Deuteron-deuteron elastic and three- and four-body breakup scattering using the Faddeev-Yakubovskii equations

Abstract

The deuteron-deuteron elastic and three- and four-body breakup scattering cross section have been calculated using the Faddeev-Yakubovskii (FY) chain-of-partition momentum-space equations. In this calculation the initial two-cluster potential is split into separable and nonseparable components, and the effective potential is reduced to elastic two-body and three- and four-body breakup open channels and a closed-channel many-body contribution. The closed-channel contribution is determined by minimizing a variational bound. The Coulomb interaction was included by expanding the initial and final Coulomb states in a Coulomb-Sturmian basis. The three sets of chain-of-partition integral equations were solved for the elastic and three- and four-body breakup scattering amplitudes. The calculations were performed for the $S=2\mathrm{spin}/L=0$ angular-momentum state. The elastic and double-breakup calculations were performed for energies up to $E=5.48\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$, while the single-breakup calculations were performed for energies up to $E=4.17\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$. In the case of elastic scattering, the calculated scattering length of ${}^{5}{a}_{dd}=7.8\ifmmode\pm\else\textpm\fi{}0.3$ fm is in good agreement with a FY cluster reduction calculation. The calculated phase shift is smaller than that predicted by the resonating group model and this difference is believed to be due to the differences in the potential and calculation methods. The breakup cross sections were calculated as a function of initial deuteron momentum and fragmented-deuteron momentum. The $d+d\ensuremath{\rightarrow}d+n+p$ cross sections were compared with neutron yield measurements and, while the measurements also included the $Lg0$ components, the general features were consistent. Estimates of the calculational uncertainties/bias are provided.