We consider the spin-exchange ( SE ) cross section in electron scattering from ^ { 3 } He II , which drives the hyperfine-changing 3.46 cm ( 8.665 GHz ) line transition .
Both the analytical quantum defect method — applicable at very low energies — and accurate R-matrix techniques for electron-He ^ { + } scattering are employed to obtain SE cross sections .
The quantum defect theory is also applied to electron collisions with other one-electron ions in order to demonstrate the utility of the method and derive scaling relations .
At very low energies , the hyperfine-changing cross sections due to e - He ^ { + } scattering are much larger in magnitude than for electron collisions with neutral hydrogen , hinting at large rate constants for equilibration .
Specifically , we obtain rate coefficients of K ( 10 { K } ) = 1.10 \times 10 ^ { -6 } cm ^ { 3 } / s and K ( 100 { K } ) = 3.49 \times 10 ^ { -7 } cm ^ { 3 } / s .