On the Possibility of the Effective Isotope-Selective Infrared Dissociation of 235UF6 Molecules Vibrationally Excited by Bichromatic Laser Radiation

Using the spectroscopic data on the 235UF6 and 238UF6 molecules and on the lasing frequencies of CF4 and para-H2 lasers and recent results, a method has been proposed to increase the efficiency of the isotope-selective infrared laser dissociation of 235UF6 molecules under nonequilibrium thermodynamic shock conditions. The method involves two processes: (i) the resonant multiphoton excitation of 235UF6 molecules to the 3ν3 or 2ν3 vibrational states by the bichromatic infrared radiation of two CF4 or para-H2 lasers and (ii) the irradiation of 235UF6 molecules with SF6 molecules serving as sensitizers resonantly absorbing the radiation of these lasers. The essence of the method has been described. Schemes and parameters for isotope-selective dissociation of 235UF6 molecules using this method has been presented.

Two important problems of laser separation of uranium isotopes involving UF 6 molecules are (i) a small isotopic shift in infrared absorption spectra of laserexcited ν 3 vibrations of 235 UF 6 and 238 UF 6 molecules and (ii) the absence of intense and efficient laser sources for isotope-selective vibrational excitation and dissociation of UF 6 molecules. The isotopic shift in the ν 3 vibrational mode ( cm -1 [26]) for 235 UF 6 and 238 UF 6 molecules is cm -1 [26]. Because of a small isotopic shift and a comparatively large width (about 20 cm -1 ) of the infrared absorption band of molecules at room temperature [2,27], iso-tope-selective infrared dissociation of UF 6 molecules is possible only at a low temperature of the gas when the infrared absorption band of UF 6 molecules with different U isotopes is much narrower [1,2,27].
Two tunable radiation sources in the 16 μm range were developed for projects on uranium MLIS using isotope-selective infrared multiphoton dissociation of UF 6 molecules. These are a molecular CF 4 laser optically pumped by the intense radiation of a CO 2 laser [28,29] and the so-called para-H 2 laser source based on the shift of the radiation frequency of the CO 2 laser to the 16 μm range caused by the stimulated Raman scattering on rotational transitions of para-hydrogen molecules [30,31]. These lasers in many parameters satisfy the requirements for operation at megafacilities [2]. However, significant disadvantages of both CF 4 and para-H 2 lasers in application to uranium isotope separation are discreteness of the frequency tuning and the absence of strong tunable lasing lines in the region of the Q branch of the ν 3 vibrational mode of 235 UF 6 molecules (in the 628.32 cm -1 range [26]).

OPTICS AND LASER PHYSICS
excited and unexcited UF 6 molecules with HCl molecules are different. For this approach, high-power CO lasers [35,36] generating in the 5.3 μm range are being produced; they are planned to be used to excite 235 UF 6 molecules. However, the efficient excitation of 3ν 3 states of UF 6 molecules by infrared radiation with a wavelength of ≈5.3 μm is problematic because absorption of UF 6 molecules at the vibrational transition is weak. The integral absorption of the overtone band of UF 6 molecules is about a factor of 1.8 × 10 4 lower than the integral absorption of the main band of UF 6 molecules [32]. Consequently, the search for alternative schemes for isotope-selective excitation and dissociation of 235 UF 6 molecules is a very important relevant task. In this work, we propose a new method for the efficient isotope-selective laser infrared dissociation of 235 UF 6 molecules.

FOUNDATIONS OF THE METHOD
The proposed method is based on the process of resonant three-or two-photon excitation of 235 UF 6 molecules to the 3ν 3 or 2ν 3 vibrational states by the bichromatic infrared radiation of two pulsed CF 4 or para-H 2 lasers [18,19] and on the irradiation of excited 235 UF 6 molecules with SF 6 molecules serving as sensitizers resonantly absorbing the radiation of these lasers [16,17,23]. In addition, it is proposed to perform the excitation of molecules under nonequilibrium thermodynamic shock conditions formed in front of a solid surface on which a gas-dynamically cooled intense supersonic molecular flow is incident [1,2,24,25].
As shown in [37,38], radiation pulses of the CO 2 laser can efficiently excite SF 6 molecules to the high 2ν 3 and 3ν 3 vibrational states by means of the resonant two- [37] and three-frequency [38] excitation of SF 6 molecules cooled in a gas-dynamic jet. Recent studies [16,23] demonstrate the possibility of a strong increase in the dissociation yield of CF 2 HCl molecules irradiated under shock conditions together with CF 3 Br sensitizer molecules resonantly absorbing the laser radiation. It was established that the processes mentioned above are also applicable to other molecules [16,23,37], in particular, UF 6 molecules. These processes are involved in the proposed method implemented under nonequilibrium thermodynamic shock conditions.
To form the molecular flow, it is proposed to use the UF 6 /SF 6 /CH 4 molecular mixture with a pressure ratio of about 1/3/10 [39], where SF 6 molecules serve as sensitizers and CH 4 molecules are used as acceptors of F atoms produced in the dissociation of UF 6 and SF 6 molecules. At the indicated pressure ratio of used gases, the vibrational temperature of UF 6 molecules (and SF 6 molecules) in the flow incident on the surface and in the compression shock will be K [27,39]. The population of the ground vibrational state of UF 6 molecules at this vibrational temperature is about 50% [2,27], and UF 6 molecules have comparatively narrow (a FWHM of about 7-8 cm -1 ) infrared absorption bands [39].
The same laser pulses exciting 235 UF 6 molecules also resonantly excite SF 6 molecules used as sensitizers. The frequency of the ν 4 vibrational mode of SF 6 molecules (≈ 615 cm -1 [40,41]) is in very good resonance with high-lying transitions of vibrationally excited 235 UF 6 molecules. For this reason, the energy is efficiently transferred from SF 6 molecules excited by the CF 4 or para-H 2 lasers to vibrationally excited 235 UF 6 molecules. As a result, the efficient isotopeselective dissociation of 235 UF 6 molecules is ensured by radiative and collisional excitation processes [16,17,23].
It is noteworthy that SF 6 molecules were used as sensitizers for the excitation and dissociation of UF 6 molecules in many works (see, e.g., [2,42] and references therein). However, SF 6 molecules were used in those works for the preliminary accumulation of the vibrational energy through their excitation by the pulsed radiation of the CO 2 laser. SF 6 molecules have an intense absorption band in the 10.6 μm range (ν 3 vibrational mode at a frequency of ≈948 cm -1 [43]). Subsequently, the energy accumulated by SF 6 molecules was transferred to the ν 3 mode of UF 6 molecules through the ν 4 mode resonant to the former, which led to their excitation and dissociation [2,42].
Unlike the cited works, sensitizer and 235 UF 6 molecules in the proposed method should be excited simultaneously by the resonant radiation of CF 4 or para-H 2 lasers, which significantly increases the efficiency of the dissociation of 235 UF 6 molecules [16,17,23]. Since the dissociation energy of UF 6 molecules (≈68 kcal/mol [44]) is much lower than that of SF 6 molecules (≈92 kcal/mol [45]), the dissociation of UF 6 molecules in the process of irradiation of the mixture will occur at a much lower vibrational temperature than the dissociation of SF 6 molecules. As a result, under certain conditions possible at a low fluence of excited laser radiation ( J/cm 2 ), UF 6 molecules will be dissociated, whereas the dissociation of SF 6 molecules will not occur [16,17,23].
The translational, rotational, and vibrational temperatures of polyatomic molecules in the gas-dynamically cooled molecular flow are related as [46] . In the compression shock [47], because of the different translational, rotational, and

T T T
vibrational relaxation rates [48], inverse nonequilibrium relation occurs [1,2,24]. The subscripts 1 and 2 indicate the temperatures of molecules in the incident flow and compression shock, respectively. In this case, because of a long vibrational-translational relaxation time of molecules (e.g., μs Torr for SF 6 [49], 32 μs Torr for UF 6 [50]), the vibrational temperature of molecules in the compression shock in the case of the pulsed rarefied gas flow can be approximately equal to the vibrational temperature of molecules in the incident flow , whereas the translational and rotational temperatures of molecules in the compression shock are much higher than the respective temperatures in the unperturbed flow: and . Thus, new nonequilibrium conditions are formed in the compression shock, where the vibrational temperature of molecules is much lower than their translational and rotational temperatures.
For the resonant excitation of the 2ν 3 and 3ν 3 vibrational states of 235 UF 6 molecules by the radiation of two pulsed infrared lasers, it is necessary [51] to satisfy the following relations between the frequencies and of these lasers and the frequency ν 3 of the excited vibrational mode of 235 UF 6 molecules: One can quite easily ensure resonance conditions for the excitation of high vibrational levels of molecules using two or three lasers with different frequencies, particularly, high-pressure lasers with smooth radiation frequency tuning. To carry out such experiments, it is necessary to exactly know the frequencies (energies) of high vibrational levels of the studied molecules. These data for the SF 6 [52] and UF 6 [53] molecules were obtained at the Los Alamos National Laboratory in the course of projects on the molecular laser separation of uranium isotopes.
Advantages of the irradiation of 235 UF 6 molecules with an SF 6 sensitizer resonantly absorbing laser radiation to increase the efficiency of their dissociation are illustrated in Fig. 1. This figure shows the infrared absorption band of the ν 4 vibrational mode (frequency of 615 cm -1 [41,54]) of molecules of SF 6 resonantly absorbing the radiation of the CF 4 laser at a temperature of K [54] and the infrared absorption band of the ν 3 vibrational mode ( 627.72 cm -1 [26]) of UF 6 molecules cooled in a supersonic gas-dynamic jet in a mixture with argon at a temperature of K [39]. The vertical arrows in Fig. 1 The horizontal arrows indicate the direction of the redshift of the absorption bands of the UF 6 and SF 6 molecules under their vibrational excitation.
Because of the anharmonicity of vibrations, the resonant excitation of 235 UF 6 molecules to the 2ν 3 and 3ν 3 vibrational states by bichromatic infrared laser radiation leads to the shift of their infrared absorption band to the low-frequency range coinciding with the infrared absorption band of the ν 4 vibrational mode of SF 6 molecules. As a result, the effective resonant radiation-collisional excitation of vibrationally excited 235 UF 6 molecules and SF 6 molecules occurs [16,17,23,42]. Laser-excited SF 6 molecules transfer the absorbed energy to 235 UF 6 molecules through the vibrational-vibrational (V-V) energy exchange, increasing their dissociation yield. The process of V-V energy exchange between molecules is highly efficient because it occurs at small frequency detuning between vibrational transitions in SF 6 and UF 6 molecules [42,55]. This high efficiency is also due to a comparatively high density of particles in the compression shock [≈(5-7) × 10 16 [23,24]] and high vibrational and rotational temperatures of molecules (≥550 K [23,24]).

SCHEMES AND PARAMETERS FOR RESONANT EXCITATION OF THE 2ν 3 AND 3ν 3 STATES OF 235 UF 6 MOLECULES
We calculated the 2ν 3 and 3ν 3 states of 235 UF 6 molecules taking into account the isotopic shift   [26] in the absorption band of the ν 3 vibrational mode for 235 UF 6 and 238 UF 6 . The isotopic shift in the 2ν 3 and 3ν 3 states is taken as 1.21 and 1.81 cm -1 , respectively. The 2ν 3 and 3ν 3 energy levels of 235 UF 6 molecules are shifted by these values toward higher energies. Two infrared lasers allow the efficient isotope-selective excitation of both 2ν 3 and 3ν 3 vibrational states of 235 UF 6 and 238 UF 6 molecules [18,19]. We consider the excitation of only those 2ν 3 and 3ν 3 states of 235 UF 6 molecules through which 235 UF 6 molecules can be resonantly excited to higher 4ν 3 and 6ν 3 vibrational states. Figure 2а shows the scheme of excitation of the 3ν 3 F 1 vibrational state of 235 UF 6 molecules (1877.41 cm -1 [53]) by radiation of two CF 4 lasers at frequencies of cm -1 and cm -1 . The threephoton bichromatic excitation of the 3ν 3 F level is performed with the detuning in the final state cm -1 (2ν L1 + ν L2 = 1877.3 cm -1 ). For this case, the solid arrows in Fig. 2b mark the frequencies of the lasing lines of the CF 4 lasers with respect to Q branches of the ν 3 mode of 238 UF 6 and 235 UF 6 molecules in the gas-dynamically cooled molecular flow at a temperature of K [27]. The solid arrows in Fig. 2b mark the frequencies of the lasing lines of the para-H 2 lasers for the excitation of the 3ν 3 F 1 state of 235 UF 6 molecules. When choosing the schemes for resonant excitation of molecules, we took into account only the most intense radiation lines of the CF 4 [56] and para-H 2 lasers. The lasing frequencies of the lasers are neither individually nor pairwise in resonance with low-lying transitions in UF 6 molecules.
Possible schemes proposed for the resonant twophoton bichromatic excitation of 2ν 3 vibrational states of 235 UF 6 molecules by the infrared radiation of two CF 4 lasers and two para-H 2 lasers are summarized in Table 1. Table 2 presents the schemes proposed for the resonant three-photon bichromatic excitation of 3ν 3 vibrational states of 235 UF 6 molecules by the infrared radiation of two CF 4 lasers and two para-H 2 lasers. According to Tables 1 and 2, both types of lasers can provide the resonant excitation of the 2ν 3 and 3ν 3 states of 235 UF 6 molecules with a small frequency detuning in the final state, which promotes a high selectivity of the excitation of 235 UF 6 molecules. In all schemes presented in Tables 1 and 2 for the excitation of the 2ν 3 and 3ν 3 states of 235 UF 6 molecules, the 4ν 3 and 6ν 3 states of 235 UF 6 molecules can also be resonantly populated by the same laser pulses. This possibility is valuable because this ensures [57] a more efficient excitation of molecules to high vibrational states and their subsequent dissociation. The conditions for the optimal isotope-selective population of the 2ν 3 and 3ν 3 states of 235 UF 6 and 238 UF 6 molecules were discussed in [19].

CONCLUSIONS
A method has been proposed to increase the efficiency of the isotope-selective infrared laser dissociation of 235 UF 6 molecules under nonequilibrium thermodynamic shock conditions. The method is based on the selective excitation of the and vibrational states in 235 UF 6 molecules by the bichromatic radiation of two CF 4 or para-H 2 lasers using SF 6 molecules that serve as a sensitizer resonantly absorbing the radiation of these lasers. Schemes and parameters for resonant two-and three-photon bichromatic exci- tation of the and states in 235 UF 6 molecules, which are cooled in a gas-dynamic flow to a temperature of K, by the radiation of the mentioned lasers are given. The results can be applied when using laser infrared dissociation of molecules to separate isotopes.   Table 1. Schemes of the resonant two-photon bichromatic excitation of 2ν 3 vibrational states of 235 UF 6 molecules by the infrared radiation of two CF 4 (schemes 1 and 2) and two para-H 2 (schemes 3 and 4) lasers. Upon stimulated Raman scattering on rotational levels of para-hydrogen, the lasing frequency of the CO 2 laser decreases by 354. 33