Non-hydrogenic wavefunctions in momentum space

Abstract

Quantum defect theory is applied to the calculation of non-hydrogenic radial wavefunctions in the momentum space representation, given in the form of Hankel transform integrals of the position space functions in the Coulomb approximation. It is shown that, even for low excited states, the momentum space functions for important values of the momentum are insensitive to the inner-core region of the atom. Analytical expressions are presented and illustrative examples are given for some Rydberg states in sodium, magnesium and caesium.

Multiphoton ionization of unsaturated hydrocarbons

“…In connection with the MPI of rare gas atoms (Larochelle et al 1998) it is found that this wavefunction gives a satisfactory result. Using equation ( 16) in equation ( 10) and performing the three-dimensional Fourier transform using the Hankel transform (Hoang Binh et al 1997) the rate of MPI of the molecule was calculated for any fixed orientation of the electric field F . Averaging over all possible orientations of the molecule (equation ( 11)), the average rate of MPI of the molecule is obtained.…”

Dissociative ionization of benzene in intense ultra-fast laser pulses

“…where λ = 800 nm is the wavelength, I 0 is the peak intensity, w 0 = 49 µm is the 1/e 2 radius of the focal spot and τ = 200 fs is the full width at half maximum (FWHM) of the pulse. Finally, the three-dimensional Fourier transform in equations (7) and (8) is calculated using Hankel transforms [31]. Equipped with all of these, equations (6) were solved and the time-and position-dependent probabilities P 1 (r, t) and P 2 (r, t) were determined.…”

“…where λ = 800 nm is the wavelength, I 0 is the peak intensity, w 0 = 49 µm is the 1/e 2 radius of the focal spot and τ = 200 fs is the full width at half maximum (FWHM) of the pulse. Finally, the three-dimensional Fourier transform in equations ( 7) and ( 8) is calculated using Hankel transforms [31].…”

Momentum-space non-hydrogenic wavefunction of quantum defect theory

“…In contrast, the non-hydrogenic wavefunctions of QDT require irregular Whittaker functions for their description [5]. This feature appears as an awkward analytical constraint to express Seaton's non-hydrogenic wavefunction of QDT in momentum space and in most applications use is made of a truncated asymptotic expansion of the irregular Whittaker function [6,7]. Only after further approximations of the irregular Whittaker function, can an analytic form of Seaton's wavefunction be obtained in momentum space.…”

“…In this work, we present an exact hypergeometric-function representation for Seaton's asymptotic non-hydrogenic wavefunction in momentum space, which can be used for both the ground and excited states of the valence electron. Using this wavefunction, we study the momentum (q)-space wavefunction of the Rydberg states 3 Li(2s), 24 Mg(6s) and 37 Rb(5s) and compare them with those obtained from a QDT approximate [6,7,9] wavefunction.…”