Theoretical Study of the $d(d,p){}^3\mathrm{H}$ and $d(d,n){}^3\mathrm{He}$ Processes at Low Energies

We present a theoretical study of the processes $d(d,p){}^3\mathrm{H}$ and $d(d,n){}^3\mathrm{He}$ at energies of interest for energy production and for big-bang nucleosynthesis. We accurately solve the four body scattering problem using the ab initio hyperspherical harmonics method, starting from nuclear Hamiltonians which include modern two- and three-nucleon interactions, derived in chiral effective field theory. We report results for the astrophysical $S$ factor, the quintet suppression factor, and various single and double polarized observables. A first estimate of the theoretical uncertainty for all these quantities is provided by varying the cutoff parameter used to regularize the chiral interactions at high momentum.

Figure 1

The astrophysical $S$ factor for the processes $d(d,n){}^3\mathrm{He}$ (left panel) and $d(d,p){}^3\mathrm{H}$ (right panel) calculated with the $\mathrm{N}3\mathrm{LO}500/\mathrm{N}2\mathrm{LO}500$ and $\mathrm{N}3\mathrm{LO}600/\mathrm{N}2\mathrm{LO}600$ interactions. The width of the bands reflects the spread of theoretical results using $\mathrm{\Lambda }=500$ or 600 MeV cutoff values. See the main text for more details. The experimental values are from Refs. [14, 15, 18, 19, 20, 21].

Figure 2

The QSF for the processes $d(d,n){}^3\mathrm{He}$ and $d(d,p){}^3\mathrm{H}$ shown as bands, in analogy of Fig. 1. We report also the results obtained with other theoretical approaches: $T$ matrix [51]; $R$ matrix [27]; RRGM [32, 33]; FY Uzu [35]; FY Deltuva [7]. The red solid [black dashed] lines connecting the red [black] symbols denote the QSF calculated in the literature for the $d(d,p){}^3\mathrm{H}$ [$d(d,n){}^3\mathrm{He}$] reaction.

Figure 3

The observables $A_{zz,0}$ and $A_{xx,0}-A_{yy,0}$ for the $\overrightarrow{d}(d,p){}^3\mathrm{H}$ and $\overrightarrow{d}(d,n){}^3\mathrm{He}$ processes at $T_d=21\mathrm{keV}$. The (cyan) bands show the results of the present calculations. The experimental values are taken from Ref. [27].

Figure 4

The polarization observables $A_{z,z}$ and $A_{zz,zz}$ calculated for the $\overrightarrow{d}(\overrightarrow{d},p){}^3\mathrm{H}$ and $\overrightarrow{d}(\overrightarrow{d},n){}^3\mathrm{He}$ processes at various laboratory energies. The calculations have been performed for the $\mathrm{N}3\mathrm{LO}500/\mathrm{N}2\mathrm{LO}500$ interaction. The associated theoretical error is of the order of 5%.