Beta-particle Sources Research Articles

Beta Particle Transmission Currents in Solid Dielectrics

The current from a beta particle source measured through a thin dielectric cannot be predicted simply from the absorption curve. A model is considered in which the space charge formation in the medium results in a component of current in addition to that of the betas transmitted. Calculations developed from this model give a close approximation to experimental results.

BETA RADIATION SOURCES, USES, AND DANGERS IN TREATMENT OF THE EYE

Beta radiation from radium, radon, and radium D-E has been used in the treatment of certain external ocular conditions for about 40 years because of the relatively superficial effects and accurate localization of the radiation. More recently, radioactive strontium (Sr 90 )-yttrium (Y 90 ) applicators have become available as a source of beta particles or electrons for ocular use. The early enthusiastic reports of the efficacy of beta radiation have been tempered by the appearance of certain secondary complications including cataract. Therefore, it becomes more important that the clinician be aware of the sources, rationale, uses, contraindications, dosages, and dangers of beta therapy. Characteristics of Various Sources of Beta Radiation Various sources and applicators have differing characteristics in surface output, depth dose, and amount of gamma rays. A comparison of available data 1 on these applicators is given in table 1. The differences in the construction of the applicators, their

The dosimetry of beta sources in tissue; the point-source function.

The widespread use in medicine and biology of radioactive nuclides emitting beta particles has focused attention on the problem of the dose distribution in tissue corresponding to non-uniform distributions of the radioactivity. The problem has two aspects. First, the distribution of absorbed energy (i.e., dose) about a point source of beta particles must be inferred in some fashion. Second, this point-source energy-distribution function must be integrated over some distributed source, real or hypothetical, to get the dose distribution. For purposes of radiation dosimetry, it would clearly be convenient if the point-source distribution could be described by a reasonably simple mathematical function. The purpose of this paper is first to present such a function, then to indicate the extent to which this function fits available experimental data, and last to discuss the application of this function to beta sources distributed in tissue. Experimentally, the problem has been approached in two ways, indirect and direct. The first experimental work was done with the indirect method (5), which consisted in attempts to deduce the point-source distribution function from the appropriate mathematical manipulation of measurements made on plane sources in polystyrene. Some of the results by this method have already been reported (6). The direct experimental approach consists in measurements on point sources of beta particles in air. Such measurements have been made by Sommermeyer and Waechter in Germany (10, 11), Clark, Brar, and Marinelli in Chicago (1), and Emery in England (2). The data from these three sets of observers give a relatively complete and consistent picture of the point-source distribution in air. When representing the experimental data with a function for dosimetry purposes, it is quite satisfactory to account for 90 or 95 per cent of the energy, with reasonable accuracy. The remainder of the energy, distributed over the last quarter or third of the beta-particle range, will, in general, be of little biological significance. This allows the function to be run to infinity, which greatly simplifies the mathematics. The measurements on point beta-particle sources in air can be represented, with this degree of accuracy, by the following function: (1) This can be somewhat more conveniently written in terms of the dimensionless variable r = μx, and c = μx1. Then Equation 1 becomes (2) Now I is the point-source distribution function, that is, the absorbed energy per gram per disintegration, at a distance r = μx from a point source of beta particles.

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.

Extrapolation Chamber for the Measurement of Beta Sources

Construction and operation of a variable-spacing, parallel-plate ionization chamber is described. It has been designed for the measurement of beta-particle sources of medical and biological interest. It has concentric collecting electrodes of 1, 3, 10, and 30 mm diameter. The air gap in which ionization is measured can be adjusted from 0.04 to 10 mm. Ionization current is measured with a commercial vacuum tube voltmeter which has a full scale sensitivity of 2×10−13 amp. The instrument sensitivity is about 0.4 esu/cc-sec using a one mm diameter collecting electrode with a collecting air gap of 0.2 mm, and about 4×10−5 esu/cc-sec using a 30 mm diameter collecting electrode with an air gap of 2 mm. Conditions are described in detail for the determination of ionization per cc in vanishingly small air gaps between polystyrene electrodes, with an accuracy of a few percent.