Showing papers in "Acta Physica Academiae Scientiarum Hungaricae in 1969"

Study of the electronic structure of molecules. X

Abstract: All electrons SCF-LCAO-MO computations for adenine, cytosine, guanine and thyamine are reported. In addition, to compute the total energies and wave functions we have computed the relative gross charges and the dipole moment. Analysis of the orbital energy for the inner shell indicates that there are three effects which govern the orbital energies splitting for inner shell a) the gross charge, or ionicity degree, of the atom in consideration, b) its valency state, c) the neighbor atoms ionicities. The first two effects are sufficient for determining the relative location of the inner shell as well as for estimating the extrema of the splitting of the inner shell electrons of a given type of atoms.

Some accurate results for three-particle systems

Abstract: Results of a variational calculation of the nonadiabatic ground state energy of H 2 + are presented. Diagonal corrections for nuclear motion have also been calculated for the electronic ground state of H 2 + . The adiabatic potential energy curve has been employed to calculate the rotational and vibrational levels for the H 2 + ion and for muonic molecules. Nonadiabatic energy corrections are discussed. Forpμd the adiabatic wave function is compared with the corresponding nonadiabatic result.

ON THE SHELL EFFECT IN (n,2n) REACTION CROSS SECTIONS.

Abstract: Shell effects are investigated by comparing measured (n,2n) cross-sections with predictions from a phenomenological equation which is insensitive to threshold energy The results suggest that only the threshold energy of (n,2n) reaction can be held responsible for any shell effect in the value of the cross-section

On the canonical transformation in classical and quantum mechanics

Abstract: A more exact formulation for Dirac’s proposition on the analogy between the unitary transformations in quantum theory and the contact transformations in classical theory is given It is shown that approximate expressions for the matrix elements of the unitary operator defining the transformation can be constructed in terms of classical quantities One can thus speak not only of an analogy between unitary and contact transformations, but also of an approximate equality between the quantum mechanical and semi-classical expressions for the corresponding quantities

Das Kombinierte Näherungsverfahren

Abstract: Die Valenzelektronenniveaus von Alkalimetall- und Kupfer-Atomen werden mittels der Pseudopotentialmethode berechnet. Von den verschiedenen Naherungsformeln liefert das kurzlich vonGombas hergeleitete statistischeG korr-Besetzungsverbotpotential die besten Ergebnisse. Von empirischen effektiven Potentialen ist ein solches mit ausgepragter Mulde am geeignetsten. Die Wechselwirkungsenergie der Atomrumpfe eines Molekuls wird unter Verwendung statistischer Methoden abgeschatzt.

Remarks concerning the theoretical explanation of Hund’s rule

Abstract: According to the accepted theoretical explanation ofHund’s rule the electronic interaction energy is smallest in the ground state which is of the highest multiplicity A breakdown of the total energy into one- and two-electron contributions in the case of carbon atom based on self-consistent field calculations and configuration interaction treatment shows that this assumption is not valid According to our results the main differences in the energies of different terms arising from the same electronic configuration are due to differences in the one-electron energies

Simulation of the influence of core electrons by a pseudopotential II

Abstract: Pseudopotential theory is combined with the Hartree-Fock and natural expansion method to calculate the molecular constantsD e, Re andk e for Na2, K2, NaCs and BeH2. We treat these molecules as two- or four-electron problems respectively in the pseudopotential field of their cores. We then analyze the energies and wave functions in terms of the contributions of the different natural orbitals to the correlation energy. The calculated equilibrium distances agree well with the experimental ones. The dissociation energies are in better agreement with experiment than those of previous calculations.

First-Order magnetic phase transitions

Abstract: The general properties of the first-order magnetic phase transitions between ordered structures have been investigated. The number of possible models has been limited by supposing the sensitivity of the exchange energy to the interatomic distance to be responsible for the phase transition. It is shown that the magnetic phase transition occurs as a result of a signchange in the proper combination of the exchange parameters. The transition may be influenced by the variation of the pressure and the magnetic field. The actual phase transition is, however, hindered in both directions by the elastic energy wall, separating the free energy minima of the different phases. TheT-P phase diagram has been calculated and the conditions for the existence of a triple point in theT-P plane have been investigated in the case of antiferromagnetic ⇆ ferromagnetic transitions. The temperature hysteresis, i.e. the difference between the upper (T sup) and lower (T inf) transition temperatures has been determined at different pressures and for both temperatures a linear dependence has been obtained. The character of the disappearance of the magnetic order has been also studied and it has been found that under certain conditions the order of the ferromagnetic-paramagnetic transition may be different from that of the antiferromagnetic-paramagnetic one. TheT-H coexistence curve between the ferromagnetic and the spin-flop antiferromagnetic phases has been determined. The upper and the lower phase transition temperature versus magnetic field curves are calculated and it is found that with increasing magnetic field and decreasing temperature the difference between these two curves (i. e. the hysteresis width) becomes increasingly small until at a critical field (H t) and temperature (T t) they end in a common point with the coexistence curve. BelowT t the variation of the magnetic field does not lead to a first-order antiferromagnetic ⇆ ferromagnetic transformation. The ferromagnetic phase is nothing, but the antiferromagnetic phase in a magnetic field strong enough to turn the moments parallel to the field direction. AboveH t but belowH c the variation of the temperature brings about also a second-order ferromagnetic ⇆ antiferromagnetic transition. The discontinuous change of the lattice parameter and that of the sublattice magnetization have been calculated at the coexistence temperature and at both the upper and lower transition temperatures. It has been shown that the entropy change of the transition has two contributions: one of them is associated with the volume change while the other with the magnetization change. Under certain conditions the order of magnitude of both contributions may be the same.

Theory of one-dimensional lattice in pseudoharmonic approximation

Abstract: The properties of the monoatomic linear chain are considered in pseudoharmonic approximation at a fixed length and at constant external tension. It is whown that in the latter case the chain becomes unstable at a sufficiently high temperature or at a sufficiently high zero-point energy.

The hydrodynamical model of wave mechanics@@@Гидродинамическая модель волновой механики: The many body problem@@@Задача многих тел

Abstract: The problem of how to extend the hydrodynamical model — described in previous publications — to many body problems is discussed and it is shown that the difficulties which arise in such an attempt are not of mathematical nature, but they reflect upon a physical problem which in our opinion is unsolved so far. It is suggested that in the correct treatment of a many body problem one should try to select between the possible wave functions such functions which are very likely in a statistical sense. This proposed selection resembles the selection of the very likely configurations in statistical mechanics.РезюмеДискутируется проблема расширения гидродинамической модели-описанной в предыдущих работах — к задаче многих тел. Показывается, что появляющиеся в приложении трудности не математического характера, они отображают физическую проблему, не решенную по нашему мнению до настоящего времени. Оказывается возможным, что в точном решении проблемы многих тел удается выбирать из возможных волновых функций те, которые очень подобны в статистическом смысле. Предполагаемый отбор напоминает отбор очень подобных конфигураций в статистической механике.

Negative magnetoresistance of compensatedn-type GaAs at 77° K temperature

Abstract: The magnetoresistance of strongly compensatedn-type GaAs doped with Cr and O has been measured at 77°K temperature. The electron concentrations of the samples were between 3.8×1017 and 1.6×1018 cm−3 at room temperature. In low magnetic fields negative magnetoresistance was observed at liquid nitrogen temperature. The characteristics of this anomalous negative magnetoresistance were shown to be very similar to those observed at liquid He temperatures in heavily doped semiconductors. In weak fields the negative magnetoresistance was proportional to the square of the magnetic field, and showed saturation in the magnetic field range of 4000–6000 G. To account for the observed effects it was postulated that metal-like impurity band conduction is the dominant mechanism of the charge carrier transport in our samples. The observed features of the negative magnetoresistance are shown to be consistent with the model of scattering of electrons in the impurity band by localized magnetic moments. For the average value of the localized magnetic moments a value of the order of 2–3 Bohr magneton was deduced from the experimental data. It is shown that the strong compensation may play an important role in the formation of impurity band at 77°K temperature and above it.

On the numerical solution of Hartree — Fock equations independent of coupling scheme

Abstract: The solution of Hartree—Fock equations by a numerical method on computers, type BESM, is described. The minimization of the input information is reached by using the equations independent of coupling scheme and the universal potential field for obtaining the initial radial wave functions. The results obtained are compared with those evaluated from the solutions of conventional Hartree—Fock equations.

Einige Bemerkungen zum Kombinierten Näherungsverfahren und zum effektiven potential

Abstract: Nach einer kurzen Einfuhrung in das kombinierte Naherungsverfahren werden dami die Bindungsenergien und Abstande der Alkalimolekulionen berechnet und die Frage nach der Existenz von Alkalihydridmolekulionen aufgeworfen. Bezuglich einer Verbesserung des Verfahrens wird ein Atomfunktionenansatz benutzt, der sich nur aus Exponentialausdrucken aufbaut, Weitere Verbesserungsmoglichkeiten werden diskutiert.

Developments in the separated pair theory

Abstract: In recent years, it has become possible to compute strongly orthogonal geminals for several smaller systems and to investigate the effectiveness of the conventional separated pair theory. The results are compared with those obtained by other many-electron theories and the sources of the main deficiencies are pointed out. Extensions of the separated pair theory using the optimized orbitals of the single antisymmetrized geminal product wave function are also discussed.

Some problems of investigating periodicities of cosmic ray time series

Abstract: A generalization of the method of the analysis of variance is given to investigate the existence and the shape of a periodicity with given length of period. Allowance is made for slow variations of the intensity of cosmic rays as well as for meteorological effects. In addition to the exact test of the existence of the periodicity, maximum likelihood estimates both of the constants characterizing the shape of the periodicity and of the mean square amplitude of the periodic function are given, together with their respective statistical errors, in the case of an arbitrary number of meteorological factors affecting the intensity of the cosmic radiation.

Angular distributions of the reaction12C(d,p)13C belowE d=2 MeV

Abstract: Excitation functions of the12C(d, p0) and12C(d, d) reactions were measured at 90° in the rangeE d=900−2000 keV in 10 keV steps. Angular distributions of the12C(d, po)13C reaction were measured in steps of 25 keV. The experimental data are interpreted in terms of interfering compound levels. Interference phenomena suggest additional new levels in14N.

On the kinetics of the phase transformation of CsCl crystals II

Abstract: The time and temperature dependence of the electrical conductivity of CsCl was measured in the temperature range of theα⇆β transformation. The results point to some cooperative ionic movement in very small regions of the crystals. Selected area electron diffraction experiments supported this assumption.

General form of the centrifugal term in the rotational spectra

Abstract: The explicit form of the centrifugal term is known so far only for the Hund’s limiting cases. The present paper presents its explicit form in the intermediate case between Hund’s case a) and b) for terms of any kind.

An effective field approach for many-body forces between ions of a metal

Abstract: For calculating the phonon spectrum of a metal lattice a self-consistent field approximation is used. At a given lattice deformation the restoring forces between the ions have a many-body character because of the effects of the periodic field. The condition of self-consistency and the use of first order Bloch functions for correcting the dielectric tensor lead to a physical understanding of a formula proposed earlier for calculating the elements of the dynamical matrix arising from many-body forces.

Quenching of fluorescence of eosin in solutions

Abstract: Absorption and fluorescence spectra and the relative quantum yield of fluorescence of solutions of eosin-blue in various solvents have been studied and the data interpreted in terms of the non-radiative processes occurring in the solution, dimer formation and the dipole moment of eosin. The results seem to suggest a lower value for the dipole moment of the eosin molecule in the excited state than in the ground state.

Study ofV-centres stable at room temperature in NaCl(Ca) crystals

Abstract: Following X-irradiation of OH-free NaCl(Ca) crystals at room temperature, the authors observed new absorption bands at 360, 336 and 193 nm wavelengths, in addition to theV2 band appearing in pure crystals at 223 nm. These new bands were assigned toVF,V1M andV2M centres, respectively.

Integration of the dynamical symmetry groups for the −1/r potential

Abstract: Finite dynamical symmetry transformations of the Kepler motion are given in closed analytic form.

Sum rules and covariance

Abstract: A representation of commutator matrix elements is derived in Lehmann-Symanzik-Zimmermann formalism and applied to current density algebra sum rules in an arbitrary frame of reference. The sum rules take a remarkably simple form if the current correlation functions obey multiple integral representations in the current masses. The reference frame dependence of the sum rules becomes explicit.

New foundations for the Thomas — Fermi model

Abstract: It is demonstrated that the atomic model, in which the zero order approximations to the one electron orbitals are hydrogen like orbitals, always leads to a model which imitates very closely the Thomas—Fermi model of the statistical theory of the atoms.

Интерпретация метода хартри-фока как метода частичного суммирования атомных фейнмановских диаграмм

Abstract: На методе Хартри-Фока [1, 2, 3] основываются почти все проводимые в настоящее время атомные и молекулярные расчеты, и поэтому его интерпретация как метода суммирования определенного класса атомных фейнмановских диаграмм [4] является очень важной. Она позволяет глубже понять смысл приближений, заложенных в методе Хартри-Фока, и причины той особой эффективности этого метода, которая проявляется при конкретных расчетах энергий, в частности, основных состояний легких атомов. В результате удается более осмысленно строить на основе метода Хартри-Фока различные теории электронной корреляции.

π-N resonance widths in the broken SL(2, C) model

Abstract: The elastic decay width of some πN resonances is evaluated in the SL(2, C) model of Regge poles. Two families of resonances are examined in the first order of symmetry breaking, one of them has isotopic spinI=1/2, the otherI=3/2. The width of other resonances along the trajectories is calculated in symmetry limit and the differential cross-section is examined for πN backward scattering. The results are in good agreement with experiments.

Quantum probability weighted paths

Abstract: The paper is concerned with the generalization ofFeynman’s method A real “probability” measure is introduced for weighting trajectories and this is expressed as the boundary case of a measure containing one real parameter For the finite values of the real parameter an equation of motion of the Fokker-Planck type is used In the zero boundary case a Schrodinger equation is derived A simple deduction is given for theWigner phase space distribution by using the differentiability of quantum trajectories, which is also proved It is suggested that the equations of motion obtained for the finite values of the real parameter included in the theory describe real processes

On the infinite component wave equations

Abstract: The form factors obtained in the study of the infinite components wave functions are compared with the ones obtained in a much more conventional way through the use of the Schrodinger equation. The classical problem like the elastic scattering of photons by a hydrogen atom is treated in detail.

On the spur of the product of Dirac matrices

Abstract: In this paper several methods for the evaluation of the spur of the product ofγ 5 matrix and any number of Dirac matrices have been established. The formulae for the determination of the various types of products of two spurs whenγ y ,γ i γ j ,γ i γ j γ k ,γ i γ j γ k γ l and these terms associated withγ 5 matrix occur in both of the spurs, have been derived. It has been shown that the product of two spurs each involvingγ 5 matrix, can be equated to an expression involving noγ 5 matrix. One useful identity for spurs involvingγ 5 matrix has been deduced.

K l3 form factors, current algebra and double integral representations

Abstract: Predictions of current algebra for theK l3 form factors are considered using double integral representations of the current correlation functions. TheK l3 form factor parameters ξ, λ± and the mass and width of the κ=K(0+) meson are calculated in good agreement with currently known experimental values.