A postgraduate note contains this working: "The deuteron is a bound state

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

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

Problem

A postgraduate note contains this working: "The deuteron is a bound state, so its scattering length must be negative. From the binding energy

B=2.2246\,\mathrm{MeV}

and the reduced mass

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

\kappa=\sqrt{2\mu_{\mathrm{red}}B}/\hbar c=0.2316\,\mathrm{fm^{-1}}

, so

1/\kappa=4.32\,\mathrm{fm}

, and therefore the triplet scattering length is

a_t=-4.32\,\mathrm{fm}

." Find the error, and give the correct sign, and (using the measured effective range

r_{e,t}=1.75\,\mathrm{fm}

and the effective-range expansion

1/a=\kappa-\tfrac{1}{2}r_e\kappa^2

) the correct value of

a_t

to compare with the measured

+5.42\,\mathrm{fm}