10,195 research outputs found
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
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 5 at
g cm. 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. is well determined by the single-nucleon
approximation while 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
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 () collisions is enabled which may alter
the spectra of SN neutrinos relative to calculations where energy-conserving
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
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
The top 500 mathematics pins: Analysis of elementary mathematics activities on Pinterest
A 2017 study found that 87% of elementary teachers reported consulting Pinterest when planning mathematical lessons (Hertel & Wessman-Enzinger, 2017). When searching for resources on Pinterest, preservice teachers identified looking at the number of pins to determine their quality (Sawyer & Meyers, 2018). This leaves teacher educators wondering, what is the quality of materials that preservice and inservice teachers are finding on Pinterest? We conducted a document analysis on the top 500 elementary mathematics pins found on Pinterest to determine what kinds of elementary mathematics materials are available, what mathematics topics are represented, the level of cognitive demand of the elementary mathematics activities, and how the image found on the activities relates to the level of cognitive demand. We found that less than two percent of activities are the highest level of cognitive demand and decorative images are correlated with lower level elementary mathematics activities. With this information, teacher educators could help prepare teachers to decide which resources they should use and what they should look for to increase the level of cognitive demand of elementary mathematics activities they implement in their classroom
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