Boson-fermion mapping of collective fermion-pair algebras

We construct finite Dyson boson-fermion mappings of general collective algebras extended by single-fermion operators. A key element in the construction is the implementation of a similarity transformation which transforms boson-fermion images obtained directly from the supercoherent state method. In addition to the general construction, we give detailed applications to SO(2N), SU(l+1), SO(5), and SO(8) algebras.Comment: 22 pages, latex, no figure

Rush (Original writing, Screenplay).

Rush is a screenplay, set in Las Vegas, Nevada. The story revolves around the troubles of the protagonist, Mark Theseus. After arriving in Vegas for a real estate conference, Mark becomes addicted to gambling. The addiction hits him quickly, and rather than get back on the airplane and leave, he chooses to stay in Vegas. The story is based on the myth of Theseus and the Minotaur, and many of the characters, themes and images help to identify it as such. But the story is also about traps and labyrinths, physical and mental spaces where people can become lost. Once Mark decides to stay in Vegas, he has sprung his own trap. And Like Theseus, he must now fulfill a quest in order to secure his freedom. Source: Masters Abstracts International, Volume: 43-05, page: 1436. Adviser: Darryl Whetter. Thesis (M.A.)--University of Windsor (Canada), 2004

RPA vs. exact shell-model correlation energies

The random phase approximation (RPA) builds in correlations left out by mean-field theory. In full 0-hbar-omega shell-model spaces we calculate the Hartree-Fock + RPA binding energy, and compare it to exact diagonalization. We find that in general HF+RPA gives a very good approximation to the ``exact'' ground state energy. In those cases where RPA is less satisfactory, however, there is no obvious correlation with properties of the HF state, such as deformation or overlap with the exact ground state wavefunction.Comment: 6 pages, 7 figures, submitted to Phys Rev

On the correlation between the binding energies of the triton and the alpha-particle

We consider the correlation between the binding energies of the triton and the alpha-particle which is empirically observed in calculations employing different phenomenological nucleon-nucleon interactions. Using an effective quantum mechanics approach for short-range interactions with large scattering length |a| >> l, where l is the natural low-energy length scale, we construct the effective interaction potential at leading order in l/|a|. In order to renormalize the four-nucleon system, it is sufficient to include a SU(4)-symmetric one-parameter three-nucleon interaction in addition to the S-wave nucleon-nucleon interactions. The absence of a four-nucleon force at this order explains the empirically observed correlation between the binding energies of the triton and the alpha-particle. We calculate this correlation and obtain a prediction for the alpha-particle binding energy. Corrections to our results are suppressed by l/|a|.Comment: 4 pages, 1 ps figure, references update

Beyond mean-field description of the low-lying spectrum of 16O

Starting from constrained Skyrme-mean-field calculations, the low-energy excitation spectrum of 16O is calculated by configuration mixing of particle-number and angular-momentum projected mean-field states in the framework of the Generator Coordinate Method. Without any adjustable parameters, this approach gives a very good description of those states and their transition moments that can be described with our restriction to axially and reflection-symmetric shapes. The structure of low-lying 0+ states is analyzed in terms of self-consistent 0p-0h, 2p-2h, and 4p-4h Hartree-Fock states.Comment: 15 pages LATEX, 6 figures, 3 tables, revision of sections 4 and

A mixed-mode shell-model theory for nuclear structure studies

We introduce a shell-model theory that combines traditional spherical states, which yield a diagonal representation of the usual single-particle interaction, with collective configurations that track deformations, and test the validity of this mixed-mode, oblique basis shell-model scheme on $^{24}$Mg. 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 results suggest that a mixed-mode shell-model theory may be useful in situations where competing degrees of freedom dominate the dynamics and full-space calculations are not feasible.Comment: 20 pages, 8 figures, revtex 12p

Microscopic calculation of the inclusive electron scattering structure function in O-16

We calculate the charge form factor and the longitudinal structure function for $^{16}$O and compare with the available experimental data, up to a momentum transfer of 4 fm$^{-1}$. The ground state correlations are generated using the coupled cluster [exp(S}] method, together with the realistic v-18 NN interaction and the Urbana IX three-nucleon interaction. Center-of-mass corrections are dealt with by adding a center-of-mass Hamiltonian to the usual internal Hamiltonian, and by means of a many-body expansion for the computation of the observables measured in the center-of-mass system

Ground state correlations and mean-field in 16^{16}O: Part II

We continue the investigations of the $^{16}$O ground state using the coupled-cluster expansion [$\exp({\bf S})$] method with realistic nuclear interaction. In this stage of the project, we take into account the three nucleon interaction, and examine in some detail the definition of the internal Hamiltonian, thus trying to correct for the center-of-mass motion. We show that this may result in a better separation of the internal and center-of-mass degrees of freedom in the many-body nuclear wave function. The resulting ground state wave function is used to calculate the "theoretical" charge form factor and charge density. Using the "theoretical" charge density, we generate the charge form factor in the DWBA picture, which is then compared with the available experimental data. The longitudinal response function in inclusive electron scattering for $^{16}$O is also computed.Comment: 9 pages, 7 figure