Real-time semiclassical initial value method and threshold tunneling probabilities

The semiclassical initial value representation (SCIVR) approach to tunneling is applied to a barrier which does not have a harmonic component and vanishes asymptotically. The lack of a harmonic approximation near the barrier top combined with the use of the primitive Van Vleck–Gutzwiller approximation provides a fairly stringent test for the SCIVR approach. In this paper we show that the primitive IVR performs rather well in obtaining the threshold tunneling probabilities for the nonharmonic barrier. In particular, we demonstrate that the threshold tunneling probabilities are reliable even in situations wherein the cutoff distances are large enough for tunneling loops to be formed.