Dhe. Gross et R. Heck, WHAT IS WRONG WITH THE BETHE-FORMULA FOR THE NUCLEAR LEVEL-DENSITY - MEASURABLE DIFFERENCES BETWEEN GRANDCANONICAL AND THE MICROCANONICAL TREATMENTS, Physics letters. Section B, 318(3), 1993, pp. 405-409
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.