  The original Calogero and Sutherland models describe N quantum particles on
the line interacting pairwise through an inverse square and an inverse
sinus-square potential. They are well known to be integrable and solvable. Here
we extend the Calogero and Sutherland Hamiltonians by means of new interactions
which are PT-symmetric but not self adjoint. Some of these new interactions
lead to integrable PT-symmetric Hamiltonians; the algebraic properties further
reveal that they are solvable as well. We also consider PT-symmetric
interactions which lead to a new quasi-exactly solvable deformation of the
Calogero and Sutherland Hamiltonians.
