Model the deuteron as a neutron and proton bound in a square well of range (a…

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

The Nucleus Resolved, Ch The deuteron and what two nucleons do to each other

Problem

Model the deuteron as a neutron and proton bound in a square well of range

R_{\rm w} = 1.9\,\mathrm{fm}

(a narrower range than the

2.1\,\mathrm{fm}

fitted from scattering data). Take the measured binding energy

B = 2.2246\,\mathrm{MeV}

, the reduced mass

\mu_{\rm red}c^2 = 469.46\,\mathrm{MeV}

, and

\hbar c = 197.327\,\mathrm{MeV\,fm}

. Using the matching condition

k_{\rm in}\cot(k_{\rm in}R_{\rm w}) = -\kappa

, with

\kappa = \sqrt{2\mu_{\rm red}B}/\hbar c

and local kinetic energy inside the well

V_0 - B = \hbar^2 k_{\rm in}^2/2\mu_{\rm red}

, find the well depth

V_0