Calculation of Proton-Deuteron Elastic Scattering at 10 MeV with a Realistic Potential

Abstract

We present the first results of a calculation of the differential cross section and of polarization observables for proton-deuteron elastic scattering at 10 MeV proton laboratory energy, for the Paris potential. The method used is the "screening and renormalization approach" which allows one to correctly take into account the Coulomb repulsion between the two protons. Comparison is made with the precise experimental data of Sagara et al. [Phys. Rev. C 50, 576 (1994)] and of Sperison et al. [Nucl. Phys. A422, 81 (1984)]. [S0031-9007(98)07756-4] PACS numbers: 25.10. + s, 03.65.Nk, 25.40.Cm During the past decade, the theoretical calculation of neutron-deuteron ͑nd͒ scattering observables has become feasible using the most up-to-date models of the nucleonnucleon ͑NN͒ interaction including three-nucleon forces [1]. The goal behind this endeavor is to get a better understanding of interesting physical phenomena such as three-nucleon forces and off-shell behavior of the nuclear interaction; but also signatures of the quark substructure may be obtainable. Furthermore, extraction of NN on-shell information which is difficult to deduce from NN scattering experiments could be possible. Such expectations are, however, to be confronted with the experimental situation which for neutrons as projectiles is rather unsatisfactory: despite great efforts, the available data are sparse and of an accuracy which as yet does not allow one to meaningfully differentiate between all of the various theoretical assumptions entering the calculations.For the proton-induced reaction ͑pd͒, on the other hand, a rich body of accurate data is available and is still being continuously expanded. There, however, the theoretical situation has been unsatisfactory until now. Either, when being of similar sophistication as in the nd case, reliable calculations had to be confined to energies below the deuteron breakup threshold [2,3] or, when performed at positive energies, had to resort to a simple ansatz for the nuclear interaction [4]. But the few cases where experiments have been performed for the nd and the pd reaction, for the same observable, at the same energy, clearly show that the presence of the Coulomb force in the latter case, in general, modifies the observables appreciably. Hence, the standard procedure of comparing "realistic" nd calculations with pd data must be considered unsatisfactory in that the expected (smaller) effects of the above-mentioned interesting topics might be more or less veiled by the neglected Coulomb effects.Thus, in order to make adequate use of the high precision pd data it is of foremost importance to reliably estimate the influence of the Coulomb repulsion between the two protons, for all energies, with realistic nuclear forces.In this paper, we present the first results obtained along these lines for various pd elastic scattering observables, at an energy above the deuteron breakup threshold. For our calculations we use the screening and renormalization approach [5,6] (for a recent review, see [7]) as formulate...

Proton-deuteron elastic scattering from 2.5 to 22.7 MeV

“…For this reason we have performed calculations with the realistic Paris potential. First results have been published recently [27,28]. Here, we present some extended calculations of differential cross sections and various polarisation observables for elastic pd scattering.…”

“…Recently we have communicated the first successful calculation of proton-deuteron scattering observables for the Paris potential using this same approach [27,28]. Here, results for many more energies will be presented and compared with experimental data.…”

Low-Energy Proton-Deuteron Scattering with a Coulomb-Modified Faddeev Equation

“…[15,16] is that we express the Faddeev equation as an integral equation in coordinate space, and then, solve the equation with an iterative method, which we called the Method of Continued Fractions [17,18]. This is in contrast with some different approaches proposed so far to accommodate the Coulomb force in three-nucleon (3N) continuum calculations: the screening and renormalization approach in momentum space Faddeev integral equations [19,20,21,22], the partial differential equation approach in configuration space [23,24,25], the three-potential formalism with the Coulomb-Sturmian separable expansion method [26], the Kohn variational method with the Pair-correlated Hyperspherical Harmonic (PHH) basis [27,28].…”

Faddeev equations and the method of hyperspherical harmonics in the problem of three-nucleon continuum

“…If Eq. (47) is rewritten as follows: (49) then, it is seen that upon "switching off" nuclear inter actions between particle 1 and two others (i.e., at V 12 = V 31 = 0) the solution to the following equation (50) will be given by the function Ψ = χ (23) . This is also seen from initial equations (39) and (40), because here we have:…”

“…Note that in [48], where Faddeev equations were solved in the momen tum representation for an analogous problem of pd scattering, it was found that for the screening radius varied within the limits from 100 to 2000 fm the calcu lated scattering phase shifts differ by no more than 1%. In [49] while computing the cross sections of pd scat tering (E p = 10 MeV) with Lippmann-Schwinger equations and separable Paris potential PEST 1-6 used, the screening radius was also 100 fm increasing up to 300 fm in the calculations of polarization char acteristics. To calculate the phase shifts of pd scattering let us apply the procedure described above.…”