In external beam radiation therapy, radioactive beams offer the best clinical solution to simultaneously treat and in vivo monitor the dose delivery and tumor response using PET or PET-CT imaging. However, difficulties mainly linked to the low production efficiency have so far limited their use. This study is devoted to the analysis of the production of high energy (11)C fragments, preferably by projectile fragmentation of a stable monodirectional and monoenergetic primary (12)C beam in different absorbing materials (decelerators) in order to identify the optimal elemental composition. The study was performed using the Monte Carlo code SHIELD-HIT07. The track length and fluence of generated secondary particles were scored in a uniform absorber of 300 cm length and 10 cm radius, divided into slices of 1 cm thickness. The (11)C fluence build-up and mean energy variation with increasing decelerator depth are presented. Furthermore, the fluence of the secondary (11)C beam was studied as a function of its mean energy and the corresponding remaining range in water. It is shown that the maximum (11)C fluence build-up is high in compounds where the fraction by weight of hydrogen is high, being the highest in liquid hydrogen. Furthermore, a cost effective alternative solution to the single medium initially envisaged is presented: a two-media decelerator that comprises a first liquid hydrogen section followed by a second decelerating section made of a hydrogen-rich material, such as polyethylene (C(2)H(4)). The purpose of the first section is to achieve a fast initial (11)C fluence build-up, while the second section is primarily designed to modulate the mean energy of the generated (11)C beam in order to reach the tumor depth. Finally, it was demonstrated that, if the intensity of the primary (12)C beam can be increased by an order of magnitude, a sufficient intensity of the secondary (11)C beam is achieved for therapy and subsequent therapeutic PET imaging sessions. Such an increase in the intensity might be easily achieved with a superconducting cyclotron.