Vol. XIII (1954)
Fasc. 1, pages 3–77
Die Rolle der Beugungswelle in den Fraunhoferschen Beugungserscheinungen
Acta Phys. Pol. 13, 3 (1954)
abstract
Die Fraunhoferschen Beugungserscheinungen lassen sich im Rahmen der Kirchhoffschen Theorie der Beugung durch die Interferenz der von den einzelnen Elementen des beugenden Randes ausgehenden Beugungswellen erklären. Die „Fraunhofersche Beugungswelle“ kann dabei durch einen einfachen Grenzübergang aus dem vom Verfasser (1917) für den Fresnelschen Fall angegebenen Ausdruck gewonnen werden. Dabei kann der beugende Rand auch durch eine Raumkurve gegeben sein. Im Gegensatz zu den Fresnelschen Beugungserscheinungen kommt im Falle einer ganz im Endlichen liegenden Beugungsöffnung die direkt einfallende Lichtwelle in der gesamten Beugungserscheinung gar nicht speziell zur Geltung. Der angegebene Ausdruck für die Fraunhofersche Beugungswelle erleichtert die Behandlung von Spezialfällen dieser Beugungserscheinungen, vornehmlich in dem Falle, wo der beugende Rand aus einer Raumkurve besteht.
On a Regular Field Theory II (Quantized)
Acta Phys. Pol. 13, 15 (1954)
abstract
A non-local field theory constructed in a domain restricted by two hypersurfaces is quantized by a Lagrangian method developed by Schwinger. The usual canonical commutation relations hold for pairs of points on either of the two hypersurfaces. No representations connected with intermediate surfaces exist. The Schrödinger equation does not exist. The two boundary hypersurfaces are physically distinguished by the fact that interactions with the apparatus of measurement take place on them. Probability amplitudes for transitions between states on these surfaces are computed. A method of a direct quantization of the field equations is discussed. Sufficient conditions for the existence of analytic solutions are given in the case of a quantized field coupled to an external field. The general case of two interacting quantized fields is discussed and some necessary conditions for the existence of regular solutions are formulated.
Relativistic Quantum Dynamics of a System of Interacting Particles
Acta Phys. Pol. 13, 29 (1954)
abstract
The relativistic problem of interacting particles is quantized by use of an approximation method. The solutions of the equations of motion are represented as expansions in powers of the interaction constant. In lowest order of approximation they obey the equations for non-interacting particles and therefore may be quantized directly. Higher order approximations may be expressed in terms of the lowest approximation allowing all physically important quantities to be expressed as expansions in powers of the interaction constant with coefficients depending on the unperturbed operators with simple commutation rules. Equations determining the \(S\)-matrix for scattering problems are given. As an example the explicit solution for \(S\) is calculated to first approximation.
Note on the Problem of Coordinate Conditions and Equations of Motion in General Relativity Theory
Acta Phys. Pol. 13, 45 (1954)
abstract
It is shown that in the approximation method of Einstein and Infeld (Canad. J. Math., 1, 209, 1949) the equations of motion in Newtonian approximation and in the next one are independent of an arbitrary function \(a_0\) appearing in the solutions of the field equations. This result together with the results of Einstein and Infeld concerning \(a_s\) and \(b_0\) lead to the conclusion that in their new approximation method the equations of motion in Newtonian and first beyond Newtonian approximation are uniquely determined by adopting the Newtonian potential as solution of the first field equation.
On the Energy of Bound States in Quantum Field Theory I
Acta Phys. Pol. 13, 51 (1954)
abstract
An equation for the eigenvalues of the energy of two body systems is derived from field theoretical first principles. The simple model of non-relativistic spinless charged fields is treated as an example. Since the energy eigenvalue problem refers to a fixed time instant, the explicit consideration of retardation may be avoided and the instantaneous electromagnetic field may be represented as a sum of two terms: the first in the form of free waves, the second in the form of a stationary solution. The energy field operator splits into several parts: the kinetic energy of charged fields, the energy of photons, the interaction energy between photons and the charged fields, several self-energy terms (due to the interaction between a charged field and the electromagnetic field produced by the same charged field), cross terms (due to the interaction between a charged field and the stationary electromagnetic field produced by the other charged field). The cross terms may be transcribed to the configuration space and yield, besides the Coulomb interaction and the Breit terms, some other corrections. The equation for the energy eigenvalues, i.e. the generalized time independent Schrödinger equation, is written in terms of relative coordinates of the two particles.
The Influence of Hindered Rotation on the Scattering of Slow Neutrons by Bound Protons
Acta Phys. Pol. 13, 67 (1954)
abstract
The cross section of the proton bound in a molecule which has an additional degree of torsional freedom is calculated. It is shown that the cross section of the proton for the collisions which are elastic with respect to the hindered internal rotation but exciting the rotation of the whole molecule about the axis of the hindered rotation, is smaller than that of a proton bound in a rigid molecule. It follows from the theory that the lowering of the cross section depends on the energy of the incident neutrons and on the thermal energy of the scattering molecules.
On the Mass Spectrum of Elementary Particles
Acta Phys. Pol. 13, 77 (1954)
abstract
Generalized field equations (Schrödinger–Gordon and Dirac equations) together with reciprocal supplementary conditions postulated within the framework of the non-local (bilocal) field theory are shown to lead to mass quantization. Families of particles may be classified with respect to (integer or half integer) values of the spin and of the isotopic spin. The mass spectra of the nucleon and pion families are given. The masses consist of two parts: a proper mass and a field mass. The existence of a field mass is responsible for a fine structure of the mass levels.Fasc. 2, pages 91–151
Magnetic Rotation of the Plane of Polarization of Broadened Resonance Lines
Acta Phys. Pol. 13, 91 (1954)
abstract
According to Weisskopf’s theory of resonance fluorescence the rotation of the plane of polarization of resonance radiation by weak magnetic fields is not the same throughout the whole breadth of the line, as one should expect on ground of a semi-classical explanation of the effect given by Hanle, but depends on frequency. Weisskopf,s equation, valid for the case of resonance lines not broadened by pressure and/or by Doppler effect, giving the dependence of the angle of rotation on frequency is generalized so as to include also the case of broadened lines.
On a Regular Field Theory III
Acta Phys. Pol. 13, 95 (1954)
abstract
A perturbation method applicable to local as well as to non-local field theories is presented and applied to the computation of the probability amplitude that a vacuum state remains a vacuum state. In order to secure convergence it is necessary to assume (besides the non-localizability of interaction) a finite space-time domain. It is shown also that in the non-local field theory the probability amplitudes are not expressible in terms of the causal functions of Stueckelberg and Feynman.
Über die Fortpflanzung Unstetiger Elektromagnetischer Signale in Wellenleitern
Acta Phys. Pol. 13, 115 (1954)
abstract
Es wurde die strenge Lösung für das Problem der Fortpflanzung eines unstetigen elektromagnetischen Signals in einem Wellenleiter angeben, das entsteht falls in den Wellenleiter eine monochromatische elektromagnetische Welle von einem bestimmten Zeitpunkt an eingestrahlt wird. Ist die Wellenlänge der monochromatischen Welle kleiner als die zum gleichen Wellentyp gehörige Grenzwellenlänge, so entsteht auf diese Weise eine fortschreitende Welle, die aus zwei Teilen nämlich aus den Vorläufern und der Hauptwelle zusammengesetzt ist.
Differential Structure of Non-local Theories, I
Acta Phys. Pol. 13, 135 (1954)
abstract
It is shown on an example of a one-dimensional linear integro-differential equation how to obtain a differential description of non-local systems. In Section 2 the equivalence of integro-differential and pure differential equations of the same order is proved under certain conditions about the kernel. In Sections 3 and 5 the discussion of the coefficients of the differential equation is carried out. Section 4 is devoted to the canonical quantization of the system. Finally, in Section 6, another direct approach to the considered problem is given.
L’allongement du Palier des Compteurs GM a Cathode en Verre
Acta Phys. Pol. 13, 145 (1954)
abstract
Le compteur du type Maze possède un palier sensiblement plus long qu’un compteur à cathode métallique. On a étudié les deux facteurs qui causent cette propriété du compteur Maze: la grande résistance du verre insérée dans le circuit cathodique et la présence d’une surface de verre au lieu d’une surface métallique à l’intérieur du compteur. En premier lieu on doit l’allongement du palier à ce dernier facteur.
A Mains Voltage Stabilizer with Iron-Hydrogen Current Regulators
Acta Phys. Pol. 13, 151 (1954)
abstract
A circuit based on the negative feedback principle using series connected magnetic amplifiers and a non-linear bridge has been constructed and checked. The control bridge consists of two iron-hydrogen current regulators and two constantan wire-wound resistors. This bridge delivers a voltage proportional to any deviation of the stabilized voltage from the level for which the bridge is balanced. This voltage is transformed up, rectified, and fed to the grid circuit of a vacuum triode. The anode current of this triode is then used to control the a.c. voltage drop across both magnetic amplifiers in such a manner that the stabilized voltage fluctuations caused by the mains voltage and load changes are minimized. Experimental results are given and some design problems briefly discussed.Fasc. 3, pages 159–225
Untersuchungen über die Konzentrationsabhängigkeit der Oberflächenspannung und der Viskosität der Lösungen von Stark Polaren Substanzen in Polaren und Unpolaren Lösungsmitteln
Acta Phys. Pol. 13, 159 (1954)
abstract
In der vorliegenden Arbeit wurde die Konzentrationsabhängigkeit der Oberflächenspannung und der Viskosität der Lösungen von stark polaren Substanzen untersucht. In fast allen Fällen kann die funktionelle Abhängigkeit der Oberflächenspannung von der Konzentration durch die Szyszkowskische Gleichung dargestellt werden. Nur im Falle der Aethylalkohol–Benzol und der Pyrocatechin–Wasser–Lösungen ist die betreffende Abhängigkeit von ganz anderer Art.-Bemerkenswert ist auch das Verhalten der Parachore der Lösungen, die sich als streng additive Funktionen der Parachore der Komponenten nur für die Alkohol–Benzol Lösungen erweisen.
Scattering of 80\(^\circ \) K-Neutrons by CH\(_3\)OH and CH\(_3\)I Molecules
Acta Phys. Pol. 13, 167 (1954)
abstract
Experiments on the scattering of slow neutrons by rigid molecules of a liquid show that the theory of Sachs and Teller may be applied to many liquids. The cross-section for the scattering of slow neutrons is then independent of the energy of the neutrons. This was verified for the CH\(_3\)I-molecule using 300\(^\circ \)K- and 80\(^\circ \)K-neutrons. Measurements of the cross-section for CH\(_3\)OH-molecules give the value (\(180 \pm 6)\times 10^{-24}\) cm\(^2\) for 300\(^\circ \)K-neutrons and (\(227 \pm 10)\times 10^{-24}\) cm\(^2\) for 80\(^\circ \)K-neutrons. The cross-section obtained from the theory of Sachs and Teller is \(247\times 10^{-24}\) cm\(^2\). These results are interpreted as the influence of torsional oscillations between OH and CH\(_3\) groups in the CH\(_3\)OH-molecule in agreement with the theory given by W. Kołos.
Quenching of Photoluminescence of Solutions
Acta Phys. Pol. 13, 175 (1954)
abstract
The present theory of quenching of photoluminescence of solutions is based on following assumptions. The quenching molecules in solutions carry out constantly irregular oscillations about their actual equilibrium position, which they change from time to time. The frequency of changes of the equilibrium position depends ceteris paribus on the viscosity of the solution and of its temperature. To every distance of the equilibrium position of a quencher from that of the luminescent molecule belongs a certain time proportional quenching probability. The above distance of the equilibrium positions is assumed to be discrete — the quencher may be present in the first, second, and so on, shell constituted of the molecules of the solvent surrounding the excited luminescent molecule (the “shell model” of the luminescent centre). The behaviour of a system of such luminescent centres is described by a system of differential equations. The theory is applied to some simple cases, and expressions are obtained describing the decay of the total (i.e. emitted in all directions) photoluminescence intensity as well as expressions giving the quantum yield of photoluminescence as a function of concentration of quenchers and other factors. Apart from quenching by quenchers also the “inner quenching” of luminescent molecules and the quenching during the “initial shock” (disturbance in the motion of nuclei in the centre caused by electronic transition and, lasting a very short time) are taken into account in these expressions. The problem in question is solved rather generally for the case of solid solutions in which the equilibrium positions of the quenchers do not change. Only approximate expressions are obtained for the more involved case of liquid solutions. Several expressions given so far by different writers result as particular approximations from the present theory.
On the Motion of Bodies in General Relativity Theory
Acta Phys. Pol. 13, 187 (1954)
abstract
The object of this paper is to give a simple derivation of the non-Newtonian equations of motion following from the field equations in general relativity theory. This is achieved through the use of Dirac’s \(\delta \) functions in the energy-momentum tensor. All calculations (with the exception of the most trivial ones) are included.
Note on the \(Z\)-Dependence of the Cross-section for Pair Production
Acta Phys. Pol. 13, 205 (1954)
abstract
A new interpretation of experimental results of previous works of the author on this subject is given. The \(Z\)-dependence of the cross-section for pair production by \(\gamma \)-rays of ThD (2.62 MeV) was found to be consistent with the theory of Jaeger and Hulme.
On the Mutual Influence of Spheres in Vibrating Air
Acta Phys. Pol. 13, 209 (1954)
abstract
The force acting on small spheres in a Kundt tube placed at different distances from each other with their line of centres normal to the vibration vector has been investigated. When the spheres are close together this force is shown to be one of attraction or repulsion according to the size of the spheres as well as to the frequency and intensity of air vibrations. The contradiction of R.S. Cook’s and E.N. da C. Andrade’s results is thus explained, the conditions of their experiments differing considerably.
The Deuteron Polarizability and Its Effect on the Rutherford Scattering
Acta Phys. Pol. 13, 225 (1954)
abstract
Kruse, Malenka and Ramsey (1953) have published two papers in which the deuteron polarizability in an electrical field and the deviations from the Rutherford scattering due to the deuteron spatial structure were discussed, and the cross-section was evaluated by classical method, the deuteron energy in the Coulomb field of the nucleus being ...Fasc. 4, pages 231–309
Localisation des Substances Radioactives dans une Roche Par l’Application de la Methode des Plaques Transparentes de Granit et des Emulsions Nucleaires
Acta Phys. Pol. 13, 231 (1954)
abstract
On a étudié quelques plaques minces de granit à l’aide d’une émulsion nucléaire appliquée, collée ou versée sur les échantillons. On a noté que les centres radioactifs sont liés à la présence de zircon dans la biotite et que le réseau cristallin de la biotite est détruit dans le voisinage du zircon. On pourrait se baser sur l’observation des enveloppes pour établir l’âge des roches.
Yield of Anti-stokes Fluorescence of Dye Solutions
Acta Phys. Pol. 13, 239 (1954)
abstract
A new explanation is suggested of the much discussed phenomenon of the abrupt drop in the anti-Stokes region of the curve representing the quantum yield of fluorescence of dye solutions as a function of the wave-length of the exciting light. The writer believes that this drop is due to the long wave-length tail of the absorption band of non-luminescent dimers superimposed on that of (luminescent) monomers and even extending beyond it.
Cross-sections of Atomic Nuclei for the (n,p) Reaction
Acta Phys. Pol. 13, 243 (1954)
abstract
The cross-sections of \(^{25}\)Mg, \(^{27}\)Al, \(^{52}\)Cr, \(^{56}\)Fe, \(^{75}\)As, \(^{116}\)Sn, and \(^{118}\)Sn nuclei was measured for the reaction (\(n,p\)). Neutrons were used from the reaction Li (\(d,n\)) with the deuteron energy \(= 0,75\) MeV. A simple method was worked out for determining the correction for scattering and absorption of \(\beta \)-electrons in the material of the irradiated samples. Two new reactions: \(^{116}\)Sn(\(n,p\)) \(^{116}\)In and \(^{118}\)Sn(\(n,p\)) \(^{118}\)In were discovered during the experiments. The results obtained were compared with cross-sections calculated on the basis of Weisskopf’s and Ewing’s theory. The causes of discrepancies are discussed, taking into consideration the dependence of the cross-sections on the radius and temperature of the nucleus, and on the threshold of the reaction.
On the \(\beta \)-Formalism of Kemmer and Its Quantization on the Basis of Schwinger’s Variational Principle
Acta Phys. Pol. 13, 275 (1954)
abstract
The “\(\beta \)-formalism” of Kemmer and its canonical quantization is deduced in a fully relativistic form on the basis of the quantum dynamical variational principle of Schwinger. A detailed investigation of the problem of constraints is given. In spite of the special type of constraints inherent in Kemmer’s formalism and a somewhat symbolic character of the division into dynamically independent and dependent field components, the results are quite identical with those of the original Kemmer formulation. The canonical commutation relations for independent, dependent and total field variables (the last being sums of the two preceding) are obtained. Some precautions are necessary (in the case of first order field equations treated here), in consequence of the mutual dependence of the field variables and their canonical conjugates. The comparison of the canonical commutation relations obtained in this way with those of Kemmer and with the relativistic form of the commutation relations given by Pauli shows their full conformity and equivalence. It is also shown that the Duffin–Kemmer matrices \(\beta _\mu \) and the Dirac matrices \(\gamma _\mu \) are the only possible Hermitian operators with eigenvalues 0, \(\pm 1\) (or \(\pm 1\)) leading to the field equations of the Dirac type.
Quantization of Non-linear Electrodynamics
Acta Phys. Pol. 13, 291 (1954)
abstract
Non-linear electrodynamics of Born and Infeld is put into Hamiltonian form by the method of Dirac’s Canadian papers.
Czesław Białobrzeski (1878–1953)
Acta Phys. Pol. 13, 301 (1954)not a regular article
Stefan Pieńkowski (1883–1953)
Acta Phys. Pol. 13, 309 (1954)not a regular article