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.
Hale, Gerald Mallory (1970). A coupled channel model for four nucleons. Doctoral dissertation, Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -177882.