Band crossing and the prealignment B(E2) anomaly in 126Ba

A theoretical interpretation of the reduction in E2 strengths in ¹²⁶Ba prior to backbending is presented. A shell model basis is built from normal parity orbilals organized into multiplets of a pseudo SU(3) symmetry coupled to $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ configurations restricted to states of seniority zero and two. Within the framework of the model the scattering of a pair of protons from normal parity to the $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ orbital produces band crossing and a corresponding reduction in E2 transition strengths prior to pair alignment which is the principal mechanism of the backbending.     

E2 polynomial strengths: A comparison with shell-model results

Polynomial-expansion E2 strengths and sum rules involving (J,T)=(0, 0)and(2, 0) states of (ds)⁶ are compared with shell-model results. The agreement is excellent. The strength distribution is describable as a narrow linear ridge in the energy space. The level-to-level fluctuations in the total strength are small, as expected from a theorem of Dyson and Mehta; fluctuations in the first and second moments are also small. The effect of collectivity and the partitioning of the sum rules into exothermic and endothermic parts are discussed.     

Spectral averaging for single-nucleon-transfer sum rules

Spectral averaging methods are used to calculate, directly in terms of the Hamiltonian matrix elements, the quantities determined by the non-energy-weighted and linear-energy-weighted sum rules for single-nucleon addition and removal. Occupancies and strength centroids, and their isospin decomposition, are given throughout the spectrum for some ds-shell cases.     

Experimental and theoretical results for 21Ne(6Li,d)25Mg

Alpha-particle spectroscopic strengths extracted from ²¹Ne(⁶Li, d) angular distributions agree in both magnitude and multipolarity with predicted strengths. Secondly, strengths calculated using eigenfunctions determined in large shell-model computations are remarkably consistent with pure SU₃ symmetry limit results.     

Alpha-particle strengths from the 16O(6Li,d)20Ne reaction

The ¹⁶O(⁶Li, d)²⁰Ne reaction has been studied at bombarding energies of 20, 32 and 38 MeV. The α-particle spectroscopic strengths have been extracted for levels up to 12.15 MeV in excitation. Nondirect processes appear to contribute significantly to all levels at 20 MeV and to high spin levels (6⁺ and 8⁺) at 32 MeV. Strengths extracted for members of the ground state band assuming (sd)⁴ transfer are unequal at both 32 and 38 MeV, in marked contrast to theoretical predictions. To explain this, particle-hole correlations in ¹⁶O(g.s.), inelastic channel coupling in the reaction and perhaps other effects as well, have to be considered. Strengths extracted for members of excited bands and α-decay reduced widths compare poorly with each other and with simple SU(3) predictions.     

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.     

A nucleon-pair and boson coexistent description of nuclei

We study a mixture of s-bosons and like-nucleon pairs with the standard pairing interaction outside an inert core. Competition between the nucleon-pairs and s-bosons is investigated in this scenario. The robustness of the BCS-BEC coexistence and crossover phenomena are examined through an analysis of pf-shell nuclei with realistic single-particle energies, in which two configurations with Pauli blocking of nucleon-pair orbits due to the formation of the s-bosons is taken into account. When the nucleon-pair orbits are considered to be independent of the s-bosons, the BCS-BEC crossover becomes smooth, with the number of the s-bosons noticeably more than that of the nucleon-pairs near the half-shell point, a feature that is demonstrated in the pf-shell for several values of the standard pairing interaction strength. As a further test of the robustness of the BCS-BEC coexistence and crossover phenomena in nuclei, results are given for B(E2; 0_1~+→2_1~+) values of even-even~(102-130) Sn with~(100)Sn taken as a core and valence neutron pairs confined within the 1d_(5/2), 0g_(7/2), 1d_(3/2), 2s_(1/2), 1h_(11/2)orbits in the nucleon-pair orbit and the s-boson independent approximation. The results indicate that the B(E2) values are reproduced well.     

Analytic expressions for energy centroids and widths in the microscopic collective model

Analytic formulae are given for the U(3) centroids of the collective Bohr-Mottelson potential in the microscopic collective model. In particular, formulae are reported for the centroids of the quadratic [Q · Q ～ β²] and cubic [Q · (Q × Q ～ β³cos 3γ] rotational scalars in the microscopic quadrupole operator. Favorable comparisons for ground-state intensities are achieved between shell-model diagonalizations and statistical predictions based upon the gaussian approximation to the energy density. These results suggest that statistical measures can be used reliably for truncation of the infinite-dimensional representation spaces of the microscopic symplectic collective theory.     

A Class of Quasi-exact Solutions of Rabi Hamiltonian

A class of quasi-exact solutions of the Rabi Hamiltonian, which describes a two-level atom interacting with a single-mode radiation field via a dipole interaction without the rotating-wave approximation, are obtained by using a wavefunction ansatz. Exact solutions for part of the spectrum are obtained when the atom-field coupling strength and the field frequency satisfy certain relations. As an example, the lowest exact energy level and the corresponding atom-field entanglement at the quasi-exactly solvable point are calculated and compared to results from the Jaynes-Cummings and counter-rotating cases of the Rabi Hamiltonian.