acta physica slovaca

Abstract: For a one-dimensional stationary system, we derive a third order equation of motion representing a first integral of the relativistic quantum Newton's law. We then integrate this equation in the constant potential case and calculate the time spent by a particle tunneling through a potential barrier.

Abstract: The grand canonical partition function of the electron plasma in metals is calculated by using the formalism of functional integrals. Within the framework of this formalism the Coulomb interaction between electrons is expressed naturally as an interaction mediated by bosons. The grand canonical partition function of the electron plasma is then represented as a product of two partition functions corresponding to the free electron gas and to a boson gas with a given energy spectrum and of a factor describing correlation effects between the electrons and bosons.

Abstract: Amorphous conductors such as liquid metals and alloys are subject to dc conductivity $\sigma$ calculation here. Principal aim is to explore the impact on $\sigma$ of the constitutive equation $\alpha^{*}=1$, formulated and developed in the preceding papers. The nearly free electrons (NFE) model has been applied. Alkali metals are assumed to fit this model well, and sodium the best. Consequently, the results on these metals have been assumed reliable and relevant for conclusions making. The conclusion we made is: instead of the Fermi radius $k_{F}$ proper for the statistical ensemble in state of thermodynamics equilibrium, a new $k'_{F}$ number is needed to be introduced into the linear response formula when calculating $\sigma$ and $\alpha^{*}$. This $k'_{F}$ is the length of the corresponding axis of ellipsoid proper for describing the statistical ensemble in the state with dc current. In the traditional interpretation of the linear response formula (Kubo formula) this conversion has been overlooked. Parameters of the mentioned ellipsoids are determined in this paper for a number of liquid metals of valency numbers 1,2,3,4, in addition to a selection of some binary and ternary conducting alloys. It is up to experimental measurements to decide how real this concept of restructuring the statistical ensemble is.

Abstract: An abundance of the strangeness that can be induced in thermalized quark-gluon plasma (QGP) is considered as a signal of the QGP phase appearing in the intermediate state of ultra-relativistic heavy-ion collisions. As a quantitative characteristic of this signal, we take the ratio $R_{K^+ K^-} = N_{K^+}/N_{K^-}$ of the multiplicities of the production of $K^{\pm}$ mesons. This ratio is evaluated for $K$ mesons produced from thermalized QGP phase and also for $K$ mesons produced by the quark-gluon system out of the QGP phase. For a thermalized QGP phase, the ratio $R_{K^+ K^-}$ has been found a smooth function of a 3-momentum of the $K^{\pm}$ meson and in the region $160\,{\rm MeV} < T <200\,{\rm MeV}$. We show that at $T= 175\, {\rm MeV}$ our prediction for the ratio $R_{K^+K^-}(q,T = 175) = 1.80^{+ 0.04}_{-0.18}$ agrees well with the experimental data of NA49 and NA44 collaborations on central ultra-relativistic Pb+Pb collisions at 158 GeV/A, $R^{\exp}_{K^+K^-} = 1.80\pm 0.10$. For the $K^+$ and $\pi^+$ multiplicities we have obtained the value $R_{K^+\pi^+}(q,T = 175) = 0.134\pm 0.014$ agreeing well with the experimental value $R^{\exp}_{K^+\pi^+} = 0.137\pm 0.008$ obtained by NA35 collaboration in the nucleus-nucleus collisions at 200\,GeV/A.

Abstract: The aim of this paper is to present a model based on the neutron-proton pairing vibrations for the doublets of the excited 0$^{+}$ states that were observed in some deformed nuclei in the rare earth region. To prove our hypothesis on these states we have calculated their excitation energies using the Quasiparticle Random Phase Approximation (QRPA) method.

Abstract: In the frame of the hyperspherical formalism, the electromagnetic properties of $^{3}$He are investigated for values of high momentum transfer up to 32\,fm$^{-2}$. Calculations of electromagnetic form factors have been performed for momentum transfer up to 22\,fm$^{-2}$ and 32\,fm$^{-2}$ for the charge and magnetic form factors, respectively. The charge radii (rms) for $^{3}$He are also calculated. Gaussian shaped spin-isospin potentials are used in generating complete mixed and mixed symmetric wave functions to be used in the form factors calculations. Contributions of partial waves are also taken into account. The present calculations are in good agreement with the experimental high momentum transfer measurements as well as the previous calculations using variational and Faddeev methods including the meson exchange current contributions.