65 



picture the size of the region containing the hydrogen atoms is much smaller 

 than 150 A, something which you can also conclude simply from the depend- 

 ence of the molecular hydrogen yield on the ionization density. If you have a 

 particle track with clusters strung along it, then as you increase the ioniza- 

 tion density these clusters will start to coalesce, and as the clusters coal- 

 esce the yield of molecular product will increase. From the rather frag- 

 mentary information available, it seems clear that the hydrogen yield does 

 not greatly increase until you reach an ion density corresponding to that of 

 an electron of the order of 3,000 or 4,000 ev. If you put in the numbers 

 for the average ionization density and assume a random distribution of these 

 clusters along the track, it is clear that the diameter of these groups of 

 radicals cannot be much greater than 10 or 15 A. 



The point I was making is that the radical distribution picture may be 

 obtained pretty well inductively rather directly from the experimental data, 

 as I discussed at the Faraday Society meeting (14). It is very nice to find 

 that Dr. Magee's more theoretical treatment is in agreement. 



Another point is that if the peroxide yield is greater than the hydrogen 

 yield it will not be possible to compare these numbers 0.Z3 and 0.32 very 

 directly with experiments, because the experiment refers to the hydrogen 

 yield; and in the case of tritium betas particularly, I think there is some 

 evidence that the peroxide yield may be several times greater than the hy- 

 drogen yield. It is a little hard to know what number to compare with this 

 0.32, since it is based on a theory which does not take into account this dif- 

 ference between the hydrogen and peroxide yields. 



FANO: I have been thinking at various times about recombination-diffu- 

 sion theories. I learned that it is very convenient, in discussing these prob- 

 lems, to keep in the forefront a very few theoretical facts. The main fact is 

 this: if two particles start diffusing at a distance r from one another and if 

 they have a joint collision radius cr , their probability of ever colliding 

 amounts to cr /r. If their probability of combination upon collision is p, their 

 total probability of combination is p cr/r. If there are scavengers around, 

 which may capture one of the two particles prior to its colliding with the oth- 

 er, the probability of collision follows the law ""/r exp(-r/a). 



If the particles are ions pulled by an electric field E in opposite direc- 

 tions at an angle with the initial separation of the ions, their collision 

 probability is ( <r/ r ) exp [ - eE_ r (i +cos e)] This formula leads to Jaffe's 



RT 

 theory, of one takes <r r e /kT and integrates over the distribution of initial 

 separations in a column of ions. 



In all these formulas the element of primary importance is the ratio °"/r. 

 The large value of this ratio for small values of r, nearly as small as cr , 

 may give the mistaken impression that recombination is important only for 

 particles that happen to start in close proximity. This is not necessarily 

 time, because the chance of starting at large distances may be very great. 

 If the probability cr/r is multiplied by a volume element 4tt r^dr, large val- 

 ues of r clearly give an overwhelming contribution. Even for a linear ( or 

 columnar)distribution , °"/r is multiplied by dr and, upon integration, the 

 large values of r would give a logarithmically infinite contribution if they were 

 not discriminated against by scavenger action, field separation, or other par- 

 asite effects. 



MAGEE: In the case I was discussing, a chemical scavenger was pres- 



