We consider the M -> 0 limit for tagged particle diffusion in a
1-dimensional Rayleigh-gas, studied originaly by Sinai and
Soloveichik, and by Szasz and Toth. In this limit we derive
a new type of model for tagged particle diffusion, for which the two 
central particles, in addition to elastic collisions with the rest of
the gas, interact with Calogero-Moser-Sutherland (i.e. inverse quadratic) 
potential. Computer simulations on this new model reproduce exactly the 
numerical value of the limiting variance obtained by Boldrighini, Frigio 
and Tognetti.