Four-body calculation of ${}^2\mathbf{H}(d,p){}^3\mathrm{H}$ and ${}^2\mathrm{H}(d,n){}^3\mathrm{He}$ reactions above breakup threshold

Nucleon transfer reactions in deuteron-deuteron collisions at energies above the three- and four-body breakup threshold are described using exact four-body equations for transition operators that are solved in the momentum-space framework. Differential cross sections, analyzing powers, polarizations, and spin transfer coefficients are obtained using realistic two-nucleon potentials and including the Coulomb repulsion between protons. Overall good agreement between predictions and experimental data is found. Most remarkable discrepancies are seen around the minima of the differential cross section at higher energies and in the outgoing nucleon polarization at lower energies.

Figure 1

Differential cross section for the ${}^2\mathrm{H}(d,p){}^3\mathrm{H}$ reaction as a function of the c.m. scattering angle at deuteron beam energies ranging from 5.0 to 25.3 MeV. Results are obtained using the INOY04 potential (solid curves) and, at 10.0 and 25.3 MeV, also the CD Bonn + $\mathrm{\Delta }$ (dashed-dotted curves), CD Bonn (dotted curves), and N3LO (double-dotted–dashed curves) potentials. Experimental data are from Refs. [20] and [21] (filled squares), Ref. [22] (open squares), and Ref. [23] (filled circles).

Figure 2

Differential cross section for the ${}^2\mathrm{H}(d,n){}^3\mathrm{He}$ reaction as a function of the c.m. scattering angle at deuteron beam energies ranging from 5.0 to 25.3 MeV. Curves are as in Fig. 1. Experimental data are from Refs. [24] (filled squares), Ref. [25] (crosses), Ref. [22] (open squares), Ref. [26] (filled triangles), and Ref. [23] (filled circles).

Figure 3

Deuteron analyzing powers for the ${}^2\mathrm{H}(d,p){}^3\mathrm{H}$ reaction at $E_d=5.5$, 7.0, 10.0, and 13.0 MeV. Curves are as in Fig. 1. Experimental data are from Ref. [21].

Figure 4

Deuteron analyzing powers for the ${}^2\mathrm{H}(d,n){}^3\mathrm{He}$ reaction at $E_d=5.5$, 7.0, 10.0, and 13.0 MeV. Curves are as in Fig. 1. Experimental data are from Refs. [27] (exes), [20] (crosses), and [28] (open squares).

Figure 5

Outgoing nucleon polarization of the ${}^2\mathrm{H}(d,p){}^3\mathrm{H}$ (left) and ${}^2\mathrm{H}(d,n){}^3\mathrm{He}$ (right) transfer reactions at deuteron beam energies ranging from 6 to 14 MeV. Curves are as in Fig. 1. Experimental data are from Refs. [29] and [30] for the ${}^2\mathrm{H}(d,p){}^3\mathrm{H}$ and ${}^2\mathrm{H}(d,n){}^3\mathrm{He}$ reactions, respectively.

Figure 6

Outgoing proton polarization $P_y$ and deuteron-to-proton polarization transfer coefficients for the ${}^2\mathrm{H}(d,p){}^3\mathrm{H}$ reaction at 10.15-MeV deuteron energy. Curves are as in Fig. 1. Experimental data are from Ref. [32].

Figure 7

Total cross sections for transfer and breakup reactions in deuteron-deuteron collisions as functions of the beam energy. In addition, results for the proton-deuteron breakup are represented by the dotted curve. Experimental data for transfer reactions are from Refs. [20, 21, 21], [24], and [25].