Test of bound-state approximations in a three-body model of rearrangement collisions

Abstract

A common approximation in atomic, molecular, and nuclear rearrangement processes is to neglect $n$-body breakup contributions ($n\ensuremath{\ge}3$) by replacing the full wave function by (sums of) product wave functions, each of which is related to a specific asymptotic arrangement channel. We test this bound-state approximation in a simple three-body model of nuclear stripping by comparing bound-state approximation calculations with exact and distorted-wave Born-approximation-type calculations. Calculated are the stripping and elastic amplitudes and cross sections for deuteron energies ${E}_{d}=1.78, 6.7, 11.2, \mathrm{and} 15.12$ MeV. The bound-state approximation is best below the breakup threshold (${E}_{\mathrm{BU}}=2.225$ MeV), where it provides an excellent fit in the forward direction and a qualitative fit over the whole angular range. For ${E}_{d}=6.7$ MeV the breakup cross section is still very small; however, the intermediate continuum states already play an important role and the bound-state approximation becomes quite poor. At this energy the distorted-wave Born approximation-type calculation, which is based on exact elastic wave functions and therefore accounts partly for the continuum, is still quite good. For the two higher energies both continuum and multistep effects appear to be very important, rendering both distorted-wave Born approximation and bound-state approximation poor approximations outside the forward region. The qualitative features of the elastic cross sections are explained in terms of the momentum dependence of the bound-state wave functions and two-body $T$ matrices.NUCLEAR REACTIONS Quality of DWBA and bound-state approximations; Three-body methods; Model ($d$,$p$) calculations at ${E}_{d}=1.7\ensuremath{-}15$ MeV; Multistep effects