3.1 Particle identification

Two processes were performed in the experiment. Firstly, a silicon detector with a thickness of 300 μm was inserted into the beam line between PPAC2 and the plastic scintillation detector at T2 as an E detector to stop the beam. The plot of E-TOF for beam particle identification is shown in Fig. 2. Since the flight distance is fixed with the calibration values of TOF and the total kinetic energy, E, each beam component can be distinguished (marked in Fig. 2). Depending on the magnetic rigidity, Bρ, set for the last dipole magnet, D4, the energy of each component can be estimated. Then the calibrated energies are compared to the estimated ones in order to check their validity. In this way, it is found that the present calibrated components correspond to the experimental data. Therefore, we can tell the identification of beam particles is reliable.

Figure 2:Full-screen View

The plot of E-TOF for beam particle identification.

Secondly, the silicon detector was removed from the beam line. Therefore, the TOF signal is essential for particle identification. From Fig. 2, it is observed that there are large differences of TOF among ¹⁶O, ¹⁷F, and ¹⁷O, so that the events of incident ¹⁷F and ¹⁷O can be excluded by selecting a correct TOF window. Meanwhile, ¹⁶O and the other components have a similar TOF value as shown in Fig. 2. However, due to the significant energy differences, none of the other scattered components can be mixed into the scattered ¹⁶O events on the energy spectrum of scattering particles. Since ¹⁶O has a large energy difference in comparison with ¹⁷F and ¹⁷O, it is still possible for ¹⁶O to be distinguished from the energy spectrum of DSSDs without TOF windows. In practice, the secondary beam includes a lot of unexpected components in RIB experiments. For our case, in cooperation with TOF signals, the precision of our experimental results can be improved.

3.2 The distributions of particles on PPAC and DSSD

In the experiment, due to the large beam spot of secondary beam on the target, the trajectories of particles have to be tracked one by one. In order to achieve this goal, two PPACs are mounted at the secondary target, ⁸⁹Y.

PPAC is often used in the nuclear reaction experiments because of its many advantages such as good position resolution, a large sensitive area, and easy to fabricate, etc. It is composed of two anode planes and one cathode plane. All electrode planes are put in parallel to assure the uniformity of the electric field. The cathode plane, which is made of mylar foil coated with a thin gold layer on both sides, lies in the middle of the PPAC. The two anode planes, which are made of gold-plated tungsten wires, are symmetrically positioned on both sides of the cathode plane. Both the entrance and exit windows are covered by mylar foils with about 12 μm in thickness, and the grids made of fishing line support the mylar foils to resist high gas pressure. The wires on both two anode planes, with a sensitive area of 80 × 80 mm², are perpendicular to each other to give the X and Y direction positions. There are 80 wires on the X and Y directions, respectively. The span between each two wires is 1 mm for each direction. The signals of wire electrodes are connected to each other by delay cables. The time difference between two read-out signals of the anode planes gives the position information of beam particles.

Fig. 3 (a) and (b) present the distributions of incident ¹⁶O on PPAC1 and PPAC2. The spot on PPAC2 is smaller than that on PPAC1, which corresponds to the fact that T2 is a focal point. This demonstrates that this set of PPACs can reflect the beam trajectory and precisely give the position coordinates of each particle on PPAC1 and PPAC2. Then the incident points on ⁸⁹Y target can be determined. It is important to determine the scattering angle of each particle.

Figure 3:Full-screen View

The distributions of incident ¹⁶O on PPACs. (a) on PPAC1; (b) on PPAC2.

The distributions of scattered ¹⁶O on two DSSDs (L1 and R1 placed symmetrically with the beam line) are shown in Fig. 4. According to the sequences of silicon strips, which is shown in Fig. 1, for L1, the silicon strips from No. 1 to No. 16 correspond to angles from forward to backward. For R1, the silicon strips from No. 1 to No. 16 correspond to angles from backward to forward. On the basis of kinematic principle, the energies of scattered particles at forward angles are larger than those at backward angles, as shown in Fig. 4 (a) and (b).This means that the present DSSDs can give the kinematic trends of scattered particles. The scattering angle of each particle can be obtained event by event.

Figure 4:Full-screen View

The distributions of scattered ¹⁶O on DSSD. The horizontal axis denotes the channels of X-strips of DSSD. (a) L1; (b) R1.

Figure 5 indicates the experimental angular distribution of scattered ¹⁶O on ⁸⁹Y target (solid line). It is shown that in the ranges of 20° to 60° and over 80°, with the increase of scattering angles, the number of events decreases. However, around 65° a sudden decrease occurs due to the influence of target and the connection position of the detectors, which has been described in Fig. 1 and Section 2. The experimental results correspond to the geometry of detector setup. Therefore, the determination of scattering angles is acceptable. The present DSSDs can not only give the reasonable kinematic trends of scattered particles, but also provide the precise angular information of scattered particles.

Figure 5:Full-screen View

The angular distributions of ¹⁶O on ⁸⁹Y target as a function of scattering angles. The solid and dashed lines represent the experimental data and the simulation results, respectively.

3.3 Simulation

In the angular distribution of elastic scattering, the differential cross sections of this reaction are normalized to the differential cross sections of the Rutherford scattering. The ratios are plotted as a function of scattering angles. Since the beam spots of RIBs on the target cannot be viewed as a point with respect to the distance between the target and the detector, the Monte Carlo method is applied to simulate the Rutherford scattering.

In the simulation program we took into account (1) the kinematics of elastic scattering process; (2) the energy spread of the secondary beam; (3) the Gaussian distributed beam spot with σ =6.5 mm on the target; (4) the real geometry design of detector system; (5) the energy loss in the target evaluated by TRIM code [15]. In addition, the reaction position along the beam direction inside the target is random. The simulation results are shown in Fig. 5 (dashed line). It is observed that the inflection position is almost identical. Therefore, the simulation method and results are reasonable.

3.4 Results and discussions

The ratios of reaction differential cross sections to the differential cross sections of Rutherford scattering are obtained by

where the parameter, C, is a normalization constant, which is determined by supposing that the elastic scattering is a pure Rutherford scattering in a region of small scattering angles (much smaller than the grazing angle). N(θ) and N_Ru(θ) are the elastic scattering events and Rutherford scattering events with the same solid angle at any scattering angle, θ, in the frame of laboratory system, respectively. In this experiment, at a laboratory angle θ, N(θ) is the experimental counts of ¹⁶O scattering on ⁸⁹Y target, and N_Ru(θ) is obtained from the Monte Carlo simulation.

For ¹⁶O at 50 MeV, the experimental scattering events are normalized to the simulation events at the angle of 22° where the elastic scattering is expected to be a pure Rutherford scattering. The results are shown in Fig. 6 as a function of scattered angles in the laboratory frame. Here only statistic error is considered. It presents that in the ranges of 10° to 35° and 75° to 110° the ratios almost keep the unity, because at this energy, the scattering of ¹⁶O on ⁸⁹Y target is pure Rutherford scattering. It demonstrates that the normalized method is reasonable. This detection system can effectively determine the elastic scattering angular distributions and give the precise angular calibration.

Figure 6:Full-screen View

The angular distribution of elastic scattering of ¹⁶O + ⁸⁹Y at 50 MeV.

In summary, for this detector setup, PPACs can precisely determine the beam trajectories before the target and DSSDs can correctly determine the positions of scattered particles. The deduced scattering angles are reasonable. The simulation about Rutherford scattering is correct. The normalization results of elastic scattering angular distributions can prove that the angular calibration is precise. As a result, this detector setup can be used for the study of heavy-ion elastic scattering at energies around the Coulomb barrier on HIRFL-RIBLL.