Volume 46, Number 56, 2001
General Physics
Elasticity of an Axially Anisotropic Solid Body B.F. Apostol Romanian Journal of Physics 46,
273278 (2001)
The elastic energy of an axially anisotropic solid body is derived by starting from the general principles of linear elasticity. The elastic waves propagating in such a body are obtained by solving the equations of motions with the aid of two suitable canonical transformations. The relevancy of the corresponding elastic constants is discussed in connection with the axial symmetry, and a comparison is made with other similar calculations.
General Physics Quantum Mechanics
Floquet Solutions for QuasiFree Electrons in TwoDimensional Crystalline Lattice Radu Paul Lungu Romanian Journal of Physics 46,
279312 (2001)
The quasienergies and the reduced floquet eigenvectors corresponding to an electron in 2dimensions, interacting with a timedependent monochromatic, linearly polarized electromagnetic field, and in the presence of a weak, spatial periodic field (varying in both directions) are calculated. These computations are performed using a variant of the stationary perturbation theory in the extended Hilbert space, adapted for the eigenvalue equation of the Floquet Hamiltonian. The perturbative corrections, in the first orders, show that the quasienergy spectrum has gaps at the boundaries of the Brillouin zones, and the Floquet eigenfunctions have Bloch forms. These results have similarities to those of the quasifree electron model.
Mathematical Physics
SelfValidating GaussKronrod Quadrature Gh. Adam, S. Adam, E. Papp Romanian Journal of Physics 46,
313330 (2001)
We investigate the reliability of the local error estimates returned by GaussKronrod quadrature rules under the use of several error estimators: GaussKronrod, quadpack, as well as their selfvalidation with natural conditions inferred from the study of the outputs of typical elementary integrals. The error estimator which gathers all the validation conditions is found to yield the sharpest and the most reliable error estimates. The selfvalidating scheme of the local error estimates is easy to implement and adds little supplementary computing effort. It strengthens considerably the correctness of the decisions within the automatic quadrature.
Mathematical Physics  Quantum Fields
Tensors, $R$ Matrices and Hermiticity on Hopf Algebras M. Micu Romanian Journal of Physics 46,
331337 (2001)
We define irreducible tensors on the simplest hopf algebra $su_q(2)$ and introduce the $R$ matrices enabling us to write hermitian expressions for the spin orbit interaction.
Condensed Matter
Quanta of Viscosity M. Apostol Romanian Journal of Physics 46,
339343 (2001)
It is shown that the viscosity is quantized in $h/m$ quanta, where $h$ is Planck's constant and $m$ denotes the particle mass.
Metallic Clusters L. C. Cune, M. Apostol Romanian Journal of Physics 46,
345364 (2001)
Large metallic clusters of heavy atoms are described within the quasiclassical theory, by means of a variational approach to the linearized ThomasFermi model. Effective interatomic potentials are derived and equilibrium spatial structures are given; these structures are universal for homoatomic metallic clusters, in the sense that they are independent of the chemical nature of the atoms. The binding energies, interatomic distances, and the vibration spectra are computed as functions of the effective number of "valence" electrons; this effective valence is estimated from the atomic screening. Magic numbers are obtained, corresponding to close spatial packings; these geometric magic numbers are also universal for homoatomic metallic clusters, in the sense that they do not depend on the atomic species. The quadrupoledeformed potential for the electrons in a metallic cluster is also derived. The extension of the theory to including ionic or covalent bonds is discussed.
Nuclear Physics
Phenomenological Three Center Model D.N. Poenaru, W. Greiner, R.A. Gherghescu, Y. Nagame, J. H. Hamilton, A.V. Ramayya Romanian Journal of Physics 46,
365381 (2001)
Experimental results on ternary fission of ^{252}Cf suggest the existence of a shortlived quasimolecular state. We present a threecenter phenomenological model able to explain such a state by producing a new minimum in the deformation energy at a separation distance very close to the touching point. The shape parametrization chosen by us allows to describe the essential geometry of the system in terms of one independent coordinate: the distance between the heavy fragment centers. The shell correction (also treated phenomenologically) only produces quantitative effects; qualitatively it is not essential for the new minimum. Halflives of some quasimolecular states which could be formed in ^{10}Be accompanied fission of ^{236}U, ^{236}Pu, ^{246}Cm, ^{252}Cf, ^{252,256}Fm, ^{256,260}No, and ^{262}Rf are roughly estimated.
Qualitative and Quantitative Description of Fission M. Mirea, V. Cartaş Romanian Journal of Physics 46,
383398 (2001)
A model is used to determine the fission products of ^{238}U. The deformation energy of the decaying system is obtained within the microscopicmacroscopic model using a twocenter nuclear shape parametrization. This model takes into account the excitation energy of the target nucleus and the evaporation of prompt neutrons. The isotopic yields of the induced fission are obtained for all mass partitions.
