No abstract

We discuss the ability of the generator coordinate method (GCM) to select collective states in microscopic calculations. The model studied is a singlej shell with hamiltonian containing the quadrupole-quadrupole interaction. Quadrupole collective excitations are constructed by means of the quadrupole single-particle operator. Lowest collective bands for j=31/2 and particle numbers N =4,6,8,10,12, and 14 are found. For lower values of j, exact solutions are obtained and compared with the GCM results.

Flow in unsaturated porous media is commonly described by the Richards equation. This equation is strongly nonlinear due to interrelationships between water pressure head (negative in unsaturated conditions), water content and hydraulic conductivity. The accuracy of numerical solution of the Richards equation often depends on the method used to estimate average hydraulic conductivity between neighbouring nodes or cells of the numerical grid. The present paper discusses application of the computer simulation code VS2DI to three test problems concerning infiltration into an initially dry medium, using various methods for inter-cell conductivity calculation (arithmetic mean, geometric mean and upstream weighting). It is shown that the influence of the averaging method can be very large for coarse grid, but that it diminishes as cell size decreases. Overall, the arithmetic average produced the most reliable results for coarse grids. Moreover, the difference between results obtained with various methods is a convenient indicator of the adequacy of grid refinement.

The influence of quadrupole and hexadecapole residual interactions on rotational bands is investigated in a single-j shell model. An exact shell-model diagonalization of the quadrupole-plus-hexadecapole Hamiltonian demonstrates that the hexadecapole-hexadecapole interaction can sometimes produce a staggering of energy levels in the yrast sequence; however, long and regular ∆I=2 sequences are not obtained. The shell-model results are discussed in terms of the intrinsic deformations extracted by means of the self-consistent Hartree-Fock method. The angular momentum dependence of intrinsic quadrupole and hexadecapole moments Q 2µ and Q 4µ is investigated.

A role of the multipole interaction in the description of the △I=4 staggering phenomenon is investigated in a model consisting of a single-j shell filled by identical nucleons. Exact diagonalization of the quadrupole-plushexadecapole Hamiltonian shows that the hexadecapole-hexadecapole interaction can produce a △I=4 periodicity in the yrast sequence.