  We derive a general relation in two-body scattering theory that more directly
relates the change of density of states (DDOS) due to interaction to the shape
of the potential. The relation allows us to infer certain global properties of
the DDOS from the global properties of the potential. In particular, we show
that DDOS is negative at all energies and for all partial waves, for potentials
that are more repulsive than $+1/r^2$ everywhere. This behavior represents a
different class of global properties of DDOS from that described by the
Levinson's theorem.
