  The kinetics of geminate subdiffusion-assisted reactions (SDARs) of
interacting particles is analyzed in detail with the use of the non-Markovian
fractional Smoluchowki equation (FSE). It is suggested that the interparticle
interaction potential is of the shape of potential well and reactivity is
located within the well. The reaction kinetics is studied in the limit of deep
well, in which the FSE can be solved analytically. This solution enables one to
obtain the kinetics in a simple analytical form. The analytical expression
shows that the SDAR kinetics fairly substantially depends on the mechanism of
reactivity within the well. Specific features of the kinetics are thoroughly
analyzed in two models of reactivity: the subdiffusion assisted activated rate
model and the first order reaction model. The theory developed is applied to
the interpretation of experimental kinetics of photoluminescence decay in
amorphous $a$-Si:H semiconductors governed by geminate recombination of
electrons and holes which are recently found to undergo subdiffusive relative
motion. Analysis of results demonstrates that the subdiffusion assisted
activated rate mechanism of reaction is closer to reality as applied to
amorphous $a$-Si:H semiconductors. Comparison of experimental and theoretical
kinetics allowed for obtaining some kinetic parameters of the systems under
study: the rate of escaping from the well and the parameter characterizing the
deviation of the subdiffusive motion from the conventional one.
