The Dosimetry of Beta Radiations

With uniform distributions of beta emitters in large volumes dosimetry is relatively simple, and has been adequately treated by various authors (1, 2). The dosimetry of small or non-uniform sources, on the other hand, has received little attention. It is with the physics aspects of this problem that the present paper is concerned. The basic physical information required for beta particle dosimetry is the distribution of absorbed energy around a point source of beta particles in an absorbing material. If this point source energy distribution function were known, we could, at least in theory, compute the distribution of absorbed energy for any known distribution of a beta emitter. If such a point source function could be computed for monoergic electrons from the theory of scattering and energy loss, it could be integrated with a known beta spectrum to give the point source function for a beta emitter. To date, the computation has not been made in useful form, and an experimental approach must be adopted. Some direct measurements have been made on very small beta sources in air, for which preliminary results only are available (3). The present paper describes measurements made on very thin plane sources, from which the information for a point source can be computed. The simple theory, along with a statement of preliminary results of measurements on P32, has already been published (4). The theory may be briefly stated as follows. If we suppose a point source of beta particles in a homogeneous absorbing medium larger in all directions than the maximum range of the particles, then the absorbed energy per unit volume must be a radially-symmetrical function of distance from the source. Let this function be represented by I(x) , and call it the “point source energy distribution function.” If now we suppose an infinite thin plane source in the medium, then the distribution of absorbed energy in a direction normal to the plane is given by where R0 is the maximum beta range, z is the perpendicular distance to the plane source, and the point source function I(x) is in units of energy/c.c.-dis. Conversely, it can be shown (4) that if D(z) is known, then I(x) can be determined by suitable differentiation: where Ē being the average energy per disintegration for the beta spectrum. The last equation expresses the condition that the energy absorption takes place in a sphere of radius equal to the maximum beta range, R0. Consideration of Equations 2 and 3 shows that the experiment need give only relative values of D(z), since multiplying D by any constant does not change the value of I(x) computed according to Equation 2. Now it is feasible to make a thin plane source, and measurements can be made of absorption in planes parallel to it. Measurements of this type have been made on a number of beta emitters, using a variablespacing, parallel-plate ionization chamber, usually referred to as an extrapolation chamber.