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 radius, in each cutoff function is adjusted so as to reproduce well-established reference values (scattering lengths and binding energies) in calculations. 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, which enable one to find the parameter value for an electron by fitting a positron calculation to a reference value, or vice versa. In other words, the number of adjustable parameters is reduced to a single effective radius for each target regardless of the projectile.