Rapid convergence of the Weinberg expansion of the deuteron stripping amplitude

Abstract

Theories of (d, p) reactions frequently use a formalism based on a transition amplitude that is dominated by the components of the total three-body scattering wave function where the spatial separation between the incoming neutron and proton is confined by the range of the n-p interaction, V np . By comparison with calculations based on the continuum discretized coupled channels method we show that the (d, p) transition amplitude is dominated by the first term of the expansion of the three-body wave function in a complete set of Weinberg states. We use the 132 Sn(d, p) 133 Sn reaction at 30 and 100 MeV as examples of contemporary interest. The generality of this observed dominance and its implications for future theoretical developments are discussed.

Implications for(d,p)reaction theory from nonlocal dispersive optical model analysis ofCa40(d,pWaldecker1, Timofeyuk2 2016Phys. Rev. CSelf Cite201251View full textAdd to dashboardCite

“…Following Johnson-Tandy [2] we retain only the first Weinberg component of the A + n + p system in the (d, p) transfer amplitude since this amplitude is sensitive only to those parts of this wave function in which the neutron n is close to the proton p. Recently, exact continuum-discretized coupled channel calculations confirmed that this component indeed dominates [26]. The first Weinberg component is a product of the deuteron wave function φ 0 (r) times the d − A relative motion wave function χ(R) which is the solution of the twobody Schrödinger equation with an adiabatic potential constructed from p − A and n − A optical potentials.…”

Surface-integral formalism of deuteron stripping

“…These constraints follow from the ones in the original matrix element (33). Replacing the exact scattering wave function Ψ has not yet been reached.…”

“…The first correct proof of Eq. (49) was presented by Goldberger and Watson [29] and extensively used by Johnson and coworkers in the formulation of the ADWA and its applications [26,[30][31][32][33].…”

“…As we mentioned, it allows one to approximate the CDCC wave function by the first term of the Weinberg states expansion [33] and this significantly simplifies the calculation of the initial state scattering wave function.…”

Optical model potential for deuteron elastic scattering with1p-shell nuclei

“…In three-body models of the (d, p) and (p, d) reactions proton and neutron potentials are used instead of the deuteron-target potentials [25][26][27]. The deuteron-target OMPs are necessary in many other reactions, for instance, the ( 3 He, d) reactions, for which the distorted wave Born approximation is usually still valid [28,29].…”