What is wrong with the Bethe-formula for the nuclear level-density? measurable differences between grandcanonical and the microcanonical treatments

Abstract

The familiar Bethe formula is the leading term (∝ volume) in an asymptotic leptodermous expansion of the nuclear level-density for very large neutron ( N), proton ( Z) number, and excitation energy E ∗ . It is shown that for realistic finite nuclei it has a wrong dependence on mass and energy by which the internal phase-space for the split of a heavier nucleus into two similar pieces is reduced. This leads e.g. to a substantial and - measurable - suppression of statistical fragmentation into larger fragments of intermediate mass which contradicts 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 corrections are incorporated.