Isotopic tiling theory for hyperbolic surfaces

In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on Delaney-Dress combinatorial tiling theory using an extension of mapping class groups to orbifolds, in turn using this to study tilings of covering spaces of orbifolds. Moreover, we study finite subgroups of these mapping class groups. Our results can be used to extend the Delaney-Dress combinatorial encoding of a tiling to yield a finite symbol encoding the complexity of an isotopy class of tilings. The results of this paper provide the basis for a complete and unambiguous enumeration of isotopically distinct tilings of hyperbolic surfaces

Estimates of weak and electromagnetic nuclear decay signatures for neutrino reactions in Super-Kamiokande

We estimate possible delayed β decay signatures of the neutrino induced reactions on 16O in a two-step model: the primary neutrino (ν,l) process, where l is the lepton in the final state, is described within the random phase approximation, while the subsequent decay of the excited nuclear state in the final channel is treated within the statistical model. We calculate partial reaction cross sections leading to β unstable nuclei. We consider neutrino energies up to 500 MeV, relevant for atmospheric neutrino detection in Super-Kamiokande, and supernova neutrino spectra

Weak reactions on 12C within the Continuum Random Phase Approximation with partial occupancies

We extend our previous studies of the neutrino-induced reactions on 12C and muon capture to include partial occupation of nuclear subshells in the framework of the continuum random phase approximation. We find, in contrast to the work by Auerbach et al., that a partial occupation of the p1/2 subshell reduces the inclusive cross sections only slightly. The extended model describes the muon capture rate and the 12C(nu_e,e-)12N cross section very well. The recently updated flux and the improved model bring the calculated 12C(nu_mu,mu^-)12N cross section (~ 17.5 10^{-40} cm^2) and the data (12.4 +/- 0.3(stat.) +/- 1.8(syst.) 10^{-40} cm^2) closer together, but does not remove the discrepancy fully.Comment: 12 pages, 2 figure

The role of ν\nu-induced reactions on lead and iron in neutrino detectors

We have calculated cross sections and branching ratios for neutrino induced reactions on ^{208}Pb and ^{56}Fe for various supernova and accelerator-relevant neutrino spectra. This was motivated by the facts that lead and iron will be used on one hand as target materials in future neutrino detectors, on the other hand have been and are still used as shielding materials in accelerator-based experiments. In particular we study the inclusive ^{56}$Fe(\nu_e,e^-)$^{56}Co and ^{208}$Pb(\nu_e,e^-)$^{208}Bi cross sections and calculate the neutron energy spectra following the decay of the daughter nuclei. These reactions give a potential background signal in the KARMEN and LSND experiment and are discussed as a detection scheme for supernova neutrinos in the proposed OMNIS and LAND detectors. We also study the neutron-emission following the neutrino-induced neutral-current excitation of ^{56}Fe and ^{208}Pb.Comment: 23 pages (including 7 figures

Quasielastic neutrino scattering from oxygen and the atmospheric neutrino problem

We examine several phenomena beyond the scope of Fermi-gas models that affect the quasielastic scattering (from oxygen) of neutrinos in the 0.1 -- 3.0 GeV range. These include Coulomb interactions of outgoing protons and leptons, a realistic finite-volume mean field, and the residual nucleon-nucleon interaction. None of these effects are accurately represented in the Monte Carlo simulations used to predict event rates due to $\mu$ and $e$ neutrinos from cosmic-ray collisions in the atmosphere. We nevertheless conclude that the neglected physics cannot account for the anomalous $\mu$ to $e$ ratio observed at Kamiokande and IMB, and is unlikely to change absolute event rates by more than 10--15\%. We briefly mention other phenomena, still to be investigated in detail, that may produce larger changes.Comment: In Revtex version 2. 14 pages, 3 figures (available on request from J. Engel, tel. 302-831-4354, [email protected]

Neutrino–nucleus reactions and nuclear structure

The methods used in the evaluation of the neutrino–nucleus cross section are reviewed. Results are shown for a variety of targets of practical importance. Many of the described reactions are accessible in future experiments with neutrino sources from the pion and muon decays at rest, which might be available at the neutron spallation facilities. Detailed comparison between the experimental and theoretical results would establish benchmarks needed for verification and/or parameter adjustment of the nuclear models. Having a reliable tool for such calculation is of great importance in a variety of applications, e.g. the neutrino oscillation studies, detection of supernova neutrinos, description of the neutrino transport in supernovae and description of the r-process nucleosynthesis

Muon capture on nuclei with N > Z, random phase approximation, and in-medium renormalization of the axial-vector coupling constant

We use the random phase approximation to describe the muon capture rate on ${}^{44}$Ca,${}^{48}$Ca, ${}^{56}$Fe, ${}^{90}$Zr, and ${}^{208}$Pb. With ${}^{40}$Ca as a test case, we show that the Continuum Random Phase Approximation (CRPA) and the standard RPA give essentially equivalent descriptions of the muon capture process. Using the standard RPA with the free nucleon weak form factors we reproduce the experimental total capture rates on these nuclei quite well. Confirming our previous CRPA result for the $N = Z$ nuclei, we find that the calculated rates would be significantly lower than the data if the in-medium quenching of the axial-vector coupling constant were employed.Comment: submitted to Phys. Rev.

Neutrino induced transitions between the ground states of the A=12 triad

Neutrino induced reactions on $^{12}$C, an ingredient of liquid scintillators, have been studied in several experiments. We show that for currently available neutrino energies, $E_{\nu} \le$ 300 MeV, calculated exclusive cross sections $^{12}$C$_{gs}(\nu,l)$$^{12}$N$_{gs}$ for both muon and electron neutrinos are essentially model independent, provided the calculations simultaneously describe the rates of several other reactions involving the same states or their isobar analogs. The calculations agree well with the measured cross sections, which can be therefore used to check the normalization of the incident neutrino spectrum and the efficiency of the detector.Comment: 9 pages REVTEX, 2 postscript figures, text and figures available at http://www.krl.caltech.edu/preprints/MAP.htm