Three-body break-up in deuteron-deuteron scattering at 65 MeV/nucleon

In an experiment with a 65 MeV/nucleon polarized deuteron beam on a liquid-deuterium target at Kernfysisch Versneller Instituut, several multibody final states in deuteron-deuteron scattering were identified. For these measurements, a unique and advanced detection system, called the Big Instrument for Nuclear-polarization Analysis, was utilized. We demonstrate the feasibility of measuring vector and tensor polarization observables of the deuteron break-up reaction leading to a three-body final state. The polarization observables were determined with high precision in a nearly background-free experiment. The analysis procedure and some results are presented.

Figure 1

Side view of the forward part of BINA which consists of a multiwire proportional chamber (MWPC) and an array of thin plastic scintillators ($\Delta$E), followed by a wall of thick segmented scintillators (E). The backward ball is not shown in this picture, since it was not used in the analysis presented in this paper.

Figure 2

Results for the vector (top panel) and tensor (bottom panel) polarizations of the deuteron beam. The filled circles and squares are the measured values by BINA and LSP, respectively. The shaded bands represent the result of a constant-value fit through all the data points.

Figure 3

Energy correlation between protons and deuterons in coincidence for the three-body break-up reaction in $\mathrm{d⃗}+d$ scattering shown as $S$ curves for several kinematical configurations. The kinematics are defined by (${\theta }_d,{\theta }_p,{\varphi }_{12}$), the polar scattering angles of the deuteron and proton, respectively, and their relative azimuthal angle.

Figure 4

Measured $\Delta$TOF for two particles that are detected in coincidence in the forward wall. The scattering angle of both particles is fixed to be ${25}^{°}\pm 2^{°}$ and the difference between the azimuthal angles of the two particles is ${180}^{°}\pm 5^{°}$.

Figure 5

The correlation between the calibrated energy of the two outgoing particles ( proton or deuteron) in the deuteron-deuteron break-up process is shown for the coplanar configuration (${\theta }_1,{\theta }_2,{\varphi }_{12})=({25}^{°},{25}^{°},{180}^{°}$) before PID (top left panel) and after PID (other panels). The bottom panel on the left-hand side depicts events from the four-body break-up reaction, and the two panels on the right-hand side correspond to the three-body break-up channels. The solid curves represent the relativistic $S$ curves that are calculated from the energy and momentum conservation for the selected configuration.

Figure 6

Calculated mass of the undetected particle in the three-body break-up reaction in deuteron-deuteron scattering. The energy and polar and azimuthal angles of the detected protons are used in the calculation. The dashed (solid) curve represents values of the calculated mass of the missing particle before (after) applying the identification cut in Fig. 4. The scattering angle of both detected particles is fixed to be ${25}^{°}\pm 2^{°}$ and the difference between the azimuthal angles of the two detected particles is ${180}^{°}\pm 5^{°}$.

Figure 7

Correlation between the energies of the deuteron and proton originating from the three-body break-up channel in one selected configuration. The projection of the events from one $S$ bin onto the $D$ axis is shown in the inset.

Figure 8

Ratio of the spin-dependent cross section to the unpolarized one for a pure vector-polarized deuteron beam (top panel) and a pure tensor-polarized deuteron beam (bottom panel) for (${\theta }_d={25}^{°},{\theta }_p={25}^{°},{\varphi }_{12}={180}^{°},S=230$ MeV).

Figure 9

Vector- and tensor-analyzing powers at $({\theta }_d,{\theta }_p)=({15}^{°},{15}^{°})$ (open squares) and $({\theta }_d,{\theta }_p)=({25}^{°},{25}^{°})$ (filled circles) as a function of $S$ for different azimuthal opening angles. The gray lines in all panels show the zero level of the analyzing powers. Only statistical uncertainties are indicated.