Dalgarno-Lewis method for second-order energies of Rydberg states of neon

The quadrupole moment and dipole polarizibilities of the ${\mathrm{Ne}}^{+}$ ground state are obtained from previous experimental data using nondegenerate perturbation theory and the method of Dalgarno and Lewis. A modified finite-difference approach to numerically solve the resulting differential equations is discussed in detail. The value of the quadrupole moment of the ${}^2{P}_{3/2}$ ground state of ${\mathrm{Ne}}^{+}$ is thereby found to be $-0.204{015\left(26\right)\mathrm{ea}}_0^2,$ in disagreement with the value from atomic structure calculations. Comparison of the results with those obtained by other approaches used to extract the same parameters from the experiment suggests that the results of the present method are more reliable. Furthermore, the present method is faster, requires no initial theoretical input for the core parameters, and provides sufficient precision to form a restrictive test for theoretical predictions of the quadrupole moment and other ${\mathrm{Ne}}^{+}$ parameters.