Oblique-basis shell-model calculations

A one-dimensional harmonic oscillator in a box is used to introduce the oblique-basis concept. The method is extended to the nuclear shell model by combining traditional spherical shell model states, which yield a diagonal representation of the usual single-particle interaction, with SU(3) shell model collective configurations that track deformation. An application to ²⁴Mg, using the realistic two-body interaction of Wildenthal, is used to explore the validity of this mixed-mode shell-model scheme. The theory is also applied to lower pf-shell nuclei, ^44–48Ti and ⁴⁸Cr, using the Kuo-Brown-3 interaction. These nuclei show strong SU(3) symmetry breaking due mainly to the single-particle spin-orbit splitting. Nevertheless, the results also show that yrast band B(E2) values are insensitive to fragmentation of SU(3) symmetry. Specifically, the quadrupole collectivity as measured by B(E2) strengths remains high even though the SU(3) symmetry is rather badly broken. The results suggest that an oblique-basis mixed-mode shell-model theory may be useful in situations where competing degrees of freedom dominate the dynamics.     

New approach in theory of Clebsch-Gordan coefficients foru(n) andU q(u(n))

A new method for calculation of Clebsch-Gordan coefficients (CGCs) of the Lie algebrau(n) and its quantum analogU _q(u(n)) is developed. The method is based on the projection operator method in combination with the Wigner-Racah calculus for the subalgebrau(n−1) (U _q(u(n−1))). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form of the projection operator ofu(n) andU _q(u(n)). It is shown that theU _q(u(n)) CGCs can be presented in terms of theU _q(u)(n−1)) q−9j-symbols. Presented at the 9th International Colloquium: “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. Supported by Russian Foundation for Fundamental Research, grant 99-01-01163. Supported in part by the U.S. National Science Foundation under Grant PHY-9970769 and Cooperative Agreement EPS-9720652 that includes matching from the Louisiana Board of Regents Support Fund.     

Simple Entanglement Measure for Multipartite Pure States

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.     

Towards a shell-model description of the low-energy structure of deformed nuclei II. Electromagnetic properties of collective M1 bands

A shell-model theory, called the pseudo SU(3) model, which was proposed previously for giving the structure of low-lying states in heavy deformed nuclei is used to predict the number of 1⁺ states with strong M1 transitions to ground states for the nuclei ¹⁵⁴Sm, ^{156 160}Gd, ¹⁶⁴Dy, ¹⁶⁸Er, ¹⁷⁴Yb of the rare earth region and the actinide species ²³²Th, ^{234 240}U, ²⁴²Pu. Results are also given for E2 and M3 transition strengths in these nuclei. The measures provide a rigorous test of the theory, which in reality is a many-particle Nilsson scheme, because the real M1, E2, and M3 operators are used in the calculations. It is found that the results for E2 strengths using the real quadrupole operator differ by less than 5% from those of calculations that use the operator which is a generator of the pseudo SU(3) symmetry. This is so even for weak interband transitions. To further test the theory additional experimental information on the 2_γ⁺ states is necessary. In particular, the 1⁺ → 2_γ⁺ decay strengths are needed to differentiate between theories for the structure of the giant M1 states.     

Evidence for symplectic symmetry in Ab initio no-core shell model results for light nuclei

Clear evidence for symplectic symmetry in low-lying states of 12C and 16O is reported. Eigenstates of 12C and 16O, determined within the framework of the no-core shell model using the J-matrix inverse scattering potential with A相似文献   

Towards a shell model description of the low-energy structure of deformed nuclei I. Even-even systems

A microscopic shell model theory for the low-lying collective states of heavy deformed nuclei is described. Basis selection is guided by the Bohr-Mottelson-Nilsson picture of collective motion in nuclei. The necessary further truncation is achieved by exploiting an SU(3) symmetry inherent to the structure of the normal parity states and by restricting abnormal parity configurations to states with low seniority. An effective interaction comprised of operators which form an integrity basis for the SU(3) → R(3) algebra is shown to be sufficient to reproduce almost exactly, within a single leading irreducible representation of SU(3), the ground and gamma band rotational structure of eight rare earth (¹⁶⁰Dy, ¹⁶²Dy, ¹⁶⁴Dy, ¹⁶⁴Er, ¹⁶⁶Er, ¹⁶⁸Er, ¹⁶⁶Yb, ¹⁶⁸Yb) and four actinide (²³²Th, ²³⁴U, ²³⁶U, ²³⁸U) nuclei. The concomitant interband and intraband E2 strengths are also shown to be accurately reproduced. Extensions of the theory and necessary further theoretical investigations are reviewed.     

Symplectic shell-model calculations for 20Ne with horizontal configuration mixing

The symplectie shell model, which incorporates vertical $\text{(2n}\text{h}\text{?}\text{ω; n = 1, 2…)}$ major shell configuration mixing as dictated by a quadrupole interaction, is augmented with horizontal (0?ω) mixing induced by realistic single-particle energies and a monopole-pairing interaction. The excitation spectrum and B(E2) rates of the ²⁰Ne ground band are accurately reproduced without the use of an effective charge. The degree of horizontal and vertical mixing is found to be on the order of 20% in the ground state and up to as much as 50% for the 8⁺ level.     

Translation planes admitting a pair of index three homology groups

It is shown that a translation plane of order which admits two homology groups of order must in fact admit symmetric homology groups of this order. It is further shown that a plane admitting such symmetric index 3 homology groups is, with a finite number of exceptions, a generalized André plane. A list of the possibly exceptional orders is determined. Received 20 March 2000.