285                                NEUTRON    PRODUCTION AND ASORPTION
 
emitted by the source is indicated by the activity of the solution in the tank when the irradiation is
carried out with empty cans surrounding the source. We obtained a measure of this number by
taking into account that in our solution about 20 percent of the neutrons are captured by
manganese and the rest by hydrogen. In order to obtain, in the same units, a measure of the
number of neutrons absorbed by uranium we proceeded in the following way: A mixture of sand
and manganese powder, having the same thermal neutron absorption as uranium oxide replaced
the uranium oxide in 1/4 of the cans which were distributed uniformly among the other uranium
oxide-filled cans. After irradiation, all this powder was mixed together, a ten-percent MnSO4
solution was prepared from a sample, and its activity was measured with our ionization chamber.
     In this way we found that about 50 percent of the neutrons emitted by the source are
absorbed as thermal neutrons by uranium in our arrangement. It follows that, if uranium absorbed
only thermal neutrons, the observed ten-percent increase in activity obtained with uranium present
would correspond to an average emission of about 1.2 neutrons per thermal neutron absorbed by
uranium..This number should be increased, to perhaps 1.5, by taking into account the neutrons
which, in our particular arrangement, are absorbed at resonance in the nonthermal region by
uranium, without causing neutron emission.
     From this result we may conclude that a nuclear chain reaction could be maintained in a
system in which neutrons are slowed down without much absorption until they reach thermal
energies and are then mostly absorbed by uranium rather than by another element. It remains an
open question, however, whether this holds for a system in which hydrogen is used for slowing
down the neutrons.
     In such a system the absorption of neutrons takes place in three different ways: The
neutrons are absorbed at thermal energies, both by hydrogen and uranium, and they are also
absorbed by uranium at resonance before they are slowed down to thermal energies. Our result is
independent of the ratio of the concentrations of hydrogen and uranium, insofar as it shows that,
for thermal neutrons, the ratio of the cross section for neutron production and neutron absorption
in uranium is greater than one, and probably about 1.5. What fraction of the neutrons will reach
thermal energies without being absorbed will, however, depend on the ratio of the average
concentrations of hydrogen and uranium. Since there is an appreciable absorption even far from
the center of the resonance band, it follows that the fraction of neutrons absorbed by uranium at
resonance will increase with decreasing hydrogen concentration. This has to be taken into account
in discussing the possibility of a nuclear chain reaction in a system composed essentially of
uranium and hydrogen. A chain reaction would require that more neutrons be produced by
uranium than absorbed by uranium and hydrogen together. In our experiment the ratio of the
average concentration of hydrogen to uranium atoms was 17 to 1, and in the experiment of von
Halban, Joliot and Kovarski this ratio was 70 to 1. At such concentrations the absorption of
hydrogen in the thermal region will prevent a chain reaction. By reducing the concentration of
hydrogen one would obtain the following effect: On the one hand a larger fraction of those
neutrons which reach thermal energies will be absorbed by uranium;on the other hand fewer
neutrons reach the thermal region due to an increased absorption by uranium at resonance. Of
these two counteracting factors the first is more important for high hydrogen concentrations and
the second is more important for low hydrogen concentrations. Starting with high hydrogen
concentrations, the ratio of neu'tron production to total neutron absorption will thus first rise,
then pass through a maximum, and, as the hydrogen concentration is decreased, thereafter
decrease. We attempted to estimate the quantities involved from the information available about
resonance absorption in uranium  and from the observed net gain of 0.2 in the number of neutrons
in our experiment. The effect of the absorption at resonance turns out to be so