524 L. H. GRAY 



tion, which vary Unearly with dose and are independent of intensity 

 for high ion density radiations, and for which biological effectiveness 

 increases with ion density, may be suspected a priori of belonging to 

 this class. In such cases impulse radiation may be expected to show 

 enhanced efficiency. There is doubtless a limitation both in space 

 and in time for the cooperative action of ion clusters. The spatial 

 limitation will define a minimum dose per impulse, the temporal a 

 maximum duration of the impulse. 



Inhomogeneous Electron Beams. Almost all our knowledge 

 of the biological effects of electron ionization has been gained by 

 exposing specimens to electrons having a continuous distribution of 

 energies from zero to a maximum value. This is, of course, true of 

 tissues exposed to the secondary electrons generated by any kind of 

 X radiation (see Chapter XIV) and all tissues exposed to the rays 

 from radioactive sources. The great variety of artificial radioactive 

 sources now available makes it possible to choose continuous j8-ray 

 distributions having almost any desired mean energy. In almost 

 every case so far investigated the mean energy, E^, with which the 

 electron is emitted from the disintegrating atom lies between 30 and 

 45% of the upper limit £"0 of the /3-ray spectrum, which is the quan- 

 tity generally listed in tables of radioactive isotopes. 



The values of E^ for 23 isotopes have been calculated by Marinelli, 

 Brinckerhoff, and Hine (55) and lie between 120 kv. (Fe^^) and 1.39 

 m.e.v. (CPS). S35 and C^* for which E^ would be about 50 kv. and 

 tritium (H^) for which it is probably of the order of 4 kv. are not 

 included in the fist. The value of E^ is the mean value of the energy 

 of the electrons with which a thin biological specimen would be- ir- 

 radiated when exposed to a source in which both self-absorption and 

 back-scatter from the source support were negligible. The corre- 

 sponding mean Hnear ion density may be read from Figure 1. When 

 a thick layer of tissue is irradiated by an external jS-ray source, or 

 when the radioactive material is incorporated in the tissues the mean 

 energy of the electrons by which each volume of tissue is ionized is, of 

 course, a good deal less than the value of E^ for the source in question 

 because each electron contributes ionization at all energies below 

 that with which it is emitted. In this case the mean in which we are 

 interested can only be properly evaluated when the form of the /S-ray 

 spectrum is knoA\Ti. A very rough value of the mean ion density may, 

 however, be found by dividing E^ expressed in volts by the product 



