Bohr Phenomena for Laplace-Beltrami Operators

Cataloged from PDF version of article.We investigate a Bohr phenomenon on the spaces of solutions of weighted Laplace-Beltrami operators associated with the hyperbolic metric of the unit ball in ℂN. These solutions do not satisfy the usual maximum principle, and the spaces have natural bases none of whose members is a constant function. We show that these bases exhibit a Bohr phenomenon, define a Bohr radius for them that extends the classical Bohr radius, and compute it exactly. We also compute the classical Bohr radius of the invariant harmonic functions on the real hyperbolic space. © 2006 Royal Netherlands Academy of Arts and Sciences

Improved search for invisible modes of nucleon decay in water with the SNO+ detector

This paper reports results from a search for single and multi-nucleon disappearance from the $^{16}$O nucleus in water within the \snoplus{} detector using all of the available data. These so-called "invisible" decays do not directly deposit energy within the detector but are instead detected through their subsequent nuclear de-excitation and gamma-ray emission. New limits are given for the partial lifetimes: $\tau(n\rightarrow inv) > 9.0\times10^{29}$ years, $\tau(p\rightarrow inv) > 9.6\times10^{29}$ years, $\tau(nn\rightarrow inv) > 1.5\times10^{28}$ years, $\tau(np\rightarrow inv) > 6.0\times10^{28}$ years, and $\tau(pp\rightarrow inv) > 1.1\times10^{29}$ years at 90\% Bayesian credibility level (with a prior uniform in rate). All but the ($nn\rightarrow inv$) results improve on existing limits by a factor of about 3.info:eu-repo/semantics/publishedVersio

Observation of Antineutrinos from Distant Reactors using Pure Water at SNO+

The SNO+ collaboration reports the first observation of reactor antineutrinos in a Cherenkov detector. The nearest nuclear reactors are located 240 km away in Ontario, Canada. This analysis used events with energies lower than in any previous analysis with a large water Cherenkov detector. Two analytical methods were used to distinguish reactor antineutrinos from background events in 190 days of data and yielded consistent observations of antineutrinos with a combined significance of 3.5 $\sigma$.Comment: v2: add missing author, add link to supplemental materia

Measurement of neutron-proton capture in the SNO+ water phase

The SNO+ experiment collected data as a low-threshold water Cherenkov detector from September 2017 to July 2019. Measurements of the 2.2-MeV $\gamma$ produced by neutron capture on hydrogen have been made using an Am-Be calibration source, for which a large fraction of emitted neutrons are produced simultaneously with a 4.4-MeV $\gamma$. Analysis of the delayed coincidence between the 4.4-MeV $\gamma$ and the 2.2-MeV capture $\gamma$ revealed a neutron detection efficiency that is centered around 50% and varies at the level of 1% across the inner region of the detector, which to our knowledge is the highest efficiency achieved among pure water Cherenkov detectors. In addition, the neutron capture time constant was measured and converted to a thermal neutron-proton capture cross section of $336.3^{+1.2}_{-1.5}$ mb

Measurement of the 8B solar neutrino flux in SNO+ with very low backgrounds

A measurement of the 8B solar neutrino flux has been made using a 69.2 kt-day dataset acquired with the SNO+ detector during its water commissioning phase. At energies above 6 MeV the dataset is an extremely pure sample of solar neutrino elastic scattering events, owing primarily to the detector’s deep location, allowing an accurate measurement with relatively little exposure. In that energy region the best fit background rate is 0.25+0.09−0.07  events/kt−day, significantly lower than the measured solar neutrino event rate in that energy range, which is 1.03+0.13−0.12  events/kt−day. Also using data below this threshold, down to 5 MeV, fits of the solar neutrino event direction yielded an observed flux of 2.53+0.31−0.28(stat)+0.13−0.10(syst)×106  cm−2 s−1, assuming no neutrino oscillations. This rate is consistent with matter enhanced neutrino oscillations and measurements from other experiments

Current Status and Future Prospects of the SNO+ Experiment

SNO+ is a large liquid scintillator-based experiment located 2 km underground at SNOLAB, Sudbury, Canada. It reuses the Sudbury Neutrino Observatory detector, consisting of a 12 m diameter acrylic vessel which will be filled with about 780 tonnes of ultra-pure liquid scintillator. Designed as a multipurpose neutrino experiment, the primary goal of SNO+ is a search for the neutrinoless double-beta decay (0] ) of 130 Te. In Phase I, the detector will be loaded with 0.3% natural tellurium, corresponding to nearly 800 kg of 130 Te, with an expected effective Majorana neutrino mass sensitivity in the region of 55-133 meV, just above the inverted mass hierarchy. Recently, the possibility of deploying up to ten times more natural tellurium has been investigated, which would enable SNO+ to achieve sensitivity deep into the parameter space for the inverted neutrino mass hierarchy in the future. Additionally, SNO+ aims to measure reactor antineutrino oscillations, low energy solar neutrinos, and geoneutrinos, to be sensitive to supernova neutrinos, and to search for exotic physics. A first phase with the detector filled with water will begin soon, with the scintillator phase expected to start after a few months of water data taking. The 0] Phase I is foreseen for 2017

Reproducing kernels of harmonic Besov spaces on the ball

Cataloged from PDF version of article.Besov spaces of harmonic functions on the unit ball of Rn are defined by requiring sufficiently high-order derivatives of functions lie in harmonic Bergman spaces. We compute the reproducing kernels of those Besov spaces that are Hilbert spaces. The kernels turn out to be weighted infinite sums of zonal harmonics and natural radial fractional derivatives of the Poisson kernel. To cite this article: S. Gergün et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences