A new isotopic fragments identification with Lagrange Multipliers in the FOOT experiment

Hadrontherapy is one of the available techniques used nowadays to treat cancer. Specifically, it employs beams of protons or heavier ions with initial energies of hundreds of MeV/u. Hadrontherapy has an advantageous energy release in the patient, allowing to irradiate the cancer volume in a more precise way and to spare the healthy tissues surrounding it. The main drawback of this kind of therapy is the nuclear interaction of the primary beam with the nuclei constituting the irradiated tissue. Target and projectile nuclear fragmentation could have a dangerous biological effect on tissues surrounding the tumor. Specifically, target fragments have a very short range and are difficultly detected. For this reason the experimental panorama is very poor, thus reducing the precision in the evaluation of success or induced risk of hadrontherapy treatments. For this purpose, the FOOT (FragmentatiOn Of Target) experiment has been designed. It aims at filling the gap both in projectile and target fragmentation experimental data, measuring the fragment production cross section by using in the latter an inverse kinematic technique. At larger energies, the FOOT measurements will be useful to evaluate the interaction of the space radiation field with materials composing the spaceship hull in a long term space mission (typically on Mars), in order to assess the radiation-induced damage on astronauts’ health and electronics on board. The FOOT apparatus allows to identify nuclear fragments by measuring their charge Z and their number of mass A. The latter is measured in three redundant ways, which need to be combined to obtain a best estimation of A. In the present thesis, the technique of Lagrange Multipliers used for the constrained minimization of functions, will be introduced and implemented in the FOOT analysis code to reconstruct the number of mass of nuclear fragments. Moreover, the results of the method will be compared to the ones already implemented in the experiment.