Discretization methods of the breakup continuum in deuteron-nucleus collisions

Two methods of discretization of the s-wave n-p breakup continuum are compared, and their effect on the elastic deuteron-nucleus scattering matrix elements is numerically investigated. In one of the methods, the continuum eigenstates of the n-p Hamiltonian are averaged over discretized momentum bins of size Δk. In the other, which is a form of the $L^2$ diagonalization method, the continuum is expanded in a set of normalizable basis functions, which physically correspond to placing the n-p potential into a box. It is found, in the case of ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$(d,d) at incident deuteron energies $E_d$=21.6 and 45 MeV, that those two discretization techniques consistently display the same physics and yield the same results. However, the lower the incident deuteron energy, the less well do the momentum discretized answers converge to a final result. The diagonalization method is found to perform better in this respect. The theoretical expectation that the long range tails of the potentials in breakup space do not sensitively affect the elastic S-matrix elements is demonstrated numerically. This result provides the mathematical reason why the discretization of the breakup continuum is a viable and practical procedure of including the breakup effects.