Symmetry properties of tunneling states in JT systems

SYMMETRY PROPERTIES OF TUNNELING STATES IN JAHN-TELLER SYSTEMS 

one can see that these are A2l, and 7ju of Oh. Each includes Alu of D3d just once. The 4-fold tunneling multiplet sphts into A2u + 7ju of Oh. 

To find the symmetry-adapted combinations Ffy that represent the tunneling multiplet, we can apply symmetry projection  

With these relationships for off-diagonal matrix elements, equation (3) can be written in the following general form  

The rate factors rr interrelate just two wells, the well 1 and the well r. For just one barrier separating the two wells, the classical path under the barrier does not split into branches. The classical path in the restricted area is approximately separable (see Section 5 later). Therefore, in JT systems, after the weight factors mr(r) are established, the multidimensional tunneling problem reduces to a one-dimensional consideration. 

---