Numerical computations of ionization efficiency and isotope selectivity of $^{176}{\rm Lu}$ have been carried out for the following three-step ladder type photoionization scheme, $5d6{s^2}^2\, D_{3/2}(0.0\;{\rm cm}^{- 1})\mathop{-\!\!-\!\!-\!\!\longrightarrow}\limits^{540.4068\,{\rm nm}} 5d6s6p$${}^4\!F_{5/2}^o(18504.58\;{\rm cm}^{- 1})\,\mathop{-\!\!-\!\!-\!\!\longrightarrow}\limits^{535.0626\,{\rm nm}}\,$$5d6s7s\,{}^4\!D_{3/2}({37193.98\;{\rm cm}}^{- 1})\,\mathop{-\!\!-\!\!-\!\!\longrightarrow}\limits^{618.0061\,{\rm nm}}\, 53375\;{{\rm cm}^{- 1}}\,{\rm Autoionization}\,{\rm State}\, \to$${{\rm Lu}^ +}$, 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 $^{176}{\rm Lu}$ have been identified.
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Table of Ionization Efficiencies, Isotope Ratio Enhancement Factors, and Selectivities Along with Optimum Power of Excitation and Ionization Lasers for Various Half-Angle Divergencesa
Peak Power ()
Counter-Propagating Beams of Lasers-1 & 2
Co-Propagating Beams of Lasers-1 & 2
Half-Angle Divergence (Degrees)
540.4068 nm
535.0626 nm
Ionization Laser
S
IRE (Natural Lu)
Degree of Enrichment of
S
IRE (Natural Lu)
Degree of Enrichment of
Doppler free
80
40
40,000
0.202
75.96
2.027
66.96
0.202
75.96
2.03
66.96
Fully expanding beam
120
120
40,000
0.161
19.14
0.511
33.80
0.154
19.89
0.53
34.68
10°
80
50
40,000
0.200
63.54
1.695
62.90
0.201
64.39
1.72
63.21
5°
80
40
40,000
0.201
74.89
1.998
66.65
0.201
75.46
2.01
66.82
2.5°
80
40
40,000
0.202
75.73
2.021
66.90
0.202
75.85
2.02
66.93
Spectral bandwidth of both excitation lasers is taken as 100 MHz.
Table 7.
Table of % Atomic Flux in the Interaction Region Relative to the Fully Expanded Beam and the Half-Angle Divergence
Half-Angle Divergence (Degrees)
Flux Relative to the Fully Expanding Beam (%)
20°
38.4%
10°
19.7%
5°
10.0%
2.5°
5.0%
Table 8.
Effect of Power of Ionization Laser on Ionization Efficiency and Degree of Enrichmenta
Peak power of Laser-1 ${80}\;{{{\rm W}/{\rm cm}}^2}$; peak power of Laser-2 ${40}\;{{{\rm W}/{\rm cm}}^2}$. Both the excitation lasers are counter-propagating to each other.
Average power calculated for beam diameter of 25 mm, pulse width of 30 ns, PRF: 10 KHz.
Table 9.
Comparison of the Production Rates and Degree of Enrichment Reported by D’yachkov et al. [4] and Present Work
Table of Ionization Efficiencies, Isotope Ratio Enhancement Factors, and Selectivities Along with Optimum Power of Excitation and Ionization Lasers for Various Half-Angle Divergencesa
Peak Power ()
Counter-Propagating Beams of Lasers-1 & 2
Co-Propagating Beams of Lasers-1 & 2
Half-Angle Divergence (Degrees)
540.4068 nm
535.0626 nm
Ionization Laser
S
IRE (Natural Lu)
Degree of Enrichment of
S
IRE (Natural Lu)
Degree of Enrichment of
Doppler free
80
40
40,000
0.202
75.96
2.027
66.96
0.202
75.96
2.03
66.96
Fully expanding beam
120
120
40,000
0.161
19.14
0.511
33.80
0.154
19.89
0.53
34.68
10°
80
50
40,000
0.200
63.54
1.695
62.90
0.201
64.39
1.72
63.21
5°
80
40
40,000
0.201
74.89
1.998
66.65
0.201
75.46
2.01
66.82
2.5°
80
40
40,000
0.202
75.73
2.021
66.90
0.202
75.85
2.02
66.93
Spectral bandwidth of both excitation lasers is taken as 100 MHz.
Table 7.
Table of % Atomic Flux in the Interaction Region Relative to the Fully Expanded Beam and the Half-Angle Divergence
Half-Angle Divergence (Degrees)
Flux Relative to the Fully Expanding Beam (%)
20°
38.4%
10°
19.7%
5°
10.0%
2.5°
5.0%
Table 8.
Effect of Power of Ionization Laser on Ionization Efficiency and Degree of Enrichmenta
Peak power of Laser-1 ${80}\;{{{\rm W}/{\rm cm}}^2}$; peak power of Laser-2 ${40}\;{{{\rm W}/{\rm cm}}^2}$. Both the excitation lasers are counter-propagating to each other.
Average power calculated for beam diameter of 25 mm, pulse width of 30 ns, PRF: 10 KHz.
Table 9.
Comparison of the Production Rates and Degree of Enrichment Reported by D’yachkov et al. [4] and Present Work
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