Atomic selective ionization processes provide critical ionization probability and isotopic selectivity in laser isotope separation. Aimed at the general principles of transition cross sections and ionization probabilities under various atomic hyperfine structures and laser parameters, and the optimization of atomic multi-channel photo-excitation and ionization processes of non-zero nuclear spin isotopes, the semi-classical density matrix theory of an imaginary two-step photoionization process is established with the consideration of magnetic sublevels of near-resonantly excited hyperfine levels. For determining the dimensionless transition cross sections of hyperfine transition channels, two methods are proposed in this article, i.e. the saturated excitation line-shape comparison method and weak excitation signal strength method, and a good agreement is achieved between numerical dimensionless transition cross sections and experimental results for several non-zero nuclear spin isotopes. The dependence of saturated ionization probability on laser polarization is studied systematically, and the hyperfine transition of Δ F = +1 is found to be superior to Δ F = −1, 0 in terms of saturated ionization probability. A general formula of oversaturated ionization probability is summarized for different hyperfine transitions. An interesting phenomenon called “magnetic sublevel coherence trapping” is employed to explain the inadequate ionization probability of the Δ F = −1 hyperfine transition even under the oversaturated excitation condition, and its mechanism is discussed through the temporal evolution of the density matrix elements. These numerical studies can provide beneficial references for laser isotope separation of isotopes with non-zero nuclear spin, as well as atomic laser spectroscopy.
Atomic selective ionization processes provide critical ionization probability and isotopic selectivity in laser isotope separation. Aimed at the general principles of transition cross sections and ionization probabilities under various atomic hyperfine structures and laser parameters, and the optimization of atomic multi-channel photo-excitation and ionization processes of non-zero nuclear spin isotopes, the semi-classical density matrix theory of an imaginary two-step photoionization process is established with the consideration of magnetic sublevels of near-resonantly excited hyperfine levels. For determining the dimensionless transition cross sections of hyperfine transition channels, two methods are proposed in this article, i.e. the saturated excitation line-shape comparison method and weak excitation signal strength method, and a good agreement is achieved between numerical dimensionless transition cross sections and experimental results for several non-zero nuclear spin isotopes. The dependence of saturated ionization probability on laser polarization is studied systematically, and the hyperfine transition of Δ F = +1 is found to be superior to Δ F = −1, 0 in terms of saturated ionization probability. A general formula of oversaturated ionization probability is summarized for different hyperfine transitions. An interesting phenomenon called “magnetic sublevel coherence trapping” is employed to explain the inadequate ionization probability of the Δ F = −1 hyperfine transition even under the oversaturated excitation condition, and its mechanism is discussed through the temporal evolution of the density matrix elements. These numerical studies can provide beneficial references for laser isotope separation of isotopes with non-zero nuclear spin, as well as atomic laser spectroscopy.
The atomic selective multi-step photoionization process is a critical step in laser isotope separation. In this work, we study three-step photoionization processes with non-monochromatic laser fields theoretically based on the semi-classical theory. Firstly, three bandwidth models, including the chaotic field model, de-correlation model, and phase diffusion model, are introduced into the density matrix equations. The numerical results are compared with each other comprehensively. The phase diffusion model is selected for further simulations in terms of the correspondence degree to physical practice. Subsequently, numerical calculations are carried out to identify the influences of systematic parameters, including laser parameters (Rabi frequency, bandwidth, relative time delay, frequency detuning) and atomic Doppler broadening, on photoionization processes. In order to determine the optimal match among different systematic parameters, the ionization yield of resonant isotope, and selectivity factor are adopted as evaluation indexes to guide the design and optimization process. The results in this work can provide a rewarding reference for laser isotope separation.
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.
The selectivity of three-step pulse photo-ionization of atoms versus the detuning delta of exciting radiation frequencies from intermediate resonance is investigated in powerful laser fields where the power broadening of the resonant transitions is at least of the order of isotope shifts. The Doppler broadening of the resonant transitions is taken into account and it is assumed that the sum frequency of both exciting laser radiations is tuned to the line centre of the two-photon transition of a selected isotope. It is shown that in this situation the photo-ionization selectivity increases so greatly with the absolute detuning mod delta mod that even in such strong fields the process of photo-ionization can be highly selective. The optimization of selective photo-ionization of atoms is discussed in connection with the decrease in the selective isotope yield with increase of the absolute detuning mod delta mod . Analytical consideration of selective three-step pulse photo-ionization in powerful laser fields, based on the density matrix formalism, is presented together with the results of numerical simulation of the 40 Ca- 48 Ca laser isotope separation process as an example.
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.
It is proposed and studied a new optimal theoretical scheme for the laser photoionization sensor of the separating isotopes, nuclear isomers and nuclear reactions products, which is based on the selective laser excitation of the isotope atoms into excited Rydberg states and further stochastic collisional ionization mechanism. The operator perturbation theory and FockerPlank stochastic equation method are used for description of stochastic collisional ionization process. The optimal laser action model and density matrices formalism is used for numeric calculation of the optimal scheme of the Na, U, Cs and Cf isotopes (ions, nuclei) sensing.
Ytterbium enriched in 176Yb is used for the production of the 177Lu radioisotope, which has applications in cancer treatment. We have theoretically studied the two-step resonant, three-step photoionization of the 176Yb isotope using the density-matrix approach. To simulate experimentally realistic conditions, the Doppler averaging, magnetic sublevel degeneracy, time-varying Rabi frequencies, ionization rate, angular divergence, and laser bandwidth have all been incorporated into the theoretical model. Calculations have been carried out to identify the optimized Rabi frequencies for evaluating the separation factor. The effect of the laser line shape on the excitation profile has also been thoroughly studied. We could obtain large separation factors of ~5000 for the 176Yb isotope, and the excitation conditions identified in this work may be utilized in the separation of the desired isotope.