Relative Properties of Smooth Terminating Bands

The relative properties of smooth terminating bands observed in the A~110 mass region are studied within the effective alignment approach. Theoretical values of $i_{eff}$ are calculated using the configuration-dependent shell-correction model with the cranked Nilsson potential. Reasonable agreement with experiment shows that previous interpretations of these bands are consistent with the present study. Contrary to the case of superdeformed bands, the effective alignments of these bands deviate significantly from the pure single-particle alignments of the corresponding orbitals. This indicates that in the case of smooth terminating bands, the effects associated with changes in equilibrium deformations contribute significantly to the effective alignment.Comment: 15 pages, 8 PostScript figures, RevTex, uses 'epsf', submitted to Nucl. Phys.

Polarization Effects in Superdeformed Nuclei

A detailed theoretical investigation of polarization effects in superdeformed nuclei is performed. In the pure harmonic oscillator potential it is shown that when one particle (or hole) with the mass single-particle quadrupole moment q_{nu} is added to a superdeformed core, the change of the electric quadrupole moment can be parameterized as q_{eff}=e(bq_{nu}+a), and analytical expressions are derived for the two parameters, $a$ and $b$. Simple numerical expressions for q_{eff}(q_\nu}) are obtained in the more realistic modified oscillator model. It is also shown that quadrupole moments of nuclei with up to 10 particles removed from the superdeformed core of 152Dy can be well described by simply subtracting effective quadrupole moments of the active single-particle states from the quadrupole moment of the core. Tools are given for estimating the quadrupole moment for possible configurations in the superdeformed A 150-region.Comment: 28 pages including 9 figure

Homotopy Type of the Boolean Complex of a Coxeter System

In any Coxeter group, the set of elements whose principal order ideals are boolean forms a simplicial poset under the Bruhat order. This simplicial poset defines a cell complex, called the boolean complex. In this paper it is shown that, for any Coxeter system of rank n, the boolean complex is homotopy equivalent to a wedge of (n-1)-dimensional spheres. The number of such spheres can be computed recursively from the unlabeled Coxeter graph, and defines a new graph invariant called the boolean number. Specific calculations of the boolean number are given for all finite and affine irreducible Coxeter systems, as well as for systems with graphs that are disconnected, complete, or stars. One implication of these results is that the boolean complex is contractible if and only if a generator of the Coxeter system is in the center of the group. of these results is that the boolean complex is contractible if and only if a generator of the Coxeter system is in the center of the group.Comment: final version, to appear in Advances in Mathematic