On some singularities of the correlation functions that determine neutrino opacities

Certain perturbation graphs in the calculation of the effects of the medium on neutrino scattering in supernova matter have a nonintegrable singularity in a physical region. A number of papers have addressed the apparent pathology through an ansatz that invokes higher order (rescattering) effects. Taking the Gamow-Teller terms as an example, we display an expression for the spin-spin correlation function that determines the cross-sections. It is clear from the form that there are no pathologies in the order by order perturbation expansion. Explicit formulae are given for a simple case, leading to an answer that is very different from one given by other authors.Comment: 8 page

Numerical Toy-Model Calculation of the Nucleon Spin Autocorrelation Function in a Supernova Core

We develop a simple model for the evolution of a nucleon spin in a hot and dense nuclear medium. A given nucleon is limited to one-dimensional motion in a distribution of external, spin-dependent scattering potentials. We calculate the nucleon spin autocorrelation function numerically for a variety of potential densities and distributions which are meant to bracket realistic conditions in a supernova core. For all plausible configurations the width of the spin-density structure function is found to be less than the temperature. This is in contrast with a naive perturbative calculation based on the one-pion exchange potential which overestimates the width and thus suggests a large suppression of the neutrino opacities by nucleon spin fluctuations. Our results suggest that it may be justified to neglect the collisional broadening of the spin-density structure function for the purpose of estimating the neutrino opacities in the deep inner core of a supernova. On the other hand, we find no indication that processes such as axion or neutrino pair emission, which depend on nucleon spin fluctuations, are substantially suppressed beyond the multiple-scattering effect already discussed in the literature. Aside from these practical conclusions, our model reveals a number of interesting and unexpected insights. For example, the spin-relaxation rate saturates with increasing potential strength only if bound states are not allowed to form by including a repulsive core. There is no saturation with increasing density of scattering potentials until localized eigenstates of energy begin to form.Comment: 14 latex pages in two-column format, 15 postscript figures included, uses revtex.sty and epsf.sty. Submitted to Physical Review

Absence of resonant enhancements in some inclusive rates

A toy model is defined and solved perturbatively with the aim of examining some claimed "resonant" enhancements of certain reaction rates that enter popular models of leptogenesis. We find: a) that such enhancements are absent; and b) that the perturbative solution, as done correctly using finite- temperature field theory, is well defined without the "resumming" procedures found in the literature. The pathologies that led to the perceived need for these procedures are an artifact of uncritical use of weighted vacuum cross- sections in the determination of rates, without adequate attention to the effects of the medium upon the single particle states within it.Comment: 11 pages, no figures. Some typos corrected. More typos correcte

Fringe Science: Defringing CCD Images with Neon Lamp Flat Fields

Fringing in CCD images is troublesome from the aspect of photometric quality and image flatness in the final reduced product. Additionally, defringing during calibration requires the inefficient use of time during the night to collect and produce a "supersky" fringe frame. The fringe pattern observed in a CCD image for a given near-IR filter is dominated by small thickness variations across the detector with a second order effect caused by the wavelength extent of the emission lines within the bandpass which produce the interference pattern. We show that essentially any set of emission lines which generally match the wavelength coverage of the night sky emission lines within a bandpass will produce an identical fringe pattern. We present an easy, inexpensive, and efficient method which uses a neon lamp as a flat field source and produces high S/N fringe frames to use for defringing an image during the calibration process.Comment: accepted to PAS

Many-Body Corrections to Charged-Current Neutrino Absorption Rates in Nuclear Matter

Including nucleon--nucleon correlations due to both Fermi statistics and nuclear forces, we have developed a general formalism for calculating the charged--current neutrino--nucleon absorption rates in nuclear matter. We find that at one half nuclear density many--body effects alone suppress the rates by a factor of two and that the suppression factors increase to $\sim$5 at $4\times10^{14}$ g cm$^{-3}$. The associated increase in the neutrino--matter mean--free--paths parallels that found for neutral--current interactions and opens up interesting possibilities in the context of the delayed supernova mechanism and protoneutron star cooling.Comment: 11 pages, APS REVTeX format, 1 PostScript figure, uuencoded compressed, and tarred, submitted to Physical Review Letter

A Self-Consistent Approach to Neutral-Current Processes in Supernova Cores

The problem of neutral-current processes (neutrino scattering, pair emission, pair absorption, axion emission, \etc) in a nuclear medium can be separated into an expression representing the phase space of the weakly interacting probe, and a set of dynamic structure functions of the medium. For a non-relativistic medium we reduce the description to two structure functions S_A(\o) and S_V(\o) of the energy transfer, representing the axial-vector and vector interactions. $S_V$ is well determined by the single-nucleon approximation while $S_A$ may be dominated by multiply interacting nucleons. Unless the shape of S_A(\o) changes dramatically at high densities, scattering processes always dominate over pair processes for neutrino transport or the emission of right-handed states. Because the emission of right-handed neutrinos and axions is controlled by the same medium response functions, a consistent constraint on their properties from consideration of supernova cooling should use the same structure functions for both neutrino transport and exotic cooling mechanisms.Comment: 33 pages, Te

Maxillary Periapical Actinomycosis: A Case with an Unusual Roentgenographic Appearance

Actinomycosis was once a fairly common disease and one that has a long history. “It was undoubtedly observed early in the 19th Century, as actinomycotic lesions were described erroneously in 1826 by LeBlanc as osteosarcomas and later in the 1800s Bollinger (1876) first recognized it as a specific entity which he named ‘lumpy jaw.’” The most frequent clinical form of actinomycosis is the cervicofacial type which is seen in 60% of reported cases, the other forms being abdominal (20%), pulmonary (15%) and cutaneous (5%). Young adult males are most frequently affected with actinomycosis. The actinomycetes, the so-called “higher” bacteria, are among the more common microorganism found within the oral cavity; however, they seldom exist as pathogens within the oral cavity, and Goldstein et al (1972) report that there are fewer than 50 cases of actinomycosis of the maxilla reported in the English literature. Periapical actinomycosis is seen even less frequently. Browne and O’Riordan reported a case of periapical actinomycotic granuloma and found that only ten such cases were on record before 1966. In 1975 Samanta et al reported that the analysis of cases reported subsequently to those of Browne and O’Riordan revealed only five additional cases in which colonies of actinomycetes were demonstrated on histologic studies of the periapical tissue

Nucleon Spin Fluctuations and the Supernova Emission of Neutrinos and Axions

In the hot and dense medium of a supernova (SN) core, the nucleon spins fluctuate so fast that the axial-vector neutrino opacity and the axion emissivity are expected to be significantly modified. Axions with m_a\alt10^{-2}\,{\rm eV} are not excluded by SN~1987A. A substantial transfer of energy in neutrino-nucleon ($\nu N$) collisions is enabled which may alter the spectra of SN neutrinos relative to calculations where energy-conserving $\nu N$ collisions had been assumed near the neutrinosphere.Comment: 8 pages. REVTeX. 2 postscript figures, can be included with epsf. Small modifications of the text, a new "Note Added", and three new references. To be published in Phys. Rev. Let

Evaluation of the Illinois Soil Nitrogen Test in the North Central Region

Data from 96 locations across the North Central Region was complied to evaluate the usefulness of the Illinois soil nitrogen test (ISNT) in identifying fields where corn will not respond to additional N fertilizer and predicting the yield optimizing N rate (YONR) for each field. The ISNT could not accurately predict non-responsive sites, nor could it predict YONR. Sub-setting the data based on soil drainage class and previous crop did not improve the predictive capability of the ISNT. The ISNT was related to soil organic matter and was measuring a constant fraction of total soil N. The ISNT is not a meaningful tool upon which N rate decisions should be based

Spin susceptibility of neutron matter at zero temperature

The Auxiliary Field Diffusion Monte Carlo method is applied to compute the spin susceptibility and the compressibility of neutron matter at zero temperature. Results are given for realistic interactions which include both a two-body potential of the Argonne type and the Urbana IX three-body potential. Simulations have been carried out for about 60 neutrons. We find an overall reduction of the spin susceptibilty by about a factor 3 with respect to the Pauli susceptibility for a wide range of densities. Results for the compressibility of neutron matter are also presented and compared with other available estimates obtained for semirealistic nucleon-nucleon interactions by using other techniques