Abstract: Since the upsilon(tau) ((upsilon) over bar (tau))A(Z) -> tau(-/+) X reaction is notoriously difficult to be directly measured, the information on the dynamics of this nuclear process should be extracted from the analysis of the energy and angular distributions of the tau decay visible products. These distributions depend, in addition to d(2)sigma / (dE(tau)d cos theta(tau)), on the components of the tau-polarization vector. We give, for the first time, the general expression for the outgoing hadron (pion or rho meson) energy and angular differential cross section for the sequential upsilon(tau) A(Z) -> tau(-) (pi(-)upsilon(tau,) rho(-)upsilon(tau))X and (upsilon) over bar (tau)A(Z) -> tau(+) (pi(+)(upsilon) over bar (tau), rho(+)(upsilon) over bar (tau)) X reactions. Though all possible nuclear reaction mechanisms contribute to the distribution, it may be possible to isolate/enhance one of them by implementing appropriate selection criteria. For the case of the quasi-elastic reaction off oxygen and neutrino energies below 6 GeV, we show that the pion distributions are quite sensitive to the details of the tau-polarization components. We find significant differences between the full calculation, where the longitudinal and transverse components of the tau polarization vector vary with the energy and the scattering angle of the produced tau, and the simplified scheme in which the polarizations are set to one and zero, being the latter their respective asymptotic values reached in the high energy regime. In addition to its potential impact on neutrino oscillation analyses, this result can be used to further test different nuclear models, since these observables provide complementary information to that obtained by means of the inclusive nuclear weak charged-current differential cross section. We also study the effects on the cross section of the W-4 and W-5 nuclear structure functions, which contributions are proportional to the charged lepton mass, and therefore difficult to constrain in muon and electron neutrino experiments.

Abstract: In medicine, computed tomographic images are reconstructed from a large number of measurements of X-ray transmission through the patient (projection data). The mathematical model used to describe a computed tomography device is a large system of linear equations of the form AX = B. In this paper we propose the QR decomposition as a direct method to solve the linear system. QR decomposition can be a large computational procedure. However, once it has been calculated for a specific system, matrices Q and R are stored and used for any acquired projection on that system. Implementation of the QR decomposition in order to take more advantage of the sparsity of the system matrix is discussed.

Abstract: A method to improve light collection efficiency of gamma-ray imaging detectors by using retroreflector arrays has been tested, simulations of the behaviour of the scintillation light illuminating the retroreflector surface have been made. Measurements including retroreflector arrays in the setup have also been taken. For the measurements, positron emission tomography (PET) detectors with continuous scintillation crystals have been used. Each detector module consists of a continuous LSO-scintillator of dimensions 49x49x10 mm(3) and a H8500 position-sensitive photo-multiplier (PSPMT) from Hamamatsu. By using a continuous scintillation crystal, the scintillation light distribution has not been destroyed and the energy, the centroids along the x- and y-direction and the depth of interaction (DOI) can be estimated. Simulations have also been run taking into account the use of continuous scintillation crystals. Due to the geometry of the continuous scintillation crystals in comparison with pixelated crystals, a good light collection efficiency is necessary to correctly reconstruct the impact point of the gamma-ray. The aim of this study is to investigate whether micro-machine retro-reflectors improve light yield without misestimation of the impact point. The results shows an improvement on the energy and centroid resolutions without worsening the depth of interaction resolution. Therefore it can be concluded that using retroreflector arrays at the entrance side of the scintillation crystal improves light collection efficiency without worsening the impact point estimation.