Someone argues: "The liquid-drop model gets the fission value right to within a few…

PHYSICS · Subjective · Fermi University Physics · Nuclear Physics · The nuclear force and nuclear models · Fission, fusion and nuclear energy

The Nucleus Resolved, Ch Fission: the double-humped barrier and the shells the drop cannot see

Problem

Someone argues: "The liquid-drop model gets the

{}^{235}\mathrm{U}

fission

Q

value right to within a few MeV out of about

200\,\mathrm{MeV}

, an accuracy of order 1%. The same model's fission barrier for

{}^{240}\mathrm{Pu}

E_f^{\rm bar} = 4.3\,\mathrm{MeV}

from the fissility parameter. Since the model is accurate to 1%, this barrier must also be correct to about

0.04\,\mathrm{MeV}

, so the true barrier lies between

4.26

and

4.34\,\mathrm{MeV}

." Find the error in this reasoning, and quote the measured inner barrier for comparison.