Polarization Potentials for Positron- and Electron-Atom Systems

Semiempirical polarization potentials with several cutoff functions are investigated for positron- and electron-atom interactions. A disposable parameter, an effective target radius, in each cutoff function of the polarization potential is adjusted so as to reproduce well-established reference values (scattering lengths and binding energies) for targets containing one or two electrons. Striking regularities in fitted parameter values are found despite the very wide variety of cutoff functions examined. The parameter exhibits a strong dependence upon spin and angular momentum in the electronic systems, which is rationalized in terms of the Pauli exclusion principle. Simple semiempirical relations between the effective radii for positronic systems and those for the corresponding electronic systems are proposed. The method for constructing model polarization potentials for electron- and positron-atom systems for targets containing up to two electrons is extended to neon and argon targets by considering pairwise interactions. For the electronic systems a local exchange potential has been devised with parameters which are adjusted to generate the correct static-exchange phase shifts and Hartree-Fock scattering length without explicitly considering the orthogonality conditions for the scattering wave. In spite of great simplicity of our method, our results for the electronic systems are very accurate even at low energy, where most other elaborate calculations yield less accurate results. For positronic systems, which are more sensitive to errors in potentials, our method produces reasonably good results. The coupled static approximation is then employed with including the polarization effect through the model polarization potential in each channel. The effect of the virtual positronium formation to the elastic scattering below the positronium formation threshold has been also investigated by using the same semiempirical polarization potentials for both atoms and found to be very large even at zero incident positron energy. Our approximation with various sets of the effective hydrogen and positronium radii, however, has failed to reproduce the most reliable variational results below and above the positronium formation threshold, although our results by adjusting the effective radii for the best s-wave phase shifts below the threshold are better than the other results from the non-variational methods. The results may indicate that the static coupling potentials are insufficient to describe the correct couplings between channels