Global Properties of fp-Shell Interactions in Many-nucleon Systems

Spectral distribution theory, which can be used to compare microscopic interactions over a broad range of nuclei, is applied in an analysis of two modern effective interactions based on the realistic CD-Bonn potential for $0\hbar\Omega$ no-core shell model calculations in the fp shell, as well as in a comparison of these with the realistic shell-model GXPF1 interaction. In particular, we explore the ability of these interaction to account for the development of isovector pairing correlations and collective rotational motion in the fp shell. Our findings expose the similarities of these two-body interactions, especially as this relates to their pairing and rotational characteristics. Further, the GXPF1 interaction is used to determine the strength parameter of a quadrupole term that can be used to augment an isovector-pairing model interaction with Sp(4) dynamical symmetry, which in turn is shown to yield reasonable agreement with the low-lying energy spectra of $^{58}$Ni and $^{58}$Cu.Comment: 21 pages, 3 figures, accepted in Nuclear Physics

M-body Pure State Entanglement

The simple entanglement of N-body N-particle pure states is extended to the more general M-body or M-body N-particle states where $N\neq M$. Some new features of the M-body N-particle pure states are discussed. An application of the measure to quantify quantum correlations in a Bose-Einstien condensate model is demonstrated.Comment: 9 pages, 2 figure

Mixed-Mode 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 states, which yield a diagonal representation of the usual single-particle interaction, with 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. Specifically, the correct binding energy (within 2% of the full-space result) as well as low-energy configurations that have greater than 90% overlap with full-space results are obtained in a space that spans less than 10% of the full-space. The theory is also applied to lower pf-shell nuclei, 44Ti-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 the 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 IBM and broken-pair models are considered as alternative basis sets for future oblique-basis shell-model calculations.Comment: 3 pages, no figures, summary of a poster present at the Nuclear Structure Conference: Mapping the Triangle. Grand Teton National Park, Wyoming USA, May 22-25, 200

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 a 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 is 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 nucleonpairs 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^{+}_{g}->2^{+}_1) values of even-even 102-130Sn with 100Sn taken as a core and valence neutron pairs confined within the 1d5/2, 0g7/2, 1d3/2, 2s1/2, 1h11/2 orbits in the nucleon-pair orbit and the s-boson independent approximation. The results indicate that the B(E2) values are well reproduced.Comment: 5.1 pages, 3 figures, LaTe

Exact solution of the two-axis countertwisting Hamiltonian for the half-integer JJ case

Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any (integer and half-integer) $J$ are derived based on the Jordan-Schwinger (differential) boson realization of the $SU(2)$ algebra after desired Euler rotations, where $J$ is the total angular momentum quantum number of the system. It is shown that solutions to the Bethe ansatz equations can be obtained as zeros of the extended Heine-Stieltjes polynomials. Two sets of solutions, with solution number being $J+1$ and $J$ respectively when $J$ is an integer and $J+1/2$ each when $J$ is a half-integer, are obtained. Properties of the zeros of the related extended Heine-Stieltjes polynomials for half-integer $J$ cases are discussed. It is clearly shown that double degenerate level energies for half-integer $J$ are symmetric with respect to the $E=0$ axis. It is also shown that the excitation energies of the `yrast' and other `yrare' bands can all be asymptotically given by quadratic functions of $J$, especially when $J$ is large.Comment: LaTex 12 pages, 3 figures. Major cosmetic type revision. arXiv admin note: text overlap with arXiv:1609.0558