The measured neutron separation energies of two zirconium isotopes bracketing the…

PHYSICS · Subjective · Fermi University Physics · Nuclear Physics · The nuclear force and nuclear models · The nuclear force and nuclear models

The Nucleus Resolved, Ch The shell model: a mean field, a spin-orbit term and the magic numbers

Problem

The measured neutron separation energies of two zirconium isotopes bracketing the

N=50

shell closure are

S_n(^{90}\mathrm{Zr}) = 11.97\,\mathrm{MeV}

and

S_n(^{91}\mathrm{Zr}) = 7.19\,\mathrm{MeV}

. Using the same method used for the

N=126

gap in lead, estimate the size of the

N=50

shell gap in zirconium.