abstract
The spectral distribution of photosensitivity and optical quenching of photocurrent at various temperatures in CdSe single crystals grown in a reducing atmosphere had been investigated. Negative photoconductivity had been observed in some CdSe single crystals in the 7150–7500 Å region at room temperature. There were determined three bands of optical quenching of photocurrent induced by excitation in the intrinsic absorption region, the long-wave limits of which amount to 7800, 12000 and 20000 Å , respectively. The observed effects of negative photoconductivity (in the 7150–7500 Å region) and optical quenching (in the 7150–12000 Å region), and the shape of spectral distribution of photosensitivity are explained as effect of surface defects of the crystal lattice.
Investigations of the Nuclear Matrix Elements (n. m.e.) of the Outer Group of the \(\beta \)-transition \(\left (W_0 = 5.26\, m_0c^2\right )\) in 140La–140Ce
Acta Phys. Pol. 30, 943 (1966)
abstract
The \(\beta \)–\(\gamma \) directional correlation factor \(A_2\) of the 140La–140Ce \(\beta \)–\(\gamma \) cascade for the outer group of \(\beta \)-electrons (\(W_0 = 5.26\)) and the following \(\gamma \)-transition (\(E_{\gamma } = 1.60\) MeV) was measured as a function of the electron energy \(W\). Using the \(\xi ^2\)-test method the set of Kotani-parameters \(Y, x, u, z\) and of n. m. e. was found for this \(\beta \)-transition with best fit of the following currently known observables: \(A^{x}_2\) — reduced \(\beta \)–\(\gamma \) directional correlation factor, \(C(W)\)-shape factor, \(\omega \) — \(\beta \)–\(\gamma \) circular polarization directional correlation factor and \(ft\)-value. All the currently known sets of n. m. e. for the outer group of \(\beta \)-transition of 140La are critically analyzed with regard to the application of different nuclear models. The set of n. m.e. found in this paper is in satisfactory agreement with the conserved vector current theory. It has been shown that the measurement of the energy dependence of the w-factor can be a sensitive experimental method to choose the most reliable set of n. m. e.
Electronic Structure and Spectra of Organic Molecules Part III. SCF MO Calculations for Some Amino, Methylamino and Dimethylamino Substituted Pyridines and Pyrimidines
Acta Phys. Pol. 30, 963 (1966)
abstract
Results of the SCF MO CI calculations for some amino, methylamino and dimethylamino substituted pyridines and pyrimidines are reported. Satisfactory agreement between experimental and theoretical singlet–singlet transition energies is obtained.
Geodesic Motion in Gravitational Fields I. Internal Schwarzschild Field
Acta Phys. Pol. 30, 981 (1966)
abstract
The motion of a test body with given mass, energy and angular momentum in an incompressible fluid sphere is studied within the framework of general relativity. Conditions for the physical parameters of the test body are derived under which the motion is of a bounded type. It is found that for some choice of the physical parameters there exist two regions wherein particle motion is admitted. These two regions form two completely separated domains. The results may be applied either to the motion elementary particles in superdense stars or to the motion of celestial bodies in galaxies.
Об уровнях среднего поля ядер
Acta Phys. Pol. 30, 999 (1966)
abstract
Рассмотрен вариант приближенного решения уравнения Шредингера с потенциалом Саксона–Вуда. Нолучены волновые функции одночастичных состояний в аналитическом виде, а также некоторые интегралы от их комбинаций. Результаты могут быть использованы в различных приложениях теории ядра и ядерных реакций.
Quantitative Studies of the Pyroelectric Properties of Triglycine Sulfate Crystals by the Dynamical Method
Acta Phys. Pol. 30, 1015 (1966)
abstract
Pyroelectric properties of triglycine sulfate crystals were investigated quantitatively by the dynamical method. The pyroelectric coefficients were determined from measurements of the pyroelectric voltage and pulse-wise variations in temperature of the crystals. Pulse-wise temperature variations were measured by two methods: at temperatures remote from the Curie point, a resistivity method recurring to the temperature-dependence of the electrical resistance in thin tellurium or bismuth layers deposited by evaporation in vacuo on one surface of the crystal plate was applied, whereas near the Curie point a capacity method was used recurring to the strong temperature-dependence of its dielectric permittivity. The numerical values of pyroelectric coefficients from the dynamical method were compared with those calculated from measurements of the spontaneous polarization versus the temperature, and the results were found to be in good agreement.
Atomic Displacements of the Perovskite Strontium Titanate
Acta Phys. Pol. 30, 1037 (1966)
abstract
Neglecting all but the three largest couplings between the sublattices of SrTiO3, one can calculate the displacements associated with each normal mode. The couplings Ti–O3, Ti–O4, O3–O4 and Sr–O2 which were neglected by Joseph and Silverman have been taken into account but with the assumption that all the titanium–oxygen couplings are same. In the similar way all the strontium–oxygen couplings are same. The calculations give two possible sets of solutions for the coupling constants. Displacement calculations suggest Last’s as well as Slater’s proposal for the description of the ferroelectric mode, but it is shown that neither is exactly correct for \(T\neq T_c\).
Réponse d’une chambre d’ionisation equivalente au tissu humain sous vide poussé
Acta Phys. Pol. 30, 1045 (1966)
abstract
On a étudié la réponse d’une chambre d’ionisation en matériel équivalent au tissu humain sous vide en fonction du potentiel de l’électrode externe. On a trouvé des régions où le courant d’ionisation est proportionnel à l’intensité du rayonnement gamma dont la chambre a été irradiée.
Ionization Current in \(n\)-Octadecane in the Vicinity of the Freezing Point
Acta Phys. Pol. 30, 1049 (1966)
On the Possibility of the Use of Technical Polycrystalline Silicon in Low Temperature Thermometry (Helium Temperatures)
Acta Phys. Pol. 30, 1053 (1966)
The Sum Rule for the Four Pion Coupling Constant Resulting from Current Algebra
Acta Phys. Pol. 30, 1057 (1966)