Vol. XXIV (1963)
Fasc. 1, pages 3–135
Исследования электрических своиств нитевид- ных монокристаллов серебра в зависимости от температуры
Acta Phys. Pol. 24, 3 (1963)
abstract
В настоящей работе проведено исследование электрического сопротивления нитевидных монокристаллов серебра в диапазоне от комнатной температуры до температуты жидкого гелия, т.е. 4,2°К, а для нескольких усиков до температуры 1,77°К. Исследовано также влияние диффузионного рассеяния электронов проводимости от поверхности в зависимости от диаметра усика. Сравнено зависимость удельного сопротивления от температуры для проволочек и усиков серебра. Установ лено выступление минимум сопротивления серебряных усиков.
Стационарное поле тяготения в конформном пространстве
Acta Phys. Pol. 24, 13 (1963)
abstract
В работе дало определение конформного пространства соответствующего пространству-времени теории тяготения Эйнштейна. Затем преобразовано уравнения стационарного поля тяготения к конформному пространству. Используя эти уравнения, показано что в пустоте, решения стационарных уравнений поля представляют плоское пространство-время. В этом случае, гармонические координаты являются прямоугольными декартовыми координатами.
On the Functional Formalism of the S-matrix
Acta Phys. Pol. 24, 23 (1963)
abstract
We present a method of obtaining the \(S\)-Matrix in form of an expansion in terms of the free incoming field. This method differs slightly from the usual approach: an auxiliary c-number field \(\mit {\Phi }\) instead of the auxiliary \(c\)-number current \(J\) is used. The exponent of the generating functional is closely related to the traditional interaction Lagrangian. This procedure leads us to vacuum expectation values of the \(T\)-products expressed rather in terms of the current \(j\) than in terms of the field \(A\). The renormalization problem is clearly exhibited.
Leptons in the Isospace \(\cal {H}(R_3^c)\)
Acta Phys. Pol. 24, 31 (1963)
abstract
After giving the isobaric spin multiplets built on the polynomials \(\phi (\omega ^*)\) of the isospace \({\cal H}(R_3^c)\) and after recalling their transformation laws under the invariance group of strong interactions and under the gauge group, it is showed that one can associate to leptons some polynomials \(\phi (\omega ^*)\in {\cal H}(R_3^c)\) so that, the sets \((\phi _e,\phi _{\nu ,e})\) and \((\phi _\mu ,\phi _{\nu ,\mu })\) do not constitute isospinors which excludes the possibility of strong interactions for leptons. Then, afterwards, the Lagrangian of strong interactions is discussed.
Effect of the Cu++ Ion on Delayed Phenomena in Rochelle Salt
Acta Phys. Pol. 24, 45 (1963)
abstract
The time-dependent variations occurring in the dielectric permittivity of Cu++-dope Rochelle salt subsequent to applying or removing DC polarizing voltage were measured. The doped crystals had been grown from solutions containing 0.01 and 0.06% CuCO3\(\cdot \) CU(OH)2. The maxima of the variations observed during the measurements were found to shift towards higher polarizing field strengths with increasing Cu++ content. The Cu++ ions are presumed to favour immobilization of the domains.
On the Effect of an External Electric Field on the Emission of Electrons from Additively Coloured KCl Into a Gaseous Atmosphere (I)
Acta Phys. Pol. 24, 51 (1963)
abstract
The dependence on the accelerating voltage of photostimulated exoelectron emission from additively coloured KCl single crystals was investigated. The decay of photostimulated emission was measured versus the time at standard accelerating voltages. From the decay curves, the dependence of the decay constant 4 on the accelerating voltage applied was derived.
Optical Properties of Thin Indium Films
Acta Phys. Pol. 24, 65 (1963)
abstract
The optical properties of thin indium films deposited by evaporation in vacuo (\(p = 5\times 10^{-5}\)Tr) on glass substrate were investigated. Using a Zeiss spectrophotometer, the following coefficients of the freshly deposited films in the wave length range from 400 m\(\mu \) to 1000 m\(\mu \) were measured; reflectance on the air-side (\(R\)), reflectance at the substrate side (\(R\)’) and transmittance (\(T\)). From \(T, R, R\)’, and using Male’s graphical method, the real (\(\nu \)) and imaginary part (\(\kappa \)) of the complex refractive index was determined.
Consistent Formulation of the Chew-Low Theory for Meson–Nucleon Scattering
Acta Phys. Pol. 24, 73 (1963)
abstract
By choosing the cutoff value \(P = 4\) and by taking into account one CDD pole we achieve good agreement of the Chew–Low theory with the experimental data for \(\pi \)–\(N\) scattering up to about 500 MeV.
New Formulation of the Statistical Theory of Multiple Particle Production
Acta Phys. Pol. 24, 79 (1963)
see erratum: Acta Physica Polonica 25, 854 (1964)
Spontaneous Magnetization of Ferromagnetic Thin Films
Acta Phys. Pol. 24, 91 (1963)
abstract
The spontaneous magnetization of a ferromagnetic simple cubic thin film is calculated. The Holstein–Primakoff spin wave method is applied. A magnetic anisotropy term is included in the Hamiltonian. The dependence of the spontaneous magnetization on the temperature and thickness is investigated. The effect of possible parallel and perpendicular magnetic anisotropy is discussed.
Dielectric Saturation in Benzene–Chloroform–Hexanol-1 Three-component Mixtures
Acta Phys. Pol. 24, 107 (1963)
abstract
The variations of the dielectric permittivity in strong electric fields for benzene–chloroform–hexanol-1 solutions were measured. The high electric conductivity of the mixtures investigated rendered a pulse method necessary. The results obtained in measuring the dielectric permittivity variations referred to unit electric field strength in cgs units \(\Delta \epsilon /E^2\) are shown versus the concentration expressed in molar fractions (\(f\)) or as the number of molecules per ccm (\(N'\)).
On the Coulomb Mechanism of the Nuclear Disintegration
Acta Phys. Pol. 24, 115 (1963)
abstract
The disintegration cross section of Be3 is considered in the Coulomb field of middle and heavy nuclei in channels Be9\(\to \) Be8+ \(n\) and Be9\(\to \) Be9*\(\to \) He5+ \(\alpha \). Besides, the cross section for the Coulomb fission of heavy nuclei is calculated.
On Elastic Scattering of Heavy Ions
Acta Phys. Pol. 24, 121 (1963)
abstract
The treatment of the elastic scattering of heavy ions in the quasi-classical approximation is more detailed as compared to that of the previous paper (Kalinkin, Pustylnik 1962). The smoothness of switching on of the absorption is taken into account. The “diffraction” maximum observed in experiment is reproduced. Besides, it is established that the curve corresponding to the ratio of the cross section of elastic scattering to that of the Rutherford scattering for strictly fixed energy can have a “fine’’ structure.
Cross Section for Compound–Nucleus Formation in Heavy-ion-induced Reactions
Acta Phys. Pol. 24, 125 (1963)
abstract
The compound-nucleus formation cross section are calculated for a number of reactions. The information about the parameters of nuclear interaction between nuclei is used which was obtained from the quasi-classical analysis of experiments on heavy ion elastic scattering. It is established that the account of such an interaction is important.
Gamma–Gamma Directional Correlations in 146Eu
Acta Phys. Pol. 24, 131 (1963)
abstract
Gamma-gamma directional correlations for the triple cascade in 146Eu were measured. An alternative assignment for the decay scheme could be established.
Magnetic Balance for Measuring the Magnetic Susceptibility of Para- and Ferromagnetics
Acta Phys. Pol. 24, 135 (1963)
abstract
A magnetic balance of a new type for measuring the magnetic susceptibility of para- and ferromagnetic bodies is described. The device possesses an optical system of original design for measuring the force pulling the sample into an inhomogeneous magnetic field, consisting of two thin plane elastic mutually parallel plates and three small mirrors. The device is of a highly simple construction and is remarkable for the easiness with which it can be operated.Fasc. 2, pages 143–295
Statistical and Thermodynamical Description of Correlated Systems. IV. Time-dependent Distributions
Acta Phys. Pol. 24, 143 (1963)
abstract
The solution of master equations describing the evolution in time of correlated subsystems forming an isolated system is given. It is found that near by equilibrium or stationary state the probabilities of finding of the subsystems in their quantized states, and also the correlation coefficients are the exponential functions of momentary values of observables, and do not depend on the the initial state of the system.
Statistical and Thermodynamical Description of Correlated Systems. V. Phenomenological Equations Near by Equilibrium
Acta Phys. Pol. 24, 153 (1963)
abstract
The phenomenological equations for time-changes of entropies and of observables are obtained from time-dependent statistical probability distributions given in the preceding paper. It is found that there are two possible and admissible ways of phenomenological description of irreversible processes: (i) from the point of view of the whole isolated system, or (ii) from the point of view of a single non-isolated subsystem. These descriptions are not equivalent: in (i) one finds different formulas for the rates of irreversible changes than in (ii), i.e., the fluxes are found to be caused by different causes in different descriptions. It is also found that irreversible processes occurring in both subsystems can influence each other.
Effect of an Electric Field on the Dielectric Permittivity of Dipole Liquids
Acta Phys. Pol. 24, 165 (1963)
abstract
The values of the dielectric saturation effect \(\Delta \varepsilon \) in ethyl ether, nitrobenzene, \(o\)-nitrotoluene, \(m\)-nitrotoluene, \(o\)-nitroanisol, 1,2-dibromoethane, 1,2-dichloroethane and 1,2-dichloroethylene were measured by the heterodyne beat method. The results obtained for ethyl ether and nitrobenzene corroborate earlier authors. For solutions, varying the concentration, the saturation effect was found to present one of the following three patterns: a) The first type is represented by ethyl ether, \(o\)-nitroanisol, and their solutions in benzene; change in permittivity \(\Delta \varepsilon \) in an external electric field is here negative (\(\Delta \varepsilon \lt 0\)) at all concentrations. b) The second type is found in nitrobenzene, \(o\)-nitrotoluene and \(m\)-nitrotoluene and their solutions in benzene; the change in permittivity \(\Delta \varepsilon \) in an electric field revealing a point of inversion at a concentration characteristical for each of the liquids. For concentrations below the inversion point, \(\Delta \varepsilon \) is negative (\(\Delta \varepsilon \lt 0\)), becoming zero for pure benzene; at concentrations above the inversion point, \(\Delta \varepsilon \) is positive (\(\Delta \varepsilon \gt 0\)), assuming its largest positive value for the pure liquid. c) The third type is represented by 1,2-dichloroethane and 1,2-dibromoethane, in whose solutions in carbon tetrachloride the permittivity variations \(\Delta \varepsilon \) in an electric field are positive (\(\Delta \varepsilon \gt 0\)) at all concentrations. The temperature-dependence of the permittivity variations \(\Delta \varepsilon \) in an electric field was measured for nitrobenzene, \(m\)-nitrotoluene, and 1,2-dibromoethane. The first two reveal a strong temperature-dependence, whereas for 1,2-dibromocthane no such dependence could be ascertained unambiguously. The saturation eflect of the second kind was convincingly shown to be closely related to the presence of intermolecular interaction depending on the structure of the molecules, whereas that of the third type is related to internal rotation within the molecules. The theoretical derivation of the saturation effect in A. Piekara’s theory, which predicts both positive and negative values \(\Delta \varepsilon \) of the saturation, is discussed.
Optical Properties of \(\mathrm {Cd}_{x}\mathrm {Hg}_{1-x}\) Te Semiconductors \(\;x = 1.0; 0.9; 0.8\)
Acta Phys. Pol. 24, 191 (1963)
abstract
The value of the forbidden energy gap and its variation with the temperature were derived from measurements of the optical absorption near the fundamental absorption edge. The transitions were found to be indirect. The energy of the phonons involved were determined.
On Some Optical Properties of Thin Cd0.9 Hg0.1 Te Layers
Acta Phys. Pol. 24, 199 (1963)
abstract
A method of depositing thin Cd0.9 Hg0.1 Te layers by evaporation is considered. The dependence of the light absorption coefficient on the wavelength in the range of 0.8\(\mu \) to 2.4\(\mu \) is given. From the shape of the transmissivity curve and from the analysis of interference frings in the 1.2\(\mu \)–2.4\(\mu \) range, the layers investigated are concluded to present two refractive indexes: a “surface” index of \(n_p = 1.9\) at the air-contacting surface, inside the layer and at the surface contacting glass “volume” refractive index of \(n_0 = 3.1\).
On the Paramagnetic Effect in Superconductors in Transversal Magnetic Field
Acta Phys. Pol. 24, 209 (1963)
abstract
The magnetic moment of the tin superconducting cylinder carrying current in transversal magnetic field has been measured. When the cylinder was in the intermediate state its magnetic moment obtained a paramagnetic sign, i.e. opposite to the sign of magnetic moment in completely superconducting state. It has been found that, likewise the case of longitudinal field, the minimal current required for the appearance of the effect is, for tin, 1.2 amperes. It has been stated that this paramagnetic effect was a result of circular superconducting currents, circulating in the plane perpendicular to the direction of external magnetic field.
Sur les propriétés optiques d’une surface conique
Acta Phys. Pol. 24, 217 (1963)
abstract
Dans un cas particulier, les surfaces réfringentes des axicons peuvent être coniques. Le but de ce travail est d’étudier les propriétés d’une surface réfringente conique. Afin d’établir les équations de l’imagerie on part de la théorie de la foncion iconale angulaire. L’auteur montre qu’il existe une classe “conique” très large de surfaces dont la fonction inconale angulaire s’exprime au moyen de la même formule. On constate que les images virtuelles sont les plus intéressantes à plusieurs points de vue et on les étudie en détail.
The \(\mu \) Meson Content in a Photon–Electron Cascade Initiated by a Primary Photon of Energy 1015 eV
Acta Phys. Pol. 24, 231 (1963)
abstract
The longitudinal development of a meson cascade in an EAS initiated by a photon of 1015 eV is analysed using Landau’s equation in approximation \(\mit {\Lambda }\) and the total number of mesons created is estimated. On our assumptions concerning the multiplicity of photoproduction, multiple production in \(\pi \)-nucleus collisions and photoproduction cross section, the number of muons in a cascade should vary in the 1300—1800 range. This means that the number of penetrating particles in a photon-initiated shower includes from 3 to 5% of that in a shower of the same size but initiated by a nuclear active particle.
Ion Mobility in Liquid Cyclohexane
Acta Phys. Pol. 24, 243 (1963)
abstract
The mobility of negative and positive ions in cyclohexane is measured. The temperature dependence of the mobility can be described by the equations \(u_ - = 6.7 \times 10^{-2} \mathrm {exp}(- 3020/RT)\) cm\(^2\)V\(^{-1}\)sec\(^{-1}\) and \(u_+ = 6.8 \times 10^{-2} \mathrm {exp}(—3810/RT)\) cm\(^2\)V\(^{-1}\)sec\(^{-1}\). Moreover, for negative ions, Stokes’ law is found to be fulfilled satisfactorily. For positive ions, the dependence between mobility and viscosity is different and would seem to be determined by the different values of the activation energy for the viscosity and mobility of positive ions.
Dispersion Relation for Spin Waves in CuFeS2
Acta Phys. Pol. 24, 249 (1963)
abstract
The spin wave dispersion relation in the case of CuFeS2 is studied. It was found that the spin wave frequencies as functions of the direction of \(\vec {q}\) are anisotropic. The possibility of experimental verification by the method of inelastic scattering of neutrons is discussed.
Approximate Coupled Integral Equations for Partial \(K^+\)–\(N\) Scattering Amplitudes
Acta Phys. Pol. 24, 255 (1963)
abstract
Approximate coupled integral equations for partial \(K^+\)–\(N\) scattering amplitudes are obtained using the method based on the Shirkov approach to the double integral representation technique in the low energy region.
Viscosity of Liquid Ammonia and Hydrogen Chloride
Acta Phys. Pol. 24, 269 (1963)
abstract
The viscosity of liquid NH3 and liquid HCl under the pressure of their saturated vapours was measured in the temperature ranges from 0° to \(+\)70°C for NH3 and from \(-\)32° to 45°C for HCl.
The Decay of Thermodynamical Fluctuations of Magnetization in the Constant Coupling Approximation for Heisenberg Ferromagnetism
Acta Phys. Pol. 24, 273 (1963)
abstract
We have derived the equations of diffusion and entropy production for the decay of the longitudinal fluctuations of magnetization in a Heisenberg ferromagnet with spin \(s = \frac {1}{2} \) at lattice site. Both equations have been obtained with the method of thermodynamics of irreversible processes and the diffusion equation also through the master equation approach. The calculations have been performed in the framework of the constant coupling approximation extrapolated to nonequilibrium conditions. The calculated diffusion coefficient does not vanish at the Curie temperature.
Electron Paramagnetic Absorption in \(\gamma \)-irradiated Polycrystalline Hg2(NO3)2\(\cdot \) 2H20
Acta Phys. Pol. 24, 281 (1963)
Zeeman Splitting of the 14.4 keV Gamma Line of 57Fe IN CoFe2O4 Investigated by the Mössbauer Effect
Acta Phys. Pol. 24, 283 (1963)
abstract
Zeeman splitting of the 14.4 keV gamma line of 57Fe in cobalt spinel CoFe204 has been studied. Two values of the magnetic field intensity at iron nuclei \(H_1 = (509\pm 5)\) kOe and \(H_2 = (528\pm 5)\) kOe are found.
Low Temperature Resistance Minimum in Ag and Cu Whiskers
Acta Phys. Pol. 24, 285 (1963)
Anisotropy of Electrical Conductivity in \(p\)-nitrophenol Crystals
Acta Phys. Pol. 24, 289 (1963)
Remark on the Future Tube
Acta Phys. Pol. 24, 293 (1963)
The Closure of Minkowski Space
Acta Phys. Pol. 24, 295 (1963)
Fasc. 3, pages 299–445
Zur Störungsrechnung in der Gravitationstheorie
Acta Phys. Pol. 24, 299 (1963)
abstract
Die Einsteinschen Feldgleichungen werden in erster Näherung untersucht. Als nullte Näherung wird eine beliebig vorgebbare Metrik verwendet. Mit Hilfe einer Koordinatenbedingung gelingt es, diese Gleichungen in eine einfache Form zu bringen und Aussagen über die Greenschen Funktionen dieser Gleichungen zu machen. Die Anwendbarkeit dieser Näherungsmethode wird betrachtet.
Bestimmunq einiger geometrischer Grössen für das Schwarzschildfeld
Acta Phys. Pol. 24, 313 (1963)
The Phase Jump at the Focal Point in the Case of Electromagnetic Waves
Acta Phys. Pol. 24, 317 (1963)
abstract
For the case of a converging spherical electromagnetic wave, the phase jump by \(\pi \) occurring at the focal point is proved to be of the nature of an optical-geometrical phenomenon. The proof is based on Kottler’s theory of diffraction of electromagnetic waves. Attention is drawn to the fact that a phase jump at the focal point occurs also for convergent electromagnetic waves of a highly general class corresponding to superposition of the fields of multipoles of arbitrary order and that it represents an optical-geometrical phenomenon.
Some Notes on the Theory of Pressure Effects on Spectral Lines
Acta Phys. Pol. 24, 327 (1963)
abstract
The consequences are discussed of a formula for the intensity distribution in a pressure-broadened line given by Jabłoński in his theory of the pressure effects on spectral lines. General relations between intensity distribution functions for various concentrations of the perturbing atoms are deduced in a form suited for experimental verification, and methods are presented by which the functions \(I_0(x), I(x)\) and the parameter \(\varepsilon _0\), involved in Jabłoński’s formula may be calculated from experimental data.
On the Time of Maintainment of Heterocharge on Wax Electretes, as Dependent on Screening
Acta Phys. Pol. 24, 339 (1963)
abstract
The effect of screening on the time of maintainment of heterocharge on wax electrets was investigated experimentally, and was found to depend on the time elapsing between the end of polarization process and the moment of removal of the electrodes from the surface of the specimen. The difference in shape of the curves for the case when the electrodes are shorted during storage and when they are left unshorted allows to draw conclusions as to the nature of the processes occurring during polarization.
High Energy Scattering in Systems with Anomalous Thresholds
Acta Phys. Pol. 24, 345 (1963)
abstract
An \(S\)-matrix-treatment of high energy scattering is given in the presence of anomalous thresholds. The high energy behaviour of the elastic amplitudes is governed by the Pomeranchuk pole. In the case of the scattering on a nucleus, the amplitude is proportional to the atomic number. Besides the scattering on individual constituents of the target, a non-vanishing coherent scattering on the target as a whole is found. The possible role of many-nucleon intermediate states is briefly discussed.
Longitudinal Modes of a Linear Chain with Many Neighbours Interactions
Acta Phys. Pol. 24, 351 (1963)
abstract
It has been shown that for a monoatomic linear chain taking into account the interactions with many neighbours, one can obtain the same phonon dispersion relations as in the Einstein and Debye cases.
Integral Spectrum of Nuclear Active Particles at Mountain Altitudes from the Investigation of High Ionization Pulses
Acta Phys. Pol. 24, 357 (1963)
abstract
High ionization pulses were investigated with an apparatus of an area of 10 m\(^2\) installed at mountain altitudes (3200 m above sea level) and containing 192 ionization chambers. The analysis of the results obtained showed a large part of the high ionization pulses to be caused by several nuclear active particles falling simultaneously on the apparatus. Nuclear active particles falling in groups cause that the exponent of the integral spectrum of pulses registered on the area of 10 m\(^2\) amounts to \(1.33\pm 0.03\) while the exponent of the spectrum due to individual nuclear active particles is \(\geq 1.90\pm 0.05\).
Energy Spectrum of Photons from Decay of \(\pi ^0\)-mesons Generated in Nuclear Interactions at the Altitude of 3200 m Above Sea Level
Acta Phys. Pol. 24, 373 (1963)
abstract
Apparatus of an area of 10 m\(^@\) containing 6 layers of ionization chambers placed between lead and graphite absorbers was installed at mountain altitudes 3200 m above sea level. A layer of nuclear emulsion plates served for investigating the energy spectrum of photons from the decay of \(\pi ^0\)-mesons generated in the graphite absorber. The spectrum constructed on the base of 154 events in the energy interval \(2\times 10^{10}\)–\(4\times 10^{12}\) eV had an exponent \(\gamma = 2.0 \pm 0.3\).
Cascade Curves for Lead, for a Primary Photon and Electron of Energy (\(3 \times 10^8\)–\(10^{14}\))eV
Acta Phys. Pol. 24, 381 (1963)
abstract
Calculations of cascade curves for lead, made by Ott [1], have been repeated. Additional curves for primary electron and photon energies between (\(3 \times 10^{11}\)–\(10^{14}\)) eV are given.
On the Determination of the Octopole Moment of Tetrahedrail Molecules from Investigation of the Second Virial Coefficients
Acta Phys. Pol. 24, 389 (1963)
abstract
The possibilities are discussed of deriving information on the value of the octopole moment of tetrahedral molecules from the investigation of the second virial coefficients of the equation of state for a gas or gas mixture, the dielectric polarization, the molecular refraction, the molecular scattering of light and the molecular Kerr and Cotton–Mouton constants. The respective coefficients are computed for the general case of molecules of different kinds and the results contain various contributions from molecular interactions of the octopole and mixed types (e.g. octopole–dipole, octopole–quadrupole etc.). Some of the expressions derived contain, in addition to the octopole moment \(\mit {\Omega }\), the hyperpolarizabilities \(\beta \), \(\gamma \) and \(\xi \), which it will be possible to determine once the appropriate experimental data become available. Numerical evaluation for methane leads to reasonable values of the octopole moment for the CH4 molecule.
A Difference Between the Two Approximation Methods in General Relativity
Acta Phys. Pol. 24, 399 (1963)
abstract
The two approximation methods in general relativity, the EIH-method and the fast motion approximation, are compared in the lowest orders. In the linear approximation the equations of the EIH-method may be derived from those of the linear fast motion approximation. In higher orders we can not get the equations of the EIH-method from those of the fast motion approximation.
Influence of Water Vapour on the Rectifying and Electroluminescent Properties of Anodic Oxide Films on Aluminium
Acta Phys. Pol. 24, 407 (1963)
abstract
The effect of water vapour on the electrical and electroluminescent properties of Al/Al2O3/ solid counterelectrode systems was investigated experimentally. Electrical asymmetry and the anodic luminescence were found to occur only in the presence of water adsorbed into the oxide from the ambient medium. On the basis of the experimental observations the suggestion is made that the mechanism of rectification is associated rather with the process of electrolysis than with the \(p\)–\(n\) or \(p\)–\(i\)–\(n\) internal structure of the oxide.
On Diagonalization of the Free Spin-waves Hamiltonian for Arbitrary Magnetic Structure
Acta Phys. Pol. 24, 415 (1963)
Partially Projected Functions in the Superfluid Model of a Nucleus
Acta Phys. Pol. 24, 419 (1963)
abstract
A new set of trial functions is suggested for solving variational problem arising in the superfluid model of a nucleus. These functions satisfy additional invariance conditions which follow from the particle-number-conservation law. From another point of view the new functions contain only small part of these superfluous component which are present in functions of standard kind. The properties of the new functions are investigated. The energy of a system in the state described by the function which satisfies the stationarity condition is found.
The Quasi-classical Analysis of the Elastic Scattering of Complex Nuclei
Acta Phys. Pol. 24, 427 (1963)
abstract
The quasi-classical analysis of the elastic scattering of heavy ions is made for a number of concrete cases. Theoretical results are in a good agreement with experimental data. The parameters characterizing the nuclear interaction proved to be sufficiently stable for different combinations of colliding nuclei.
The Angular Distribution of the Transfer Reaction Products
Acta Phys. Pol. 24, 435 (1963)
abstract
The angular distribution of the transfer reaction products is calculated on the basis of the assumption about the quasi-elastic character of collision of ions with the target-nucleus. In this case use is made of the information about the parameters of the nuclear interaction between colliding nuclei obtained from the quasi-classical analysis of experiments on the heavy ions elastic scattering. Results are in a good agreement with experimental data.
Ferrimagnetics of Composition \(\mathrm {MnFe}_{2-x} \mathrm {Cr}_{x}\mathrm {O}_{4}\) and \(\mathrm {MnFe}_{2-x} \mathrm {Al}_{x}\)O4 with \(0\ll x\lt 2\)
Acta Phys. Pol. 24, 445 (1963)
Fasc. 4, pages 451–557
Some Experimental Data on the Semiconduction Properties of Indium Sulphide Crystals
Acta Phys. Pol. 24, 451 (1963)
abstract
Indium trisulphide was synthesized in a two zone furnace under sulphur pressure. Crystals were selected by using polarization or phase-contrast microscopes. A number of monocrystals and polycrystalline plates were provided with electrodes to measure the photoconductivity, conductivity and thermoelectric power. These exhibited high photoconductivity in the visible region. For determining the refractive index, the “real over apparent depth” method was used. The dielectric constant of the crystal at radio frequencies was measured. Infrared emission was investigated.
Electromagnetic Waves in General Relativity as the Source of Information
Acta Phys. Pol. 24, 465 (1963)
abstract
Trautman’s method of obtaining wave-like solutions of the Einstein equations is applied to the case of a spacetime filled with electromagnetic radiation. The solution obtained is the well-known metric of Brinkman–Robinson–Peres.
On Lagrangians with High Derivatives
Acta Phys. Pol. 24, 471 (1963)
abstract
Starting from a Lagrangian with high order derivatives, a “canonical conjugate momentum” is defined. With this, certain commutation rules are written. The field momentum and the energy, satisfying conservation laws are introduced. Finally two examples are given.
Fraunhofer Diffraction at 0°K of Field Emitted Electrons Passing Through an Infinite Slit
Acta Phys. Pol. 24, 477 (1963)
abstract
A general wave function for electrons being emitted under the influence of an electrostatic field (1) is adapted to the special case of emission by a very thin slit of infinite length. Using this, the resolution of the field emission microscope is estimated.
Evolution of a Simple System Towards Equilibrium
Acta Phys. Pol. 24, 485 (1963)
abstract
An exact expression is given for the dependence of one of the coordinates of a model system on time. This result is compared with approximate ones following from the weak coupling, pole, and strong coupling approximations. The reliability of the approximations is discussed.
Luminescent Properties of Copper-activated Zinc Sulphide in Their Dependence on the Activator
Acta Phys. Pol. 24, 493 (1963)
abstract
A satisfactorily simple and economical method of producing luminophors was elaborated. A polarographic method is suggested for determining the copper content in the luminophors; the flame spectrophotometer was found to be inapplicable for this purpose. The spectral distribution of the fluorescence and electroluminescence intensities was investigated versus the copper concentration in the luminophors. The effect of copper concentration on: a. the decay of the blue fluorescence band of zinc, b. the crystallographical structure of the luminophors and c. the slight shift of the green fluorescence band towards shorter wavelengths was clarified.
Photon Energy Measurement in Xenon Bubble Chamber in the Energy Interval 20–1000 MeV
Acta Phys. Pol. 24, 509 (1963)
abstract
Authors present a simple and quick method of the photon energy measurement in the Xenon bubble chamber in the energy interval 20 to 1000 MeV.
On the Relation Between the Penrose Classification of Gravitational Fields and the Classification According to Group of Motions
Acta Phys. Pol. 24, 515 (1963)
abstract
The following theorem is proved: An algebraically special vacuum field with non-degenerate Weyl tensor admits of at the most a 2-parametric group of motion.
Ist die Bezeichnung elektrische oder Magnetische multipolstrahlung gerechtfertigt?
Acta Phys. Pol. 24, 519 (1963)
abstract
Die im Titel der Arbeit gestellte Frage wird durch die Angabe der Struktur der Quellen der elektrischen und magnetischen Multipolstrahlung zu beantworten versucht. Ein elektrischer bzw. magnetischer Multipol \(l\)-ter Ordnung wird dabei durch ein Debyesches Potential definiert, das durch ein Produkt aus einer Kugelfunktion der gleichen Ordnung und einer Radialfunktion gegeben wird. Die Quellen eines solchen “Kugelfunktionen-Multipols” lassen sich dann durch eine Summe von elektrischen bzw. magnetischen “Stromnetzen” von den Ordnungen \(l, l--2, l--4\), … darstellen. Ein Stromnetz \(k\)-ter Ordnung besteht dabei aus \(2^k\) Polen und \(k\, 2^{k-1}\) den Ladungsaustausch zwischen ihnen vermittelnden Stromelementen, Das System der Pole eines solchen elektrischen bzw. magnetischen Stromnetzes wird, ebenso wie ım Falle eines skalaren Feldes, nach dem bekannten Maxwellschen Verfahren der Gegenüberstellung, ausgehend von einer Punktladung in \(k\) Schritten gewonnen. Die Lage der \(k\, 2^{k-1}\) Stromelemente wird durch die Wege der Pole beim Gegenüberstellungsprozess gegeben. Die Stromrichtung in allen in einem Pole zusammentreffenden Stromelementen ist entweder auf den Pol hin, oder von ihm weg gerichtet. Die elektromagnetische Strahlung eines nach dem Maxwellschen Verfahren hergestellten Systems von \(2^k\) Polen ist nicht eindeutig definiert, da sie ja von den Strömen abhängt, die zwischen den Polen fließen. Die Bezeichnung elektrische oder magnetische Multipolstrahlung scheint daher nicht gerechtfertigt zu sein.
The Dependence of the Quenching of Fluorescence of Dyes on the Position of the Maxima of Fluorescence and Absorption
Acta Phys. Pol. 24, 555 (1963)
Le mouvement classique de la molécule diatomique dans le champ potentiel de frost et musulin
Acta Phys. Pol. 24, 557 (1963)
Fasc. 5, pages 563–693
On the Shape Parameters and the Moments of Inertia of Non-axial Nuclei
Acta Phys. Pol. 24, 563 (1963)
see erratum: Acta Physica Polonica 25, 854 (1964)
abstract
The second approximation of the shape parameter \(\beta \) for the Davydov and Filippov model (1958) is obtained by an improvement of the formula of Davydov and Filippov about the reduced transition probability \(B (E2, ^12\to ^10)\). The second approximation of the shape parameters \(\beta \) and \(\gamma \) for the Mallman model (1961) is also obtained. The shape parameters of a large number of nuclei are calculated. A simple approximate method is given to obtain the individual nucleon wave functions in the non-axial Nilsson potential. By means of these wave functions, the moments of inertia along the principal axes of the Davydov and Filippov model and the Mallman model for the nuclei Er166 and Hf178 are calculated on the basis of the cranking model with pair-correlation interaction taken into account. The calculated results agree with observation at least in order of magnitude.
Spin-wave Theory of Magnetoplumbite Ferrites
Acta Phys. Pol. 24, 583 (1963)
abstract
The theory of spin waves in ferrites having the magnetoplumbite structure is presented. The approximation of the magnetic quasisaturation is used. The spin-wave spectrum consists of five branches. The dispersion formulas have great uniaxial anisotropy.
Simplified Molecular Field Theory Applied to Cubic Antiferromagnetic Lattices
Acta Phys. Pol. 24, 591 (1963)
abstract
Molecular field theory as developed for isotropic exchange interactions is used in order to find from the complete set of geometrically possible Gersch–Koehler superstructures the most stable ones and to determine the intervals of their existence. It is shown that within the molecular field approach the antiferromagnetic collinear superstructures may be considered as a composition of two equivalent ferromagnetic sublattices when the requirement of the same numbers of like and unlike neighbours for each spin is satisfied. This requirement allows to obtain the general expression for the Néel temperature in very simple algebraic form similar to that for the net interaction energy obtained by Gersch and Koehler (1958). A simplified discussion for the first- and second-nearest neighbour interactions, based on a comparison of the Néel temperatures, is performed for all Gersch–Koehler superstructures of cubic magnetic lattices and the intervals of existences of the most stable superstructures are determined. It should be noted that all results derived here by molecular field theory and by applying the Ising model (Gersch and Koehler 1958) are identical and conformable to those previously obtained by the conventional molecular field method (Smart 1952, Adamowicz 1962 and 1963), where only regular and some non-symmetric superstructures were considered.
Intensity Ratios of Spectral Lines in the Visible Triplet of Zni in the Temperature of Liquid Nitrogen
Acta Phys. Pol. 24, 601 (1963)
abstract
The effect of reabsorption on the intensity ratios of spectral lines is discussed. The dependence of the intensity ratios of the spectral lines in the visible ZnI triplet (\(4s5s^3S_1\)– \(4s4p^3P^\mathrm {o}_{0,1,2}:4680, 4722, 4811\) Å ) on the current intensity in the liquid nitrogen-cooled Schüler type hollow-cathode lamp was determined. The relative populations of the levels \(^3P^\mathrm {o}_{0,1,2}\) were evaluated.
On the Evaluation of Certain Integrals and Their Application to Diffraction Theory
Acta Phys. Pol. 24, 611 (1963)
abstract
Certain integrals involving products of Bessel functions have been evaluated. Integrals of this type play important roles in physics and mathematics, especially in diffraction theory and analytic number theory. For particular values of the parameters and order of the Bessel functions the integral expression is a solution of the axial wave equation (Helmholtz equation in cylindrical coordinates) satisfying the boundary, Sommerfeld and Bouwkamp–Meixner conditions for the problem of diffraction by circular apertures or discs, slits or strips. The existence and domains of convergence of the series have been discussed in some detail. Furthermore it is shown that the integrals of the Bouwkamp–Levine–Schwinger type which one obtains for the calculation of the transmission coefficient, as well as, other functions of mathematical physics, such as Lommel, Struve and Lambda functions and Zernike polynomials are special cases of these integrals. Finally, Bouwkamp’s expansion of the field over the aperture or disc in terms of Legendre functions is derived in a direct way from this integral form of the solution of the wave equation and generalized to the case of oblique incidence.
Diffraction of Electromagnetic Waves by Circular Apertures and Discs. Integral Representation Method I
Acta Phys. Pol. 24, 621 (1963)
abstract
The problem of diffraction of a monochromatic plane electromagnetic wave incident obliquely on an aperture or disc has been treated the integral representation method in terms of the solution of the scalar wave equation in integral form (Whittaler’s integral), which satisfies all the conditions of the problem. By employing Hertzian or Fitzgeraldian potentials, the field quantities can be calculated, when the potentials are expressed in power series of the integral representation solution of the scalar problem. The unknown coefficients in the expansions are found to satisfy a set of infinite linear equations which are of the Bouwkamp–Levine Schwinger type. The results can be easily extended to cases where the incident wave is not a plane wave which will be considered in subsequent papers.
Some Remarks on the Foundations of Quantum Mechanics
Acta Phys. Pol. 24, 629 (1963)
abstract
Here we have shown the close connection between Birkhoff’s approach to quantum mechanics: from the asymptotic theory of differential equations and our approach from the classical dynamical equations, based on Poincaré’s fundamental theorem on the existence uniform integrals of the canonical equations and the stability condition satisfied by a dynamical system. We have shown that Birkhoff’s conditions for the existence of an invariant integral of the amplitude of the asymptotic solution squared taken over a characteristic volume, defined by the classical trajectories, which expresses the quantum mechanical condition \(\int \psi \psi ^*d(x) =\) invariant, are the same as our conditions imposed on the solution of the variational equations which determine first order stability of the classical system. A further relationship between the two methods is found to be in the similarity of the form of solution of the “principal amplitude” of the asymptotic expansion of the wave function and the solution of the variational equations of the coordinates and momenta of the dynamical system. Moreover, Chetaev’s condition for complete stability is a special case of Birkhoff’s condition for the existence of the invariant integral \(\int v_0^2d(x)\). It seems to us that both methods of approach to quantum mechanics reveal the asymptotic character of classical mechanics.
Fluoreszenzlöschung durch Zwischenmolekularen Energieubergang
Acta Phys. Pol. 24, 641 (1963)
abstract
Es werden die Messungen der Löschung der Sensibilisatorfluoreszenz an dem System: Trypaflavin \(\to \) Rhodamin 6G In Methanol durchgeführt. Die erhaltenen Messergebnisse werden mit der Försterschen und Jabłoński’schen Theorie der Löschung durch zwischenmolekularen Energieübergang verglichen. Die beobachteten Abweichungen zwischen Experiment und Theorie werden diskutiert.
On the Problem of the Effective Conductivity Tensor of a Polycrystalline Mixture, in Connection with the Theory of Metals in High Magnetic Fields
Acta Phys. Pol. 24, 651 (1963)
abstract
In polycrystalline mixtures, the particular components form connected areas, to be referred to henceforth as agglomerations. For the properties of the mixture it is essential whether the agglomerations of a component of lower concentration are isolated within a medium constituted by a component of high concentration. If the agglomerations of a component are so large as to reach to the opposite sides of the sample, the component cannot be considered to be a small admixture, quite independently of its concentration, which may be relatively small. The present paper gives, in a first approximation neglecting the correlations between different “side-branches” of an agglomeration, the greatest value of the concentration of a component in a two-components mixture for which the dimensions of the agglomerations are still finite, on the assumption that the crystals of various components have the same geometrical properties and that there is no correlation between their positions. For special simplified models of the polycrystal, numerical results are obtained. The subject of the present paper is of interest for the theory of metals in high magnetic fields.
Device for Absolute Measurement of the Capacitance
Acta Phys. Pol. 24, 663 (1963)
abstract
An improved method for the absolute measurement of the capacity is proposed bringing, particularly, improvements in the arrangement for charging and discharging the condenser allowing to vary widely the frequency and time of charging and, independently, the time of discharging and providing for durability and operational reliability.
Влияние упорядочения на диффузию кадмия в сплаве МgСd3
Acta Phys. Pol. 24, 669 (1963)
abstract
Методом интегрального остатка, применяя радиоактивный изотоп Сd115 исследовано диффузию кадмия в сплаве МgСd3. Получено следующую температурную зависимость коэффициента диффузии для упорядоченного и неупорядоченного состояния сплава: \(D_y = 11,2\cdot 10^{-5}\, \mathrm {ехр} (-12400/RТ)\,, D_{Ну} = 0074\, \mathrm {ехр} (-16700/RТ)\) .
A Simple Photoelectric Bridge Method for Determining the Lifetime of Injected Current Carriers in Semiconductors
Acta Phys. Pol. 24, 675 (1963)
abstract
A new stationary, photoelectric method for determining the current carriers lifetime is proposed. The method can be successfully used for germanium or silicon samples with \(\tau \geq 10~\mu \)s.
On the Quantum-mechanical Description of Non-isolated Systems
Acta Phys. Pol. 24, 681 (1963)
abstract
The Schrödinger equation with a time-dependent Hamiltonian is sometimes applied to the study of non-isolated systems. We show that this is correct (with a proper choice of the Hamiltonian) if and only if the state of the system is initially pure and remains so with increasing time. Further the problem of describing a non-isolated system by the density matrix of a pure state is discussed.
Hyperfine Structure of the 14.4 keV Gamma Line of 57Fe In Some Iron Oxy-hydroxides Investigated with the Mössbauer Effect
Acta Phys. Pol. 24, 689 (1963)
abstract
The hyperfine structure of the 14.4 keV gamma line of 57Fe in lepidocrocite (\(\gamma \)-FeOOH) and geothite (\(\alpha \)-FeOOH) has been studied. In lepodocrocite only the quadrupole splitting \(\Delta E = (0.45\pm 0.05)\) mm/sec is observed. In geothite, besides the quadrupole splitting \(\Delta E = (0.24\pm 0.05)\) mm/sec, two values of the magnetic field intensity at iron nuclei \(H_1 = (282\pm 5)\) kOe and \(H_2 = (342\pm 7)\) kOe are found. This indicates the existence of two sublattices in \(\alpha \)-FeQOH.
The Amplitude of Virtual Compton Scattering on Nucleons
Acta Phys. Pol. 24, 693 (1963)
abstract
It is shown that, in the virtual Compton scattering on nucleons, the amplitude depends on the charge, the anomalous magnetic moment and one new constant in an approximation linear in the wave vectors of the incoming and scattered photons.Fasc. 6, pages 697–823
Quantum Theory of Gravitation
Acta Phys. Pol. 24, 697 (1963)
see erratum: Acta Physica Polonica 25, 855 (1964)
The Stark Effect in Complex Atoms
Acta Phys. Pol. 24, 723 (1963)
abstract
In the paper we give a formula for energy eigenvalues of electrons in complex atoms in the case of an exterior, homogeneous, electric field. The formula explains a transition of the square to the linear Stark effect.
Influence of Absorbed Hydrogen on the Angular Distribution of Photons from Two-quantum Annihilation in Titanium
Acta Phys. Pol. 24, 729 (1963)
see erratum: Acta Physica Polonica 25, 855 (1964)
abstract
The angular distribution of gamma rays from two-quantum electron–positron annihilation in titanium and in H–Ti system of \(1.91 \frac {\mathrm {H}}{\mathrm {Ti}}\) concentration has been measured. Curves illustrating the two distributions and normalized to the same height in the centre have been compared. The curve corresponding to the H–Ti system seems to be broader then the one obtained for pure titanium. The experimental curves have been compared with theoretical Fermi momentum distributions calculated for 2, 3, 4, 5 and 6 free electrons per titanium atom. Usual assumption has been made that positrons are thermalized prior to annihilation and that they annihilate only with electrons of an ideal Fermi gas. From the comparison conclusion may be drawn that the number of free electrons per one titanium atom is not less than 3 in pure titanium and about 6 in the investigated H–Ti system. The results suggest that the positive ionization of the absorbed hydrogen is almost complete.
Gravitation Theory in Three-dimensional Space
Acta Phys. Pol. 24, 735 (1963)
abstract
Gravitation theory in three-dimensional space (with two space-like and one time-like dimension) is considered. In particular, a general solution of the problem of motion of point particles with finite mass is proposed: the particles move along straight lines in Euclidean space, whence by cutting out certain fragments and connecting the edges of the cutting one obtains the space produced by the bodies.
A Determination of Zeros of the Pion–Nucleon Forward Scattering Amplitude
Acta Phys. Pol. 24, 741 (1963)
abstract
The scattering amplitude \(T(^{1)}(\omega )\) of pions on nucleus is considered. A new method for its zeros determination is obtained. It is shown that it is impossible to fit the experimental data of Orear \(T^{(1)}(1) \lt 0\) to the value of \(T^{(1)}(0) \gt 0\).
Stochastic Processes in Polycrystalline Mixtures and the Problem of the Effective Conductivity
Acta Phys. Pol. 24, 749 (1963)
abstract
Polycrystals consisting of crystals of different kinds are considered. Crystals of the same kind form connected areas, called agglomerations, within the polycrystal. An agglomeration as such is a stochastic process. The purpose of this paper is to find how large the concentration of a given component must be in order that agglomerations of this component shall be infinitely extended (in an infinite polycrystalline sample). A method of finding this critical concentration is evolved for simplified models of polycrystals. It is found that a concentration of about \(30\%\), is sufficient in the three-dimensional case for the existence of infinite agglomerations (in the two-dimensional case a concentration of \(50\%\), is required).
On Functional Formulation of the S-matrix Theory
Acta Phys. Pol. 24, 763 (1963)
abstract
A functional formulation of quantum field theory is presented consisting in a unification and generalization of the three and four-dimensional functional methods. The basis for the formulation are the generating functionals for the on the mass shell S-matrix elements and their out of the mass shell generalizations restricted by the conditions of unitarity and causality. The notions of Hilbert space (of state vectors) and field operators in this space do not occur (at least not as primary notions) and, therefore, also the corresponding assumptions (as e.g. the asymptotic condition or the assumption about completeness) are avoided.
Mobility of Ions in Dielectric Liquids of High Viscosity
Acta Phys. Pol. 24, 785 (1963)
abstract
The mobility of the negative and positive ions created by X-rays has been measured in paraffin oils with viscosity coefficients 1.6 P, 0.52 P, 0.26 P and 0.044 P. The relation between ion mobility and viscosity coefficient can be expressed by the formula \(u = A\eta ^{-\kappa } (\kappa = W/W\eta \) the ratio of corresponding activation energies). For the negative ions this ratio is almost equal to unity and the Stokes law is satisfied. For the positive ions the \(\kappa \)-value is greater than unity and the above equation is close to Adamczewski’s relation \(u = A\eta ^{-3/2}\).
Preparation, Doping and Electrical Properties of Cd0.1Hg0.9Te
Acta Phys. Pol. 24, 791 (1963)
abstract
The process of preparation and crystallization of Cd0.1Hg0.9Te is discussed. The effect of various technological processes, deviations from stoichiometry (excess Cd, Te and Hg were introduced) and doping with the foreign elements Cu, In, Al and Ni on the shape of the temperature dependence of the Hall coefficient and electric conductivity between 77°K and 300°K was investigated. In the material under investigation the excess Te atoms probably occupy the sites of Hg atoms yielding donor levels. Hg dopes the semiconductor to \(p\)-type. Excess Cd produces no noticeable change. In the group of foreign atoms, Cu yields acceptor levels. Al would seem to introduce neutral centres. A method of determining the composition (the value of ) in CdxHg1-xTe crystals by measuring their density is described. The density varies linearly with the composition. Hole mobility was evaluated at \(\mu _p = 420 \mathrm {cm}^2\)/Vsec. Material was obtained wherein the value of the product \(R_H \times \sigma \) at 200° K amounted to \(4\times 10^5 \mathrm {cm}^2\) Vsec. The \(\omega (T)\) curves were found to reveal characteristic maxima at 200°C about 300°C.
On the Paramagnetic Effect in Superconductors in Transversal Magnetic Field
Acta Phys. Pol. 24, 801 (1963)
abstract
The magnetic moment of the tin superconducting cylinder carrying current in transversal magnetic field has been measured. When the cylinder was in the intermediate state its magnetic moment obtained a paramagnetic sign, i.e. opposite to the sign of magnetic moment in completely superconducting state. It has been found that, likewise the case of longitudinal field, the minimal current required for the appearance of the effect is, for tin, 1.2 amperes. It has been stated that this paramagnetic effect was a result of circular superconducting currents, circulating in the plane perpendicular to the direction of external magnetic field.
Dependence of Ionization Current in Saturated Hydro-carbon Liquids on Radiation Energy
Acta Phys. Pol. 24, 809 (1963)
abstract
The dependence of hexane-to-air ratio of ionization currents in an ionization chamber on X and gamma ray energy is discussed. The results of the measurements carried out by means of a chamber with coplanar electrodes are in good agreement with the theoretical curve drawn on the assumption that the effectiveness of ion collecting, corresponding to the extrapolated “saturation’’ current, does not depend on radiation energy and is equal to \(2.3\%\). Obtained result cannot be explained in terms of the theories of Jaffé and Kramers.
Spin-rotational Magnetic Relaxation for Nonlinear Molecules
Acta Phys. Pol. 24, 817 (1963)
abstract
Spin-rotational contributions to \(1/T_1\) and \(1/T_2\) were calculated for nonlinear molecules in liquids and gases.
Remark of the Angular Distribution of Particles in High Energy Jets
Acta Phys. Pol. 24, 823 (1963)