Differential cross section measurements for hadron therapy: 50 MeV/nucleon ${}^{12}\mathrm{C}$ reactions on H, C, O, Al, and ${}^{\mathrm{nat}}\mathrm{Ti}$ targets

During a carbon therapy treatment, the beam undergoes inelastic nuclear reactions leading to the production of secondary fragments. These nuclear interactions tend to delocate a part of the dose into healthy tissues and create a mixed radiation field. In order to accurately estimate the dose deposited into the tissues, the production rate of these fragments all along the beam path have to be taken into account. But the double differential carbon fragmentation cross sections are not well known in the energy range needed for a treatment (up to 400 MeV/nucleon). Therefore, a series of experiments aiming to measure the double differential fragmentation cross sections of carbon on thin targets of medical interest has been started by our collaboration. In March 2015 we performed an experiment to study the fragmentation of a 50 MeV/nucleon ${}^{12}\mathrm{C}$ beam on thin targets at GANIL. During this experiment, energy and angular cross-section distributions on H, C, O, Al, and ${}^{\mathrm{nat}}\mathrm{Ti}$ have been measured. The experimental set-up will be detailed as well as the systematic error study and all the experimental results will be presented.

Figure 1

A global view of the experimental set-up. The telescopes on their rotating supports, the beam monitor as well as the target wheel are represented.

Figure 2

$\mathrm{\Delta }E-E$ map (thick silicon diode vs. CsI) with a KaliVeda identification grid (red lines). Dashed circles are displayed to highlight the horizontal trails coming from the proton, $\alpha$, and ${}^{12}\mathrm{C}$ lines caused by in-detector fragmentation or by particles escaping from the sides of the detector.

Figure 3

Pulse shape analysis plot. The different isotopes are distributed along different lines and are clearly discernible for fragments with a charge below 5. The two $\alpha$ pile-up is clearly visible on a separate line.

Figure 4

Example of the misidentification effects on a ${}^3\mathrm{H}$ energy distribution at $7^{\circ }$. The distribution with red circles is the result of the KaliVeda identification and the one with blue triangles is the distribution corrected using the pulse shape analysis technique. The dotted line indicates the beam energy and the crosshatched area represents the energy threshold.

Figure 5

Relation between the value of the total reconstructed energy and its uncertainty for several isotopes.

Figure 6

${}^4\mathrm{He}$ measured cross sections for C (blue squares) and ${\mathrm{CH}}_2$ (red circles) targets and calculated cross sections for H target (hollow black circles).

Figure 7

Angular differential cross sections distributions of six isotopes from $Z=1$ to $Z=6$ for the carbon target.

Figure 8

Angular differential cross sections of ${}^4\mathrm{He}$ for all elemental targets.

Figure 9

Energy distributions for ${}^4\mathrm{He}$ and four angles from $5^{\circ }$ to ${31}^{\circ }$ for the carbon target. The dotted line indicates the beam energy and the crosshatched area represents the energy threshold.

Figure 10

Energy distributions for ${}^4\mathrm{He}$ and all elemental targets at $7^{\circ }$. The dotted line indicates the beam energy and the crosshatched area represents the energy threshold.

Figure 11

Comparison between the measured (full dots) and reconstructed (hollow dots) PMMA angular and energy cross sections (up and down, respectively). The results are displayed for protons (red circles), ${}^4\mathrm{He}$ (blue squares), and ${}^6\mathrm{Li}$ (green triangles). The dotted line indicates the beam energy and the crosshatched area represents the energy threshold.

Figure 12

Comparison with the 62 MeV/nucleon experiment at LNS [4]. The angular distributions of ${}^4\mathrm{He}$ (blue squares), ${}^6\mathrm{Li}$ (green circles), and ${}^9\mathrm{Be}$ (red triangles) are represented. The data of this work are represented by hollow symbols while the data from LNS in full symbols.