Exact second Born amplitude for the electron impact excitation of the 1s to 2s transition in atomic hydrogen

The authors report an exact calculation of the second Born amplitude for the electron impact excitation of the 1s to 2s transition in atomic hydrogen at 54.4 eV. Comparison is made between the exact results and the closure approximation to the amplitude. It is concluded that the closure approximation is not too bad in the energy range in which it is presently being used. In particular the distorted-wave second Born approximation cross section of Kingston and Walters (1980) for the 1s to 2s transition, which differs markedly from the 1s-2p-2p close-coupling cross section for this transition, is shown not to be substantially in error through the use of the closure approximation.