Electron-impact excitation of quadrupole-allowed transitions in positive ions

An asymptotic analysis of the partial collision strength for quadrupole-allowed transitions, in the limit of large angular momentum, is presented. It is shown that the infinite sum over partial collision strengths, which gives the total collision strength, is asymptotic to a geometric series of ratio k<²/k>², where k>² and k<² are the energies of the free electron before and after the collision.