Investigation of the cross section for $dd$ elastic scattering and $dd\to n{}^3\mathrm{He}$ reactions at 160 MeV

Differential cross sections of ${}^2\mathrm{H}(d,d){}^2\mathrm{H}$ elastic scattering and proton transfer ${}^2\mathrm{H}(d,{}^3\mathrm{He})n$ reactions at 160 MeV beam energy have been obtained. They have been normalized relative to the existing cross-section data for the ${}^2\mathrm{H}(d,d){}^2\mathrm{H}$ elastic scattering at 180 and 130 MeV, benefitting from the negligible energy dependence of this observable at certain range of the four-momentum transfer. The experiment was performed at KVI in Groningen, the Netherlands, using the BINA detector. The elastic scattering data are compared to theoretical predictions based on the lowest-order term in the Neumann series expansion for four-nucleon transition operators. The calculations underpredict the data. The data presented in this paper can be used to validate the future theoretical findings.

Figure 1

A schematic view of the BINA detector.

Figure 2

Ball part of the BINA detector.

Figure 3

Upper panel: Sample of $\mathrm{\Delta }E\text{−}E$ distribution with $3\sigma$ limits on ${}^3\mathrm{He}$ ions. Bottom panel: The same as in the upper panel but with zoomed-in $dE$ scale to show the fit quality for protons and deuterons, presented as solid and dashed lines, respectively.

Figure 4

Missing mass spectrum of the $d+d\to {}^3\mathrm{He}+X$ reaction at 160 MeV. A prominent peak corresponds to the mass of a neutron. A signal (Gaussian) + background function (an eighth-order polynomial) was fitted to the distribution, resulting in a Gaussian with a mean of $939.4\pm 0.1$ MeV and $\sigma =5.7\pm 0.1$ MeV.

Figure 5

Distribution of the reconstructed energy versus the polar angle for ${}^3\mathrm{He}$ ions. The solid black line represents the calculated kinematics. The dashed line indicates the energy threshold.

Figure 6

The efficiency map of the MWPC for the ${}^3\mathrm{He}$ ions. The ellipse-like structures illustrate the “dead” and malfunctioning wires.

Figure 7

A sample energy distribution of the ${}^3\mathrm{He}$ ions at $\theta ={22}^{\circ }$ within a range of $1^{\circ }$. The background is marked as the blue hatched area. The distribution obtained after the background subtraction was fitted with a Gaussian function and integrated in the range corresponding to $-3\sigma$ and $+3\sigma$ from the peak position.

Figure 8

A sample energy distribution of the deuterons registered at $\theta ={22}^{\circ }$ in a window of $2^{\circ }$. The background due to the breakup reaction is marked as the blue hatched area. The dashed lines represent the integration region for the events.

Figure 9

Relative loss of events due to hadronic interaction of deuterons (black dots) and ${}^3\mathrm{He}$ ions (red dots) in the plastic scintillator, presented as a function of the scattering angle.

Figure 10

The elastic scattering cross-section data measured at 160 MeV (red dots) are presented together with the data measured in the BBS experiment at 130 (blue squares) and 180 MeV (blue triangles) [31] (lines connecting points are used to guide the eye). The band represents systematic errors. Solid, dotted, and dashed black lines represent the calculations [25] with the use of potentials specified in the legend. The marked area refers to the region used in the normalization procedure.

Figure 11

Differential cross sections for transfer reactions in $d\text{−}d$ systems measured at various deuteron beam momenta, presented as a function of $q^2$ [30, 45]. The present data from the BINA experiment at 0.79 GeV/$c$ are shown as red points. The dark band represents systematic errors.

Figure 12

Differential cross section obtained for three different ranges of the linearization function $L$. See text for details.

Figure 13

A sample energy distribution of the elastically scattered deuterons registered as the Wall-Ball coincidences (blue hatched distribution) for the Ball element 47 and an angular cover in the Wall of $\left(\theta ={22}^{\circ }\pm 0.5^{\circ },\phi =-7^{\circ }\pm 5^{\circ }\right)$. The distribution is compared to one obtained for the single tracks in the Wall at the same polar angle. The inset shows the same comparison after applying the background subtraction procedure as described in Sec. 3.