Energetics of a Decay

We will consider the general features of a emission, and then we will describe them in terms of a simple quantum mechanical model. It turns out that a emission is a beautiful example of the quantum mechanical process of tunneling through a barrier that is forbidden in classical mechanics. 

For example, one of the heaviest naturally occurring isotopes, 238U (with a mass defect, A of +47.3070 MeV) decays by a emission to 234Th (A = +40.612 MeV) giving a Qa value of  

The Qa values generally increase with increasing atomic number, but the variation in the mass surface due to shell effects can overwhelm the systematic increase (Fig. 7.2). 

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. 

Example Problem Calculate the Q value, kinetic energy T, barrier Vc, for the primary branch of the a decay of 212 208Pb. 

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The third technique for establishing a reference axis for angular correlations can be applied to nuclear reactions when the direction of a particle involved in the reaction is detected. This direction provides a reference axis that can be related to the angular momentum axis, but each nuclear reaction has its own pecu-larities and constr aints on the angular momentum vector. For example, the direction of an a particle from a decay process that feeds an excited state can be detected as indicated in Figure 9.7, but, as is discussed in Chapter 7, the energetics of a decay... 

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