Abstract
Microscopic calculations of four-body scattering become very challenging in the energy regime above the threshold for four free particles. We consider mixed-isospin four-nucleon reactions initiated by the proton-3 H, neutron-3 He, or deuteron-deuteron collisions. We solve the Alt, Grassberger, and Sandhas equations for the four-nucleon transition operators in the momentum-space framework. The complex-energy method with special integration weights is applied to deal with the complicated singularities in the kernel of AGS equations. Results for the differential cross section and spin observables in elastic, charge-exchange, transfer, and breakup reactions using realistic potentials are presented.
Highlights
The four-nucleon (4N) continuum is an important “theoretical laboratory" for a quantitative test of the two-nucleon (2N) and three-nucleon (3N) interaction models
The reliability of all these methods was confirmed in a benchmark calculation [9] for neutron-3H (n-3H) and proton-3He (p-3He) elastic scattering observables
The symmetrized version for the four-particle transition operators Uβα is derived in ref. [7], where the nucleons are treated as identical particles in the isospin formalism, i.e., U11 = − (G0 t G0)−1P34 − P34U1G0 t G0 U11 + U2G0 t G0 U21, (1a)
Summary
The four-nucleon (4N) continuum is an important “theoretical laboratory" for a quantitative test of the two-nucleon (2N) and three-nucleon (3N) interaction models. Exact four-particle scattering equations have been formulated 50 years ago by Faddeev and Yakubovsky (FY) [1] and by Alt, Grassberger, and Sandhas (AGS) [2, 3]. In the last decade accurate numerical calculations for low-energy nucleon-trinucleon elastic scattering have been performed using both coordinate-space and momentum-space rigorous approaches, namely, the hyperspherical harmonics (HH) expansion method [4, 5], the Faddeev-Yakubovsky (FY) equations [1] for the wave function components [6], and the Alt, Grassberger and Sandhas (AGS) equations [3] for transition operators [7, 8].
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