A nucleon inside a nucleus with mass number (a typical fission fragment) occupies a…

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

A nucleon inside a nucleus with mass number A=90A = 90 (a typical fission fragment) occupies a single-particle state 15 MeV15\,\mathrm{MeV} above the Fermi energy ϵF=37 MeV\epsilon_F = 37\,\mathrm{MeV}. Take the unblocked mean free path as λ0=1/(ρ0σ)≈0.45 fm\lambda_0 = 1/(\rho_0\sigma) \approx 0.45\,\mathrm{fm}, using ρ0=0.16 fm−3\rho_0 = 0.16\,\mathrm{fm^{-3}} and an average free nucleon-nucleon cross section σ≈14 fm2\sigma \approx 14\,\mathrm{fm^2}. Estimate the Pauli-blocked mean free path using the near-surface blocking factor [(ϵ−ϵF)/ϵF]2[(\epsilon-\epsilon_F)/\epsilon_F]^2 (the ratio here is not small, so treat the result as an order of magnitude), and compare it with the nuclear diameter (take the equivalent sharp radius R=1.2 A1/3 fmR = 1.2\,A^{1/3}\,\mathrm{fm}) to judge whether treating this nucleon as an independent particle moving in a smooth field is reasonable at this excitation.

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