Single eta production in heavy quarkonia: Breakdown of multipole expansion

The η production in the (n,n′) bottomonium transitions ϒ(n)→ϒ(n′)η, is studied in the method used before for dipion heavy quarkonia transitions. The widths Γη(n,n′) are calculated without fitting parameters for n=2,3,4,5, n′=1. Resulting Γη(4,1) is found to be large in agreement with recent data. Multipole expansion method is shown to be inadequate for large size systems considered.