Study of the time and space distribution of beta+ emitters from 80 MeV/u carbon ion beam irradiation on PMMA

Proton and carbon ion therapy is an emerging technique used for the treatment of solid cancers. The monitoring of the dose delivered during such treatments and the on-line knowledge of the Bragg peak position is still a matter of research. A possible technique exploits the collinear $511\text{kilo}\text{electronvolt}$ photons produced by positrons annihilation from ${\beta }^{+}$ emitters created by the beam. This paper reports rate measurements of the $511\text{kilo}\text{electronvolt}$ photons emitted after the interactions of a $80\text{mega}\text{electronvolt}\mathrm{/}u$ fully stripped carbon ion beam at the Laboratori Nazionali del Sud (LNS) of INFN, with a Poly-methyl methacrylate target. The time evolution of the ${\beta }^{+}$ rate was parametrized and the dominance of ${}^{11}C$ emitters over the other species (${}^{13}N$, ${}^{15}O$, ${}^{14}O$) was observed, measuring the fraction of carbon ions activating ${\beta }^{+}$ emitters $A_0=(10.3\pm 0.7)\cdot {10}^{-3}$. The average depth in the PMMA of the positron annihilation from ${\beta }^{+}$ emitters was also measured, $D_{{\beta }^{+}}=5.3\pm 1.1\text{milli}\text{meter}$, to be compared to the expected Bragg peak depth $D_{Bragg}=11.0\pm 0.5\text{milli}\text{meter}$ obtained from simulations.