Fractional Reaction-Diffusion Equation

A fractional reaction-diffusion equation is derived from a continuous time random walk model when the transport is dispersive. The exit from the encounter distance, which is described by the algebraic waiting time distribution of jump motion, interferes with the reaction at the encounter distance. Therefore, the reaction term has a memory effect. The derived equation is applied to the geminate recombination problem. The recombination is shown to depend on the intrinsic reaction rate, in contrast with the results of Sung et al. [J. Chem. Phys. {\bf 116}, 2338 (2002)], which were obtained from the fractional reaction-diffusion equation where the diffusion term has a memory effect but the reaction term does not. The reactivity dependence of the recombination probability is confirmed by numerical simulations.Comment: to appear in Journal of Chemical Physic

Dispersive diffusion controlled distance dependent recombination in amorphous semiconductors

The photoluminescence in amorphous semiconductors decays according to power law $t^{-delta}$ at long times. The photoluminescence is controlled by dispersive transport of electrons. The latter is usually characterized by the power $alpha$ of the transient current observed in the time-of-flight experiments. Geminate recombination occurs by radiative tunneling which has a distance dependence. In this paper, we formulate ways to calculate reaction rates and survival probabilities in the case carriers execute dispersive diffusion with long-range reactivity. The method is applied to obtain tunneling recombination rates under dispersive diffusion. The theoretical condition of observing the relation $delta = alpha/2 + 1$ is obtained and theoretical recombination rates are compared to the kinetics of observed photoluminescence decay in the whole time range measured.Comment: To appear in Journal of Chemical Physic

Design and construction of a new detector to measure ultra-low radioactive-isotope contamination of argon

Large liquid argon detectors offer one of the best avenues for the detection of galactic weakly interacting massive particles (WIMPs) via their scattering on atomic nuclei. The liquid argon target allows exquisite discrimination between nuclear and electron recoil signals via pulse-shape discrimination of the scintillation signals. Atmospheric argon (AAr), however, has a naturally occurring radioactive isotope, 39Ar, a β emitter of cosmogenic origin. For large detectors, the atmospheric 39Ar activity poses pile-up concerns. The use of argon extracted from underground wells, deprived of 39Ar, is key to the physics potential of these experiments. The DarkSide-20k dark matter search experiment will operate a dual-phase time projection chamber with 50 tonnes of radio-pure underground argon (UAr), that was shown to be depleted of 39Ar with respect to AAr by a factor larger than 1400. Assessing the 39Ar content of the UAr during extraction is crucial for the success of DarkSide-20k, as well as for future experiments of the Global Argon Dark Matter Collaboration (GADMC). This will be carried out by the DArT in ArDM experiment, a small chamber made with extremely radio-pure materials that will be placed at the centre of the ArDM detector, in the Canfranc Underground Laboratory (LSC) in Spain. The ArDM LAr volume acts as an active veto for background radioactivity, mostly γ-rays from the ArDM detector materials and the surrounding rock. This article describes the DArT in ArDM project, including the chamber design and construction, and reviews the background required to achieve the expected performance of the detector