On the calculation of mean restricted collision stopping powers Wolfgang A. Tome ´ a) and Jatinder R. Palta b) Department of Radiation Oncology, University of Florida, College of Medicine, Gainesville, Florida 32610-0385 Received 10 September 1996; accepted for publication 19 February 1998 An analytical method for the calculation of ratios of mean restricted collision stopping powers ( L  /  ) g m averaged over the charged particle spectra and the photon spectrum that is accurate to first order has been developed, and it has been explored whether a moderate change in the photon fluence spectrum with field size has an effect on the mean restricted collision stopping power ratio in high-Z materials. The results of this study indicate that for the case of a miniphantom, moderate changes in the photon fluence spectrum have only a weak effect on the ratios of mean restricted collision stopping powers. © 1998 American Association of Physicists in Medicine. S0094-24059800505-7 Key words: collision stopping power, charged particle spectra, photon spectrum, dosimetry, calibration I. INTRODUCTION The total stopping power of a medium is the average rate at which charged particles lose energy at any point along their tracks in the medium. It is customary to separate total stop- ping power into two components: i the collision stopping power, which is the average energy loss per unit pathlength due to inelastic Coulomb collisions with atomic electrons of the medium resulting in ionization and excitation; ii the radiative stopping power, which is the average energy loss per unit pathlength due to the emission of bremsstrahlung. The collision stopping power is an important parameter in the well-known Bragg–Gray theory, which relates the ab- sorbed dose to a cavity gas and the absorbed dose in the surrounding medium. This theory allows the use of cavity ionization chambers for the determination of absorbed dose to a medium from a photon or electron beam. The practical application of the Bragg–Gray theory re- quires a schematization in which the collision stopping power is restricted to energy losses less than some specified cutoff energy. Spencer and Attix 1 introduced such a schema- tization that forms the basis for the TG-21 dose calibration protocol. 2 The accuracy of dose calibration is critically de- pendent upon the selection of appropriate stopping power ratios, which, in turn, depend upon the spectrum of the pho- ton or electron beam incident on the dosimetry phantom. TG 21 uses a methodology described by Cunningham and Schluz 3 in which the stopping power ratio for a photon beam is indexed to a beam quality indicator that is characterized by the ratio of ionization measured at two depths. The calcula- tional method summarized in their paper is not clear on how the presence of photon spectrum and the resultant distribu- tion of secondary electrons is accounted for in the determi- nation of mean collision stopping power. On the other hand, several authors have done extensive Monte Carlo simulations using various Monte Carlo codes to obtain stopping power ratios of water and water equivalent materials for the use in radiation dosimetry. Berger et al. 4,5 have done extensive Monte Carlo calculations for the case of electron beams using ETRAN to obtain the electron fluence spectrum  T . Their stopping power ratios are used for elec- tron beam dosimetry in the TG-21 and IAEA dosimetry protocols. 2,6 Nahum 7 first recognized the importance of the track-end term in the calculation of stopping power ratios for photon beams using the Monte Carlo method. Andreo and Brahme 8 have preformed extensive Monte Carlo simulations to obtain stopping power ratios for clinical photon beam spectra. In their extensive calculations they have treated pos- itrons in the same way as electrons, except that they take annihilation of the positrons into account when they come to rest. Malmut et al. 9 made the next step forward by calculat- ing water/air stopping-power ratios using EGS4, taking the electron–positron differences into account explicitly. The motivation for this paper is to describe a method for the calculation to first order of mean restricted collision stop- ping powers for materials of any Z value that are accurately averaged over the total electron–positron spectra and the photon spectrum. We describe all the fundamental equations and the inherent assumptions used in the derivation of this quantity. We find that in the case of water our values for water/air restricted collision stopping-power ratios agrees to better than 1.2% with the previously reported values for this quantity. 8–10 Furthermore, we have also explored whether a change in the photon spectrum with field size has any effect on the mean restricted collision stopping-power ratio ( L  /  ) cap air in materials typically used as buildup cap material in-air mea- surements in high-energy photon beams. If it turns out that the restricted collision stopping power ratio changes signifi- cantly due to changes in the incident photon spectrum with field size, it can invalidate the measurement of relative out- put factors in air, where it is inherently assumed that ioniza- tion is directly proportional to dose under electronic equilib- rium. 758 758 Med. Phys. 25 „5…, May 1998 0094-2405/98/25„5…/758/15/$10.00 © 1998 Am. Assoc. Phys. Med.