The neutron-proton system binds in the spin-triplet channel

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

The neutron-proton system binds in the spin-triplet channel, with scattering length

a_t=+5.42\,\mathrm{fm}

, and does not bind in the spin-singlet channel, with

a_s=-23.7\,\mathrm{fm}

. A study group argues: "since

|a_s|

is more than four times

|a_t|

, the singlet channel must have the stronger nuclear force." Using the square-well depths at a common range of

2.1\,\mathrm{fm}

(triplet

33.7\,\mathrm{MeV}

, singlet

21.6\,\mathrm{MeV}

, both against a just-bound depth of

23.2\,\mathrm{MeV}

at this range), decide whether the claim is correct, and explain what the large magnitude of

a_s

actually reflects.