Question

1. The Heidelberger Ionenstrahl-Therapiezentrum (HIT) has a particle accelerator capable of reaching beam kinetic energies of 500 MeV per nucleon. Instead of using protons or alpha particles, Dr. X wants to investigate the effects of high LET radiation in a tissue irradiation experiment with a ¹²C (A=12, Z=6) ion beam with a kinetic energy of 6000 MeV. The carbon ion beam (stripped of electrons) will be impinging on a radially symmetric (e.g. cylindrical) tissue-equivalent target.
   1. Using the Bethe-Bloch equation, calculate the stopping power of the carbon ion beam in the tissue target. Assume the tissue target has water-equivalent properties. (Hint: Determine the F(β) and β for a proton traveling at the same velocity as the carbon ion in water).  
   2. What is the maximum range of the carbon ion?
   3. What is the range of delta rays from the carbon ion? What is the minimum radius of a cylindrical (radially symmetric) tissue-equivalent target needed to measure the absorbed dose from collisional interactions from charged particles from the carbon ion beam?
   4. If the delta electron has a range of 5X10^-6 g/cm², what is the fraction of the electron’s kinetic energy is converted to bremsstrahlung? (Assume here Z equivalent for the water-equivalent cell tissue is 7.7)
   5. At what kinetic energy would the collisional and radiative stopping power of the delta particle be equivalent? How would this energy change if the accelerator were irradiating Al instead of tissue? Pb instead of tissue?