Theoretic Considerations of the Radiation Dose from Discrete Tritium Sources

The preparation by one of us, (W. L. H.), of tritium-labeled thymidine of high specific activity permits the localizing of tritium within cell nuclei, and the question of the radiation dose from single tritium disintegrations assumes considerable practical importance. Tritium β− particles have unusually low kinetic energies, the average being about 5.7 kev. Associated with this low energy is a short range, the figure usually cited being 0.23 mg./cm.2 as measured in helium gas (1), or about 2.3 µ in soft tissue. On this basis, the radiation dose from tritium sources localized in cell nuclei is delivered largely within the nuclei. The formulas for dose calculation which involve an assumption of homogeneous distribution are obviously not satisfactory for evaluation of the results in this situation. The formulas given by Loevinger (2) for the radiation dose from discrete sources also fail for tritium β− particles. Therefore, the present calculations have been made. The shape of the tritium β− spectrum is well established (3, 4) and fits very closely a Fermi plot for the appropriate Z number and maximum energy. For present purposes, the spectrum was divided into eighteen 1-kev intervals, and the relative number of disintegrations in each interval was calculated. Since none of the empirical formulas relating range and energy (5, 6) is satisfactory at these low energies, a smooth curve drawn through the published experimental values of ranges for monoergic electrons (7, 8) has been used. According to this curve, the maximum range of tritium β− particles of maximum energy (18 kev) should be about 6 or 7 µ. The previously measured range of 2.3 µ corresponds to a maximum energy of only 9.5 kev. The straggling which occurs at these low energies, however, makes experimental determination of the range very difficult. Differentiation of the range-energy curve gives the rate of loss of energy per unit path length and thus provides a basis for radiation dose calculations. Calculations based on the use of the Bethe-Block formula for the rate of energy loss along the path of electrons give fairly closely similar results. Given the above basic information, the integrated energy loss in the volume surrounding a point source of tritium was calculated by multiplying the rate of energy loss by the average frequency of emission over 1-kev intervals as functions of distance at 0.5-µ intervals. Appropriate corrections for the volume factor and conversion from kev/µ3 to rad gives the final curve of the average radiation dose rate as a function of distance from a point source. In the inner ½ µ radius sphere (0.52 µ3) a single disintegration gives an average of 53.5 rad (or about 2 rad per 10−6 µc-sec) while in the next ½ µ shell (3.7 µ3) the average dose is only 5.8 rad/dis. The 10 per cent of the total disintegrations having energies of 2 to 3 kev give an average of 82.5 rad per disintegration in the inner sphere.