Closed decay energy cycles

The masses for many short-lived nuclei are unknown although their decay modes and energies have been determined. From this the nuclear masses may be calculated, and consequently Q-values of different imknown decay modes can be obtained. This can be done through the use of closed decay energy cycles. 

The generally smooth variation of Qa with Z, A of the emitting nucleus and the two-body nature of a decay can be used to deduce masses of unknown nuclei. One tool in this effort is the concept of closed decay cycles (Fig. 7.3). Consider the a and (3 decays connecting j7Np,, 721 Am, 1 Pu, and IpU. By conservation of energy, one can state that the sum of the decay energies around the cycle connecting these nuclei must be zero (within experimental uncertainty). In those cases where experimental data or reliable estimates are available for three branches of the cycle, the fourth can be calculated by difference. 

Suppose we need to know if can decay to Th through a-emission. Of course this is a simple calculation if the masses of U and " Th are known, but let us assume they are not. We have data that decays through jU-emission ( max 0-248 MeV) followed by 7-decay (Ey 0.267 MeV). Th decays through /3-emission 1.230 MeV) directly to " Pa. Wp undergoes a-decay to Pa with E = 4.79 MeV. We may construct a closed cycle including these decay energies... 

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