Measurement of charge- and mass-changing cross sections for ${}^4\mathrm{He}+{}^{12}\mathrm{C}$ collisions in the energy range 80–220 MeV/u for applications in ion beam therapy

${}^4\mathrm{He}$ ions are considered to be used for hadron radiotherapy due to their favorable physical and radiobiological properties. For an accurate dose calculation the fragmentation of the primary ${}^4\mathrm{He}$ ions occurring as a result of nuclear collisions must be taken into account. Therefore precise nuclear reaction models need to be implemented in the radiation transport codes used for dose calculation. A fragmentation experiment using thin graphite targets was conducted at the Heidelberg Ion Beam Therapy Center (HIT) to obtain new and precise ${}^4\mathrm{He}$-nucleus cross section data in the clinically relevant energy range. Measured values for the charge-changing cross section, mass-changing cross section, as well as the inclusive ${}^3\mathrm{He}$ production cross section for ${}^4\mathrm{He}+{}^{12}\mathrm{C}$ collisions at energies between 80 and $220\mathrm{MeV}/\mathrm{u}$ are presented. These data are compared to the ${}^4\mathrm{He}$-nucleus reaction model by DeVries and Peng as well as to the parametrizations by Tripathi et al. and by Cucinotta et al., which are implemented in the treatment planning code trip98 and several other radiation transport codes.

Figure 1

Schematic of the experimental setup used at HIT to measure the charge- and mass-changing cross sections of ${}^4\mathrm{He}$ ions in graphite. The primary ${}^4\mathrm{He}$ ions coming out of the beam nozzle impinged on a start scintillator, which triggered the data acquisition of the Tektronix DSA 72004C oscilloscope and penetrated through a graphite target of variable thickness where some of the ions fragmented. The remaining ${}^4\mathrm{He}$ ions or the generated fragments leaving the target entered a $\mathrm{\Delta }E-E$-telescope whose scintillation pulses were recorded by the oscilloscope. They can later be analyzed to calculate the relative number of primary ions that have fragmented within the target. Examples of signals recorded for the three detectors are shown in the oscilloscope panel. The pulses from the BC-400 plastic scintillators (signals 1 and 2) are very short, while the ${\mathrm{BaF}}_2$ signal (signal 3) consists of a short and a long component. The ${\mathrm{BaF}}_2$ pulse shape can be analyzed for improving the particle identification.

Figure 2

Examples of ${\mathrm{BaF}}_2$ signals normalized to their peak value recorded for monoenergetic protons (${}^1\mathrm{H}$ ions), ${}^4\mathrm{He}$ ions and ${}^{12}\mathrm{C}$ ions at $200\mathrm{MeV}/\mathrm{u}$. The signals were averaged over 100 events with full energy deposition to reduce the noise. Due to the normalization to the peak value the area below the curves represents the pulse shape $PS$.

Figure 3

Examples of (a, c) $\mathrm{\Delta }E-E$ spectra and (b, d) $\mathrm{\Delta }E$-pulse-shape spectra for $130\mathrm{MeV}/\mathrm{u}{}^4\mathrm{He}$ ions with (a, c) no target and (c, d) after traversing $1\mathrm{cm}$ of graphite. Double hits and noise events were excluded. The thresholds T1 and T2 have been set by hand to separate the He events in the upper right corner of the $\mathrm{\Delta }E$-pulse-shape plots from their H fragments. The origin of the event clusters visible in the spectra for $1\mathrm{cm}$ graphite is indicated by the arrows. A detailed description is given in the text.

Figure 4

Example of a $\mathrm{\Delta }E$ spectrum for $130\mathrm{MeV}/\mathrm{u}{}^4\mathrm{He}$ ions after traversing $1\mathrm{cm}$ of graphite. Double hits and noise events are already excluded (see text). The thresholds T1 and T2 (see Fig. 2) were applied to separate the $\mathrm{He}$ ions from the $\mathrm{H}$ fragments. The identified He events are shown together with the fits to separate the ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ ions as well as with the raw spectrum, showing the overall events.

Figure 5

Nuclear attenuation curves in graphite measured for ${}^4\mathrm{He}$ ions with incident energies of 90, 130, 180, and $220\mathrm{MeV}/\mathrm{u}$. The open circles show the relative number of $\mathrm{He}$ ions and the closed squares show the relative number of ${}^4\mathrm{He}$ ions leaving the targets. The corresponding dashed lines are exponential fits, which were calculated to obtain the charge-changing cross section ($\mathrm{He}$ ions as a function of target thickness) and the mass-changing cross section (${}^4\mathrm{He}$ ions as a function of target thickness). The given $\lambda$ values are the mean interaction lengths of the fit functions according to Eq. (2).

Figure 6

Measured cross sections for ${}^4\mathrm{He}+{}^{12}\mathrm{C}$ collisions in comparison to published ${\sigma }_{\mathrm{\Delta }A}$ values [23, 36, 37, 38, 39, 40, 41] as well as to nuclear reaction models [11, 42, 43]. The solid line shows the optical model calculation by DeVries and Peng and the dashed lines show the parametrizations by Tripathi and Cucinotta (dotted: mass-changing cross section, short dashed: charge-changing cross section, long dashed: ${}^3\mathrm{He}$ production cross section). The prediction for the charge-changing cross section was calculated by ${\sigma }_{\mathrm{\Delta }Z}={\sigma }_{\mathrm{\Delta }A}-{\sigma }_{{}^3\mathrm{He}}$.