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Journal of Nuclear Science and Technology

Laser Power Balance for Effective Multi-Step Photoionization of Degenerate Atoms

Katsuhiko Nakahara, Junko Watanabe, Kunihiko Nakayama, Tadashi Yoshida

Published Jan 1, 1993• 5 citations
Publisher

Abstract

Optimization of laser power balance is studied numerically for effective multi-step photoionization of degenerate atoms. To date, a large number of similar studies have been executed for simple nondegenerate atoms and, therefore, the emphasis in this study is placed on investigating the role of the level degeneracy. It is concluded that a monotonically increasing J-value in the excitation ladder of levels is preferable, which is followed by some variations thereof. It should also be noted that a reasonably high ionization rate is attainable, in any case, provided that the Rabi-frequencies are optimized at the expense of the sizable laser powers required. The computer code employed here, which deals with the population evolution among numerous magnetic sublevels, has been tested against experiments in advance of the above numerical study.

DOI
10.1080/18811248.1993.9734472

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Optimization of laser power balance is studied numerically for effective multi-step photoionization of degenerate atoms. To date, a large number of similar studies have been executed for simple nondegenerate atoms and, therefore, the emphasis in this study is placed on investigating the role of the level degeneracy. It is concluded that a monotonically increasing J-value in the excitation ladder of levels is preferable, which is followed by some variations thereof. It should also be noted that a reasonably high ionization rate is attainable, in any case, provided that the Rabi-frequencies are optimized at the expense of the sizable laser powers required. The computer code employed here, which deals with the population evolution among numerous magnetic sublevels, has been tested against experiments in advance of the above numerical study.
Based on rate equation a theoretical study on laser power balance in a resonance multi-step ionization process of atoms has been presented in this paper.The calculation results made for a typical three-level atom show that there is an optimization laser power assignment when the total pumping laser power is limited,and under the optimization laser power assignment the ionization probability of a three-level atom can reach its maximum value.This conclusion is very different from that obtained under saturation excitation conditions.The method used here can be applied to more complicated multi-step ionization process of atoms.
Numerical computations of ionization efficiency and isotope selectivity of 176 L u have been carried out for the following three-step ladder type photoionization scheme, 5 d 6 s 2 2 D 3 / 2 ( 0.0 c m − 1 ) − − − ⟶ 540.4068 n m ⁡ 5 d 6 s 6 p 4 F 5 / 2 o ( 18504.58 c m − 1 ) − − − ⟶ 535.0626 n m 5 d 6 s 7 s 4 D 3 / 2 ( 37193.98 c m − 1 ) − − − ⟶ 618.0061 n m 53375 c m − 1 A u t o i o n i z a t i o n S t a t e → L u + , by invoking the density matrix formalism for the laser–atom interactions. Equations of motion have been derived for the odd isotopes by inclusion of hyperfine levels. The line shapes and their effect on the ionization efficiency and isotope selectivity have been discussed in detail. The effects of power of excitation and ionization lasers, spectral bandwidths, pulse delays, Doppler broadening of the atomic ensemble on the ionization efficiency, and degree of enrichment have been presented. Optimum conditions for the power of excitation, detunings, and other system parameters for the selective yet efficient photoionization of 176 L u have been identified.
The effect of a dc magnetic field on the rate at which a ground-level, Zeeman-degenerate atom is photoionized via a short-lived autoionizing level is calculated. We consider single-step as well as two-step photoionization; in the latter case we allow the light to be either resonant or far from resonance with an intermediate level. In all cases we find that the magnetic field may raise the fraction of the atoms available for photoionization and consequently increase the photoion fraction produced by a light pulse of given fluence. In the resonant case we find that if the magnetic-field Zeeman splitting of the ground and intermediate level is much larger than the rate at which population enters or leaves that level then the Zeeman-state populations are decoupled from one another and there exist simple conditions under which they obey rate equations. In the nonresonant case an additional condition for two-photon rate equations is that the optical Stark shift of the ground state be much smaller than the magnetic Zeeman splitting. These results apply specifically to excitation by lasers whose spectral widths are narrow compared to the homogeneous linewidths of the corresponding atomic transitions, but appear to be generalizable to the opposite limit, in which the laser spectral widths are much broader than the homogeneous linewidths.
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 theoretical model of two-step resonant ionization which includes an autoionizing state is developed. The effects examined include interactions with a multimode laser and Zeeman and hyperfine multiplets. We approach this problem starting from first principles by treating the atom-radiation system as a unit. Theoretical analysis and numerical calculations of ionization probabilities are given. The intermode scattering is investigated in detail, and a simple physical interpretation of the dynamical effect is given. Comparisons of ionization probabilities for two-step processes with first-step excitations by single-mode or two-mode lasers are made. It is found that, if the mode spacing in a multimode-laser beam is less than the Doppler width of the atom, the multimode laser can more effectively produce ions than a single-mode laser does. This leads to the conclusion that the resonance effect is more important than the power-broadening effect. This is shown to be also true when Zeeman and hyperfine multiplets are included.
The dynamical process of photoexcitation and photoionization of alkali atoms is studied with three-step laser pulses, focusing on the similarities and differences between Li and Cs atoms on their properties by making a comparison of them. Based on several excitation schemes, the present work not only establishes the rate equations of atom population for all related transition states, but also obtains the analytical solutions of photoexcitation and photoionization process. The mathematical solutions are simplified significantly by restricting the most general case to the several special cases, either designed or selected carefully, in order to highlight the main factors and obtain the physical insight underlying the complicated mathematical expressions. With self-programming, the possible impact of time configuration of laser pulses on the three-step laser excitation process of the photoexcitation and photoionization is calculated and studied systematically. Variation of the ionization efficiency with the laser parameters is investigated and discussed. With the same time configuration of laser pulses, the dependences of atom population for all the related transition states on the two different excitation paths are compared and analyzed, reflecting the impact of changing the atomic parameters. Under the similar excitation conditions, the differences of ionization efficiency between Li and Cs atoms are explored. Finally, based on the present study, several means for optimizing ionization efficiency are proposed.