MOMENTUM-TRANSFER DISPERSION-RELATIONS FOR ELECTRON-ATOM CROSS-SECTIONS

We derive momentum-transfer dispersion relations by showing that at fixed impact energy the electron-atom differential cross sections are analytic functions of the momentum transfer squared K2 in a complex plane cut from - infinity to 0, along the real axis. It is therefore natural to introduce sets of interpolating rational functions of K2 to fit experimental data. The most suitable are the Pade approximations. We find that the zeros and the poles of these approximations split into two families. One family is made of poles and zeros that sit on the cut, yielding a good simulation of it. The other family takes care of the noise in the data: poles and zeros appearing in pairs very near each other. We can therefore first filter the noise by eliminating those pairs. Among the remaining poles, one pole is extremely near K2=0 for the inelastic differential cross sections. We apply this technique to recompute both elastic and inelastic cross sections for Xe, Kr, and Ar atoms, at impact energies of 100, 400, and 500 eV. In this way, we get the optical oscillator strength for two optically connected states. Our results are compared with other experimental as well as theoretical results.