Neutron suppression in polarizedddfusion reaction

Abstract

We report a model-independent partial-wave analysis of polarized $\mathrm{dd}$ fusion reactions at low energies. The radial transition amplitudes, designated by the central, spin-orbit, and tensor forces, are determined by fitting angular distributions of the tensor and vector analyzing powers ${A}_{\mathrm{XZ}}(\ensuremath{\theta}),$ ${A}_{\mathrm{ZZ}}(\ensuremath{\theta}),$ ${A}_{\mathrm{XX}\ensuremath{-}\mathrm{YY}}(\ensuremath{\theta}),$ and ${A}_{Y}(\ensuremath{\theta}),$ and the unpolarized cross section ${\ensuremath{\sigma}}_{0}(\ensuremath{\theta}).$ The polarized fusion cross section ${\ensuremath{\sigma}}_{1,1}(\ensuremath{\theta})$ is then predicted from these radial transition amplitudes. We stress that this is feasible only when these amplitudes are separated according to the tensor rank of the interaction. This study includes the D-state components of the deuteron, triton, and ${}^{3}\mathrm{He},$ and the partial-wave expansion is done up to the d wave for both the entrance and exit channels. Experimental data at ${E}_{\mathrm{lab}}=30,$ 50, 70, and 90 keV for the $d(d,p)t$ reaction are very well fitted with this method. It is found that the ratio of polarized to unpolarized cross sections is about 86% at 30 keV and goes down to 22% at 90 keV. The implication of the suppression of a polarized $\mathrm{dd}$ fusion reaction is discussed in the context of the neutron-lean fusion reactor with polarized D-${}^{3}\mathrm{He}$ fuel. It turns out that the important range of energy for suppressing the $d(d,p)t$ and ${d(d,n)}^{3}\mathrm{He}$ reactions at the plasma temperature $T=60$ keV is ${E}_{d}=80$--600 keV. More experimental data are needed in this range to make a detailed study of the neutron suppression.