For a nucleus with (mid-mass

PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Nuclear Physics · 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

For a nucleus with

A = 120

(mid-mass, similar to tin), estimate the excitation energy

\epsilon - \epsilon_F

above the Fermi surface

\epsilon_F = 37\,\mathrm{MeV}

at which the Pauli-blocked mean free path first becomes smaller than the nuclear diameter. Use the same unblocked path

\lambda_0 \approx 0.45\,\mathrm{fm}

, the near-surface blocking factor

[(\epsilon-\epsilon_F)/\epsilon_F]^2

, and

R = 1.2\,A^{1/3}\,\mathrm{fm}

for the nuclear radius. This locates, for a nucleus of this size, where the independent-particle picture starts to fail.