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Physical Review A

Theory of doubly resonant ionization by broad-band radiation applied to the determination of isotopic abundances

A. Lyras, B. Zorman, P. Lambropoulos

Published Jul 1, 1990• 21 citations
Publisher

Abstract

We present a theoretical study of doubly resonant three-photon ionization with radiation of sufficiently broad bandwidth to overlap all hyperfine levels of the resonant intermediate states. We demonstrate that isotopic selectivity in ionization is apt to occur under a variety of circumstances, although the degree may vary from negligible to quite significant, depending on the relative values of atomic and radiation parameters. Our theory provides a satisfactory quantitative interpretation of recent experimental data in Sn.

DOI
10.1103/physreva.42.543

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We present a theoretical study of doubly resonant three-photon ionization with radiation of sufficiently broad bandwidth to overlap all hyperfine levels of the resonant intermediate states. We demonstrate that isotopic selectivity in ionization is apt to occur under a variety of circumstances, although the degree may vary from negligible to quite significant, depending on the relative values of atomic and radiation parameters. Our theory provides a satisfactory quantitative interpretation of recent experimental data in Sn.
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We present a theory of Stark splitting in doubly resonant three-photon ionization (three-level system) with nonmonochromatic fields. The asymmetry of the peaks of the resonance curve due to Stark splitting is shown to be reversed when the laser bandwidth is larger than the width of the atomic transitions of the resonant states. It is further shown that ionization as well as the probe field have a significant effect on the features of the splitting. Similar effects are found with monochromatic fields in the presence of an additional level near the initial level (four-level system). The results of the analysis are in general qualitative agreement with existing observations.
We have studied two-photon resonant three-photon ionization of atomic sodium vapor. A dye laser tuned to either the 4d or 5s two-photon allowed transition was used to excite the atom and a second more intense laser (λ = 7000 Å) was used for ionization. The ion yield was measured as a function of resonant laser intensity and detuning, the nonresonant laser intensity, and the temporal overlap of the exciting and ionizing laser pulses. We have found1 that at high laser intensities the photoionization yield decreases as the nonresonant laser intensity is increased. When tuned to the 5s level a value of ~−0.6 was obtained for the exponential index even with the resonant laser tuned to maximize the ion yield. A theoretical model including the effects of Stark shift of the ground state, power broadening of the intermediate level due to saturation of the two-photon transition and by rapid transitions to the ionization continuum was used to predict the experimental results. Good agreement between theory and experiment required the use of a photoionization cross section for the 5s level which was ~20 times greater than the accepted value. Results for photoionization from the 4d level are also presented.
The manifestation of double resonances upon the three-photon ionization of the samarium atom has been studied in a frequency range of 17200–18400 cm −1 . Thirty peaks caused by double resonances have been found in the dependence of the yield of Sm + ions on the laser radiation frequency. The majority of these peaks greatly exceed in amplitude the peaks associated with ordinary two-photon resonances. The influence of double resonances on the three-photon ionization has been theoretically analyzed using the density matrix approximation. The calculations show that the probability of the three-photon resonance ionization can increase by more than two orders of magnitude due to the additional one-photon population of an intermediate level. The double resonance slows down the rate of increase in the probability of ionization with an increase in the laser radiation intensity compared to ordinary two-photon resonance.
Selective photoionization of ytterbium isotope is studied numerically based on a three-step photoionization scheme, 4f146s2 1S0 (0 cm−1) → 4f146s6p 3P1 (17992.008 cm−1) → (4f136s26p) (7/2, 3/2)2 (35196.98 cm−1) → auto-ionization state (52353 cm−1) → Yb+, by the density matrix theory with the consideration of atomic hyperfine structures and magnetic sublevels. To examine the physical model, the numerical isotopic abundance of ytterbium is compared with that from mass spectroscopy experiment, showing that they are in good agreement with each other. The excitation process and ionization process of ytterbium, especially for odd isotopes, are discussed and analyzed in detail on this basis. The effects of frequency detuning, power densities, spectral bandwidths, polarization of two excitation lasers, and atomic Doppler broadening on the total ionization yield and isotopic abundance are investigated numerically and the optimal excitation conditions for 176Yb enrichment are identified semi-quantitatively.
A general theory is developed to treat two-photon ionization through a single intermediate state in which an arbitrary degree of relaxation may occur. The method is set up to probe the parameters governing the relaxation, by determination of the angular distribution of photoelectrons. The method is applied to the ionization of Na atoms, through the 3p2P123p^{2}P_{\frac{1}{2}}3p2P21​​ and 3p2P323p^{2}P_{\frac{3}{2}}3p2P23​​ intermediate states.