WHAT IS WRONG WITH THE BETHE-FORMULA FOR THE NUCLEAR LEVEL-DENSITY - MEASURABLE DIFFERENCES BETWEEN GRANDCANONICAL AND THE MICROCANONICAL TREATMENTS

The familiar Bethe formula is the leading term (is-proportional-to vol ume) in an asymptotic leptodermous expansion of the nuclear level-dens ity for very large neutron (N), proton (Z) number, and excitation ener gy E. It is shown that for realistic finite nuclei it has a wrong dep endence on mass and energy by which the internal phase-space for the s plit of a heavier nucleus into two similar pieces is reduced. This lea ds e.g. to a substantial and - measurable - suppression of statistical fragmentation into larger fragments of intermediate mass which contra dicts to existing data of multifragmentation. Consequently one cannot extrapolate the level-density with the Bethe formula beyond the region of experimental control even if various higher leptodermous correctio ns are incorporated.