Explicit Integration of Extremely-Stiff Reaction Networks: Quasi-Steady-State Methods

A preceding paper demonstrated that explicit asymptotic methods generally work much better for extremely stiff reaction networks than has previously been shown in the literature. There we showed that for systems well removed from equilibrium explicit asymptotic methods can rival standard implicit codes in speed and accuracy for solving extremely stiff differential equations. In this paper we continue the investigation of systems well removed from equilibrium by examining quasi-steady-state (QSS) methods as an alternative to asymptotic methods. We show that for systems well removed from equilibrium, QSS methods also can compete with, or even exceed, standard implicit methods in speed, even for extremely stiff networks, and in many cases give somewhat better integration speed than for asymptotic methods. As for asymptotic methods, we will find that QSS methods give correct results, but with non-competitive integration speed as equilibrium is approached. Thus, we shall find that both asymptotic and QSS methods must be supplemented with partial equilibrium methods as equilibrium is approached to remain competitive with implicit methods.Comment: Updated reference

Solution of the Nuclear Shell Model by Symmetry-Dictated Truncation

The dynamical symmetries of the Fermion Dynamical Symmetry Model are used as a principle of truncation for the spherical shell model. Utilizing the usual principle of energy-dictated truncation to select a valence space, and symmetry-dictated truncation to select a collective subspace of that valence space, we are able to reduce the full shell model space to one of manageable dimensions with modern supercomputers, even for the heaviest nuclei. The resulting shell model then consists of diagonalizing an effective Hamiltonian within the restricted subspace. This theory is not confined to any symmetry limits, and represents a full solution of the original shell model if the appropriate effective interaction of the truncated space can be determined. As a first step in constructing that interaction, we present an empirical determination of its matrix elements for the collective subspace with no broken pairs in a representative set of nuclei with $130\le A \le 250$. We demonstrate that this effective interaction can be parameterized in terms of a few quantities varying slowly with particle number, and is capable of describing a broad range of low-energy observables for these nuclei. Finally we give a brief discussion of extending these methods to include a single broken collective pair.Comment: invited paper for J. Phys. G, 57 pages, Latex, 18 figures a macro are available under request at [email protected]

Temperature-dependent gap equations and their solutions in the SU(4) model of high-temperature superconductivity

Temperature-dependent gap equations in the SU(4) model of high-Tc superconductivity are derived and analytical solutions are obtained. Based on these solutions, a generic gap diagram describing the features of energy gaps as functions of doping P is presented and a phase diagram illustrating the phase structure as a function of temperature T and doping P is sketched. A special doping point P_q occurs naturally in the solutions that separates two phases at temperature T = 0: a pure superconducting phase on one side (P > P_q) and a phase with superconductivity strongly suppressed by antiferromagnetism on the other (P < P_q). We interpret P_q as a quantum phase transition point. Moreover, the pairing gap is found to have two solutions for P < P_q: a small gap that is associated with competition between superconductivity and antiferromagnetism and is responsible for the ground state superconductivity, and a large gap without antiferromagnetic suppression that corresponds to a collective excited state. A pseudogap appears in the solutions that terminates at P_q and originates from the competition between d-wave superconductivity and antiferromagnetism. Nevertheless, this conclusion does not contradict the preformed pair picture conceptually if the preformed pairs are generally defined as any pairs formed before pairing condensation.Comment: 23 pages, 5 color figure

Neutrino-driven supernovae: Boltzmann neutrino transport and the explosion mechanism

Core-collapse supernovae are, despite their spectacular visual display, neutrino events. Virtually all of the 10^53 ergs of gravitational binding energy released in the formation of the nascent neutron star is carried away in the form of neutrinos and antineutrinos of all three flavors, and these neutrinos are primarily responsible for powering the explosion. This mechanism depends sensitively on the neutrino transport between the neutrinospheres and the shock. In light of this, we have performed a comparison of multigroup Boltzmann neutrino transport (MGBT) and multigroup flux-limited diffusion (MGFLD) in post-core bounce environments. Differences in the mean inverse flux factors, luminosities, and RMS energies translate to heating rates that are up to 2 times larger for Boltzmann transport, with net cooling rates below the gain radius that are typically 0.8 times the MGFLD rates. These differences are greatest at earlier postbounce times for a given progenitor mass, and for a given postbounce time, greater for greater progenitor mass. The increased differences with increased progenitor mass suggest that the net heating enhancement from MGBT is potentially robust and self-regulated.Comment: 7 pages, 2 figures, 1 table; LaTex using iopconf.sty; To appear in: Proceedings of The Second Oak Ridge Symposium on Atomic & Nuclear Astrophysic

Theoretical nuclear structure and astrophysics. Progress report for 1996

This research effort is directed toward theoretical support and guidance for the fields of radioactive ion beam physics, gamma ray spectroscopy, computational and nuclear astrophysics, and the interface between these disciplines. The authors report substantial progress in all those areas. One measure of progress is publications and invited material. The research described here has led to more than 43 papers that are published, accepted, or submitted to refereed journals, and to 15 invited presentations at conferences and workshops

Theoretical nuclear structure and astrophysics. Progress report for 1993--1995

This research effort is directed toward theoretical support and guidance for the developing fields of radioactive ion beam (RIB) physics, computational and nuclear astrophysics, and the interface between these disciplines. The authors are concerned both with the application of existing technologies and concepts to guide the initial RIB program, and the development of new ideas and new technologies to influence the longer-term future of nuclear structure physics and astrophysics. The authors report substantial progress in both areas. One measure of progress is publications and invited material. The research described here has led to more than 70 papers that are published, accepted, or submitted to refereed journals, and to 46 invited presentations at conferences and workshops

Universality of Symmetry and Mixed-symmetry Collective Nuclear States

The global correlation in the observed variation with mass number of the $E2$ and summed $M1$ transition strengths is examined for rare earth nuclei. It is shown that a theory of correlated $S$ and $D$ fermion pairs with a simple pairing plus quadrupole interaction leads naturally to this universality. Thus a unified and quantitative description emerges for low-lying quadrupole and dipole strengths.Comment: In press, Phys. Rev. Lett. 199