New methodical developments for GRANIT

New methodical developments for the GRANIT spectrometer address further improvements of the critical parameters of this experimental installation, as well as its applications to new fields of research. Keeping in mind an extremely small fraction of ultra cold neutrons (UCN) that could be bound in gravitational quantum states, we look for methods to increase statistics due to: developing UCN sources with maximum phase-space density, counting simultaneously a large fraction of neutrons using position-sensitive detectors, and decreasing detector backgrounds. Also we explore an eventual application of the GRANIT spectrometer beyond the scope of its initial goals, for instance, for reflectometry with UCN. (authors)