Vol. XXXIII (1968)
Fasc. 1, pages 3–155
On the Field Theory with Infinite Multiplets in the SU(2,2) Symmetry
Acta Phys. Pol. 33, 3 (1968)
abstract
Two series of degenerate unitary representations of the group \(SU (2,2)\) (the principal and the supplementary ones) were found in the previous papers [13], [14]. The reduction \(SU(2,2)\supset \{SU(2)\otimes SU(2)\otimes U(1)\}_p\) where \(p\) is the four-momentum of particles and the classification of particles according to the irreducible representations of the maximal compact subgroup were also given. The vertex of the interaction of an infinite multiplet with a singlet field is considered in the present paper. The expression of a “unique propagator” of an infinite boson and fermion multipletis given. The true propagator of a particle with definite spin can be obtained from the “unique propagator” with the help of projection operators. Besides it is shown by using the “unique projection” that in many cases the field theory with infinite multiplets leads to convergent diagrams while they are divergent in the conventional field theory.
On the Critical Magnetic Scattering of Neutrons
Acta Phys. Pol. 33, 13 (1968)
abstract
Critical magnetic scattering of neutrons in ferromagnets and antiferromagnets has been investigated on the basis of a model of the scattering system, which represents a continuation of the ideas of Smoluchowski in the theory of critical opalescence. A fluctuation in magnetic moment in a ferromagnet or in antiferromagnetic ordering in an antiferromagnet is treated as subsystem in a reservoir. The general formalism of Van Hove has been modified in order to account for the features of the assumed model of the scattering system. The cross section has been calculated in two forms, which depend on the static spin correlation formula. For external magnetic field and magnetic moment chosen as thermodynamic variables in the calculation of the internal energy of the fluctuation, the static correlation between spins within the fluctuation is determined by the Ornstein–Zernike formula. The essential difference in the calculated cross section as compared with that derived by Van Hove appears in the replacement of the factor \(N\) which determines the number of spins in the scattering system by the product of two factors \(N_\mathrm {f} N_1\), of which \(N_\mathrm {f}\) determines the number of maximal fluctuations in the system and \(N_1\) the number of spins in a single fluctuation. In the case of external plus molecular field (in the Weiss sense) and magnetic moment chosen as thermodynamic variables in the calculation of the internal energy of the fluctuation, the static correlation between spins within the fluctuation has the form \(|\sin \chi _2 r|/4\chi _2 r\). The presence of diffraction minima represents the characteristic feature of the cross section calculated with this correlation formula. This cross section differs from that derived in our previous paper in the replacement of the factor \(N\) by the product \(N_\mathrm {f} N_1\). For an antiferromagnet only a general cross section formula has been derived, whose final form depends on the knowledge of the evolution in time in a fluctuation in antiferromagnetic ordering.
Exoelectron Emission from Thin Layers of NaCl
Acta Phys. Pol. 33, 27 (1968)
abstract
Photostimulated emission of electrons from thin layers of NaCl excited with X-rays had been investigated. It was found that the maximum depth of photoelectron emergence from layers evaporated in vacuum equalled approximately 400 nm. The emissive properties of a system of metal —NaCl—silver layers and of NaCl crystals coated with a thin layer of silver (from 1 to 50 nm) has also been looked into. It was found that the silver coating on the emitter causes a drop in the emission jatensity and a rise in its rate of decay. The mean range of an electron in a silver layer of thickness \(L\backsimeq 2\) nm had been determined. A model is proposed for explaining the emissive properties of electrons from thin NaCl layers and NaCl layers overlain with silver.
Polarization Parameters and Resonance Decay Distributions in High-energy Two-body Processes. I. Baryon–Baryon Collisions
Acta Phys. Pol. 33, 37 (1968)
abstract
The cross sections, polarization parameters and resonance decay distributions for the simplest types of two-body reactions are expressed in terms of independent transversity amplitudes. Crossing relations are explicitly written down for each type of process. Implications of discrete symmetries are taken into account. The case of a polarized target is also considered. Finally, the discussion of the number of independent parameters, which can be found by performing various measurements, is presented for each reaction.
Polarization Parameters and Resonance Decay Distributions in High-energy Two-body Processes. II Meson–Baryon Collisions
Acta Phys. Pol. 33, 51 (1968)
abstract
The polarization and resonance decay parameters of several familiar meson-initiated two-body processes are expressed in terms of the transversity amplitudes. The problem of finding all the amplitudes (together with their relative phases) from the quantities which are directly measurable is discussed in each case.
Molecular Light Scattering in Dense Mixtures
Acta Phys. Pol. 33, 63 (1968)
abstract
Additivity of the scattered light intensity \(l^\mathrm {S}\) holds only in mixtures of ideal gases, but breaks down in mixtures of real gases or liquids as a result of molecular correlations. Here, by statistical methods, \(l^\mathrm {S}\) is derived for multi-component systems as a power series in the molar fractions \(x\), the first term (linear in \(x\)) describing the additive properties of an ideal mixture and higher terms (nonlinear with regard to \(x\)) accounting for deviations from additivity due to various (pairwise, triple etc.) molecular correlations. The theory proposed is discussed in detail for certain molecular models taking into consideration the various multipolar interactions.
The Jet Analysis by the Method of Principal Axis
Acta Phys. Pol. 33, 81 (1968)
abstract
The analysis of six prong jets at 8 GeV/\(c\, \pi ^+ p\) interactions by the method of principal axis does not show the existence of well separated bodies which could be identified as the known resonances. The shape of the jets does not show the significant flatness.
Second Harmonic Light Scattering by Dense Isotropic Media
Acta Phys. Pol. 33, 89 (1968)
abstract
A semi-macroscopic method is applied to derive the intensity tensor \(I^8_{\sigma \tau }\) of light elastically scattered in the general case by a dense isotropic medium on which an intense (laser) beam of intensity \(I\) is incident: \(I^8_{\sigma \tau } = (P^{\omega }+ P^{2\omega }I+ P^{3\omega }I^2 + \dots ) I\delta _{\omega \tau }+(Q^{\omega })+Q^{2\omega }I + Q^{3\omega }I^2 + \dots ) I_{\sigma \tau }; P^{\omega }Q^{\omega }\) denote linear Rayleigh scattering with the ground frequency \(\omega \), whereas \(P^{2\omega }, Q^{2\omega }\), etc. define nonlinear scattering with the double frequency \(2\omega \) and higher harmonics \(3\omega \), etc. The angular dependence of nonlinear scattering is discussed, and Krishnan’s reciprocity relation is shown to hold. A molecular-statistical discussion of the quantities \(P^{2\omega }\) and \(Q^{2\omega }\) is given involving bi-molecular radial and orientational correlation functions. Applications to special cases, in particular to interacting tetrahedrally- and axially-symmetric as well as dipolar, quadrupolar and octupolar molecules, are given. A detailed analysis of the results allows to predict that second harmonic scattering measurements will provide information concerning molecular: correlations, anisotropy of nonlinear polarizability of isolated molecules, and their quadrupole or octupole moments.
Fission-like Disintegrations of Medium-mass Nuclei Induced by High Energy Protons
Acta Phys. Pol. 33, 105 (1968)
abstract
An analysis of 788 fission-like interactions of the 25 GeV/\(c\) protons with Ag and Br nuclei in low sensitivity emulsion has been performed. Several possible models which might describe these interactions are analysed and a new model is discussed on the assumption that the target nucleus breaks up in an explosion.
A Revised Theory of General Relativity and Quantization of the Gravitational Field I.
Acta Phys. Pol. 33, 119 (1968)
abstract
The theory of General Relativity, if applied to the case of isolated gravitational fields, bears no resemblence to other field theories because a non-vanishing energy of limited gravitational wave packets cannot be defined, or such packets do not exist. This and other peculiarities necessitate a revision of the foundations of General Relativity. The process of time measurement is analysed. The Principle of General Covariance is criticised and revised. A distinguished class of normal coordinate systems, deserving the name of ‘‘inertial with respect to a set of (compatible) hypersurfaces of measurements”, is introduced, and Hilbert’s variational principle is modified by taking account of the coordinate conditions. The modified theory also satisfies the principles of Equivalence, General Relativity, and of General Covariance (though in a weaker sense). The modified theory admits a more general class of solutions, may be easily put into a canonical form, and quantized. In the quantized version there appears a new sort of complementarity: if the hypersurface of measurement is determinate, the number of scalar and longitudinal gravitons is completely indeterminate and vice versa.
On a Radical Removal of the Convergence Difficulties
Acta Phys. Pol. 33, 129 (1968)
abstract
The possibility of formulating a divergence-free, relativistic, gauge invariant, and macro-causal electrodynamics is discussed. A non-local interaction involving a formfactor dependent upon the total energy-momentum is investigated. In this formalism the four-momentum is defined only implicitly and bootstraps itself. Such a theory is meaningful under some restrictions upon the quantum mechanical interpretation. The class of physically meaningful pure states is to be restricted to those representing coherent phenomena.
О точности вычислеия одночастичных состояний деформированных ядер
Acta Phys. Pol. 33, 135 (1968)
abstract
В статье обсуждается точность метода вычисления энергий и волновых функций одночастичных состояний деформированных аксиально-симметричных ядер, предложенного авторами. Результаты расчетов как энергий так и структуры состояний находятся в хорошем соответствии с данными, полученными более точным, но и более громоздким способом. Обсуждаемый метод обладает важными достоинствами. С одной стороны, учитывается сложная форма реалистического потенциала, имеющего размытый край. Это приводит к наиболее последовательному определению уровней энергии и Вволновых функций (в особенности их поведение на границе и периферии ядра). С другой стороны, метод позволяет производить расчеты весьма быстро, а найденные волновые функции представить в аналитическом виде. Это делает его особенно удобным в приложениях.
Higher-order Elastic Scattering of Laser Light
Acta Phys. Pol. 33, 141 (1968)
abstract
A formal theory predicting various higher-order scattering processes in dense isotropic media transmitting a strong laser beam is proposed.
The Unit Cell and Space Group of Crystals of 1-Phenyl-6-Benzyl-7,7-Dichlor-3,5-Diaza-Bicyclo-122-Hepten-5-On-2
Acta Phys. Pol. 33, 145 (1968)
Magnetization Curve of Uniaxially Deformed Ferromagnetic Monocrystals
Acta Phys. Pol. 33, 147 (1968)
abstract
On the basis of results obtained from analysis of the influence of external magnetic field and lattice deformation on domain structure (Acta Phys. Pol., 31, 555 (1966)) the influence of lattice deformation on the magnetization curve is established.
Remark on a Theorem of Araki
Acta Phys. Pol. 33, 151 (1968)
abstract
A different proof of a Theorem of Araki published in Progr. Theor. Phys. 32, 844 (1964) is given in the framework of the theory of local observables.
Über eine empirische Formel für die Mesonenmassen
Acta Phys. Pol. 33, 155 (1968)
abstract
Im Zusammenhang mit einer neuen Klassifikation der Mesonen wird eine empirische Formel für die Mesonenmassen angegeben, die im Einklang mit den bestehenden Ingtervall-regeln ist. Diese Formel liefert sehr gute Werte für 23 Mesonen; 6 weitere Resonanzen ergeben sich als Differenzen von Massen. Die neue Klassifikation zwingt zu einer Abhänderung der Ladungsformel von Gell-Mann und Nishijima.Fasc. 2, pages 165–343
Leopold Infeld Obituary
Acta Phys. Pol. 33, 165 (1968)not a regular article
On the Magnetization Curve of a Polycrystalline Ferromagnetic
Acta Phys. Pol. 33, 171 (1968)
abstract
A new method of application of the phase theory to the analysis of magnetization process of polycrystalline ferromagnetics is presented. The accepted model of magnetization process is more general than that of Lawton and Stewart [3]. Under certain assumptions concerning state of the specimen, the considerations are based on the analysis of equilibrium conditions which define the course of a quasi-static magnetization process. The scheme of magnetization process derived can be applied as the basis for plotting the magnetization curve for arbitrary distribution of grain orientations.
Magneto-Conductivity Tensor in the Presence of a Strong a.c. Electric Field
Acta Phys. Pol. 33, 183 (1968)
abstract
The nonlinear Boltzmann equation for a strong a.c. electric field is solved. The electric current density and magneto-conductivity tensor are calculated. The effect of higher harmonics generation is predicted as to be associated with the nonlinearities in the Boltzmann equation.
Electron Conductivity on Dislocation Lines in Ge
Acta Phys. Pol. 33, 193 (1968)
abstract
When excess current carriers are locally injected into a germanium crystal at nearly liquid nitrogen temperature then a small fraction of them are transmitted for a long distance, causing a change of conductivity there. Such a process occurs preferably along dislocations introduced by plastic bending. It is argued that the effect results from conduction of accepted electrons along dislocation lines. The lower limit of electron mobility on dislocation has been estimated as \(5\times 10^3\) cm\(^2\)/Vs.
Pion–Nucleon Coupling Constant from Spin–Flip Dispersion Relation
Acta Phys. Pol. 33, 203 (1968)
abstract
Single variable dispersion relation for the spin–flip part of the pion–nucleon scattering amplitude is used to obtain a value of the pion–nucleon coupling constant. The method has the advantage of the using accurately known phase-shifts from the recent analyses.
Нарушенная симметрия SU\(_W\)(6) и девятый псевдоскалярный мезон
Acta Phys. Pol. 33, 209 (1968)
abstract
Обсуждаются возможные нарушения симметрии SU\(_W\)(6) на примере массовых формул. Для барионов полученные результаты такие же, как и в случае статической группы SU(6). Известное различие в классификациях мезонов по \(W\)-спину и обычному спину в SU\(_W\)(6) приводит к тому, что при всех возможных нарушениях девятый псевдоскалярный мезон должен иметь массу около 1.40 Гэв. Очень близким значением массы обладает \(Е\)(1420)-мезон, наиболее вероятное значение спин-четности которого по новым данным есть как раз \(0^-\). Полученные результаты справедливы и в группе \(\mathrm {SU}_X\)(6), которая обобщает SU\(_W\)(6) на случай любой бинарной реакции.
Impurity Conductivity of \(p\)-type Germanium in Low-frequency Electric Field
Acta Phys. Pol. 33, 217 (1968)
abstract
The ac conductivity of \(p\)-type germanium at very low temperatures in the frequency range \(10^2\)–\(10^5\,\mathrm {sec}^{-1}\) was calculated on the bacis of the model proposed by Pollak and Geballe using the Schechter functions of acceptor ground state. The formula for the transition rate for phonon-induced hopping in deformation potential approximation is derived. Finally, the formula for the polarization conductivity is given and numerical results are presented. The range of validity of our results is also discussed.
Exoelectron Emission from \(\mathrm {BaF}_2\) and \(\mathrm {SrF}_2\) Induced by X-rays
Acta Phys. Pol. 33, 231 (1968)
abstract
Thermo- and photo-stimulated exoelectron emission from polycrystalline \(\mathrm {BaF}_2\) and \(\mathrm {SrF}_2\) tables was investigated with the use of a flow point counter operating in atmospheric air. The curve of thermostimulated emission decay was found to have three maxima: for \(\mathrm {BaF}_2\), in the vicinity of the temperatures \(T_{m_1} = 398^\circ \)K, \(T_{m_2} = 453^\circ \)K and \(T_{m_3} = 599^\circ \)K; and for \(\mathrm {SrF}_2\), in the vicinity of the temperatures \(T_{m_1} = 431^\circ \)K, \(T_{m_2} = 526^\circ \)K and \(T_{m_3} = 656^\circ \)K. In the case of the two materials tested the dependence of the total number of pulses recorded (electrons) \(N\) upon the X-ray dose within the range from \(D= 2\) to \(D = 100\) R was found to be linear. Moreover, the integrally-recorded emissivity was distinctly seen to be affected by the illumination and heating-up rate of the samples. The influence of ageing samples after X-irradiation on the total recorded number of pulses (electrons) \(N\) has also been investigated in both the case of photostimulation and thermostimulation of exoelectron emission. It was found that in the case of photostimulation the curve \(N = f(t_\mathrm {age})\) reaches maximum after three days for \(\mathrm {BaF}_2\) and after 13 days for \(\mathrm {SrF}_2\). In the case of thermo-stimulation the curves \(N = f(t_\mathrm {age})\) become saturated after an ageing time at which a maximum appears for photostimulation.
Influence of External Electric Field on Photostimulated Exoemission of Electrons in Vacuum
Acta Phys. Pol. 33, 239 (1968)
abstract
The influence of external electric field on the intensity of photostimulated exoemission of electrons from electrolytically coloured NaCl and KCl monocrystals and from the surface of roughed aluminium has been studied. It was found that an external electric field influences the decay rate of exoemission from KCl. No such influence was, however, observed in the use of roughed aluminium surface.
On the Kinetics of Intensity Growth of Exoemission of Electrons During Plastic Deformation of Aluminium Coated with Oxide Film
Acta Phys. Pol. 33, 249 (1968)
abstract
The study concerns the process of growth of the intensity of photostimulated exoemission of electrons into vacuum during plastic deformation (stretching) of aluminium coated by oxide film.
Semi-empirical Calculations of the Band Shape and Polarization of Charge-transfer Transitions
Acta Phys. Pol. 33, 267 (1968)
abstract
Width and diffuseness of charge-transfer absorption bands as well as the anomalies in their polarization state are considered as a result of the statistical distribution of intermolecular distances and orientations of complex molecules in solutions. Potential energy curves in the ground and excited state, frequencies and dipole moments of the charge-transfer transition, the dependence of the frequency and dipole moment of charge-transfer transition on deviations from the equilibrium configuration are calculated in the first approximation of the Mulliken theory of charge-transfer complexes. It is shown that the shape of the absorption band is mainly determined by the amplitude of the valence vibrations in the first \((v = 0)\) vibrational state. For nonideally oriented species the transition moments of different charge-transfer transitions are not collinear and deviate from the line joining centres of donor and acceptor molecules. A qualitative agreement with experimental values is found.
Development of Partition Function in Boltzmann Distribution I.
Acta Phys. Pol. 33, 281 (1968)
abstract
The development of a quantum mechanical expression for the grand-canonical partition function of a system, of interacting particles in powers of Maxwell–Boltzmann distribution functions is proposed. This development is somewhat related with the expansion in activity and in density. The relative magnitude of different kinds of terms arising in perturbation expansion is discussed and the main properties of the leading terms of the development are found.
Development of Partition Function in Boltzmann Distribution. II. Diagram Notation
Acta Phys. Pol. 33, 291 (1968)
abstract
A diagram notation, similar to that of Hugenholtz, and useful for calculations of quantum-mechanical grand-canonical partition function in Boltzmann approximation is introduced. The characteristics of the diagrams is discussed, and the topological properties of diagrams leading in the development, as well as their contributions are found.
New Extrapolation Formulae Defining the Molecular Mean Square Dipole Moment of a Substance in Solution with a Non-polar Solvent
Acta Phys. Pol. 33, 307 (1968)
abstract
New extrapolation formulae have been derived on the basis of the Onsager and Piekara–Zakrzewski theory, which enable calculation of the mean square dipole moment of polar molecules in non-polar solvents. In these formulae there are, independently of the physical constants, the following quantities which have to be determined experimentally: \(M_2\) and \(M_1\), the molecular weight of the substance and the solvent, respectively; \(\varepsilon _1\) and \(\eta _1\), the dielectric constant and refractive index; and the density of the solvent \(\delta =\frac {d\varepsilon _{12}}{d\omega _2}, \beta = \frac {dd_{12}}{d\omega _2},\frac {dn_{12}}{d\omega _2}\) respectively equal to the change of the dielectric constant, the change of the solution density and the change of the refractive index, as a function of the weight fraction \(w_2\), of the solute. The extrapolation formulae have been corroborated for a number of polar substances, receiving good agreement between the dipole moment determined on the basis of experiments with solutions of these substances, and that found on the basis of measurements of dipole moments in the gas phase.
Unitary-symmetrical Statistical Model of Multiple Particle Production
Acta Phys. Pol. 33, 315 (1968)
abstract
A statistical model is suggested in which particles are considered as the terms of SU(3) multiplets and transitions are possible only between states corresponding to the identical irreducible representations of the group SU(3). The processes of \(pp\) and \(pn\) annihilation at rest and the inelastic \(\pi ^+ P\) interactions in the energy range \(T \gt 1\) GeV are considered in detail. Introducing the splitting of the effective coupling constant which is due to the difference between the interactions of the \(K\)-mesons and other particles, a disagreement with experiment occurs only for channels with a small number of particles where a more detailed approach is needed.
On a Generalization of the Łopuszański Theorem
Acta Phys. Pol. 33, 327 (1968)
abstract
A generalization of the Łopuszański theorem is given with the help of a method similar to that recently used by Csikor and Pócsik in their generalization of the Jost and Schroer result. We have shown that the action of an interacting field on any vector can not be represented as a result of action of a free field operator on this vector, or even, on any linear combination of some vectors, unless the interaction vanishes.
On the Quenching of Photoluminescence of Solid Solutions by Energy Transfer
Acta Phys. Pol. 33, 331 (1968)
abstract
In order to get a better interpretation of the processes occurring in solid fluorescent solutions a modification of the layered model of a luminescent centre has been achieved in the theory of quenching with foreign absorbing substances.
Relation Between the Number of Localized \(d\) Electrons and the Atomic Magnetic Moment of Magnetic Transition Metals
Acta Phys. Pol. 33, 335 (1968)
abstract
B. Rozenfeld obtained recently from results on positron annihilation the number of collectivized electrons in d transition metals. It is shown that computing from his data the number of localized \(d\) electrons and applying to them Hund’s rule one gets to a fair approximation the atomic magnetic moment of ferro- and antiferromagnetic \(d\) transition metals.
Measurements of Proton Spin–Lattice Relaxation Time in Ordinary and Partially Deuterised Liquid Silane
Acta Phys. Pol. 33, 337 (1968)
abstract
Measurements of the proton spin–lattice relaxation time \(T_1\) in liquid silane and in partially deuterated liquid silane are reported. The obtained temperature dependence of \(T_1\) may be explained by dipolar and spin-rotational interactions.
A Remark on the Regge-pole Model for the Processes \(\pi (K)p\rightarrow \pi (K)N^*\)
Acta Phys. Pol. 33, 341 (1968)
abstract
Corrections to the Bialas–Kotanski relation, arising from low-lying trajectories, are investigated.
Determination of Oscillator Strength Ratios for Doublets of the Si II and Si IV Spectrum
Acta Phys. Pol. 33, 343 (1968)
abstract
This article gives the values of oscillator strength ratios of spectral lines in multiplets, determined theoretically by Fermi’s semi-empirical method, and compares them with several experimental values. Calculations for Si II were made for two doublets of the principal series: \(4P_{1/2,\,3/2}\rightarrow 4S_{1/2}\) and \(5P_{1/2,\,3/2}\rightarrow 4S_{1/2}\) and also for the doublet of the sharp series \(5S_{1/2}\rightarrow P_{1/2,\,3/2}\).Fasc. 3, pages 349–499
Investigation of the Thermoelectric Power in the Nickel–Hydrogen System
Acta Phys. Pol. 33, 349 (1968)
abstract
The thermoelectric power of the nickel-hydrogen system has been investigated as a function of the hydrogen content in the temperature range 77–250°K. The absolute value of the thermoelectric power increases with the increase in the hydrogen content and becomes nearly zero at the atomic ratio \(\mathrm {H/Ni} = 0.9\). For a constant hydrogen content the absolute thermoelectric power is a linear function of temperature. A different behaviour for the \(\alpha \)- and \(\beta \)-phase regions was observed. No anomaly was observed as could be expected as caused by the filling up of the \(d\)-band by the hydrogen electrons.
Zur Störungstheoretischen Berechnung von verallgemeinerten Zweipunktfunktionen in der Elektrodynamik
Acta Phys. Pol. 33, 355 (1968)
see erratum: Acta Physica Polonica 34, 1105 (1968)
abstract
Ausgehend von den klassischen Feldgleichungen der vollen Elektrodynamik werden unter Berücksichtigung einiger Voraussetzungen, die man gewöhnlich an die Wightmanfunktionen stellt, Photon- und Elektron-Zweipunktfunktionen in erster nichtverschwindender störungstheoretischer Näherung bestimmt. Das Verfahren lässt sich so einrichten, dass man die Zweipunktfunktionen der konventionellen, unrenormierten Quatenelektrodynamik erhält.
The Quantum Theory of Adsorption on Metals. II
Acta Phys. Pol. 33, 363 (1968)
abstract
The numerical results concerning adsorption heat and ionization probabilities of alkaline ans Sr and Ba atoms adsorbed on planes (100), (110), (111) of tungsten and on planes (100) and (110) of copper are given. From the results, it follows that in the case of adsorption of alkaline adsorbates on W and Cu the bond is an ionic one, and in the case of Sr and Ba the bond is partially covalent and partially ionic, but the contribution of the latter is small. The adsorption heats of different adsorbates on considered planes of tungsten are such that: \(E_{110} \gt E_{100} \gtrsim E_{111}\). For the adsorption on the planes (100) and (110) of copper it was found that \(E_{110} \gt E_{100}\). The adsorption heats of different adsorbates on W and Cu are such that for the plane with given indices (\(hkl\)) one has: \(E_\mathrm {Na} \lt E_\mathrm {K} \lt E_\mathrm {Rb} \lt E_\mathrm {Cs}\) and \(E_\mathrm {Sr}\lt E_\mathrm {Ba}\), what is in good agreement with experiment. It was shown also that in the neighbourhood of the equilibrium distance, of the adsorbate to metal, the ionization probabilities \(c\) are such that: \(c_{110} \gt c_{100} \gt c_{111}\), for the system of alkaline atoms on W, and \(c_{111} \gt c_{100} \gt c_{110}\) for the system of Sr and Ba on W. It was shown also that the one-dimensional model with a square potential barrier between adsorbate and metal gives the wrong alteration of \(c_{hkl}\). The work also contains a discussion on simplifying assumptions accepted by other authors in calculations of some integrals appearing matrix elements.
Deposition of Thin \(\mathrm {BaTiO}_3\) Films by Means of Sputtering
Acta Phys. Pol. 33, 381 (1968)
abstract
Arbitrarily thin \(\mathrm {BaTiO}_3\) films have been obtained by sputtering from a heated cathode from polycrystalline ceramic \(\mathrm {BaTiO}_3\) sample. The thin films obtained are characterized by polycrystalline structure, high degree of hardness and good adherence to arbitrary substrate. They also show an electric hysteresis curve.
EPR Investigation of Copper Complexes in Single Crystals of Rochelle Salt and Triglycine Sulphate
Acta Phys. Pol. 33, 387 (1968)
abstract
The angular dependence of the electron spin resonance spectrum of \(\mathrm {Cu}^{2+}\) has been measured in the tryglicine sulphate (TGS) and the spin-hamiltonian parameters: g-factor, the hyperfine splitting (\(A^\mathrm {Cu}\)) and the ligandhyperfine splitting (\(A^N\)) have been found. The main values of \(\hat {\hat {g}}, \hat {\hat {A}}^\mathrm {Cu}\) and \(\hat {\hat {A}}^N\) tensors were used to estimate the bonding character of copper ion in a planar complex: \(\alpha ^2 = 0.75\) and \(\beta _1^2 = 0.90\). Similar measurements of Cu\(^{2+}\) in the Rochelle salt have been done showing that \(\mathrm {Cu}^{2+}\) ion enters into Na-position. The \(\alpha ^2 = 0.83\) and \(\beta _1^2 = 0.93\) data indicate a predominant ionic bonding in the Rochelle salt.
Electric Dipole Hyperpolarizabilities for Several Open Shells of Electron Systems
Acta Phys. Pol. 33, 401 (1968)
see erratum: Acta Physica Polonica 34, 1105 (1968)
abstract
A method is derived for calculating the electric dipole hyperpolarizabilities on the case of open shells of atoms and ions by means of coupled first-and second-order Roothaan–Hartree–Fock orbital equations. A second method is also given, which involves the direct calculation of the Roothaan–Hartree–Fock wave functions of the atoms and ions, for open shell electron systems, in the presence of a constant perturbing field.
Fast Neutron Excitation of Isomeric Activities in \(^{112}\)In and \(^{114}\)In Isotopes
Acta Phys. Pol. 33, 409 (1968)
abstract
The 14.7 MeV neutron cross sections have been measured for \(^{113}\mathrm {In}(n, 2n) ^{112g,m}\mathrm {In}\) and \(^{115}\mathrm {In}(n,2n) ^{{114g,m_2}}\mathrm {In}\) reactions. Experimental results for isomeric ratios are compared with the statistical theory predictions.
Neutron Inelastic Scattering Data for Crystalline \(\mathrm {H}_3\mathrm {O}\cdot \mathrm {NO}_3, \mathrm {CH}_3\mathrm {I}\), and \(\mathrm {CH}_2\mathrm {I}_2\) and Their Comparison with Infrared and Raman Spectroscopy
Acta Phys. Pol. 33, 419 (1968)
abstract
Results on neutron inelastic incoherent scattering by crystalline nitric acid monohydrate, methyl iodide, and methylene iodide are presented and compared with infra-red and Raman spectroscopy data.
Determination of the Volume of the Uranine Molecule Together with Its Solvatation Shell
Acta Phys. Pol. 33, 441 (1968)
abstract
In an earlier paper the result were reported of the evaluation of the volume \(v\) of uranine molecule together with its solvatation shell in glycerol + ethyl alcohol or glycerol-water on ground of measurements of emission anisotropy \(\bar {r}\) and of the mean durations of fluorescence. It appeared that \(v\) grows rapidly with growing ethyl alcohol (or water) concentration in the solvent. The evaluation of \(v\) was carried out by means of the expressions (A. Jabłoński) resulting from the simplified form of the theory of rotational depolarization, based on following assumptions: 1. the rotation of luminescent molecules is governed by laws of Brownian rotations of spherical particles — there results an exponential decays of emission anisotropy with decay time of fluorescence, and 2. the total fluorescence decay according to a simple exponential law. The aim of this paper is to check how far these assumptions are justified. To this end the values of v were determined by the measurements of the diffusion rate. In the case of glycerol+ethyl alcohol solutions the values of \(v\) thus determined agree within experimental errors with those obtained by the former method, thus corroborating the assumptions on which it is based. However, in the case of uranine solutions in glycerol + water the results obtained by the two methods differ drastically. This difference may be due to the negative hydration of the uranine molecule in its ground state which affects the microscopic viscosity coefficient.
Remarks on Wallace’s Hamiltonian Perturbation Method
Acta Phys. Pol. 33, 449 (1968)
abstract
The statistical part of Wallace’s Hamiltonian perturbation method worked out in [1] for the occupation number representation is here formulated without reference to any particular representation and augmented by a formula for calculating statistical averages to order \(m+1\) if the problem is solved to order \(m\). Furthermore, two erroneous statements made in [1] are pointed out and discussed.
Semiconductive Properties of \(\mathrm {BaTiO}_3\)
Acta Phys. Pol. 33, 455 (1968)
abstract
This work deals with barium titanate doped with lanthanum oxide (one atomic per cent). Polycrystalline samples were obtained by means of the traditional ceramic technique. The semiconductive properties were the result of reduction in hydrogen atmosphere. Described here are the measuring methods and the results of research on the electric conductivity as a function of temperature within the range from —198°C to +300°C, the thermoelectromotive force (20 to 200°C) and the reflectivity in the infrared for wavelengths from \(0.7~\mu \) to \(7.4~\mu \) . An explanation of the results received is given with the use of the model of small polarons, conformably to the considerations of Gerthsen, Groth and Härdtl. A hypothesis that lanthanum affects the magnitude of the conductivity of reduced \(\mathrm {BaTiO}_3\) has been advanced.
On Stoichiometric Defects in Rutile (\(\mathrm {TiO}_{2-x}\))
Acta Phys. Pol. 33, 465 (1968)
abstract
Measurements of electric resistance as a function of temperature in the range between 20° and 1000°C were made for sintered \(\mathrm {TiO}_2\) samples which were than partly reduced in CO–CO\(_2\)-atmosphere. Some maxima have been observed in the dependence \(\ln \sigma = f (1/T)\), whose magnitude and position were dependent on the degree of reduction. In repeated measurement of \(\ln \sigma \) versus \(1/T\) dependence rectilinear section were obtained which are characteristic for semiconductors. The maxima in \(\ln \sigma \) versus \(1/T\) have been explained in terms of stoichiometric defects.
Strangeness-exchange Processes in the Quark Model
Acta Phys. Pol. 33, 471 (1968)
abstract
Two-body strangeness-exchange processes, with or without resonance production, are discussed in the framework of the generalized quark model. Relations between the cross sections and spin density matrix elements are derived and compared with the experimental data. The comparison shows a reasonable agreement for the relations between the cross sections, except for processes involving \(\mit {\Sigma }\)-hyperons. Also the density matrix elements seem to be correctly described by the model.
Numerical Calculations of Optical Kerr Constant for Several Liquids
Acta Phys. Pol. 33, 495 (1968)
abstract
Molecular optical Kerr constants calculated taking into account the effect of angular correlations on molecular reorientation are found to be in satisfactory agreement with recent measurements of laser light-induced optical birefringence of the liquids.
Note on the Ground-state Energy of a Cubic Antiferromagnet
Acta Phys. Pol. 33, 499 (1968)
abstract
Some infinite series of graphs correcting the zero-point and excited state energies of a cubic antiferromagnetic are derived.Fasc. 4, pages 505–687
On the Green’s Functions Approach in the Theory of Nuclear Matter
Acta Phys. Pol. 33, 505 (1968)
abstract
The method of Green’s functions is applied to investigate the ground-state properties of nuclear matter treated as a large bound system of fermions interacting through short-range forces. An approximation which consists in neglecting three-body correlations is considered. Since all quantities of interest can be expressed by spectral functions of Green’s functions, the latter have to be found. So, equations for the spectral functions of the self-energy and the vertex part are derived. Additional approximations are made in the case of normal systems. Damping effects are neglected or an independent-particle model is introduced to get a correspondence with the generalized ladder approximation in the perturbation theory. The Brueckner-type scheme is obtained at the low-density limit. In this scheme there appear only single-particle energies and their derivatives on the energy shell.
Polarization in High-energy Proton–Proton and Proton–Antiproton Elastic Scattering
Acta Phys. Pol. 33, 521 (1968)
abstract
Polarization in high-energy, fixed momentum transfer elastic \(pp\) and \(p\bar {p}\) scattering is discussed on the basis of the asymptotic expansion of the scattering amplitudes in terms of the real powers of c.m. energy.
Space Charge Limited Currents in \(p\)-Terphenyl and \(p\)-Quaterphenyl Monocrystals
Acta Phys. Pol. 33, 529 (1968)
abstract
The electrical properties of organic crystals of \(p\)-terphenyl and \(p\)-quaterphenyl are examined. The results obtained are suggesting the existence of the space charge limited currents. The influence of the electrode material, the temperature and the illumination are discussed. The results are showing that the current-voltage characteristic exponent cannot be related to the centre of gravity of the trap level distribution. The value can be calculated from the relation between the current and the temperature.
General Relativistic Fluid Spheres. I. New Solutions for Spherically Symmetric Matter Distributions
Acta Phys. Pol. 33, 541 (1968)
abstract
At present, when general relativity has entered astrophysics not only through cosmology but also through relativistic treatment of stellar structure, it seems appropriate 1o have on hand an abundance of models describing the internal structure of general relativistic fluid spheres. Till now, only a small number of exact solutions of the Einstein gravitational field equations in space filled with matter is known. In the present papers several new solutions are obtained which may be of use in astrophysical research; also a general mathematical scheme of generating new simple solutions is presented. Some of the solutions (which have an especially simple form) are examined and it is found that they may be used at least in certain regions of the fluid sphere; there are, of course, also some solutions being valid everywhere inside the sphere.
Thermodynamic Properties of the Heisenberg Ferromagnet. Arbitrary Spin
Acta Phys. Pol. 33, 565 (1968)
abstract
The perturbation theory of Stinchcombe et al. [1] is extended to arbitrary spin. The result of the molecular field theory is obtained. At low temperatures all leading graphs are summed to yield Dyson’s low temperature free energy.
Influence of Double-stage Excitation Energy Transfer on Resonance Quenching of Photoluminescence of Solutions by Foreign Absorbing Substances
Acta Phys. Pol. 33, 573 (1968)
abstract
Experimental studies of quenching of photoluminescence of trypaflavine by rhodamine \(B\)(I) and trypaflavine by rhodamine \(6G\) (II) have been carried out in glycerine solutions for various molar concentration ratios of trypaflavine to rhodamine \(C_T/C_R\). The experimental values of critical distance \(R_1\) determined in the present work turned out to be different for different \(C_T/C_R\)-ratios both in the case of the system (I) and (II). For \(C_T/C_R\) values ranging from 1/3 to 3 in the case of the system (I) the corresponding \(R_1\)-values vary between 45.7 A and 51 Å while in the case of the system (II), \(C_T/C_R\) changes from 1/2 to 4 are associated with \(R_1\)-changes from 44.9 A to 53.4 A. The experimental results obtained seem to indicate that in the process of resonance quenching of trypaflavine by rhodamines the electron excitation energy may be transferred from the trypaflavine molecule to that of rhodamine not only as the result of a single transfer act, but also through intermediary-previously not excited — trypaflavine molecules.
Remark on the (71°|180°) Bloch Wall in Four-axial Ferromagnets
Acta Phys. Pol. 33, 581 (1968)
abstract
When solving the variational principles for the Bloch walls in four-axial ferromagnets in [1], the periodic solution for the (71°|180°) Bloch wall was not obtained in its most general form, as it does not hold for all positive values of the first integration constant. It is shown in the present paper that this restriction can actually be avoided, as there exists a real periodic solution of the respective Euler–Lagrange equation for those values of the integration constant for which the solution given in [1] ceases to be valid.
Nonlinear Excitation of Electrons in Semiconductors
Acta Phys. Pol. 33, 585 (1968)
abstract
The effect of the nonlinear excitation of electrons in semiconductors in the presence of a strong a. c. electric field is discussed. This effect is associated with the generation of the higher harmonics in the current density. It is shown that there are two sources of the nonlinear excitation of electrons. One of these is the energy dependence of the relaxation time and the second one is the nonparabolicity of the band.
Исследование \(\gamma \)-излучения из реакции \(^{12}\mathrm {C}(^3\mathrm {He},p\gamma )^{14}\mathrm {N}\)
Acta Phys. Pol. 33, 595 (1968)
abstract
Исследовалось \(\gamma \)-излучение из реакции \(^{12}\mathrm {C}(^3\mathrm {He},p\gamma )^{14}\mathrm {N}\). Используя допплеровское уширение пиков спектра, определена верхняя граница времени жизни шести наблюдаемых уровней ядра 1*№ На основании анализа угловых распределений \(\gamma \)-квантов сделана оценка значений спинов дла некоторых возбужденных состояний ядер \(^{15}\mathrm {O}\) и \(^{14}\mathrm {N}\).
X-ray Study of Vegetable Fibres: Part I: Coir
Acta Phys. Pol. 33, 605 (1968)
abstract
X-ray diffraction patterns of coconut fibre (coir) both in the natural and treated conditions are recorded. In mature fibre a spiral orientation of 45° is obtained. (101) planes with spacing 6.1 Å tend to lie parallel to the fibre axis. The cell wall of fibre remains without collapsing and lumen is estimated to have a dimension of 50–75 microns, which may account for the high buoyancy of coir. Results of sodium chloride and sodium hydroxide treatment are given.
X-ray Study of Vegetable Fibres. Part II: Banana and Sisal Fibres
Acta Phys. Pol. 33, 609 (1968)
abstract
Fibres of different varieties of Musa sapientum and Agave sisalania have been studied by the X-ray diffraction method under normal and chemically treated conditions. Musa fibre is highly crystalline like jute and ramie, exhibiting layer lines and layer line spots. Sodium chloride treatment has no effect on these fibres. However, sodium hydroxide produces partial mercerization. Delignification produces no change in structure.
Application of Transmission Pseudo-Kossel Lines to Precise Determination of Lattice Constant in Crystals of Diamond Type
Acta Phys. Pol. 33, 613 (1968)
abstract
The divergent-beam X-ray technique has been used to determine precisely the lattice parameter of single crystal of germanium. Taking into account geometrical relations occurrings among the lines on the photographic film one can calculate the lattice parameter. Its value obtained in this investigation was \(5.6577\pm 0.0002\) Å . The method given below enables us to determine precisely the value of the lattice parameter for other cubic crystals.
Note on the Azimuthal Asymmetry of the Secondary Particle Emission in a High Energy Nuclear Reaction
Acta Phys. Pol. 33, 619 (1968)
abstract
The azimuthal asymmetry in a class of secondaries in the 780 interactions of 9 GeV negative pions with xenon nuclei is observed. The observed asymmetry is correlated with the previously established occurrence of the \(p\)–\(p\) final state interaction in the secondary particle emission.
Magnetic Levels in the Valence Band of Semiconductors with Wurtzite Structure
Acta Phys. Pol. 33, 625 (1968)
abstract
The magnetic levels of holes in the two uppermost valence bands of wurtzite type semiconductors are investigated and illustrated by examples with two sets of numerical values of the constants in the effective mass hamiltonian.
Absorption of the Electromagnetic Radiation by Hopping in \(n\)-type Germanium and Silicon at the Weak Magnetic Field
Acta Phys. Pol. 33, 635 (1968)
abstract
The absorption of the electromagnetic radiation at low temperatures in the wavelength region from 100 to 800 \(\mu \) and from 500 \(\mu \) to 2.5 cm, in the magnetic field 50 kgauss and 5 kgauss, at donor concentrations up to \(2\times 10^{18}\) cm\(^{-3}\) and \(6 \times 10^{16}\) cm\(^{-3}\) in \(n\)-type Si and Ge, respectively, is investigated theoretically on the basis of a model of direct absorption process. Compensation ratios up to 0.2 are considered. The formula for the magnetic field-dependent correction to the absorption coefficient calculated by Blinowski and Mycielski is derived and numerical results are presented. The range of validity of the results is also discussed.
The Low Temperature Specific Heat of Some Polish Tool Steels and Stainless Steel
Acta Phys. Pol. 33, 657 (1968)
abstract
Measurements of low-temperature specific heat of some Polish tool steels and stainless in the range 2.5 to 16°K are reported. The results are analyzed in terms of the usual electronic and lattice specific heat contributions. The measurements of the hardness have been also performed.
Determination of Relative Values of Transition Probabilities in Doublets of the Principal Series of ScIII, YIII and LaIII Spectra
Acta Phys. Pol. 33, 665 (1968)
abstract
The line strength ratios were determined on the basis of measured ratios of line intensities for the doublet of the principal series \(4^2P^0 \rightarrow 4^2S\) of the ScIII spectrum, found to be \(S_{3/2}:S_{1/2} = 1.61\), for the doublet \(5^2P^0\rightarrow 5^2S\) of the YIII spectrum — \(S_{3/2}:S_{1/2} \geq 1.63\), and for the doublet \(6^2P^0\rightarrow 6^2S\) of the LaIII spectrum — \(S_{3/2}:S_{1/2} \gt 2.19\). These values were calculated theoretically by Fermi’s method of accounting for spin-orbit interaction of the luminous electron. Comparison of the experimental and theoretical values indicates that Fermi’s method, which leads to goods results in the case of alkali spectra (isoelectronic with bivalent ions of scandium, yttrium and lanthanum), in this case does not give values conformable with experiment.
A Further Modification of a Strip Magnetic Balance with Controllable Sensitivity
Acta Phys. Pol. 33, 673 (1968)
abstract
The paper presents a modified version of a magnetic balance with controllable sensitivity. The modification consists in the application of additional two mirrors, the use of two plastic floats of suitable buoyancy reducing the load of elastic strips as vibration damping and a new system of bearing in the mounting of the rod which holds the specimen. The application of four mirrors has increased the sensitivity by a factor of six as compared with the earlier version while the remaining changes improved the operation of the balance.
A Thermostat for Magnetic Balances of Sucksmith’s Type for Measurements in the Temperature Range from Room Temperature to 1100°C
Acta Phys. Pol. 33, 679 (1968)
abstract
A simple thermostat for magnetic balances of Sucksmith’s type is described which permits obtainment of temperatures up to 1100°C. Its construction guarantees good thermal insulation from surroundings without the necessity of evacuation of the whole balance. The comparatively low diameter enables measurements for mutual pole piece distances from 23 mm.
\(N/D\) Solutions for the Low Equation in the Lee Model
Acta Phys. Pol. 33, 683 (1968)
abstract
In this work the solutions of the Low equation in the Lee model obtained via the \(N/D\) method are written and the correct interpretation of the bootstrap-crossing symmetry correlation is given.
La I-ére approximation de la methode WKB pour la fonction potentielle symmetrique
Acta Phys. Pol. 33, 687 (1968)
abstract
In this work is obtained the first approximation of the WKB method for the Symmetric Potential Function.Fasc. 5, pages 693–865
Tunnel Current Density-energy Distribution in the Symmetric M-I-M System
Acta Phys. Pol. 33, 693 (1968)
abstract
In this paper, the tunnel current density distribution of electron energy levels in the symmetric M-I-M system as a function of various parameters was considered. Current-energy distributions as functions of the applied voltage, height of the barrier, temperature and the barrier thickness were presented in graphical form. Most of the results described in the paper are assigned to the transition region between the tunnel and thermionic effects. The influence of the above-mentioned parameters on the change of the distribution curves in this region was considered.
On the Determination of the Radial Intensity Distribution of Radiation in Cylindrical Plasma
Acta Phys. Pol. 33, 701 (1968)
abstract
A survey is given of several numerical methods of calculation of radial intensity distribution \(i(r)\) of the radiation in the axially symmetric plasma on the basis of observed intensity distribution \(I(x)\) (see text). The influence of error of the measurement of the intensity distribution \(I(x)\) on the maximal error of calculated radial intensity distribution \(i(r)\) is discussed. A method of \(i(r)\) — distribution calculation is presented which is the least sensitive to the error of \(I(x)\)-measurement and which provides sufficient accuracy in the solution of Abel’s integral equation, occurring in the problem.
Quasilocal Terms in the Functional Formulation of the \(S\)-matrix Theory
Acta Phys. Pol. 33, 711 (1968)
abstract
Quasilocal terms in the functional formulation of the S-matrix theory are investigated. The quasilocal terms that arise in the formulation of Lehmann, Symanzik and Zimmermann and those corresponding to the interaction fuctionals \(J[g]\) that do not contain derivatives, are given.
On the Motion and Statistics of Neutrinos in Superdense Matter
Acta Phys. Pol. 33, 723 (1968)
abstract
The neutrino plays a very special role among other elementary particles: it takes part only in the weak and gravitational interactions. Its emission stage plays a central role in the evolution of late type stars. For high temperatures and densities of stellar matier the neutrino luminosity may exceed by orders of magnitude the photon luminosity of a star. On the other hand, for such strong gravitational fields as in this case, the neutrino dynamics is a result of the gravitational field only. For no other particle can one find the gravitational effects so clearly pronounced. Therefore it seemed to be meaningful to study the motion of neutrinos in various theoretically possible types of internal stellar fields; the results of studies (which have been partially reported in preceding papers by the present author) are summarized. For strong enough gravitational fields inside (and in a vicinity of the surface) of the star the neutrino emission into outer space may be rendered difficult thanks to the “gravitational trap” mechanism. Since inside a superdense star more and more nentrinos accumulate in equilibrium with other elementary particles), the problem of neutrino statistics arises. The gravito-dynamical and the statistical approaches to the neutrino problem in superdense stars may be regarded as being complementary.
On Functional \(S\)-matrix Theory. Generalization for Vector Field with Mass
Acta Phys. Pol. 33, 733 (1968)
abstract
An extension of the functional formulation of the \(S\)-matrix theory to the vector field is given. The connection between the existence of the three physical degrees of freedom and the conditions for the off mass shell \(S\)-matrix elements is investigated.
Local Transition Temperatures for Magnetic Crystals with Domain Structures
Acta Phys. Pol. 33, 743 (1968)
abstract
By applying the Heisenberg model and Bogolubov’s variational method in the molecular field approximation to uniaxial magnetic crystals with domain structures, the temperature is determined at which the local mean magnetization vanishes. It is shown that this ‘‘local transition temperature” varies within the domain structure, being highest in domains and lowest in interdomain walls. This effect is shown to exist in ferromagnets as well as in two-sublattice antiferromagnets, for arbitrary crystal lattices. This indicates that, when approaching the Curie (or Néel) temperature, first the domain walls disappear and only then the domains themselves, which would explain the origin of a similar effect discovered in recent experimental investigations. In addition, numerical calculations are presented for the difference of the mean magnetization in walls and domains as a function of temperature, for various values of the spin and the anisotropy constant.
New Force Constants of Benzene
Acta Phys. Pol. 33, 759 (1968)
abstract
Thirty four elements of the F-matrix were calculated for benzene and all deuterobenzenes in the generalized valence force field. The calculations were performed with the use of 180 inherent frequencies of the molecules: \(\mathrm {C}_6\mathrm {H}_6, \mathrm {C}_6\mathrm {H}_5\mathrm {D}\), \(p\)-\(\mathrm {C}_6\mathrm {H}_4\mathrm {D}_2\), \(s\)-\(\mathrm {C}_6\mathrm {H}_6\mathrm {D}_3\), \(p\)-\(\mathrm {C}_6\mathrm {H}_2\mathrm {H}_4, \mathrm {C}_6\mathrm {HD}_5\) and \(\mathrm {C}_6\mathrm {D}_6\). The margins of error of the individual constants were determined for the first time for benzene by the method of ‘‘least squares”. Considerable improvement has been achieved in the conformity between experimental and calculated frequencies, as compared with earlier publications. With the use of an original method of estimation, the numerical values of the four force constants associated with the change in the CC bond length have been calculated.
Spin-wave Resonance in Hexagonal Cobalt Thin Film
Acta Phys. Pol. 33, 769 (1968)
abstract
Quantum theory of SWR is applied to a hcp cobalt thin film cut perpendicularly to the hexagonal axis. A surface spin pinning parameter depending on the surface anisotropy is introduced. The relation between this parameter and the SWR spectrum is discussed, as well as the properties of surface spin-waves. It is found that the surface waves can occur in SWR up to some degree of surface spin pinning, and their absorption obeys the \(k^{-1}\)-rule. Excitation of the optical spin-waves is practically impossible.
The Integrals of the Product of Atomic Orbitals and the Sums of Plane Waves Over the Brillouin Zone
Acta Phys. Pol. 33, 785 (1968)
abstract
In certain problems of solid state theory integrals of the type \(W=N^{-1}\sum \limits _\boldsymbol {k} \exp (i \boldsymbol {k} \cdot \boldsymbol {r}){\mit \Phi }^*(\boldsymbol {r})\mathrm {d}\boldsymbol {r} = \int \xi (\boldsymbol {r}){\mit \Phi }^*(\boldsymbol {r})\mathrm {d}\boldsymbol {r}\) occur, where \({\mit \Phi }(\boldsymbol {r})\) is a linear combination of atomic orbitals centered on the lattice sites and the summation over \(\boldsymbol {k}\) runs over the entire volume of the Brillouin zone. In this paper we discuss a very simple way of evaluating such integrals in the case of cubic symmetry. In order to find their values we used the standard method of expansion of the functions in the integrand into a series of Kubic Harmonics. This procedure reduces the three-dimensional integral to a sum of one-dimensional integrals which may be very easily calculated numerically. The radial functions in the expansion of an atomic orbital centered at a lattice site are known from Léwdin’s considerations. Our main purpose was to find the radial functions in the expansion \(\xi (\boldsymbol {r})=\sum \limits _{j-0}^{\infty }g_1(r)K_j(0,\phi )\). In order to find them, Houston’s method is used. \(\xi (\boldsymbol {r})\) is analyzed for three cubic lattices: simple, face-centered and body-centered. \(W\)-integrals are written down as appropriate sums of one-dimensional integrals for face-centered cubic, body-centered cubic and NaCl-type lattices taking into account only \(s\) and \(p\) atomic orbitals.
Relaxation of the Local Temperature of Luminescent Centres in Solutions
Acta Phys. Pol. 33, 803 (1968)
see erratum: Acta Physica Polonica 34, 189 (1968)
abstract
Theory of depolarization of fluorescence of solutions by initial shock given in earlier papers is further developed. The local temperature increment (or decrement) \(\Delta T\) of luminescent centre produced by electronic transition in luminescent molecule is assumed to relax exponentially with the decay time \(t\) of fluorescence: \(\Delta T(t) = \Delta T_0 \exp (-t/\theta ), 0\) being the relaxation time of the local temperature and \(\Delta T_0 = \Delta T(t)\) at \(t =0\), i.e. at the moment of excitation of the luminescent molecule. Expressions are given for emission anisotropy of fluorescence \(\bar {r}''\) excited by steady illumination with primary light in which depolarization by torsional vibrations and Brownian rotations affected by initial shock are taken into account (for simplifying assumptions see the text). Comparison of the effect produced by initial shock at constant temperature of the solution with that resulting from change of the temperature of the solution by excitation of luminescent molecule with the purely electronic transition frequency enables the relaxation time \(\theta \) to be estimated. The experiments performed for fluorescein, eosin and erythrosin (differing only by the substituents, the number of atoms being the same) in glycol yield \(0''(4+6)\times 10^{-11}\)s, \((7+9)\times 10^{-11}\)s and \((9+12)\times 10^{-11}\)s respectively. These results show that \(\theta \) grows with growing atomic mass of the substituents.
Energy Distribution of Long Range \(\alpha \)-particles Emitted During the Thermal Neutron Fission of \(^{235}\mathrm {U}\)
Acta Phys. Pol. 33, 819 (1968)
abstract
The energy spectrum of the long range \(\alpha \)-particles emitted in the thermal neutron fission process of \(^{235}\mathrm {U}\) has been measured. A good fit has been found using the Gaussian distribution. The relative cross-section (\(Y_\mathrm {{th}}/Y_\mathrm {{res}}\)) for thermal and resonance neutrons was determined. An attempt to estimate the yields of the other charged particles emitted in the ternary fission was made.
The Influence of Aluminium Admixture on the Superconducting Properties of Tin
Acta Phys. Pol. 33, 827 (1968)
abstract
The variation of the superconducting properties of tin with different aluminium impurity concentration has been investigated. The measure of purity has been determined from the ratio \(R_{300^{\circ }\mathrm {K}}/R_{4.2^{\circ }\mathrm {K}}\). It has been found that the transition temperature, the critical current, and the critical magnetic field depend on impurity concentration. The amount of aluminium soluble in tin does not exceed 0.7% at.
\(^6\mathrm {He}_{{\mit \Lambda \Lambda }}\) with Nonlocal Separable Interactions with Hard Shell \({\mit \Lambda }\)–\({\mit \Lambda }\) Repulsion
Acta Phys. Pol. 33, 831 (1968)
abstract
The problem of \(^6\mathrm {He}_{\mit {\Lambda \Lambda }}\) treated as a \(2{\mit \Lambda } + \alpha \) system is solved exactly with a Yamaguchi nonlocal separable \({\mit \Lambda }\)–\(\alpha \) potential, \(V_{{\mit \Lambda }\alpha }\), and a nonlocal separable \({\mit \Lambda }{\mit \Lambda }\) potential, \(V_{{\mit \Lambda }{\mit \Lambda }}\), consisting of a long range attractive part plus a repulsive shell of radius \(c\). The parameters of \(V_{{\mit \Lambda }\alpha }\) and \(V_{{\mit \Lambda }{\mit \Lambda }}\) are adjusted to make the potentials equivalent to the local potentials \(V_{{\mit \Lambda }\alpha }\) and \(V_{{\mit \Lambda }{\mit \Lambda }}\) (with hard core radius \(r_c\)) discussed recently by Tang and Herndon. Numerical results for \(B_{{\mit \Lambda }{\mit \Lambda }}(^6\mathrm {He}_{{\mit \Lambda }{\mit \Lambda }}\)) show that to get agreement with the experimental value of \(B_{{\mit \Lambda }{\mit \Lambda }}\) one has to choose \(c \lt r_c\).
On the Nature of “Exoelectrons” Emitted During the Solidification of Metals in Vacuum
Acta Phys. Pol. 33, 839 (1968)
abstract
Using an experimental set-up consisting of electron multiplier as detector of particles, a system of electrodes focusing the beam at the first dynode of the multiplier and a transverse magnetic field deviating the beam it was shown that the particles emitted during the solidification of metals, the so called “exoelectrons” are electrons.
Surface Electroluminescence of Single Crystals of Seignette Salt
Acta Phys. Pol. 33, 845 (1968)
abstract
It had been found that light pulses appear during polarization of crystal samples of Seignette salt. After polarization in an adequate electric field, the surface of the Seignette salt becomes a source of light. The lowest value of strength of the polarizing electric field \(E_p\) at which the sample surface begins to glow depends uniquely on the crystallographic plane, parallel to which the sample is cut out. It is smallest for samples cut along the (100) plane. The course of the changes of the observed luminescence depends on the history of the sample quite distinctly. The obtained results of measurements imply that the observed light pulses can be treated as due to surface discharges of the gas in which the sample is stored. The possible relationship with Barkhausen noise is indicated.
Photostimulated Exoemission of Electrons from NaCl and KCl Crystals Excited by Irradiation with Electrons
Acta Phys. Pol. 33, 853 (1968)
abstract
The kinetics of photostimulated exoemission from the surface on NaCl and KCl single crystals excited by electrons is studied. The influence of exciting electron energy, external electric field, intensity of light and sample polarization time on the emission kinetics is shown.
Tribo-photostimulated Exoemission of Electrons and Triboluminescence of Coloured NaCl Single Crystals
Acta Phys. Pol. 33, 865 (1968)
abstract
Photostimulated exoemission of electrons and the luminescence during the deformation of sodium chloride single crystals has been investigated. The investigations have been carried out at various rates of the compressive force increase. The samples used in the investigations were previously coloured by X-rays. It has been found that during plastic deformation and at the force increase rates used in the experiment there is a rigorous dependence between the total number of electrons emitted by the sample and the total amount of luminescent light. When the total number of emitted electrons increases at a fixed force growth rate, the total amount of luminescence light decreases.Fasc. 6, pages 879–1025
Some Features of Neutral Pion Production in Interactions of 9 GeV Negative Pions with Xenon Nuclei
Acta Phys. Pol. 33, 879 (1968)
abstract
The energy and angle of emission of 3271 photons emitted in \(1374\pi ^-\)–Xe interactions at 9 GeV have been measured and the process leading to \(\pi ^{\circ }\) production is discussed.
Emissionsrauschen und Oberflächenwanderung bei Kaliumbedampfung von Wolframspitzen im Feldelektronenmikroskop
Acta Phys. Pol. 33, 887 (1968)
abstract
Die Bedampfung einer Wolframspitze im Feldelektronenmikroskop mit Kalium wurde bei verschiedenen Emittertemperaturen durchgeführt und das Stromrauschen sowie die Spannung für konstanten Emissionsstrom gemessen. Es wird der Zusammenhang des Rauschens mit Platzwechselvorgängen des Kaliums auf den verschiedenartigen Emitterflächen diskutiert. Außerdem wird über charakteristische Bedeckungsvorgänge bei 195°K berichtet.
Temperature Dependence of Magnetic Losses in \(\alpha \) Fe–C(N) in the Case of Snoek Relaxation
Acta Phys. Pol. 33, 899 (1968)
abstract
With the use of calculations by Krupitka and Roskovec, based on Néel’s theory of diffusion magnetic viscosity, a new formula was derived for the temperature dependence of relaxation losses associated with the Snoek process. It was shown that for \(\alpha \) Fe–C and \(\alpha \) Fe–N, and peaks of height up to 0.2, this formula is equivalent to the corrected Debye formula which takes into account the temperature-variation of relaxation intensity. The measurements, performed with the use of a Maxwell–Wien bridge for several samples of pure iron containing C and N in the form of solid solution, showed that the experimental curves \(\tan \delta _r = f(T)\) can be described by means of one or a sum of two relaxation processes satisfying the new formula. It was found that in accordance with theory the position of the maximum of the magnetic relaxation curve depends on the peak height.
Adsorption of Oxygen on Tungsten and Some Effects Associated with Thermal Desorption
Acta Phys. Pol. 33, 913 (1968)
abstract
The adsorption of oxygen on tungsten tip has been studied in the field emission electron microscope. The dependence of work function on the oxygen coverage of the surface has been measured at the temperature of 300°K. It has been found that for very small coverages (\(3\times 10^{18}\) atoms/cm\(^2\)) there is a minimum of average work function. The decrease in \(\bar {\phi }\) amounts to about 0.1 eV. The occurrence of this minimum depends on the method of measurement. In connection with this the correctness of methods used by other authors has been discussed. Characteristic changes in the emission patterns with increasing coverage have been found which may indicate a rearrangement of surface atoms of tungsten due to adsorption. Some effects occurring during the thermal desorption have been also investigated and the occurrence of oxygen atom diffusion from surface layer into the metal was found. It has been observed that at \(T = 1500\)°K the adsorption of oxygen changes the equilibrium geometrical form of the single crystal of tungsten.
Bloch Wall Energies in Unjaxial Ferromagnets in an External Magnetic Field Perpendicular to the Hexa Gonal Axis
Acta Phys. Pol. 33, 923 (1968)
abstract
The energies for all possible orientations of Bloch walls in uniaxial ferromagnets are calculated, for the case of an external magnetic field perpendicular to the direction of easiest magnetization. An alternate polarization of consecutive Bloch walls is assumed. The results show the Bloch walls perpendicular to the external field to be energetically most favourable.
Dispersion Theory of Elastic Photon–Deuteron Scattering
Acta Phys. Pol. 33, 929 (1968)
abstract
The relativistic dispersion theory for the process of elastic photon-deuteron scattering is proposed. There are presented numerical results for the differential cross sections for the scattering in the 0–100 MeV region of lab energy of the incident photon. The calculations have been performed in the approximation based on the assumption that the dominant role is played by the photodisintegration of deuteron in the low-energy elastic \(\gamma \)–d scattering. Our results are in very good agreement with the existing experimental data.
On the Method of Establishing the Stability Conditions for the Thermodynamical Equilibrium
Acta Phys. Pol. 33, 953 (1968)
abstract
The stability conditions for the thermodynamical equilibrium are discussed. It is shown that a seeming inconsistency of the method used in several textbooks can be easily removed by a more careful procedure. Moreover, it is exhibited that the most economic way is to investigate systems where restrictions are imposed on extensive quantities, as this provides the richest information about stability conditions. In this way the preference of the case of an adiabatically isolated systems is explained.
Vibrational Assignment of Tetracyanoethylene on the Basis of IR Polarized Spectra of Its Charge Transfer Complexes
Acta Phys. Pol. 33, 959 (1968)
abstract
With the aim of determining the vibrational assignmeut of TCNE, the polarized infrared spectra of two charge-transfer complexes were investigated. The particularly convenient molecular arrangement in the TCNE–HMB complex made it possible to sort out the out-of-plane vibrations. The distinction between two planar species of TCNE was found from polarized spectra of TCNE pyrene complex. The identification of the lines at the region of C \(\equiv \) N stretching vibrations was facilitated by comparison with the spectra of some other complexes of TCNE, recorded as nujol mull.
Modification of Solutions in the Froissart Model and Massless Second-order Pole
Acta Phys. Pol. 33, 969 (1968)
abstract
An operator formalism describing the free massless double pole is introduced. It is shown that the covariant decomposition formula of Froissart, describing the massive double pole, has to be essentially modified. The four-parameter family of operators describing the free massless double pole field in all Poincaré frames is introduced. It is shown that all Green functions are independent of the parametrization and invariant with respect to the Poincaré group.
Surface States of Deformed Crystals by the Tight-binding Approximation (TBA)
Acta Phys. Pol. 33, 981 (1968)
abstract
A three-dimensional model of deformed crystal with the Hamiltonian \(H = H_0+\mathrm {d}V\), where \(H_0\) is the Hamiltonian for the undeformed delimited crystal, and \(\mathrm {d}V\) describes the potential deformation due to the change of the lattice constant deformation influences the interaction between the surface atoms and their first and second neighbours. Contrary to undeformed crystals, the existence conditions for the surface states in 1-, 2-, and 3-dimensions are different.
Theoretical and Numerical Study of the \(1s\)–\(2s\) Excitation of Atomic Hydrogen by Slow Electrons
Acta Phys. Pol. 33, 991 (1968)
abstract
An approximate method is applied in calculations of the partial and total cross sections for the \(1s\)–\(2s\) excitation of atomic hydrogen by slow electrons. The method takes into account the spherically symmetrical part of the distortion of the hydrogen atom due to the incoming electron and the distortion of the incoming electron’s wave function. The values of zero-order (\(L = 0\)) partial cross sections obtained by this method are nearer to the values obtained from the close-coupling method than the values given by the Born approximation. For increasing angular momentum quantum numbers of the incoming electron the partial cross sections calculated by the method used in this paper and the Born approximation decrease too fast in comparison with the close coupling results. A possible further application of the theoretical results is indicated.
On Stability of a Circular Motion in the Relativistic Kepler Problem
Acta Phys. Pol. 33, 1007 (1968)
abstract
A circular motion of two particles with the interaction described by the Fokker action principle is found unstable. An argument is put forward that relativistic corrections to a Newtonian motion cannot be written down as a power series in \(1/c\).
Spin Waves in Ferromagnetic Thin Films with Domain Structure
Acta Phys. Pol. 33, 1013 (1968)
abstract
Spin wave procedure is adapted to ferromagnetic thin films with domain structure using the Heisenberg Hamiltonian for the Valenta’s model of the sublattices. Spin wave spectrum is obtained assuming simple hexagonal structure and domains in the form of parallel stripes along the hexagonal axis situated in the plane of the film. The anisotropic interaction between spins is taken into account. The distribution function of the magnetization is assumed constant inside the domains and as linear function of the distance from the wall middle in the domain walls.
Vibration Spectra of Polysubstituted Benzene Derivatives. II. Crystal Structure and Infrared Spectra of 2,5-dichloro-1,4-xylene and 4,5-dichloro-1,2-xylene Crystals
Acta Phys. Pol. 33, 1025 (1968)