At (laboratory energy)

PHYSICS · Multi-part · 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

At 150 MeV150\,\mathrm{MeV} (laboratory energy), npnp scattering shows triplet PP-wave phase shifts δ(3P0)=+3.7∘\delta(^3P_0)=+3.7^\circ, δ(3P1)=−17.5∘\delta(^3P_1)=-17.5^\circ, δ(3P2)=+13.8∘\delta(^3P_2)=+13.8^\circ, all with L=1L=1, S=1S=1. ((a)) Using antisymmetry, (−1)L+S+T=−1(-1)^{L+S+T}=-1, determine the isospin TT required for an L=1L=1, S=1S=1 two-nucleon state. ((b)) Two protons must also have T=1T=1 (from Tz=−1T_z=-1). Predict, using charge independence (dependence on TT, not TzT_z), what proton-proton 3P0^3P_0, 3P1^3P_1, 3P2^3P_2 phase shifts at the same energy should look like once the Coulomb interaction between the two protons has been removed, and explain why this comparison is a genuine test of charge independence whereas comparing the deuteron's 3S1^3S_1-3D1^3D_1 channel to a hypothetical pppp analogue would not be.

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