Geometric phase driven predissociation: Lifetimes of 2$^2A'$ levels of H$_3$

We discuss the role of the geometric phase in predissociation dynamics of vibrational states near a conical intersection of two electronic potential surfaces of a $D_{3h}$ molecule. For quantitative description of the predissociation driven by the coupling near a conical intersection, we developed a method for calculating lifetimes and positions of vibrational predissociated states (Feshbach resonances) for X$_3$ molecule. The method takes into account the two coupled three-body potential energy surfaces, which are degenerate at the intersection. As an example, we apply the method to obtain lifetimes and positions of resonances of predissociated vibrational levels of the 2$^2A'$ electronic state of the H$_3$ molecule. The three-body recombination rate coefficient for the H+H+H $\to$ H$_2$+H process is estimated.