A coupled channel model for four nucleons

Abstract

A charge-independent model is developed for describing the two-body scattering processes possible in a system of four nucleons. When the model wavefunction and Hamiltonian are inserted in Schrodinger's equation, coupled differential equations result for the radial functions associated with the two-body channels of the system. One need only specify a matrix of effective "potentials" to solve these equations, and to obtain scattering observables for all the two-body processes in the four-nucleon system.A simple parameterization using square-well shapes is tried for the elements of the effective potential matrix. The resulting twelve parameters are varied by a numerical search method to achieve the best fit to differential cross-sections for the reactions T(n,n)T, T(p,p)T, T(p,n)He³ , He³ (n,n)He³ , D(d,p)T, D(d,n)He³ , and D(d,d)D, at a single center-of-mass energy. A good qualitative fit to both the differential cross-sections and polarizations for all the reactions is obtained at the searched energy. Consideration of the calculated cross-sections and polarizations for the reactions at other energies indicates that the simple parameterization used does not reproduce very well the energy dependence of the scattering observables.