Three-body to three-body elastic scattering using hyperspherical harmonics

The technique of hyperspherical harmonics is used in the calculation of elastic scattering of three nucleons, $N+N+N\to N+N+N$. The calculation is done within the context of rigorous treatment of spin-isospin variables involved in the system and standard three-body theory. We obtain formulas for the differential cross section and total cross section for the scattering channel characterized by total orbital angular momentum unity, negatve parity, total spin ½, and total isospin $\frac{3}{2}$. The calculation of this specific scattering channel is investigated by analyzing the uncoupled channel, grand orbital $L=1\mathrm{}$ and the coupled channel, grand orbital $L=1.3\mathrm{}$ Two model calculations for spin-independent and spin-dependent two-body potentials of the total cross section are presented for both uncoupled and coupled channels. The convergence of the hyperspherical harmonic expansion of the wave function is discussed.