Sudden freeze - out vs continuous emission : duality in hydro - kinetic approach to A + A collisions

The problem of spectra formation in hydrodynamic approach to A+A collisions is discussed. It is analyzed in terms of the two different objects: distribution and emission functions. We show that though the process of particle liberation, described by the emission function, is, usually, continuous in time, the observable spectra can be also expressed by means of the Landau/Cooper-Frye prescription. We argue that such an approximate duality results from some symmetry properties that systems in A+A collisions reach to the end of hydrodynamic evolution and reduction of the collision rate at post hydrodynamic stage.