Optical background measurement in a potential site for the NEMO KM undersea neutrino telescope

We describe the measurement of the deep sea optical background in some sites south of Capo Passero, Sicily. A continuous flux of about 440 photons cm ^-2 s ^-1 in the wavelength interval 440-550 nm is estimated due to the decays of the ⁴⁰K contained in the sea water. Bioluminescence light bursts are also observed and an example of time evolution is reported. All the measurements were accomplished using a deep sea module also described in this article. Received: 20 April 2002 / Published online: 26 July 2002     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Smoothing minimally supported frequency wavelets: Part II

The main purpose of this paper is to give a procedure to “mollify” the low-pass filters of a large number ofMinimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA. Hence, we are able to approximate (in the L ² -norm) MSF wavelets by wavelets with any desired degree of smoothness on the Fourier transform side. Although the MSF wavelets we consider are bandlimited, this may not be true for their smooth approximations. This phenomena is related to the invariant cycles under the transformation x ↦2x (mod2π). We also give a characterization of all low-pass filters for MSF wavelets. Throughout the paper new and interesting examples of wavelets are described.     

Time-scale and excitation energy partition in sequential binary decays induced by heavy-ion collisions at ≃6 MeV·A

We studied the sequential binary decay of the systems ³²S+⁴⁵Sc, ⁷⁶Ge, ⁸⁹Y, ⁵⁹Co, ⁶³Cu and ¹⁹F+⁶³Cu induced by collisions at ≃6 MeV·A. The two stages of the process have reaction-times compatible with the dynamics of different mechanisms. The study of the excitation energy partition shows that the reaction mechanism of the first step has influence on the de-excitation of the primary fragments producing two decay components which have different time scale. Received: 25 March 1997 / Revised version: 2 December 1997