A first step in the dosimetry of fast-ion beams is the determination of acc
urate Bragg (ionization) functions. Bragg functions for several substances
have been measured and calculated for 3480 MeV carbon ions. In the measurem
ents, the ions first traverse an absorber in which the energy is reduced to
either 1900 or 1200 MeV, then a "range gauge" followed by a thin ionizatio
n chamber. Functions are calculated with an analytical method using convolu
tions of straggling functions, This approach gives results without the stoc
hastic variations implicit in Monte Carlo methods. The comparison of measur
ed and calculated functions shows how reliable the calculations are. An imp
ortant part of the calculations is the determination of the total range of
the ions, The range can be determined from the Bragg function. The measured
range is given by the sum of the thickness of the absorber and the residua
l range measured with the range gauge. For water, the range is about 150 mm
, and the precision of the measurements is +/-0.05 mm. Because the ion ener
gy at the surface of the absorber fluctuates with time, measurements with w
ater are used to define this energy. Thus the ranges (or average stopping p
owers) in absorbers are obtained relative to those in water. Measured range
s R-m are compared with ranges R-0 calculated with a current version of the
Bethe theory. For light absorbers (atomic number Z < 20), differences betw
een R-m and R-0 are less than +/-0.3 mm; for Z > 20 differences are between
0 and +/-0.6 mm, This agreement between calculated and measured ranges con
firms the value I = 80 eV for water measured earlier for protons. The ioniz
ation by nuclear fragments is obtained from the difference between measured
and calculated ionization functions, and has little influence on the range
s of the primary ions. (C) 2000 by Radiation Research Society.