Applications of Three-Body Methods to Many-Body Hadronic Systems

Continuum discretization methods in a composite particle scattering off a nucleus: Benchmark calculations

“…On the other hand, the very close agreement between the conventional CDCC approach and the fully alternative wavepacket integral method should remove any doubts reported in literature [16,18] concerning the reliability and convergence properties of the Schrödinger coupled-channel scheme in the framework of the three-body scattering problem.…”

“…This approach has been successfully applied in the field of nuclear reactions to find the scattering amplitudes of many particular processes for various types of projectiles such as deuterons, 6 Li, 6 He, 7 Li, 12 C, etc. However, a strong discussion about the validity of the method arose [16][17][18] because of some unclear issues related to the treatment of the total wave function breakup components in the asymptotic region. So, to check the accuracy and reliability of the results attained within this approach, the convergence of the elastic and breakup amplitudes (with variation of the momentum bin widths and their number) was studied in detail for various approximation schemes [9].…”

“…So, the three-body wave function for the ith excited channel has an outgoing asymptotic behavior, i.e., Therefore above the three-body breakup threshold, the total wave function (r, R) vanishes at r → ∞ (similar to the bound-state function), while the dependence of the total scattering wave function upon the projectile center-of-mass coordinate has the pure outgoing wave asymptotic behavior. Such an asymmetry for the motions along the two coordinates at energies above the breakup threshold appears to be not fully justified [16][17][18], because in this energy region the proper asymptotic behavior over all spatial variables might be important. However, for the scattering of a weakly bound projectile (e.g., deuteron or 7 Li) at relatively high incident energies (E > ∼ 40 MeV), the motion along the projectile c.m.…”

Coupled channels approach to the deuteron break-up in the field of a nucleus

“…This procedure leads us to suggest a method for inclusion of the Coulomb distortion in the break-up channel. The respective cross sections are determined consistently in this approximation, and reliability tests of these methods become more stringent because a closer comparison with three-body calculation should be possible [1]. The underlying physical model we use is simple and essentially the same as in the work of the authors mentioned 9 Proton and neutron are assumed to interact via a two-body force.…”

“…It has often been argued that for higher deuteron energies, the increasing difficulties with the application of the DWBA may, to a major part, be due to the inadequate treatment of effects arising from the break-up of the deuteron in the field of a nucleus. As the deuteron appears to be a weakly bound system for average nuclear interaction energies, the description leads-even in the reduced version where internal degrees of freedom of the nucleus are neglected-to essentially a three-body problem, and considerable work has been done along the lines of Faddeev theory [1]. Because of the numerical difficulties associated with a three-body description, one is led to consider such formulations (one specific example is outlined below) where the deuteron-nucleus system is reduced to an effective two-body problem resulting in a set of coupled equations for the center-of-mass wave function of the p-n system (for a DWBA approach see e.g.…”