# acta physica slovaca

Acta Physica Slovaca 52(2002)
• M. Demetrian, D. Kochan
Qantum mechanics on non-commutative plane
Acta Physica Slovaca 52, 1 (2002)

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.

• V. Bezák
Stationary particle transport in a randomly inhomogeneous rod
Acta Physica Slovaca 52, 11 (2002)

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.

• M. Y. M. Hassan, Z. Metawei
First and second order corrections to the eikonal phase shifts for the interactions of -particle with 12C and Ca isotopes
Acta Physica Slovaca 52, 23 (2002)

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.

• L. L. Chotorlishvili
Nuclear magnetic relaxation in hydrogen-containing niobium caused by modulation of quadruple interaction by means of tunnel two-level systems
Acta Physica Slovaca 52, 35 (2002)

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.