Composite Fermions and the First-Landau-Level Fine Structure of the Fractional Quantum Hall Effect

A set of scalar operators are employed to generate explicit representations of both hierarchy states (e.g., the series of fillings 1/3, 2/5, 3/7, ... ) and their conjugates (fillings 1, 2/3, 3/5, ...) as non-interacting quasi-electrons filling fine-structure sub-shells within the FLL. This yields, for planar and spherical geometries, a quasi-electron representation of the incompressible FLL state of filling p/(2p +1) in a magnetic field of strength B that is algebraically identical to the IQHE state of filling p in a magnetic field of strength B/(2p+1). The construction provides a precise definition of the quasi-electron/composite fermion that differs in some respects from common descriptions: they are eigenstates of L,Lz; they and the FLL subshells they occupy carry a third index I that is associated with breaking of scalar pairs; they absorb in their internal wave functions one, not two, units of magnetic flux; and they share a common, simple structure as vector products of a spinor creating an electron and one creating magnetic flux. We argue that these properties are a consequence of the breaking of the degeneracy of noninteracting electrons within the FLL by the scale-invariant Coulomb potential. We discuss the sense in which the wave function construction supports basic ideas of both composite fermion and hierarchical descriptions of the FQHE. We describe symmetries of the quasi-electrons at half filling, where a deep Fermi sea of quasi-electrons forms, and the quasi-electrons take on Majorana and pseudo-Dirac characters. Finally, we show that the wave functions can be viewed as fermionic excitations of the bosonic half-filled shell, producing at half filling an operator that differs from but plays the same role as the Pfaffian.Comment: 28 pages, 7 figures; includes discussion of the relation of the wave functions to composite fermion and hierarchical constructions; symmetries at the half filled shell including connections to Majorana and pseudo-Dirac basis states; representations of the wave functions as antisymmetric operators acting on the symmetric half-filled shell; and operator analogs of the Pfaffia

The Nuclear Physics of Solar and Supernova Neutrino Detection

This talk provides a basic introduction for students interested in the responses of detectors to solar, supernova, and other low-energy neutrino sources. Some of the nuclear physics is then applied in a discussion of nucleosynthesis within a Type II supernova, including the r-process and the neutrino process.Comment: School lecture, "New Era in Neutrino Physics, Tokyo Metropolitan University; 30 pages; 6 figures; late

Neutrino Oscillations and the Solar Neutrino Problem

I describe the current status of the solar neutrino problem, summarizing the arguments that its resolution will require new particle physics. The phenomenon of matter-enhanced neutrino oscillations is reviewed. I consider the implications of current experiments -- including the SuperKamiokande atmospheric and LSND measurements -- and the need for additional constraints from SNO and other new detectors.Comment: Reference corrected in this replacemen

Neutrino Astrophysics

A review of neutrino astrophysics is presented, including solar and atmospheric neutrinos; neutrino mass and oscillations; the supernova mechanism, supernova neutrino production, and associated nucleosynthesis; cosmological neutrinos and Big Bang nucleosynthesis; neutrino cooling and associated limits on neutrino properties; and high-energy astrophysical neutrinos.Comment: 42 pages, 15 figures; to appear in Wiley's Encyclopedia of Nuclear Physics. arXiv admin note: substantial text overlap with arXiv:0808.073

CN Neutrinos and the Sun's Primordial Core Metalicity

I discuss the use of neutrinos from the CN cycle and pp chain to constrain the primordial solar core abundances of C and N at an interesting level of precision. A comparison of the Sun's deep interior and surface compositions would test a key assumption of the standard solar model (SSM), a homogeneous zero-age Sun. It would also provide a cross-check on recent photospheric abundance determinations that have altered the once excellent agreement between the SSM and helioseismology. Motivated by the discrepancy between convective-zone abundances and helioseismology, I discuss the possibility that a two-zone Sun could emerge from late-stage metal differentiation in the solar nebula connected with formation of the gaseous giant planets.Comment: 11 pages, 3 figures; talk presented at the Carolina International Symposium on Neutrino Physics; based on Haxton and Serenelli, arXiv:0805.2013; typos fixed in this replacemen

Harmonic-Oscillator-Based Effective Theory

I describe harmonic-oscillator-based effective theory (HOBET) and explore the extent to which the effects of excluded higher-energy oscillator shells can be represented by a contact-gradient expansion in next-to-next-to-leading order (NNLO). I find the expansion can be very successful provided the energy dependence of the effective interaction, connected with missing long-wavelength physics associated with low-energy breakup channels, is taken into account. I discuss a modification that removes operator mixing from HOBET, simplifying the task of determining the parameters of an NNLO interaction.Comment: 15 pages, 5 figures; from 3rd ANL/MSU/INT/JINA RIA Worksho

Edward Teller and Nuclei: Along the Trail to the Neutrino

I discuss two of Edward Teller's contributions to nuclear physics, the introduction of the Gamow-Teller operator in beta decay and the formulation of the Goldhaber-Teller model for electric dipole transitions, in the context of efforts to understand the weak interaction and the nature of the neutrino.Comment: Talk presented at the Edward Teller Centennial Symposium; 16 pages, 5 figure

Solar Neutrinos: Models, Observations, and New Opportunities

I discuss the development and resolution of the solar neutrino problem, as well as opportunities now open to us to extend our knowledge of main-sequence stellar evolution and neutrino astrophysics.Comment: 11 pages, 8 figures; talk presented at "Nuclear Astrophysics 1957:2007: Beyond the First 50 Years," Caltech, July, 2007. To appear in the Publications of the Astronomical Society of Australi

Three Puzzles from Nuclear Astrophysics

I discuss three open problems in astrophysics where nuclear physics can make important contributions: the solar abundance problem, dark matter particle detection, and the origin of the r-process elements.Comment: 11 pages, 6 figures; talk presented at HITES 201

Theoretical Issues in Neutrino Physics

I review a number of the open questions about neutrino properties, critique recent hints of neutrino mass, and discuss one recently proposed neutrino mass matrix to illustrate the direction in which we may be headed. I also present one example of the implications of these new developments for astrophysics.Comment: Baryons '98 talk; 15 pages, 3 figures; latex Replacement contains updated reference