Test of a q-fractional V^(N-q) hartree-fock potential for the calculation of double photoionization cross sections of neon

The approach of a parametric V^(N-q) Hartree-Fock potential with fractional q is developed and applied for the first time for the calculation of the double photoionization cross sections of Ne. A minimum of the squared difference between the length-form and velocity-form cross sections is used as a criterion for calculating the values of q. It is found that the minimization procedure leads to a practically exact equality of the length-form and velocity-form cross sections for the Ne III 2s²2p⁴[³P, ¹D, ¹S], 2s¹2p⁵[³P, ¹P] and 2s⁰2p⁶[¹S] states in the exciting-photon energy region from the double-ionization threshold up to 325 eV, if q is considered as a function of the exciting-photon energy. The calculated V^(N-q) cross sections are in better agreement with the experimental data than those for the V^(N-1) and V^(N-2) potentials.