  A non-interacting electron gas on a one-dimensional ring is considered at
finite temperatures. The localized spin is embedded at some point on the ring
and it is assumed that the interaction between this spin and the electrons is
the exchange interaction being the basis of the Ruderman-Kittel-Kasuya-Yosida
indirect exchange effect. When the number of electrons is large enough, it
turns out that any small but finite interaction radius value can always produce
an essential change of the spin density oscillations in comparison with the
zero interaction radius traditionally used to model the
Ruderman-Kittel-Kasuya-Yosida effect.
