Three-body description of direct nuclear reactions: Comparison with the continuum discretized coupled channels method

Abstract

The continuum discretized coupled channels (CDCC) method is compared to the exact solution of the three-body Faddeev equations in momentum space. We present results for: i) elastic and breakup observables of d+ 12 C at E d = 56 MeV, ii) elastic scattering of d+ 58 Ni at E d = 80 MeV, and iii) elastic, breakup and transfer observables for 11 Be+p at E11 Be /A = 38.4 MeV. Our comparative studies show that, in the first two cases, the CDCC method is a good approximation to the full three-body Faddeev solution, but for the 11 Be exotic nucleus, depending on the observable or the kinematic regime, it may miss out some of the dynamic three-body effects that appear through the explicit coupling to the transfer channel.

Theory of (d,p) and (p,d) reactions including breakup: Comparison of methods

“…Table I contains the parameters for all interactions used in this application, where V 0 , r 0 , and a 0 are the depth, radius, and diffuseness of the real part, respectively; W v , W d , r i , and a i are the depth of the volume and surface imaginary potentials and their radius and diffuseness, respectively. For p + 10 Be, we use an optical potential of Woods-Saxon shape, which reproduces elastic scattering at E lab /A = 39.1 MeV [38]. (In our formulation, the Hamiltonian is energy-independent; thus this is a reasonable choice for the reactions under study, although not unique.)…”

Improved description ofAr34,36,46(p,d) transfer reactio

“…Within the adiabatic approaches, for the neutron in the initial channel we use an effective real binding potential fitted to the spectrum of nucleus A whereas in the final state the nucleon optical potential contains absorption which reproduces elastic scattering. In previous Faddeev A(p,d)B calculations V nB was real in all partial waves [25,41] while V pB was complex with parameters corresponding to the A + p state. In the present work, Faddeev calculations take V nB to be real in the partial wave with the n + B bound state but in all other partial waves V nB is taken to be complex as in the adiabatic approach in the final state.…”

“…The numerical details of solving AGS equations with potentials of general form can be found in [44,45]. Since elastic scattering, transfer, and breakup are treated on equal footing, the Faddeev/AGS framework yields the most accurate solution to the general three-body problem where all channels (elastic, transfer and breakup) are fully coupled; it already has provided important tests to other methods commonly used in reaction theory [25,46,47].…”

“…Examples include the study of optical potential uncertainties [20], the effect of the reaction mechanism [21], the uncertainties in the single particle state [22,23], the description of the deuteron continuum [24] and the inclusion of full three-body dynamics in the reaction [25].…”

Analytical transformed harmonic oscillator basis for continuum discretized coupled channels calculations

“…As a first application of the method, we consider the reaction d + 58 Ni at 80 MeV, which has been the subject of many studies in the past [3,[35][36][37]. Following our previous work [27], the proton-neutron (pn) interaction is parametrized in terms of the Poeschl-Teller potential,…”