Optical selectivity calculations have been carried out for the 91Zr isotope for two-color resonant three-photon photoionization schemes. The density-matrix equations of motion were solved numerically for collinear, counterpropagating, linearly polarized laser beams having Gaussian temporal profile. Calculations were carried out incorporating the effects of Doppler broadening, magnetic sublevel degeneracy, and laser bandwidths. The selectivities and ion yields were determined for various Rabi frequencies and ionization rates. Thereby, the optimal Rabi frequencies for the first and second excitation steps and ionizaton rate for the ionizaton step were determined. The ionization efficiency as a function of detuning of the excitation lasers was also investigated. Two of the photoionization schemes investigated yielded a selectivity of ∼10, with an ion yield of ∼23%.
Optical selectivity calculations have been carried out for the 91Zr isotope for two-color resonant three-photon photoionization schemes. The density-matrix equations of motion were solved numerically for collinear, counterpropagating, linearly polarized laser beams having Gaussian temporal profile. Calculations were carried out incorporating the effects of Doppler broadening, magnetic sublevel degeneracy, and laser bandwidths. The selectivities and ion yields were determined for various Rabi frequencies and ionization rates. Thereby, the optimal Rabi frequencies for the first and second excitation steps and ionizaton rate for the ionizaton step were determined. The ionization efficiency as a function of detuning of the excitation lasers was also investigated. Two of the photoionization schemes investigated yielded a selectivity of ∼10, with an ion yield of ∼23%.
Seven new schemes have been theoretically studied using the density-matrix approach for the ns2(1S0)→nsnp(3P01 or 1P01)→nsms(1S0) and the ns2(1S0)→nsnp(3P01 or 1P01)→np2(1S0 or 1D2) double optical resonance photoionization pathways to establish the possibility of selective ionization of the rare strontium 90Sr isotope for continuous wave laser excitation. The double-resonance excitation is followed by photoionization using a 488 nm photon. Density-matrix equations for the double-resonance ionization have been numerically integrated by incorporating the effects of Doppler broadening, velocity-dependent interaction times, time varying Rabi frequencies, and laser bandwidths. All the optical selectivity calculations were carried out on a high-speed parallel processing machine. Theoretical computations on five previously studied photoionization pathways have also been performed and tabulated for the sake of completeness. The conditions for obtaining optimum optical selectivities have been evaluated. This study results in seven new photoionization pathways. The optical selectivities are a few orders higher compared to the previously studied photoionization schemes for five out of the seven schemes studied. The remaining two schemes are slightly better than the previously studied schemes.
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.
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.
Abstract The enriched 160 Gd isotope is an important target nucleus for the production of the next-generation β -emitting therapeutic nuclide 161 Tb. To address the limitation that the J = 2 → 2 → 1 → 0 polarization ionization path, although suitable for separating odd Gd isotopes with parallel linearly polarized lasers, cannot be used to enrich even Gd isotopes, we propose an efficient and highly selective ionization scheme for 160 Gd. Based on the density matrix theory, a general four-color, three-step ionization model was established by taking into account magnetic sublevel degeneracy and hyperfine structure. Numerical calculations of photoionization dynamics were performed to optimize laser parameters such as polarization, power density, and frequency detuning, with the aim of enhancing the ionization yield and isotopic abundance of 160 Gd. The results show that, in the absence of Doppler broadening, the ionization yield obtained with orthogonal linear polarization is higher than that obtained with parallel linear polarization in both three-color, three-step and four-color, three-step schemes. To maximize ionization yield, resonant excitation is required in the three-color, three-step scheme, whereas detuned excitation is needed in the four-color, three-step schemes to mitigate the population trapping effect. When Doppler broadening is taken into account, the selective photoionization performance depends on the residual Doppler broadening and on the number of laser beams passing through the atomic vapor. The calculations indicate that the optimal ionization scheme, namely the four-color, three-step scheme with parallel linear polarization, detuned excitation, saturation power density, and a bandwidth of 0.5 GHz, can achieve a 160 Gd abundance exceeding 98% at a residual Doppler broadening of 0.45 GHz, thereby meeting the application requirements.
Optical selectivities have been calculated by use of the density matrix approach for ns2 1S0−nsnp 1P10− nsms (or np2) 1S0 double-resonance photoionization pathways to establish the possibility of selective ionization of rare calcium and strontium isotopes for continuous-wave laser excitation. Numerical integration of the density matrix equations for double-resonance ionization has been carried out by incorporation of the effects of Doppler broadening, velocity-dependent interaction times, time-varying Rabi frequencies, and laser bandwidths. The conditions for obtaining optimum selectivities have been evaluated. This study results in five new photoionization pathways (two for calcium and three for strontium) whose optical selectivities were found to be a few orders higher than the previously studied photoionization schemes. The effect of laser linewidth of the excitation lasers and Doppler width have also been investigated.
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.