Momentum-space treatment of the Coulomb interaction in three-nucleon reactions with two protons

Abstract

The Coulomb interaction between the two protons is included in the calculation of proton-deuteron elastic scattering, radiative proton-deuteron capture and two-body electromagnetic disintegration of 3 He. The hadron dynamics is based on the purely nucleonic charge-dependent (CD) Bonn potential and its realistic extension CD Bonn + ∆ to a coupled-channel two-baryon potential, allowing for single virtual ∆-isobar excitation. Calculations are done using integral equations in momentum space. The screening and renormalization approach is employed for including the Coulomb interaction. Convergence of the procedure is found already at moderate screening radii. The reliability of the method is demonstrated. The Coulomb effect on observables is seen at low energies for the whole kinematic regime. In proton-deuteron elastic scattering at higher energies the Coulomb effect is confined to forward scattering angles; the ∆-isobar effect found previously remains unchanged by Coulomb. In electromagnetic reactions Coulomb competes with other effects in a complicated way.

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

“…Observables of elastic scattering are calculated from the matrix elements with β = α, those of breakup are given by β = 0 while 0 = β = α correspond to transfer reactions. Although the original AGS equations were derived for short-range potentials, the Coulomb interaction can be included using the method of screening and renormalization [43]. The numerical details of solving AGS equations with potentials of general form can be found in [44,45].…”

Vector analyzing powers of deuteron-proton elastic scattering and breakup at 130 MeV

“…These two effects usually compete, and therefore * izabela.ciepal@uj.edu.pl the net effects of including the isobar in the potential are smaller than for approaches with the phenomenological 3NF's. When the chiral perturbation theory (ChPT) is used at the next-to-next-to-leading order (NNLO), the 3N contributions arise naturally, fully consistently with the NN force terms [4].The long-range electromagnetic component of the NN interaction was successfully implemented in CC formalism [5,6] as well as in the calculations [7] based on the AV18 NN potential combined with the Urbana IX 3NF.Besides the binding energies of the light nuclei, the importance of the 3NF was experimentally confirmed on the basis of the data originating from the nucleon-deuteron elastic scattering process [8][9][10][11][12][13][14][15][16][17]. In general, inclusion of the 3NF component improves the description of the cross-sectional data.…”

Four-nucleon scattering: a new numerical approach

“…1. Finally we use the method developed for pd elastic scattering [2,3] to include the Coulomb interaction between the protons. This means using the two-potential formula…”

“…They are the A y puzzle in elastic Nd scattering and the space star anomaly in Nd breakup, just to name a few. These problems persist even when the Coulomb interaction is added [1,2,3] and seem to be insensitive to the choice of realistic 2N + 3N force model. As it has already been highlighted in the past [4,5,6], the four-nucleon scattering problem reveals further discrepancies between theory and experiment that need clarification in terms of improved calculations using modern force models and efficient numerical algorithms that allow for a numerically converged solution of the Alt, Grassberger and Sandhas (AGS) equation [7] for the transition operators.…”

“…Given the success recently achieved in including the Coulomb interaction in pd elastic scattering and breakup [2,3], we generalize the proposed method to the four-nucleon system and study p 3 He below three-body breakup threshold.…”