General Considerations Concerning the Lattice Structure

The last two kinds of premature neutron absorption may occur in the third part of the cycle. First, the damper as well as the U absorbs slow neutrons to some extent. Evidently, the neutrons absorbed in the damper will not cause 

The last cause of neutron loss is the absorption of the thermal neutrons by the rather than the. Only the latter absorption leads to fission and the creation of daughter neutrons. The relative amount of absorption by the cannot be diminished except by increasing the percentage of in the U or by adding 49, i.e., by enriching the U. 

The so-called lattice calculations are designed to obtain the geometries (carbon to U ratio and size of lumps) in which the sum of the resonance and thermal losses is least. It turns out, for instance, that a carbon to uranium mass ratio of 6 with uranium spheres of 2 diameter gives a particularly small premature loss of neutrons. The calculations are based on numerous experimentally established nuclear constants. They have been, on the whole, well confirmed by direct observations. 

A chain reacting system will be thermally stable if it becomes less chain reacting as the temperature increases. On the other hand, if the system becomes more chain reacting as the temperature increases, it is thermally unstable. These possibilities have been described already above, by Fermi. 

Evidently, the thermal stability depends on whether or not the above detailed losses increase with increasing temperature we shall give a brief analysis of the relevant factors. It must be emphasized, however, even at the outset, that it is not possible, at present, to predict theoretically whether a given system will be thermally stable or unstable. As was pointed out by Fermi, an empirical answer to this question must also await further work. 

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A. M. Weinberg and E. P. Wigner, General Considerations Concerning the Lattice Structure , from Possibility of a Chain Reaction by Fermi, Weinberg, and Wigner, CP-383, November 16, 1942. 

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