Estimate the minimum depth of a spherical square well of range needed to bind a first…

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Central potentials and canonical three-dimensional systems · Central potentials and canonical three-dimensional systems

The Structure of Quantum Mechanics, Ch Central potentials as a rotation problem

Problem

Estimate the minimum depth V0V_0 of a spherical square well of range a=1.8 fma = 1.8\,\mathrm{fm} needed to bind a first l=1l=1 nucleon-nucleon state, treating the two nucleons (each of mass mpc2≈938 MeVm_pc^2 \approx 938\,\mathrm{MeV}) with reduced mass μc2=mpc2/2\mu c^2 = m_pc^2/2. Take ℏc=197 MeV fm\hbar c = 197\,\mathrm{MeV\,fm} and use the l=1l=1 binding threshold V0a2>π2ℏ2/2μV_0a^2 > \pi^2\hbar^2/2\mu.

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