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J. Weyssenhoff, A. Raabe
Relativistic Dynamics of Spin-Fluids and Spin-Particles
Acta Phys. Pol. 9, 7 (1947)

abstract

Following up a train of thought inaugurated by Einstein and Gromer, Mathisson and Lubański deduced the equation of motion of a material particle endowed with spin from the general principles of the theory of relativity. In the present paper we give a third method of obtaining the same equations by establishing first the laws of the dynamics of an incoherent spin-fluid and passing then to the limit. Strictly speaking, we obtain different and much simpler equations, which prove however to be equivalent to Frenkel’s and Mathisson’s. The simplification is due to the explicit introduction of the 4-vector of linear monumentum and energy \(G^\alpha \).

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J. Weyssenhoff, A. Raabe
Relativistic Dynamics of Spin-Particles Moving with the Velocity of Light
Acta Phys. Pol. 9, 19 (1947)

abstract

In the preceding paper we have deduced the equations of motion of a spin-particle moving with a velocity \(v\) smaller than that of light, \(c\). We shall now consider the equations of motion of a spin-particle moving with the velocity of light.

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J. Weyssenhoff
Further Contributions to the Dynamics of Spin-Particles Moving with a Velocity Smaller Than That of Light
Acta Phys. Pol. 9, 26 (1947)

abstract

In a preceding paper written with the late Mr. A. Raabe I worked out the equations of motion of a particle endowed with spin, by considering at first the relativistic equations of motion of a spin fluid, and passing then to the limiting case of an infinitely small portion of such a fluid with infinitely large mass-density and angular-momentum density.

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J. Weyssenhoff
Further Contributions to the Dynamics of Spin-Particles Moving with the Velocity of Light
Acta Phys. Pol. 9, 34 (1947)

abstract

In two previous papers written with the late Mr. A. Raabe we deduced among other things the relativistic equations of motion of a spin-particle moving with the velocity of light. First, in I, we found the equations of motion of a spin-particle moving with a velocity smaller than that of light by integrating the equations of motion of a spin-fluid over an infinitesimal volume of that fluid. Secondly, in II, we changed the parameter along the world-line of the particle from \(\tau \), the proper time of the particle, to an arbitrary parameter \(p\), leaving the world line of the particle unaltered, and distorted afterwards the world line in such a way as to make it everywhere tangent to the corresponding light-cone.

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J. Weyssenhoff
On Two Relativistic Models of Dirac’s Electron
Acta Phys. Pol. 9, 46 (1947)

abstract

The view has been often expressed that some at least of the difficulties of the present quantum theory of fields arise from the inadequateness of the underlying “classical model”, rather than from the inadequateness of the methods of quantization. Possibly the same may be true of Dirac’s theory of the spinning electron.

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M. Mięsowicz, L. Jurkiewicz
A Counter Apparatus for the Measurements of Cosmic Rays
Acta Phys. Pol. 9, 54 (1947)

abstract

For the measurements of the weak effects of cosmic rays, e.g. penetrating showers or the component of great depth, we must use G-M counters of large dimensions. They must stand long use, because the investigations last several months or more. We describe here the construction of counters of large dimensions, which can be made in any laboratory fairly simply, which are distinguished by mechanical solidity without being sealed in glass, and which have all the properties of good counters with respect to plateau, efficiency, stability during work, etc.

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J. Wesołowski, B. Makiej
Simple Quenching-Circuit for G. M. Counters
Acta Phys. Pol. 9, 59 (1947)

abstract

E.W. Yetter proposed a quenching circuit containing one vacuum tube connected in series with the cylinder of the counter. As the author admits, the chief disadvantages of that circuit are: (a) varying potential of the cylinder, requiring shielding and insulation if two or more counters are used, and (b) the low size of the negative output pulse. In addition a negative bias must be applied to the control grid of the quenching tube.

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J. Wesołowski
An Electronic Voltage Stabilizer
Acta Phys. Pol. 9, 61 (1947)

abstract

Several methods have been proposed for the stabilization of the output voltage operating G.-M. counters. A great simplicity and high constancy offers the Neher–Pickerung circuit in which, however, bias batteries must be used.

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J. Rzewuski
Relativistic Intensities of Multipole Radiation in the Lyman Series
Acta Phys. Pol. 9, 71 (1948)

abstract

In this paper the intensities of multipole radiation in the Lyman series are calculated on the basis of Dirac’s relativistic theory of the electron. In the non-relativistic case the corresponding calculations were carried out by Rubinowicz. It was possible to work out the selection rules, the Zeeman effect, and the sum rules for the radiation considered. In the particular case of magnetic dipole and electric quadrupole radiation our formulae are in agreement with the formulae of Rubinowicz. Finally, an example is discussed: the probability is calculated of an inversion of the spin vector under the influence of a magnetic field, assuming that the electron is in the state \(n=1\).

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J. Rayski
On the Divergence Problem in the Theory of Quantized Fields
Acta Phys. Pol. 9, 87 (1948)

abstract

By a suitable change of the definition of the four-vector of charge and current density a Lorentz-invariant formfactor has been introduced which removes the well known divergencies in the theory of quantized fields. Physically, this amounts to the introduction of an elementary length connected with the finite dimensions of particles. Connections are shown to the problem of field equations with higher derivatives.

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B. Średniawa
Relativistic Equations of Motion of Free Dipole and Quadrupole Particles
Acta Phys. Pol. 9, 99 (1948)

abstract

(1) Recapitulation of Mathisson’s variational principle for deriving the equations of motion of multipole particles. (2) Equations of motion of a dipole particle characterized by a spin bivector \(s^{\alpha \beta }\) and a dipole moment \(n^\alpha \). (3) Solutions of the equations of motion of a dipole particle of the second kind (characterized by \(n^\alpha \) only). (4) Equations of motion of a dipole-quadrupole particle. (5) Solution of the equations of motion of a quadrupole particle.

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R.S. Ingarden
Theoretical Remarks on Crane and Halpern’s Experimental Evidence for the Existence of the Neutrino
Acta Phys. Pol. 9, 109 (1948)

abstract

The relation between the recoil energy of the nucleus in the process Cl\(^{38}\overset {\beta }\rightarrow \) A\(^{38}\) and the number of droplets produced by this in a cloud chamber has been calculated on the assumption of Crane and Halpern that the number of droplets is approximately equal to the number of nitrogen and oxygen atoms dissociated in collision chains initiated by the recoil atom. The relation appears to be linear with two constants which have been evaluated. The occurrence of several ions in clusters of droplets has been explained as caused by X-rays or Auger processes releasing the fraction of the total binding energy of the orbital electrons of the atom connected with the change of the nuclear change during the beta decay. Finally | statistical errors in Crane and Halpern’s experiments have been discussed. The analysis leads to the conclusion that these experiments give a definitely positive answer in the question of the non-conservation of momentum in the «two-body» beta-decay.

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J. Rzewuski
Radiative Collisions Between Two Electrons
Acta Phys. Pol. 9, 121 (1948)

abstract

The differential cross section is calculated for a radiative collision between two particles. The assumptions are: Both particle obey the Dirac equation and their mutual interaction is static. In the limiting case when the mass of one of the particles tends to infinity we get the well known formula of Bethe and Heitler. However, in the case of great energies it is not allowed to neglect the change of momentum of the heavy particle and our formula becomes different from that of Bethe and Heitler. For equal masses our formula gives the cross section for a radiative collision between two electrons. It vanishes for small velocities of the particles. For large velocities it reaches the same order of magnitude as that of Bethe–Heitler’s cross section for “Bremsstrahlung”. The same formulae are valid, of course, for the reverse process of pair production in the field of an electron.

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J. Rayski
On Simultaneous Interaction of Several Fields and the Self-energy Problem
Acta Phys. Pol. 9, 129 (1948)

abstract

The problem of simultaneous interaction of several fields is studied within the framework of the Heisenberg–Pauli formalism. For a suitable mixture of fields of the well known types the divergent parts of the self-energy terms may be eliminated. The main interest is devoted to the problem of vacuum charge fluctuations. It is found that the photon self-energy vanishes if a suitable mixture of charged spinor and scalar fields is assumed. The calculations are performed to the second order of approximation in \(e^2\) only.

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B. Makiej
On the Existence of an Electric Field in Superconductors
Acta Phys. Pol. 9, 141 (1948)

abstract

By a generalization of Ohm’s law and its application to the electric current in superconductors the fundamental laws of electrodynamics of superconductivity are deduced by purely formal analogy with the equations of motion of a free charge in an electromagnetic field. For stationary currents the condition \(\hat {E}+\frac {1}{\rm nec}\hat {i} \times \hat {H}=0\) asserts that there exist in superconductors an electric field acting upon the superconduction electrons but producing no Joule’s heat, as its activity \(\hat {i} \cdot \hat {E} = 0\). By a train of thought starting from Hamilton’s principle the electric field is found to derive from an electric polarization inside the superconductors. The appearance of an electric polarization may be traced to a spin coupling of the electrons due to the existence of exchange forces. A calculation of the number of electrons worked out for a simplified model of a superconductor leads to a fairly good agreement with experiment.

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R.S. Ingarden
A Geometrical Interpretation of the Phase-difference Angle and Its Application to A.C. Phase Measurements by Means of the Oscillograph
Acta Phys. Pol. 9, 149 (1948)

abstract

It is well known that the trajectory of a point performing simultaneously two harmonic motions of the same frequency perpendicular to each other is an ellipse (first figure of Lissajous). It may be easily shown (see e.g. M. Born, Optik, 1933, p. 22) that between the amplitudes \(a_1\), \(a_2\), the phase difference \(\delta \) of the two motions and the lengths \(a\) and \(b\) of the semi-axes of the ellipse the following relations exist \[a^2_1+a^2_2=a^2+b^2\,,\] \[a_1a_2\sin \delta =ab\,.\]

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