The photoionization cross section of neon

Abstract

The photoionization cross section has been calculated for neon from threshold to an incident photon energy of 11.547 Rydbergs considering transitions from both the 2s and 2p shells. The results are in good agreement with recent experimental data. The bound state wave functions for the configurations Ne (1s}^2 (2s)^2 (2p)^6 , Ne+(1s)^2 (2s)^2 (2p)^5 , and Ne+(1s) 2 (2s)(2p)^6 were computed by the Hartree-Fock method. A new method for solving the radial Schrodinger equation which simplifies the numerical integration and provides total energies which are more consistent than those obtained in previous calculations is presented. As a result the computed ionization and excitation energies are in excellent agreement with experiment. Hartree-Fock equations are derived for an ion-free electron system by including the free electron function in the Slater determinant. The resulting set of equations include the polarizing effect of the free election upon the ion. However, it is shown that polarization has a negligible effect upon the field acting upon the free electron, and it is assumed that it also produces a negligible perturbation in the orbitals of the ion. The free electron functions which were used in the evaluation of the cross sections were then computed by using the orbitals of the positive ions to define the potential field and exchange terms. Both the dipole length and dipole velocity formulations were used in the evaluation of the cross section. It was found that for the photoionization of the 2p electron the cross section computed from the dipole length equation was greater than the one obtained from the dipole velocity equation, while for the photoionization of a 2s electron the dipole velocity equation gave the larger results. Due to these results, it was decided that the cross section obtained by averaging the values computed from the two formulations would be reported. This average cross section has a threshold at an incident photon energy of 1.5466 R. and then rises rapidly to a maximum of 9.85Mb at an energy of 2.5 R. The energy of the L_i edge is 3.5162 R. The theoretical curve is in good agreement with the experimental observations, both in shape and magnitude. The cross section for the ionization of the ion by the loss of a 2p electron was also computed using free electron functions whose potential and exchange terms were defined by the orbitals of neutral neon. This cross section was too large in magnitude and peaked at larger energies that did the experimental cross section, and it was shown that this indicated that the potential field as defined by the atomic orbital was weaker than the one actually acting upon the free electron. Since the cross section which was computed with free electron functions whose potential and exchange terms were defined by the orbitals of the positive ion agreed both in magnitude end photon energy of the maximum, it was concluded that the free electron does indeed move in a field that closely resembles that of the positive ion. This also indicates that polarization effects should be small.