Vol. XI (1951, 1952, 1953)
Fasc. 1, pages 1–87
Statistical Interpretation of the Klein–Gordon Equation
Acta Phys. Pol. 11, 1 (1951)
abstract
A quantum-statistical interpretation of the solutions of the Klein–Gordon equation is given. It permits calculation of cross-sections without use of field quantization.
Field Theories Without Divergences
Acta Phys. Pol. 11, 9 (1951)
abstract
In this paper a quantum statistical interpretation is given for the extended source theory of Peierls and McManus. It is shown that by use of this theory only the electron self-energy is made finite. To remove other divergences it is necessary to average the extended source Lagrangian with an appropriate weight factor over the mass of the electron. Higher order equations are discussed and it is shown that for any neutral field they are equivalent to the extended source theory. For charged fields they lead to non gauge-invariant results. In general all physically interesting possibilities seem to be already contained in the Lagrangians with first order derivatives of the fields.
On Field Theories with Non-localized Interaction
Acta Phys. Pol. 11, 25 (1951)
abstract
It is shown that a method of direct quantization of field equations (completely avoiding the canonical formalism) is applicable to a wide class of fields with a non-local interaction. In Section I the extended source theory of Peierls and McManus is quantized and discussed. The \(S\)-matrix is computed by the method of C.N. Yang. A general rule for an immediate transcription of the traditional \(S\)-matrix elements into the new form is given. In Section II another type of a non-local interaction is discussed and it is shown that all the usual convergence difficulties may be easily avoided if we give up the strict localizability of charge, energy etc., and if we abandon the postulate of gauge invariance of the second kind. This is acceptable since it is possible to guarantee the integral conservation laws without the continuity equations and to secure a vanishing photon rest mass by other devices, not necessarily by the formal gauge invariance. In the limit \(\lambda \to 0\), where \(\lambda \) is a fundamental length the discussed field theory goes over into the traditional quantum electrodynamics.
Angular Distribution of Compton-Coincidences
Acta Phys. Pol. 11, 36 (1951)
abstract
The angular distribution of coincidences due to a beam of \(\gamma \)-rays in a telescope consisting of two GM-counters was investigated. There exists a maximum of coincidence rate for an angle of c. 30\(^{\circ }\) between the axis of the telescope and the beam of the \(\gamma \)-rays. The theoretical interpretation of the curve for the angular distribution of coincidences is given. It follows from the measurements that the angular distribution of scattered \(\gamma \)-rays agrees for the energy 2,62 MeV very well with the formula of Klein and Nishina. The relatively high efficiency of a double telescope for isotropic \(\gamma \)-radiation was explained.
Relativistically Invariant Homogeneous Canonical Formalism with Higher Derivatives
Acta Phys. Pol. 11, 49 (1951)
abstract
Ostrogradsky’s canonical formalism with second derivatives in the Lagrangian function has been put in “homogeneous form” in which an arbitrary parameter plays the part of time in classical dynamics or proper time in relativistic dynamics. This doubly generalized canonical formalism makes it possible to treat the motion of a spin particle in a generally relativistic manner, independently of the velocity of the particle being less or equal to the velocity of light. Weyssenhoff’s and Raabe’s equations of motion of a spin particle and Hönl’s and Papapetrou’s equations of motion of a pole–dipole particle are both included as special cases in the new equations of motion.
A Method of Determining the Efficiency of Ra–Be Neutron Sources
Acta Phys. Pol. 11, 71 (1951)
abstract
A simple method of measuring the efficiency of Ra–Be neutron sources has been elaborated. The method is based upon neutron induced \(\beta \)-radioactivity and avoids measurements of weak secondary effects in the presence of strong direct radiation from the Ra–Be source. The accuracy of the method is comparable with that of other, more elaborate, methods now in use.
On the Absorption in Aluminium of Electron Pairs Created in Lead by Gamma-Rays of ThC
Acta Phys. Pol. 11, 75 (1951)
abstract
The absorption of pair electrons in Al was measured by the method of G.M.-counters working in coincidences. The absorption curve obtained was compared with curves calculated from the theoretical energy distributions of pair electrons given by Bethe & Heitler and Jaeger & Hulme. The experimental curve fits much better with the curve calculated on the base of the theory of Jaeger and Hulme.
Geiger–Müller Counters for Soft X-Rays
Acta Phys. Pol. 11, 81 (1951)
abstract
The dependence of the efficiency of GM-counters on argon pressure for the X-ray wave-lengths \(K_\alpha \)Fe (1.9 Å) was investigated. The results obtained agree with a formula deduced for the dependency of the efficiency upon pressure. Small discrepancies are due to the increase of dead-time at higher pressures. The investigated counter attained maximum efficiency (about 50%) at the pressure of 41 cm Hg. The work of an argon-alcohol GM-counter up to 64 cm Hg pressure was also tested.
Calculation of the \(\pi \)-meson Mass Based on an Electrodynamical Model of the Particle
Acta Phys. Pol. 11, 87 (1951)
abstract
The dispersion formula for electromagnetic waves in plasma is known to have the following form \[u=\frac {e}{\sqrt {1-\frac {\omega ^2_0}{\omega ^2}}}\,,\] where u is the phase velocity of an electromagnetic wave with an angular frequency o, o, is the plasma angular frequency !, and ¢ is the vacuum speed of light. On the other hand, an analogous dispersion formula is fulfilled by the de Broglie waves of a free particle. Thus the supposition arises that this similarity is not a fortuitous one but that there must exist an electrodynamical model of a free particle. Indeed, it will be shown here that one can build an electrodynamical model of a free non-spinning particle leading to the correct value of the \(z\)-meson mass in a surprisingly straightforward way.Fasc. 2, pages 91–201
The Influence of the Internal Stress in Dielectrics on the Polarization of Reflected Light
Acta Phys. Pol. 11, 91 (1952)
abstract
The refractive index considered as a function of the strains has been introduced into the equations describing the state of polarization of light reflected from a strained dielectric. Glass has been chosen as example since the Neumann constants are known from experiment for this material only. The relation between the rotation of the plane of polarization of reflected (plane polarized) light and uniform traction normal to the plane of incidence has been deduced, as well as a relation between the rotation of the plane of polarization of reflected light and the state of plane stress within the dielectric. The latter relation yields one equation for the determination of the two principal stresses. The second equation needed can be deduced from the fundamental equation of photoelasticity connecting the phase shift of transmitted light with the stress within the dielectric.
The Lowering of the Freezing Point in the Theory of Dipolar Coupling
Acta Phys. Pol. 11, 99 (1952)
abstract
The theory of dipolar coupling developed by the author in a previous paper (Acta Phys. Polonica, 10, 107 (1950)) has been applied to the calculation of the lowering of the freezing point of dilute solutions of polar substances in non-polar solvents. The lowering of the freezing point in these solutions (\(\Delta T\)) is less than that in “ideal” solutions (\(\Delta T_{id}\)) in which the dissolved molecules do not exert any forces on each other. The quantity \(j=(\Delta T - \Delta T_{id})/\Delta T_{id}\) has been calculated on the assumption of a “coupling of the second kind” tending to associate the dissolved molecules in antiparallel couples (for details, see the above mentioned paper). The value of \((dj/dm)_{m=0}\), where \(m\) is the molar concentration, determines the tangent to the curve \(j(m)\) at \(m=0\); it is found to depend on the shortest possible distance \(r_0\) between the molecules. The theoretically calculated tangents fit well enough with the experimental curves. It must be emphasized that for nitrobenzene, orthonitrophenol and paranitrophenol no new constants have been introduced, as the value of \(r_0=4,6\) A has been taken from the above mentioned investigation, where it was determined from a discussion of the dielectric, electro-optical and magneto-optical phenomena in solutions of nitrobenzene in non-polar solvents.
On Non-local Quantum Electrodynamics
Acta Phys. Pol. 11, 109 (1952)
abstract
A general rule for constructing observable densities enables the formulation of a non-local electrodynamics. The basic equations describing the interaction between the electromagnetic and time electronic fields are integral (or mixed integrodifferential) equations. The free waves and the non-local analogs of Green’s functions \(\Delta ^{ret}\), \(\Delta ^{adv}\) may be constructed by invoking Born’s principle of reciprocity (i.e., a symmetry between position and infinitesimal displacement operators). The \(S\)-matrix may be constructed by Yang’s method. The commutation relations for the (perturbed) fields may be computed from the field equations, provided the homogeneous integral equations possess no solution. The conservation laws are secured in spite of the absence of continuity equations. Constant electromagnetic potentials are shown to be physically meaningless. The non-local formalism is free from the usual convergence difficulties.
The Interference of the Enforced Electric Dipole Radiation and the Spontaneous Electric Quadrupole Radiation
Acta Phys. Pol. 11, 131 (1952)
abstract
This paper deals with the theory of the interference effect of the enforced electric dipole radiation and the spontaneous electric quadrupole radiation. The case is investigated when the magnetic field is parallel to the electric field, the latter enforcing the dipole radiation. The result of the calculation is that the interference effect can be expected to be observable in transversal observation. Placing a nicol askew, we can obtain such a position that one of the \(\Delta M=\pm 1\) components is extinguished. Then, the intensity of the corresponding \(\Delta M=\mp 1\) component gets its maximum. Approximative formulas for the intensity of the Zeeman components are given in the case of Russel–Saunders coupling. Their application to the first line of the \(^3D_5/_2,_3/_2\to ^2S_{1/2}\) series in the potassium spectrum leads to the conclusion that in this case one must apply an electric field of about 10 kV/cm to observe the interference effect.
The Temperature Dependence of the Working of Geiger–Müller Counters
Acta Phys. Pol. 11, 140 (1952)
abstract
The measurements were made on selfquenching argon–alcohol Geiger–Müller counters in the range of temperatures between \(-22^{\circ }\) and \(+60^{\circ }\)C. The results show that the characteristic curves remain normal up to the temperature at which the quenching vapour begins to condense, and all changes in these curves can be explained by the assumption that the only phenomenon which causes them is the condensation of the quenching vapour.
Influence of the Electrolytic Dissociation and the Hydratation of H\(_2\)SO\(_4\)-Molecules on the Scattering of Slow Neutrons
Acta Phys. Pol. 11, 146 (1952)
abstract
Coefficients of absorption of slow neutrons in H\(_2\)SO\(_4\)-water-solutions were measured. At low concentrations of acid the effect of electrolytic dissociation was observed. The results are in agreement with the theory if one assumes complete or almost complete dissociation in H\(^+\) and SO\(_4^-\) ions up to the concentration of 40 per cent (by wt.). At higher concentrations the increase of the absorption coefficient due to the hydratation of H\(_2\)SO\(_4\)-molecules was observed.
Fields Defined by Elementary Laws
Acta Phys. Pol. 11, 155 (1952)
abstract
Supposing that a given scalar field \(u\) is isotropic and homogeneous and corresponds to a linear physical law it is possible to define it by an elementary law (possibly empiric) in the form of a spherically symmetric field of a simple source \(u=f(r)\). Its partial fields are namely given by \(f(r)\) and the derivatives of \(f(r)\) with regard to Cartesian coordinates \(x,y,z\). The fields of the \(l'\)th derivatives may be interpreted as fields of multiple sources of order \(2^{l'}\)...
A Note on Perturbation Theory
Acta Phys. Pol. 11, 179 (1952)
abstract
In this paper the identity of the results of the new and the old perturbation theory is shown by a direct transition. Feynman’s method is presented in a simple form based on integral equations which is evidently invariant not only in the results but throughout the derivation. The problem of scattering on bound states is treated by means of the modern techniques.
Measuring Energy Emitted by Electrically Activated Nitrogen
Acta Phys. Pol. 11, 189 (1952)
abstract
Lord Rayleigh’s work on the measuring of energy emitted by electrically activated nitrogen was repeated, and the causes of the very high values of energy he obtained were studied. One comes to the conclusion that the results obtained by Lord Rayleigh may be easily explained.
A Note on the Franck–Condon Principle
Acta Phys. Pol. 11, 195 (1952)
see erratum: Acta Physica Polonica 12, 160 (1953)
abstract
It appears that the quantum mechanical version of the Franck–Condon principle can be obtained by applying the “sudden approximation” method to the eigenfunctions describing the nuclear motion in a system consisting of electrons and nuclei, say, in a molecule. To show it one has to use the formalism given e.g. in Schiff’s Quantum Mechanics (New York 1949) in the chapter dealing with the methods for time-dependent problems. The conditions of applicability of this method to our particular problem are much the same as those for which the first Condon approximation is valid, the approximate separability of the electronic and nuclear motion being the most important. The eigenfunctions for nuclear motions have to be obtained from Schrödinger equations involving different potential functions corresponding to different electronic states of the system.
The Derivation of Vlasov’s Equation from Fock’s Equation
Acta Phys. Pol. 11, 196 (1952)
abstract
The classical theory of plasma was given by A.A. Vlasov; its basic equation is \[\frac {\partial f}{\partial t}+\frac {p}{m}\nabla _x f+F\nabla _p f- \nabla _p f\nabla _x \int dx'K(|x-x'|)\int dp' f (x',p')=0\,,\] where \(f=f(r,p,t)\) is the distribution function of electrons, \(p\) is the momentum, \(F\) the external force, \(K(|x-x'|)=\frac {e^2}{|x-x'|}=\frac {e^2}{r(x,x')}\) Coulomb’s energy. In this equation the mutual interaction of electrons is taken into account, but changes of \(f\) due to ionization, recombination and scattering of electrons are disregarded ...
Electrostatic Neutron–Electron Interaction
Acta Phys. Pol. 11, 199 (1952)
abstract
The problem of the static interaction between neutron and electron is investigated. This problem was investigated experimentally and theoretically, but the results of several authors did not agree with each other...
A Multiple Shielding Counter
Acta Phys. Pol. 11, 201 (1952)
abstract
Seeger as well as Jürgensen and Weiss describe a Multiple Shielding Counter consisting of two coaxial cylinders and 6 anode wires enclosed in the space between the cylinders. Independently of the above mentioned research a counter almost identical in principle was built and partly investigated in our Institute as an anticoincidence shielding of internal carbon-dioxide filled counter for research carried by one of us (W.M.) as well as an anticoincidence shielding for neutron counters...Fasc. 3–4, pages 203–331
On the Connection Between Fields and Particles
Acta Phys. Pol. 11, 203 (1953)
abstract
In the present paper the connection between field equations and equations of motion of particles is studied for the case of classical electrodynamics. The equations of motion and the energy and momentum of the particles are derived from the corresponding notions for the field. The mass of the particle is purely electromagnetic and is uniquely determined either by the self-force or by the self-energy and self-momentum. Most of the results are independent of the structure of the particles.
\(\beta \)-Spectrum of RaE in the Low Energy Region
Acta Phys. Pol. 11, 215 (1953)
abstract
Electron sensitive nuclear research emulsion was used as an electron detector in a magnetic lens spectrograph for the investigation of the \(\beta \)-spectrum of RaE in the low energy region. The intensities were found by counting of some \(35\,000 \) separate electron tracks. Very thin sources were prepared by a volatilization method. The images obtained in the spectrograph were checked by a special method to prove the uniformity of the specific surface activity of the sources used. The spectrum was investigated within the energy band from 100 keV down to 4.6 keV. The results show that the energy distribution corresponding to this forbidden transition cannot be expressed simply in terms of \((E-E_0)^4\). It seems that the energy distribution curve cuts the \(P(E)\) coordinate.
A Method of Preparation of Very Thin RaE Sources
Acta Phys. Pol. 11, 226 (1953)
abstract
A volatilization method of preparation of comparatively strong but extremely thin RaE sources for \(\beta \)-spectroscopy is described. A source 50 \(\mu \)C per 1 mm\(^2\), supported by a conductive film, the whole less than 4 \(\mu \)g/cm\(^2\) thick was prepared. The authors believe that the method described is new in many details.
On the Relation Between the Energy and the Number of Grains for Low Energy Tracks in Photographic Emulsions
Acta Phys. Pol. 11, 230 (1953)
abstract
The relation between the energy and the number of grains at low energies for Ilford electron sensitive emulsion G5 was investigated. The observations were extended over energies from 37,1 keV down to 4,2 keV. A good separation of joined or overlapping grains was achieved by resoaking the emulsion before microscopic examination.
Directional Correlation for Two-Quanta Emission
Acta Phys. Pol. 11, 233 (1953)
abstract
The present paper contains correlation formulae for directions of two photons emitted simultaneously in a single act of two-quanta emission. The formulae apply to electric double-dipole radiation, i.e. where both photons are of electric dipole type. Especially interesting is the transition \(j’=0\to j=0\) forbidden for one-quantum emission. The forms of matrix elements obtained in the course of the calculations are useful not only for the electric dipole moment but also for a wider class of vectors, including i.a. the magnetic dipole moment. Measurements of directional correlations of photons are admittedly possible for \(\gamma \) radiation. Therefore the present paper refers to two quanta emission from the nucleus, although the arguments equally apply to any system of charged particles. Moreover the results are applicable after a slight and obvious change of coefficients to other simultaneous processes of second order (in double-dipole approximation) such as for instance the Raman effect.
Thermal Pseudohysteresis of the Dielectric Constant of Ferroelectric Titanates
Acta Phys. Pol. 11, 256 (1953)
abstract
Measurements of the dielectric constant of barium titanate and barium-strontium titanate were made in various temperatures with an alternating current of 2 and 5 kHz frequency and a distinct anomaly in the dependence of the dielectric constant on temperature was discovered: the curve \(\varepsilon =f(t)\) is different during the heating and the cooling of a sample. Values of the dielectric constant during cooling (above as well as below the Curie point) are higher than those measured at the same temperatures during heating. In the direct vicinity of the Curie point the value of the dielectric constant is higher by over 10 per cent during cooling than the maximum value observed during heating. We have called this phenomenon the thermal pseudohysteresis of the dielectric constant because of the characteristic appearance of the residue after the former thermal state.
On the Dependence of the Cross-section for Pair Production on the Atomic Number \(Z\)
Acta Phys. Pol. 11, 263 (1953)
abstract
The ratio of the cross-section for production of electron pairs by gamma ThC” rays (2,62 MeV) in Al, Cu and Ag to the cross-section in Pb was measured. For this purpose the G.-M. counter method was employed, using counters for beta rays working in coincidence. Possible sources of errors, the most important among which are due to Compton coincidences caused by a Compton electron and a scattered gamma photon, were carefully considered and discussed. The ratio of the cross-sections in Al and Pb was found to be much larger than the ratio theoretically calculated from Bethe and Heitler’s and Jaeger and Hulme’s theories.
On the Microstructure of the World. I. The Elementary Length
Acta Phys. Pol. 11, 273 (1953)
abstract
The main causes of the difficulties encountered by present day physics in the theory of elementary particles is attributed to (i) the indiscriminate use of Euclidean (or pseudo-Euclidean) metric both in microphysics and macrophysics and (ii) the recognition of the point (or the point-event) not only as the primitive notion of macrophysics but also of microphysics. An attempt is made to construct such a scheme of macro–micro–macrophysical space-time measurements which leads to Euclidean geometry only in macrophysics, this geometry ceasing to be even approximately valid in microphysics. This can be achieved by changing the primitive element of physical geometry from the point to that of “directed wave front” and by adopting the “concordant contact” of two wave fronts as their unique primitive relation. If the proposed theory proves to be true, than all laws of microphysics will have to be invariant under the 15-parameter group of wave-front transformations, which is isomorphic with the 15-parameter group of Lie’s sphere transformations in three-dimensional space (or the Möbius group of conformal point-transformation in four-dimensional space). At the same time the concept of elementary length is automatically introduced in the foundations of physics.
Distributions and Statistical Moments of Bosons and Fermions with Some of Their Applications
Acta Phys. Pol. 11, 298 (1953)
abstract
The present paper contains a sketch of an analytic method of solving combinatory problems concerning the distribution of particles into cells, the particles being either distinguishable or not and the different possibilities of filling the cells being possibly subject to a priori given restrictions. This method rests upon the use of so-called Laplace’s generating functions. The fundamental generating function as well as the characteristic function of a generating function have been defined and Newton’s polynomial expansion applied to the generating functions. Distributions of probabilities as well as their statistical moments have been obtained. Also application of the above method to problems in cosmic radiation, the theory of contrast in photographic emulsions, and the theory of number have been given.
On a Regular Field Theory I (Classical)
Acta Phys. Pol. 11, 314 (1953)
abstract
Regular field equations are derived from a variational principle in a finite space-time domain. The existence and uniqueness of the solutions in the form of a power series expansion is proved. Conservation laws are inferred.
Battery Pulse-Supply for G-M Counters
Acta Phys. Pol. 11, 328 (1953)
abstract
A battery pulse-supply for G-M counters is presented allowing to obtain small overall dimensions and weight of the apparatus. Working conditions for measurements with the G-M counters often require that the whole apparatus, including high voltage supply, pulse amplifier and registrator, should be transportable, light, and of small dimensions...
Sur les spectres ramaniens des mélanges de pyridine et de l’acide acétique
Acta Phys. Pol. 11, 329 (1953)
abstract
Par l’étude des spectres ramaniens des mélanges de pyridine et do l’acide acétique on a mis en évidence les changement des fréquences propres des molécules aussi quo l’apparition des fréquences nouvelles. Cette méthode mettant en évidence les modifications des fréquences permet d’étudier plus profondement les effets des associations moléculaires. Les méthodes usuelles, utilisant les mesures de tension de vapeur, de parachore, de réfraction moléculaire ne donnent que les effets globaux...
The Existence of Two OH-groups in H\(_2\)SO\(_4\) Molecules Verified by the Scattering of Thermal Neutrons
Acta Phys. Pol. 11, 330 (1953)
abstract
The scattering of slow neutrons by molecular gases is well accounted for by the theory of Sachs and Teller. This theory states that a neutron being scattered by a proton bound in a molecule may cause a rotation of the whole molecule. The cross section for the scattering of a neutron by this bound proton is...
A Remark on the Dependence of the Cross-section for Pair Production by Photons on the Atomic Number
Acta Phys. Pol. 11, 331 (1953)