  There are surface modes on the Bose-Einstein condensed Na atoms so that the
number of vortices diverges when the stirring frequency becomes equal to that
of the surface waves. We introduce the finite life time of the surface modes so
that the number of vortices becomes finite. Usually the number of vortices is a
linear function of the stirring frequency. We find that this linearity is
destroyed by the finite life time and a peaked function emerges with several
peaks, one for each surface mode. The vortices become normal, as they should
be, so that there occurs a phase transition from normal to the superfluid
state.
