Monte Carlo estimates of multiple scattering in neutron spectroscopy: an efficient algorithm

The substantial upgrade in new generation reactor-based time-of-flight (ToF) spectrometers lies in their hugely increased detection area. For such instruments, the strong improvement is clearly the high neutron-collection power, and with this the count statistics achievable in relatively short times. Dealing with thousands of time channels and several tens of thousands of detection pixels is, however, quite punishing as soon as data handling and correction for various effects in real-geometry conditions are considered. Anisotropic multiple scattering evaluation, even in an approximate way, is surely the most demanding step in the general treatment of inelastic neutron data, and becomes a very hard task when "extreme" conditions are further imposed by a widely-extended detection geometry, as that typical of new or upgraded neutron ToF spectrometers such as BRISP, IN4C or IN5 at the Institut Laue Langevin in Grenoble. For this reason, we refreshed our approach to multiple scattering calculations, in order to obtain reasonably accurate real-geometry results in nearly real-time conditions. Our new code, though conceptually originating from a long standing experience of Monte Carlo (MC) integration techniques to extract (unnormalized) double and single scattering intensities, is now made particularly efficient in computing time both by a careful application of the "importance sampling" method used to calculate some of the required MC integrals, and by the choice of programming languages which allow for a heavy but efficient use of matrix algebra. The fast matrix manipulation performances offered by some languages thus allow to avoid the (far slower) nested-loop logic required by more traditional languages. The concepts at the basis of the algorithm and several implementation details are presented.