Vol. XIV (1955)
Fasc. 1–2, pages 3–153
On the Foundations of Statistical Thermodynamics
Acta Phys. Pol. 14, 3 (1955)
abstract
The aim of this essay is to survey the logical structure of statistical thermodynamics and to realize how faithfully this theory reflects the peculiar dialectical character of the physical situation. The author tries to outline very briefly the foundations of the atomistic interpretation of the laws of thermodynamics, laying the emphasis on the physical meaning of the formal arguments. The points that he wants to make are no doubt familiar to those physicists who have cared to look into the matter; but there is still widespread confusion concerning some of them, which may afford some justification for taking up the question from a synthetic point of view. In this connexion, it is not at all superfluous to discuss the classical approach as well as the quantal one: the true significance of the latter can only be perceived by contrasting it with the former.
On a Certain Class of Unitary Transformations
Acta Phys. Pol. 14, 41 (1955)
abstract
This work is devoted to a study of linear unitary transformation which can be applied to coordinate and momentum operators. Since these operators behave like two components of a covariant spinor with respect to unimodular transformations, a formalism is developed (§1) and a notation is introduced analogous to that used in the spinor calculus. A linear group of transformations \(\tau \) and a group of linear homogeneous transformations \(\tau _h\) are introduced in §2. In §3 representations of unitary operators are introduced leading to given transformations from \(\tau _h\). A discussion of the use of general unitary operators of the form e\(^{iT}\) is given, \(T\) being a quadratic form in the momentum and coordinate operators, which lead to certain transformations from \(\tau \). In §5 an explicit form for the operator e\(^{iT}\) is formed leading to a given transformation of \(\tau \). In §6 a transformation group induced by \(\tau _h\) is discussed for three real operators which are the quadratic forms in coordinate and momentum operators (physically identical with the Hamiltonian, the Lagrangian and the action function of a harmonic oscillator respectively). This group proves to be identical with \(L_3\) i.e. with the restricted Lorentz group acting in a threedimensional Minkowski space. In §7 the possibility of reduction of quadratic forms in coordinates and momenta to each of the three possible canonical forms, effected by means of linear unitary transformations, is discussed. In §8, avoiding the problem of an explicit construction of e\(^{iT}\) leading to a given transformation from \(\tau \), a simple method is given for finding the eigenvalues of an operator which is a general elliptic quadratic form in the coordinates and momenta. Finally in §9 by specializing the general theory of the preceeding sections a detailed discussion of a number of particular unitary transformations and the corresponding unitary operators is given; at the same time the rules for applying these operators to state vectors are deduced. The formulae of this section are useful computations directly performed on operators appearing in various quantum mechanical problems. In the last (10-th) section the question of composing linear transformations and the corresponding unitary operators is discussed.
A Generalization of the Young–Rubinowicz Principle in the Theory of Diffraction
Acta Phys. Pol. 14, 77 (1955)
abstract
The paper contains a generalization of Rubinowicz’ method of decomposition of the wave behind a Kirchhoff screen into the “incident” wave \(u_I\) and the “diffracted” wave \(u_D\) for the case of an arbitrary “geometrical” wave falling on the screen. The calculations are carried out in approximation of Kirchhoff’s scalar theory for an arbitrary shape of the screen. Fock’s approximate solution of the wave equation (1950) is used for the incident wave. The result for \(u_D\) is a line integral containing a series expansion in powers of \(1/k\) (\(k\) — the wave number) as well as of \(1/R\) (\(R\) — the distance from the integration point to the observation point) and gives Rubinowicz’ formula as a special case. In the “parageometric approximation” a specially simple extension of Rubinowicz’ result is obtained, being a series whose coefficients define the aberrations of the incident wave along the diffracting edge.
Radiation Theory in Crystals
Acta Phys. Pol. 14, 93 (1955)
abstract
This paper contains the radiation theory for the atom in a crystalline medium. In the first part we obtain equations for that class of problems using the formalism of quantum electrodynamics. An apparent mass of the photon appears in that formalism. In the second part we define (with certain simplifying assumptions) the formula for the apparent mass of the photon and solve the equations of the radiation field in a crystal. The solution obtained is consistent with Ewald’s classical result. In the third part we give an estimate of the emission probability in crystals.
On a Bilocal Theory of Families of Elementary Particles
Acta Phys. Pol. 14, 107 (1955)
abstract
The generalized bilocal wave equations restricted by reciprocally invariant supplementary conditions describe families of particles with various spin and mass values. In contradistinction to a previous supposition no direct connection with the isotopic spin theory exists. A close connection with Fierz’s theory of higher spins is shown. The question of interaction is briefly discussed.
Differential Structure of Non-local Theories, II
Acta Phys. Pol. 14, 121 (1955)
abstract
A differential description of non-local systems is obtained by replacing the original integro-differential equations containing integrals over space-time by equivalent integro-differential equations containing integrals over a space-like hypersurface only. These equations provide a descriptions of the system which is local in time. The construction of the coefficients of the equation in question is carried out in the linear as well as in the general non-linear case (Sections 1, 2, 4). The calculations are illustrated on a particularly simple example (Section 3). The admissibility of form-factors containing poles in the Fourier representation (corresponding to multi-mass equations) is discussed.
Disintegration of the Be\(^9\)-Nucleus in Coulomb Field
Acta Phys. Pol. 14, 135 (1955)
see erratum: Acta Physica Polonica 15, 358 (1956)
abstract
The cross-section for the disintegration (Be\(^9 \to \) Be\(^8 + n\)) of high velocity Be\(^9\)-nuclei by heavy nuclei (\(Z\gg 1\)) and the disintegration of Be\(^9\)-nuclei by high velocity protons is calculated by Dancoff’s method. Attention is centered on those processes in which there is no direct nuclear collision and where the disintegration is due to electric forces. The cross section \(\sigma \) for 170 MeV Be\(^9\)-nuclei is of the order \(4.2 \times 10^{-29}Z^2\) cm\(^2\) and \(3.5 \times 10^{-29}Z^2\) cm\(^2\) for 265 MeV Be\(^9\)-nuclei. For 18.8 MeV protons \(\sigma \approx 4.75 \times 10^{-29}\) cm\(^2\) and for 29.14 MeV protons \(\sigma = 4.1 \times 10^{-29}\) cm\(^2\). Quantitatively this process seems usually to be less important than the disintegration involving a direct nuclear collision.
Angular Distribution of Deuterons from Be\(^9\)(p,d)Be\(^8\).I
Acta Phys. Pol. 14, 143 (1955)
abstract
The pickup process Be\(^9\)(p,d)Be\(^8\) is investigated. The differential cross section is calculated with use of Born’s approximation. Contrary to the simplifying assumptions used by Bhatia et al. the exact wave functions of beryllium are used in the calculations under the assumption of the nuclear shell model of the Be\(^9\) nucleus. A formula available for numerical calculations is obtained.
On the Problem of Systematization of Heavy Mesons and Hyperons
Acta Phys. Pol. 14, 149 (1955)
abstract
We assume tentatively that heavy particles may be classified according to spin and parity (with respect to reflections of space exes \(x, y, z\)). The \(\pi \)-meson possesses spin 0 and a minus parity (pseudoscalar), the next member of the pion family (the \(\tau \)-meson) should possess spin 1 and a plus parity (pseudovector), etc ...
An Analysis of a \({\mit \Lambda }^0\)-particle Decay in Flight Recorded in Nuclear Emulsion
Acta Phys. Pol. 14, 153 (1955)
abstract
In Ilford G5 nuclear emulsion 600 \(\mu \) thick exposed at an altitude of about 25 000 m during 6.5 hours a two prong star was found the photomicrograph of which is shown in tab. 1. Two tracks, marked \(a\) and \(b\), start from point \(S\), no trace of recoil being visible ...Fasc. 3, pages 159–269
Analyse de la Radioactivité des Minéraux Formés au Contact d’une Veine Granitique avec une Serie Calcaire
Acta Phys. Pol. 14, 159 (1955)
abstract
En employant l’émulsion nucléaire Ilford C2, on a étudié le caractère de la répartition des substances radioactives dans des échantillons de roche; on a déterminé avec quels minéraux elles ont été prélevées et on a calculé leur teneur générale en thorium et en uranium. On a relévé que ce sont des inclusions de surface différentes allant de quelques \(\mu ^2\) jusqu’à environ 1 mm\(^2\) réparties inégalement qui consitituent lea centres radioactifs. Les substances radioactives se sont concentrées avec la magnetite. La teneur générale en thorium et en uranium est du même ordre de grandeur dans tons les échantilions étudiés.
The Influence of Hindered Rotation on the Scattering of Slow Neutrons by Bound Protons II
Acta Phys. Pol. 14, 173 (1955)
abstract
The influence of rotation of a rigid molecule on the cross-section of a proton bound in the molecule is considered. The molecule is assumed to be a symmetric rotator. Using the “static approximation” of Placzek, contributions to the cross-section due to various changes of the rotation about the axis of symmetry are calculated. It was shown in Part I that this enables us to calculate the influence of hindered rotation on the proton cross-section for collisions elastic with respect to the hindered rotation. The method is applied to the methyl alcohol molecule. It is shown that the influence of hindered rotation makes the cross-section of the molecule about 13 per cent smaller compared to that of the molecule assumed to be rigid. A rough estimate shows that the remaining experimentally observed effect may be due to vibrations of the protons.
Über eine Verallgemeinerung des Reziprozitätstheorems für Lösungen der Schwingungsgleichung mit Multipolquellen
Acta Phys. Pol. 14, 183 (1955)
abstract
Der Satz von der Vertauschbarkeit von Quell- und Aufpunkt einer Greenschen Funktion der Schwingungsgleichung \({\mit \Delta } u + k^2 u=0\) wird auf den Fall zweier Lösungen \(u^{(1)}\) und \(u^{(2)}\) dieser Differentialgleichung verallgemeinert. Dabei wird vorausgesetzt, daß jede der beiden Funktionen \(u^{(1)}\) bzw. \(u^{(2)}\) nur eine einzige in dem Raumpunkte 1 bzw. 2 gelegene singuläre Stelle aufweist, die durch beliebige Multipolquellen ausdrückbar ist. Die angegebene Verallgemeinerung des Reziprozitätstheorems stellt dann eine bilineare Beziehung zwischen den nachstehenden beiden Sätzen von Koeffizienten dar: (1) den Koeffizienten, die die Stärken und Phasen der Multipole der beiden Funktionen \(u^{(1)}\) und \(u^{(2)}\) in ihren Quellpunkten 1 bzw. 2 festlegen und (2) den Entwicklungskoeffizienten der nach Kugel- und Besselschen Funktionen fortschreitenden Entwicklungen von \(u^{(1)}\) und \(u^{(2)}\) in den Raumpunkten 2 bzw. 1, in denen diese Funktionen regulär sind.
Solution of the Fluctuation Problem in the Cascade Theory by Means of the G-equations of Jánossy Without Ionization Loss
Acta Phys. Pol. 14, 191 (1955)
abstract
A new method is given for solving the G-equations of Jánossy. The plane of the independent variables \((x,\varepsilon )\) is divided into bands: \(1/(n + 1 \lt \varepsilon \leq 1/n\) (\(n\) — natural number). The solution for \(\varepsilon \gt 1\) may be easily found. Taking this solution into account, it is possible to linearize and solve the G-equations for \(\varepsilon \gt 1/2\). In each subsequent band (in the direction of increasing \(n\)) the equations can be linearized and solved in the same manner provided one knows the solution for the preceding band. Thus one obtains recurrent formulae together with explicit expressions for them for nucleon and electron–-photon cascades. Graphical representations of the solution can be given. It is also shown that this method permits to obtain immediately the factorial moments of the distribution.
The Configurational Equation of Photons
Acta Phys. Pol. 14, 197 (1955)
abstract
A covariant configuration theory of bosons is developed on the example of photons. The first part of the paper contains a configurational representation of the state vector. For this purpose the mixed representation of the Günther type is used in which \(N\) photons are treated configurationally while the electrons and the remaining photons may be treated in any other way one likes. In the second part of this paper a configurational equation is derived for photons, corresponding to the Salpeter–Bethe equation.
Fortpflanzung von Sprüngen Elektromagnetischer Feldstärken und Eindeutigkeitsbeweis für das Anfangswertproblem der Maxwellschen Gleichungen
Acta Phys. Pol. 14, 209 (1955)
abstract
Sprünge von elektromagnetischen Feldstärken, die auf mit beliebigen Geschwindigkeiten in der Richtung ihrer Normalen sich bewegenden Flächen auftreten, nehmen an der Energiebilanz eines vierdimensionalen Raum-Zeit-Gebietes im allgemeinen als Energie-Quellen oder Senken teil. Vom physikalischen Standpunkt kann man diese Energieänderungen durch elektrische und “magnetische” Ströme erklären, die in den Sprungflächen fließen. Die Maxwellschen Gleichungen zeigen, daß man sich diese Flächenstrome entstanden denken kann durch Zusammendrängen von Leitungsströmen in die Sprungflächen. Diese Ströme müssen verschwinden, damit die in Rede stehenden Sprünge keinen Beitrag zur Energiebilanz des elektromagnetischen Feldes liefern. Auf diese Weise ergeben sich Bedingungen für die physikalisch zulässigen Sprünge der elektromagnetischen Feldstärken, die u.a. besagen, daß solche Sprünge sich nur längs charakteristischer Flächen fortpflanzen können. Auch bei Vorhandensein von Sprüngen elektromagnetischer Feldstärken, die die angegebenen Bedingungen erfüllen, ist der Eindeutigkeitsbeweis für das Anfangswertproblem der Maxwellschen Gleichungen durchführbar und zwar in einer solchen Weise, daß er der endlichen Ausbreitungsgeschwindigkeit der elektromagnetischen Wellen Rechnung trägt.
Der Satz von der Erhaltung des Impulses und die Fortpflanzung von Sprüngen Elektromagnetischer Feldstärken
Acta Phys. Pol. 14, 225 (1955)
abstract
Die Forderung, daß die mit Lichtgeschwindigkeit sich bewegenden Sprungflächen elektromagnetischer Feldstärken keinen Beitrag zur Impulsbilanz eines Raum-Zeit-Gebietes liefern, ist nur mit dem Minkowskischen nicht aber mit dem Abrahamschen Ansatz für den Energie-Impulstensor vereinbar.
Singular Potentials in Relativistic Equations of Motion
Acta Phys. Pol. 14, 233 (1955)
abstract
It is shown that in the relativistic equations of motion for a particle moving in external potentials some additional forces of purely relativistic origin appear. These forces are repulsive for scalar and pseudoscalar potentials in spite of the apparently attractive character of the potential; they prevent the particle front coming too near to the singularity of the potential. An adiabatic approximation of the interaction potential for two nucleons interacting through the pseudoscalar field has been obtained. An interesting feature of this potential is a strong repulsive term acting at short distances between the nucleons.
The Solution of the G-equations of Jánossy with Ionization Loss
Acta Phys. Pol. 14, 251 (1955)
abstract
In a previous paper (Łopuszański, 1954, hereafter referred to as I) an analytical solution of the fluctuation problem was given by means of the G-equations of Jánossy for nucleon and electron–photon cascades without ionization loss. The methods developed in I will now be applied to the case of the electron–photon cascade taking into account the ionization loss. The case of a nucleon cascade with ionization loss can be dealt with in the same manner.
On the Vectorial Intensity Law in Geometrical Optics
Acta Phys. Pol. 14, 255 (1955)
abstract
In 1947 F. Friedlander published an interesting contribution to our knowledge of the asymptotic behaviour of solutions of Maxwell’s equations (Friedlander 1947). He derived a vectorial intensity law (i.e. a law concerning the vectors \(E\) and \(H\) of the electric and magnetic field and not the scalar amplitude \(u\) of the scalar theory of light) and also a law of the variation of the direction of polarization. Both laws were given in the approximation of geometrical optics for inhomogeneous and unmagnetic (\(\mu =1\)) but isotropic and continuous media. The aim of the present note is to call attention to a small but essential mistake which occurred in Friedlander’s intensity law and its derivation.
Numerical Determination of the Ground State of the Mesonic Atom
Acta Phys. Pol. 14, 257 (1955)
abstract
The distribution of electrical charge inside heavy nuclei influences considerably the energy levels of the mesonic atoms. The influence is most marked for the ground state and for high values of the atomic charge. Various charge distributions were considered: uniform, exponential, and Gaussian distributions, as well as the smoothed uniform one which according to recent reports is the most probable. The energy levels were determined numerically for the greater part of the charge distributions, the work of Hill and Ford (1954) being the most exhaustive; see also Fitch and Rainwater (1953), as well as Cooper and Henley (1953).
On the Emission of Photoelectrons from F-centers in NaCl
Acta Phys. Pol. 14, 263 (1955)
abstract
Taft and Apker (1951, see also Seitz 1954, p. 87) observed the photoelectric emission of electrons from F’-centers in RbJ at a temperature of about 85\(^\circ \) K; the maximum of the F-center absorption band for RbJ lay at about 7600 Å , corresponding to a photon energy of about 1,6 eV. Initially no photoelectric emission was observed when a sample containing F-centers was irradiated with photons of energy 1,9 eV (6500 Å ). After prolonged irradiation, however, the yield curve developed a new branch extending to as low energies as 1,6 eV. This branch could be removed by heating the sample to room temperature or by irradiating it with 1 eV photons, which are known to lie in the F’-band of RbJ. In the present note, the author wishes to mention some of his own observations which seem to confirm the interpretation of Taft and Apker’s results as emission from F’-centers.
The Asymptotic Behaviour of the Probability Distribution Function of Cosmic Cascades
Acta Phys. Pol. 14, 265 (1955)
abstract
We confine ourselves for the sake of simplicity to the case of nucleon cascade, but the results given below may be easily generalized to the case of the electron–-photon cascade. The development of the nucleon cascade is described by Jánossy’s C-equation (Jánossy 1950) ...
Evaluation of the Probabilyty Distribution of Function of Cosmic Cascades for Large Depth of the Absorber
Acta Phys. Pol. 14, 269 (1955)
abstract
We have shown in the previous letter that \[\lim _{x\to \infty }p*(1|\varepsilon ,x)=1, \qquad \lim _{x\to \infty }p*(n|\varepsilon ,x)=0\quad n\geq 2\] and ...Fasc. 4, pages 275–373
On Certain Wave-packets
Acta Phys. Pol. 14, 275 (1955)
abstract
Theorems concerning the properties of Kennard packets have been extended over all the solutions of the wave equation of a harmonic oscillator. Generalizing these theorems to the quantum theory of fields, non-spreading wave packets with classical properties have been obtained.
Self-depolarization and Decay of Photoluminescence of Solutions
Acta Phys. Pol. 14, 295 (1955)
abstract
Self-depolarization of photoluminescence of solid solutions (depolarization by migration of the excitation energy from one luminescent molecule to other luminescent molecules of the same kind) is treated in a similar way as the quenching of photoluminescence of solutions was treated in a previous paper. The problem is, however, even more complicated than that of quenching, and thus some additional simplifying assumptions have to be made. The model of a luminescent centre adopted here is the simplest one. The excited centre is assumed to consist of an excited luminescent molecule surrounded by an “active sphere”, which may contain one or more unexcited luminescent molecules of the same kind. If there are unexcited molecules within the active sphere, the excitation energy can be transferred to them and migrate several times from one molecule to another. The probability of an energy transfer is assumed to be proportional to time and be the same for transfer to ally of the unexcited molecules belonging to the same centre. It is assumed to be nil for transfer to unexcited molecules outside the centre ...
Hamiltonian Formalism and Canonical Commutation Relations in the Case of First Order Lagrange Equations
Acta Phys. Pol. 14, 309 (1955)
abstract
The problem of the Hamiltonian formalism in the case of first order equations of motion is investigated on a dynamical model with a finite number of degrees of freedom. The possibility is shown of introducing canonically conjugate variables to the generalized coordinates \(q_j\) by the usual definition \(p_j=\frac {\partial L}{\partial g_j}\), in spite of their dependence on \(q_j\) provided that a suitable symmetrization is performed. The relations between the \(q\)’s and \(p\)’s are interpreted as a canonical transformation independent of time. The canonical quantization with the aid of the correspondence principle (exploiting the properties of the Poisson brackets) is proved to be possible in this case in spite of the mutual dependences of \(q\) and \(p\). The correct canonical commutation relations with the factor \(1/2\) are obtained. The admissibility of treating the relations between the \(p\)’s and \(q\)’s as a canonical transformation is restricted to only one of the infinitely many Lagrangians giving the same equations of motion, i.e. differing by terms of the form of a time derivative, namely to the one symmetrical with respect to integration by parts. This form of the Lagrange function (connected with the canonical commutation relations possessing a factor \(1/2\)) is thus distinguished. Moreover, two other special forms allowing an immediate elimination of one half of the variables \(q\) are distinguished too; then the remaining canonical variables, already independent, fulfil the traditional commutation relations without the factor \(1/2\). These considerations are generalized for the known cases of fields obeying first order field equations (Dirac and Kemmer fields).
Simple Model of the \(^6\)Li Nucleus and the Neutron Induced Reactions on \(^6\)Li
Acta Phys. Pol. 14, 323 (1955)
abstract
A simple model of the \(^6\)Li nucleus consisting of an \(\alpha \) particle plus a deuteron is discussed. This model is applied to the calculation of the differential cross-section for the \(^6\)Li(n,t)\(^4\)He and \(^6\)Li(n,d) He reactions. For the first reaction the pickup mechanism is assumed, for the second one the mechanism of a “knock-out” of the deuteron as a whole from the \(^6\)Li nucleus. The results are compared with experiment. Fairly good agreement is obtained especially for the \(^6\)Li(n,t)\(^4\)He reaction for small angles.
Introduction to the Bilocal Theory of Elementary Particles
Acta Phys. Pol. 14, 337 (1955)
abstract
A generalized field formalism (closely connected with that of Yukawa) incorporating a fundamental length \(l\) may be regarded as a new type of field quantization: the “\(l\)-quantization”, to be distinguished from the canonical “\(h\)-quantization”. The \(l\)-quantization appears to be the mass and spin quantization and leads to a rotator (or spinrotator) model of elementary particles. The particle is represented by (the surface of) a sphere of radius \(l^2M\) (\(M\) being the rest mass). The general solution of the (first or second order) field equation includes a whole family of particles with higher spins and masses. A close connection with Fierz’s theory of higher spins is discussed. The particles are classified in families and super-families according to the type of the field equations (of the first or second order) and the type of parity. Four families of bosons and six families of fermions follow from general group-theoretical considerations. There exists a homomorphism between all single and multi-valued irreducible representations of the group of rotations and inversions and the possible types of elementary particles.
On the Surface Tension of Ideal Solutions
Acta Phys. Pol. 14, 365 (1955)
abstract
In a recent paper Puchalik (1954) has reported an experimental study on the surface tension of some solutions, made in order to investigate the association processes accompanying dissolving of one substance in another. It seems, however, that the surface tension is influenced by association processes in a very complicated manner and before drawing any conclusions from such a study changes in the surface tension of ideal solutions must be first determined.
On the Measurements of Cosmic Radiation in Horizontal Direction
Acta Phys. Pol. 14, 369 (1955)
abstract
There are in the literature very few data concerning the measurements of cosmic radiation in horizontal directions. Clay (1949) found in horizontal measurements a great excess of photons over ionizing particles; from the data given by Clay one might conclude that they refer to photons of low energy (\(\leq 10\) MeV). Rogoziński (1948) stated that the horizontal cosmic radiation should be very penetrating. He found that ...
On the Collective Motion in a System of Particles Having Different Masses and Charges
Acta Phys. Pol. 14, 373 (1955)
abstract
The problem of separating the plasma motion into the so called collective part and the individual one, was recently the subject of several papers (Bohm and Pines 1951, 1952, 1953, Hubbard 1954). An important step in this direction is, as it seems, the work of Zubariew (1953). Its fundamental idea consists in introducing into the wave function of the system additional variables \(\varrho k\), being Fourier components of the density operator of the system. The wave function depends on the components \(\varrho _k\) with indices for which \(k=|k|\leq k_0\). This cut-off procedure permits to separate out of the plasma motion their collective part. Parameter \(k_k\) is bound in the classical theory with the Debye length. After such an introduction of additional variables, the Hamiltonian of the system can be separated into three parts, which correspond successively to: free fermions, collective vibrations having a boson character and mutual interactions ...Fasc. 5, pages 379–419
Zur Frage der Additivität der Parachore von Lösungen
Acta Phys. Pol. 14, 379 (1955)
abstract
In der vorliegenden Arbeit wurde die Abhängigkeit der Parachore der Lösungen von ihrer Konzentration untersucht. Die Resultate der Messungen zeigen, dass die Additivität der Parachore der Lösungen nur in verhältnismässig seltenen Fällen zutrifft. Es wurden zwei Gleichungen vorgeschlagen, die die funktionelle Abhängigkeit der Parachore der Lösungen von ihrer Konzentration ausdrücken. Bemerkenswert ist die Abnahme der Parachore der stark verdünnten Lösungen mit wachsender Konzentration im Fällen, in denen das Parachor der gelösten Substanz das des Lösungsmittels weit ubertrifft.
An Integrating Apparatus for the Schrödinger Equation. II
Acta Phys. Pol. 14, 385 (1955)
abstract
Several improvements have been introduced in the integrating apparatus for the Schrödinger equation, (Antonowicz 1953). The apparatus was calibrated by means of the Morse potential and its harmonic approximation. For verification purposes eigenvalues were determined for the harmonic oscillator and the Morse potential. The eigenvalues obtained by means of the apparatus agree within 1 per cent with the theoretical values. One of the eigenfunctions for Morse’s potential was compared with a theoretical curve. A very good agreement between them was found.
Dependence of the Dielectric Properties of Ceramic BaTiO\(_3\) for High Frequency Currents on the Technology of the Preparation of Samples
Acta Phys. Pol. 14, 395 (1955)
abstract
The dependence of the dielectric constant and the ceramic BaTiO\(_3\) losses on the way of preparing samples has been investigated. The method of measurements of the dielectric constant of materials having very high dielectric constants has been worked out with the help of high frequency currents, as well as the method of measurements of losses. Four groups of BaTiO\(_3\) samples, marked \(A, B, C, D\), have been prepared, each of them being obtained from the previous one by means of thorough grinding, pressing, and resintering at a temperature of about 1350\(^\circ \)C. The last group \(D\) remained particularly long in the oven: about 130 hours, including the time of heating and cooling. It has been proved that the dielectric constant of each successive group of samples is at all temperatures considerably higher than the dielectric constant of the previous group. The losses of samples in the row \(A, B, C, D\) decrease gradually but not very significantly.
Angular Distribution of Deuterons from \(^9\)Be(p,d)\(^8\)Be. II
Acta Phys. Pol. 14, 407 (1955)
see erratum: Acta Physica Polonica 15, 431 (1956)
abstract
The formula for the Born approximation cross-section for the \(^9\)Be(p,d)\(^8\)Be pickup reaction obtained with the help of the “\(^8\)Be + neutron” model of the \(^9\)Be nucleus is compared with the experimental data for 6,5 and 22 MeV protons. The best agreement is obtained for the \(^8\)Be-neutron square well radius \(r_0=5\times 10^{-13}\) cm. The angular distributions for larger angles lie under the experimental curves mostly due to the compound state formation. The absolute values of the cross section obtained by taking into account the Coulomb correction seem to be too great because of the neglect of the \(^8\)Be-proton interaction. Comparison with the results of the Butler approximation determines the limits of validity of this approximation. The same model of the \(^9\)Be nucleus is applied for the calculation of the Born cross section for the \(^9\)Be(d,t)\(^8\)Be reaction. The results are compared with experiment for 7,7 MeV deuterons. The “\(^8\)Be + neutron” model of the \(^9\)Be nucleus is discussed.
Electronic Interaction in the Free-electron Model for Non-branched Conjugated Systems
Acta Phys. Pol. 14, 419 (1955)
abstract
The ASMO CI method for molecular orbitals of a free-electron for non-branched bond systems of conjugated molecules is presented here in close analogy to the ASMO CI theory as developed by Goeppert-Mayer and Sklar and Craig for molecular orbitals in the form of the linear combination of atomic 2p orbitals. This scheme was used to calculate the energy levels in two cases: ethylene and butadiene. The results are in a better agreement with experimental data than those which can be obtained by analogical computations with LCAO MO method. This is the case especially in the singlet–triplet separation for the first excited states. In addition a significant decrease in the configurational interaction effect compared with the LCAO MO method was obtained.Fasc. 6, pages 435–501
Über die Ausbreitung “Exponential Begrenzter” Wellen von Endlicher Amplitude
Acta Phys. Pol. 14, 435 (1955)
abstract
Es wird die Ausbreitung einer akustischen Welle in einer Exponentialbegrenzung untersucht, wobei das Problem mit Hilfe der krummlinigen Koordinaten als ein eindimensionales Problem formuliert wird. Die Wellen sind durch harmonische Schwingungen eines Kolbens, der sich im engen Teil der Begrenzung befindet, hervorgerufen. Den Ausgangspunkt bilden die hydrodynamischen Bewegungsgleichungen in Lagrangeschen Koordinaten, die dadurch linearisiert werden, dass alle Grössen nach Potenzen der Relativamplitude \(A=2\pi \alpha /\lambda \) entwickelt werden, wo \(\alpha \) die Amplitude der harmonischen Schwingungen des Kolbens ist und \(\lambda \) die Wellenlänge, die der Kreisfrequenz \(\omega \) der Kolbenschwingungen entspricht ...
The Yield of Anti-stokes Fluorescence of Very Viscous Dye Solutions
Acta Phys. Pol. 14, 447 (1955)
abstract
The results of measurement of the relative yield of fluorescence of fluorescein in glycerol and glucose are given. In the first case the yield decreases with increasing wave-length of the exciting light, in the second case, however, it does not — remaining practically constant. An explanation of the experimental results is put forward, according to which the course of the yield as a function of the exciting wave-length depends on the relative concentration of non-luminescent dimers.
Remarks on the Relativistic Two Body Problem in the Classical Scalar Meson Field Theory
Acta Phys. Pol. 14, 455 (1955)
abstract
In §1 some general remarks are given on the Cauchy problem for the system: scalar meson field + particles. In §2 an exact solution of the two-body problem in the case of a circular motion is given for \(\mu =0\). This solution is compared with the solutions in the cases of some different approximations. In §3 some remarks are given on the rectilinear motion concerning the problem of the repulsive forces for small distances between the nucleons in the scalar field theory. It is shown that some physical contradictions result from the theory neglecting retardation.
The Localized Molecular Orbitals and the Structure of Some XH\(_3\) Molecules
Acta Phys. Pol. 14, 471 (1955)
abstract
The method of equivalent orbitals in the two-centres approximation for bond orbitals is used to calculate the variation with bond angle of the total energy of the NH\(_3\) and PH\(_3\) molecules. A modification of the orthogonality conditions for the orbitals enables to calculate the bond angles of the equilibrium configuration in a qualitative agreement with experiment. It is shown that the theory in this approximation over-emphasizes the hybridization of the lone pair orbital as compared to that of the bond orbitals, and over-emphasizes the part played by the lone pair electrons in determining the molecular structure.
New Low Dead Capacity Condensers for Measuring Dielectric Constants of Liquids
Acta Phys. Pol. 14, 483 (1955)
abstract
A new construction of cylindrical condensers for measuring dielectric constants of liquids has been described. Several condensers of different capacities up to 140 pF have been constructed. An absolute measurement of the dielectric constant of commercial, chemically pure benzene has been made, and then by means of this benzene the dead capacities of the above mentioned condensers have been determined. It has been proved that they had a dead capacity of the order of 0,1 pF and extremely small losses. The volume of the liquid necessary for the filling of the condenser amounted to 10–15 cm\(^3\).
The Retarding Potential as a Stabilizing Factor for the Working Conditions of Aluminium G–M Counters
Acta Phys. Pol. 14, 489 (1955)
abstract
It is well known that aluminium walled G–M counters show a marked instability in working plateau and background, during fast rate counting (Veksler 1949, Loeb 1950, p. 482). In these works on the excited emissivity problem, it is proved that the instability phenomenon, often called “counter self excitement” is due to the excitement of the cathode (Kramer 1951, 1952; Sujak 1953, 1955; Bohun 1954, Lepper 1955). Counter cathode exciting seems to be looked on as a production process of some donor centres with a rather low effective work-function in the oxidized metal layer or in the layer of the decomposed quenching component of the counter filling (Sherb 1949, Nassenstein 1954). The nature of the centres seems to be like the F- or F’- centres in alkali halides (Sujak 1953, 1955; Bohun 1954).
Energy Integrals for 3D Electrons in Body-centered Iron
Acta Phys. Pol. 14, 493 (1955)
abstract
To carry out quantitatively the programme of the tight binding approximation for solids one requires the knowledge of the numerical values of the energy integrals. Fletcher and Wohlfarth (1951) in their pioneer work have calculated these integrals for Ni as the two-center integrals between the atomic 3d functions. The atomic functions have been calculated by Hartree (1936) for Cu\(^+\) in the Hartree–Fock approximation. The example of Ni is a particularly good one as in the two-center approximation reasonable values of the energy integrals can be obtained in such cases when the atomic functions of neighbouring atoms overlap only slightly: moreover, as it is well known, the ratio of the interatomic distance to the radius of the \(3d\) function is particularly large for Ni.
Note on the Theory of the Polarization of Photoluminescence of Solutions
Acta Phys. Pol. 14, 497 (1955)
abstract
A theory of the fundamental polarization of photoluminescence of solutions was put forward long ago (Jabłoński, 1935). Recently a new form was given to the expressions resulting from that theory (Jabłoński, 1950), viz ...
On the Influence of the Shape of the Nickel Point on the Electron Image in the Müller Microscope
Acta Phys. Pol. 14, 501 (1955)