Metastable state decay through tunneling

A potential corresponding to this problem is Figure 1.1(b). Metastable states supported by the potential well decay through tunneling. The corresponding diagram is shown in Figure 2.10. 

B. Decay of Metastable State through Tunneling (Predissociation)... 

The theory developed for tunneling splitting can be easily extended to the decay of the metastable state through multidimensional tunneling, namely, tunneling predissociation of polyatomic molecules. In the case of predissociation, however, the instanton trajectory cannot be fixed at both ends, but one end should be free (see Fig. 17). The boundary conditions are... 

This result verifies the correctness of the expression for r given in Ref. [7], where it was just a guess based upon the analogy with the one-dimensional E <8> e case. It has the same clear-cut physical meaning, r represents the probability of decay of the metastable state in the well. It is proportional to the number of particle collisions with the barrier wall per second, u>/2it, and to the exponential factor, that is the probability of tunneling through the barrier at each of these collisions. 

In the first part of this section, the instanton theory [2] is explained by taking the motion of a particle of mass m in one-dimensional potential V x). Tunneling splitting in a symmetric double well potential and decay of metastable state by tunneling through a potential barrier are employed as examples. In the second subsection, it is shown that the results can be reproduced by the WKB method with slight modification. 

Next, let us consider the decay of a metastable state through tunneling [see Figure 1.1(b) and Figure 2.10]. The formulation can be done in the similar way as in the case of tunneling splitting [44]. The decay rate is given by... 

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