acta physica slovaca

Abstract: One of the simplest example of non-commutative (NC) spaces is the NC plane. In this article we investigate the consequences of the non-commutativity to the quantum mechanics on a plane. We derive corrections to the standard (commutative) Hamiltonian spectrum for hydrogen-like atom and isotropic linear harmonic oscillator (LHO) and formulate the problem of the potential scattering on the NC plane. In the case of LHO we consider the non-commutativity of the momentum operators, too.

Abstract: The paper concerns the stationary solution of the one-speed transport equations of the rod model known in the theory of the neutron transport. The solution is presented in view of an arbitrary absorption cross section $\sigma(x)$ and of the scattering cross section equal to $c\sigma(x)$ where $c$ is taken as a constant. The author treats the `albedo problem' with a given value of the influx of particles upon the rod from the left and with no influx from the right. He recalls, at first, the exact `albedo solution', accentuating one important statement: the transmitted fraction $\cal T$ and the reflected fraction $\cal R$ of the fluxes of the particles are functions of one single variable, namely of the `optical length' ${\mit\Lambda}=\int_0^L{\rm d}x\:\sigma(x)$ of the rod. ($L$ is the geometrical length of the rod.) If $\sigma(x)$ is defined as a random function, then ${\mit\Lambda}$ and, consequently, $\cal T$, $\cal R$ become random variables. The statistical moments ${\langle}{\cal T}^n\rangle$ and ${\langle}{\cal R}^n\rangle$ are calculated for $n$ = 1, 2. As $\cal T$ and $\cal R$ are nonlinear functionals of $\sigma(x)$, the random variables $\cal T$ and $\cal R$ need not be Gaussian even if $\sigma(x)$ is defined as a Gaussian random function. Conditions are discussed under which $\cal T$ and $\cal R$ may be approximated as two correlated Gaussian random variables.

Abstract: The high-energy double-folding optical potential approximation to the exact nucleus-nucleus multiple scattering series derived by Wilson has been used to calculate the optical potential and the elastic scattering differential cross-section for the interactions of -particle with 12C and Ca isotopes at energy 1370 MeV. The Pauli correlation effect has been considered. The first- and second-order corrections to the optical potential and to the eikonal phase shifts have been calculated for our reactions. Also, the transparency function has been calculated.

Abstract: Nuclear magnetic relaxation in niobium and hydrogen nuclei caused by modulation of quadruple interaction by means of a tunnel two-level system (TLS) has been investigated. It is shown that at low temperatures and high density of states, the relaxation caused by TLS dominates the relaxation of conduction electrons.