Microscopic models for exotic nuclei

Starting from successful self-consistent mean-field models, this paper discusses why and how to go beyond the mean field approximation. To include long-range correlations from fluctuations in collective degrees of freedom, one has to consider symmetry restoration and configuration mixing, which give access to ground-state correlations and spectroscopy.Comment: invited talk at ENAM0

Projective Geometry and PT\cal PT-Symmetric Dirac Hamiltonian

The $(3 + 1)$-dimensional (generalized) Dirac equation is shown to have the same form as the equation expressing the condition that a given point lies on a given line in 3-dimensional projective space. The resulting Hamiltonian with a $\gamma_5$ mass term is not Hermitian, but is invariant under the combined transformation of parity reflection $\cal P$ and time reversal $\cal T$. When the $\cal PT$ symmetry is unbroken, the energy spectrum of the free spin-$\frac {1}{2}$ theory is real, with an appropriately shifted mass.Comment: 7 pages, LaTeX; version accepted for publication in Phys. Lett. B; revised version incorporates useful suggestions from an anonymous refere

Multiple-Scale Analysis of the Quantum Anharmonic Oscillator

Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an infinite reordering and resummation of the conventional perturbation series. Multiple-scale analysis provides a good description of the classical anharmonic oscillator. Here, it is extended to study the Heisenberg operator equations of motion for the quantum anharmonic oscillator. The analysis yields a system of nonlinear operator differential equations, which is solved exactly. The solution provides an operator mass renormalization of the theory.Comment: 12 pages, Revtex, no figures, available through anonymous ftp from ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at http://euclid.tp.ph.ic.ac.uk/Papers/papers_95-6_.htm

Systematics of quadrupolar correlation energies

We calculate correlation energies associated with the quadrupolar shape degrees of freedom with a view to improving the self-consistent mean-field theory of nuclear binding energies. The Generator Coordinate Method is employed using mean-field wave functions and the Skyrme SLy4 interaction. Systematic results are presented for 605 even-even nuclei of known binding energies, going from mass A=16 up to the heaviest known. The correlation energies range from 0.5 to 6.0 MeV in magnitude and are rather smooth except for large variations at magic numbers and in light nuclei. Inclusion of these correlation energies in the calculated binding energy is found to improve two deficiencies of the Skyrme mean field theory. The pure mean field theory has an exaggerated shell effect at neutron magic numbers and addition of the correlation energies reduce it. The correlations also explain the phenomenon of mutually enhanced magicity, an interaction between neutron and proton shell effects that is not explicable in mean field theory.Comment: 4 pages with 3 embedded figure

Beyond-mean-field-model analysis of low-spin normal-deformed and superdeformed collective states of S32, Ar36, Ar38 and Ca40

We investigate the coexistence of spherical, deformed and superdeformed states at low spin in S32, Ar36, Ar38 and Ca40. The microscopic states are constructed by configuration mixing of BCS states projected on good particle number and angular momentum. The BCS states are themselves obtained from Hartree-Fock BCS calculations using the Skyrme interaction SLy6 for the particle-hole channel, and a density-dependent contact force in the pairing channel. The same interaction is used within the Generator Coordinate Method to determine the configuration mixing and calculate the properties of even-spin states with positive parity. Our calculations underestimate moments of inertia. Nevertheless, for the four nuclei, the global structural properties of the states of normal deformation as well as the recently discovered superdeformed bands up to spin 6 are correctly reproduced with regard to both the energies and the transition rates.Comment: 14 pages revtex4, 15 eps figures, 8 table

Green Functions for the Wrong-Sign Quartic

It has been shown that the Schwinger-Dyson equations for non-Hermitian theories implicitly include the Hilbert-space metric. Approximate Green functions for such theories may thus be obtained, without having to evaluate the metric explicitly, by truncation of the equations. Such a calculation has recently been carried out for various $PT$-symmetric theories, in both quantum mechanics and quantum field theory, including the wrong-sign quartic oscillator. For this particular theory the metric is known in closed form, making possible an independent check of these approximate results. We do so by numerically evaluating the ground-state wave-function for the equivalent Hermitian Hamiltonian and using this wave-function, in conjunction with the metric operator, to calculate the one- and two-point Green functions. We find that the Green functions evaluated by lowest-order truncation of the Schwinger-Dyson equations are already accurate at the (6-8)% level. This provides a strong justification for the method and a motivation for its extension to higher order and to higher dimensions, where the calculation of the metric is extremely difficult

Model of supersymmetric quantum field theory with broken parity symmetry

Recently, it was observed that self-interacting scalar quantum field theories having a non-Hermitian interaction term of the form $g(i\phi)^{2+\delta}$, where $\delta$ is a real positive parameter, are physically acceptable in the sense that the energy spectrum is real and bounded below. Such theories possess PT invariance, but they are not symmetric under parity reflection or time reversal separately. This broken parity symmetry is manifested in a nonzero value for $$, even if $\delta$ is an even integer. This paper extends this idea to a two-dimensional supersymmetric quantum field theory whose superpotential is ${\cal S}(\phi)=-ig(i\phi)^{1+\delta}$. The resulting quantum field theory exhibits a broken parity symmetry for all $\delta>0$. However, supersymmetry remains unbroken, which is verified by showing that the ground-state energy density vanishes and that the fermion-boson mass ratio is unity.Comment: 20 pages, REVTeX, 11 postscript figure

Pairing correlations beyond the mean field

We discuss dynamical pairing correlations in the context of configuration mixing of projected self-consistent mean-field states, and the origin of a divergence that might appear when such calculations are done using an energy functional in the spirit of a naive generalized density functional theory.Comment: Proceedings of the XIII Nuclear Physics Workshop ``Maria and Pierre Curie'' on ``Pairing and beyond - 50 years of the BCS model'', held at Kazimierz Dolny, Poland, September 27 - October 1, 2006. Int. J. Mod. Phys. E, in prin

Visual stimulation of saccades in magnetically tethered Drosophila

Flying fruit flies, Drosophila melanogaster, perform `body saccades', in which they change heading by about 90° in roughly 70 ms. In free flight, visual expansion can evoke saccades, and saccade-like turns are triggered by similar stimuli in tethered flies. However, because the fictive turns in rigidly tethered flies follow a much longer time course, the extent to which these two behaviors share a common neural basis is unknown. A key difference between tethered and free flight conditions is the presence of additional sensory cues in the latter, which might serve to modify the time course of the saccade motor program. To study the role of sensory feedback in saccades, we have developed a new preparation in which a fly is tethered to a fine steel pin that is aligned within a vertically oriented magnetic field, allowing it to rotate freely around its yaw axis. In this experimental paradigm, flies perform rapid turns averaging 35° in 80 ms, similar to the kinematics of free flight saccades. Our results indicate that tethered and free flight saccades share a common neural basis, but that the lack of appropriate feedback signals distorts the behavior performed by rigidly fixed flies. Using our new paradigm, we also investigated the features of visual stimuli that elicit saccades. Our data suggest that saccades are triggered when expanding objects reach a critical threshold size, but that their timing depends little on the precise time course of expansion. These results are consistent with expansion detection circuits studied in other insects, but do not exclude other models based on the integration of local movement detectors