3.1. Binary Rare Gas-Fluorine Mixtures

Both fluorescence and absorption spectra of rare gases change with adding fluorine but, in the case of fluorescence, the change is drastic and related to emission of RgF* and Rg₂F* (Rg is rare gas symbol) excimers, see, e.g., Huestis et al. (Reference Huestis, Marowsky, Tittel and Rhodes1984) and Brau (Reference Brau and Rhodes1984).

Adding fluorine to krypton leads, first of all, to strong well-known KrF (B-X) emission at λ ~ 248 nm. Besides, there arise 275-nm KrF (C-A) and broad Kr₂F (4²Γ → 1,2²Γ) bound-free emission bands (Molchanov, Reference Molchanov2006; Zvorykin, 2007; Huestis et al., Reference Huestis, Marowsky, Tittel and Rhodes1984; Brau, Reference Brau and Rhodes1984). The fluorescence spectrum shown in Figure 1a was recorded using a 248-nm broadband cut-off filter, which reduced the magnitude of all KrF fluorescences; nevertheless, 248-nm emission reveals itself in the second order. Kr₂F* emission band has a bell-shaped profile (half-width of about 65 nm) with a maximum at λ ~ 410–420 nm. Noticeable self-absorption related to Kr I lines is seen at the red wing of the emission profile. The absorption spectrum of Kr/F₂ mixture shown in Figure 1b is seen to be blue-shifted with respect to the spectrum of Kr₂F* fluorescence and overlapped with it. A blue wing of the recorded fluorescence profile is thus distorted because of volumetric absorption. The fluorescence spectrum has been corrected for volumetric absorption using formula (Shannon et al., Reference Shannon, Killeen and Eden1988)

(2)

where I _a(λ) and A(λ) are recorded fluorescence and absorption and I _na(λ) is “true” fluorescence signal that would have been recorded if the absorption had been absent. Corrected fluorescence spectrum I _na(λ) is shown in Figure 1a; its maximum is just slightly shifted to shorter wavelength compared with the recorded spectrum. The absorption spectra of Kr/F₂ mixture and pure Kr in Figure 1b are similar in the position of maximum absorption, but different in shape of the long-wavelength tail. Whereas absorbing species in pure Kr is Kr₂⁺ (Levchenko et al., Reference Levchenko, Ustinovskii and Zvorykin2010a), in Kr/F₂ mixture there are also Kr₂F* triatomic molecules. UV absorption spectrum of the latter related to (9²Γ ← 4²Γ) transition (as well as all the other spectroscopic properties) was predicted to be very similar to the absorption spectrum of Kr₂⁺ (Wadt & Hay, Reference Wadt and Hay1978). Experimental study (Geohegan & Eden, Reference Geohegan and Eden1988) reported the Kr₂F* absorption profile different from that of Kr₂⁺ within spectral range 335–360 nm. However, more recent study (Schloss et al., Reference Schloss, Tran and Eden1997) based on monitoring the products of photoabsorption showed the absorption profile similar to that of Kr₂⁺ predicted in (Wadt, Reference Wadt1980) but more narrow, with half-width of about 33 nm. Similarly, in our measurements, the bandwidth of absorption in Kr/F₂ mixture is smaller than in pure Kr. Line absorption referred to Kr* (see Levchenko et al. (Reference Levchenko, Ustinovskii and Zvorykin2010a)) in Kr/F₂ mixture is certainly lower than in pure Kr. As Kr* atoms are mainly produced via dissociative recombination of Kr₂⁺ ions, it is reasonable to assume that UV absorption recorded in the mixture is mainly related to Kr₂F (9²Γ ← 4²Γ) transition rather than to absorption by Kr₂⁺.

Fig. 1. Spectra of (a) fluorescence (recorded with a broadband 248-nm cut-off filter), measured and corrected for volumetric absorption, and (b) absorption in Kr/F₂ = 99.5/0.5 mixture and in pure Kr at p = 1.05 atm.

Fluorescence spectra of Ar/F₂ mixture at different pressures are shown in Figure 2a. Origin of the fluorescence peaks at 248 nm (497 nm, in the second diffraction order) is caused by traces of Kr in the mixture (KrF (B-X) transition). ArF* is responsible for the fluorescence peak at 193 nm (386 nm). The emission continuum centered at λ ~ 275 nm shows a broad symmetrical profile with a full width at half maximum (FWHM) of about 60 nm; its blue wing recorded in the second order is seen at the long-wavelength part of the spectral range under study. It is assigned, following literature (e.g., Molchanov (Reference Molchanov2006) and Marowsky et al. (1984)) to Ar₂F fluorescence. We have recorded no broadband emission centered at λ ~ 435 nm observed in (Sauerbrey et al., Reference Sauerbrey, Zhu, Tittel and Wilson1986) high pressure Ar/F₂ mixtures and ascribed to the four-atomic Ar₃F rare-gas halide complex. It is seen in Figure 2a that pressure dependence of the Ar₂F fluorescence intensity is somewhat non-monotonic: it increases with pressure up to p ~ 1 atm, and then slowly decreases up to the highest used pressure of 1.8 atm. Non-monotonic dependence of Ar₂F fluorescence on the mixture total pressure p can be extracted from the literature: one can infer from Figure 6a in Marowsky et al. (Reference Marowsky, Glass, Tittel, Hohla, Wilson and Weber1982) that maximum of Ar₂F fluorescence in Ar/F₂ = 99.7/0.3 mixture occurs at p ~ 0.7 atm, at least in the pressure range 0.5–1.1 atm. The pressure dependence of the 193-nm ArF fluorescence (monitored by an independent photodiode) demonstrates monotonic growth with pressure.

Fig. 2. Spectra of (a) fluorescence from Ar/F₂ = 99.7/0.3 mixture at p = 0.2 (1), 0.4 (2), 0.6 (3), 0.8 (4), 1.05 (5), and 1.8 (6) atm and (b) absorption in Ar/F₂ and pure Ar at p = 1.8 atm.

Absorption spectrum of Ar/F₂ mixture shown in Figure 2b is a bell-shaped continuum with half-width of about 120 nm and maximum at λ ~ 300 nm. It was recorded using a Cu target, and the region of faulty recording around λ ~ 327 nm (see, Levchenko et al. (Reference Levchenko, Ustinovskii and Zvorykin2010a)) shown by dashed arc is reconstructed. For the sake of direct comparison, Figure 2b also shows absorption spectrum of pure Ar. To our knowledge, no experimental data on UV absorption continuum in Ar/F₂ mixture have been reported in the refereed literature. Our data are in very good agreement with UV absorption spectra presented in the Los Alamos scientific report (Bigio et al., Reference Bigio, Czuchlewski, Mccown and Taylor1990) and ascribed to Ar₂F and Kr₂F (9²Γ ← 4²Γ) transitions. Like in the case of Kr/F₂, in Ar/F₂ mixture line absorption (by Ar I) and particularly narrow-band absorption corresponding to Ar₂*(npπ ³Π_g) ← Ar₂*(4sσ ³Σ_u⁺) (see Levchenko et al. (Reference Levchenko, Ustinovskii and Zvorykin2010a)) transitions are greatly reduced. Consequently, the absorption at λ ~ 325 nm in the mixture is very unlikely related to photoionization of Ar₂*(4sσ ³Σ_u⁺). In view of those reasons, we assign the absorption continuum in Figure 2b mainly to Ar₂F. Contrary to the case of Kr/F₂ mixture, the fluorescence spectrum of Ar₂F is somewhat blue-shifted with respect to the absorption spectrum of Ar₂F, which seems strange at first glance. However, such an opposite behavior was predicted in Wadt and Hay (Reference Wadt and Hay1978) based on the calculated potential curves. In Wadt and Hay (Reference Wadt and Hay1978), the predicted maximums of the emission from and absorption by Rg₂F (4²Γ) state are, respectively, blue- and red-shifted with regard to those shown in Figures 1 and 2, and so in the case of Ar₂F predicted “opposite shift” between the absorption and fluorescence continuums was even larger than that of about 25 nm seen in Figure 2. In the case of Ar/F₂ mixture, because of closeness of the wavelengths corresponding to the absorption and fluorescence peaks, correcting for volumetric absorption (Eq. (2)) leads to no noticeable wavelength shift of the fluorescence maximum but to increase in its magnitude (approximately two-fold at p = 1.8 atm). Since absorption increases with pressure, such correcting eliminates above-mentioned non-monotonicity in the pressure dependence of Ar₂F fluorescence. Under the conditions of present experiments, it is the absorption by Ar₂F which seems to be responsible for absence of lasing on Ar₂F molecule rather than absorption by Ar₂⁺ and Ar₂* claimed in Marowsky et al. (Reference Marowsky, Glass, Tittel, Hohla, Wilson and Weber1982).

3.2. Ternary Ar(He, Ne)/Kr/F₂ Gas Mixtures

Ternary mixtures of rare gases with fluorine (fluorine donor) are common gain mixtures of rare-gas halide lasers (Molchanov, Reference Molchanov1988). Fluorescence and absorption spectra of Ar/Kr/F₂ = 90.7/9/0.3 mixture, which is a conventional gas mixture of high-power KrF lasers (Zvorykin et al., Reference Zvorykin, Didenko, Ionin, Kholin, Konyashchenko, Krokhin, Levchenko, Mavritskii, Mesyats, Molchanov, Rogulev, Seleznev, Sinitsyn, Tenyakov, Ustinovskii and Zayarnyi2007), are shown in Figure 3. Kr₂F (4²Γ → 1, 2²Γ) emission band is clearly seen at p ≥ 0.6 atm. However, at such pressures KrF emission is very strong and must be suppressed with cut-off filter, which makes recording the short-wavelength part of spectrum not possible. The short-wavelength spectrum constituents can be seen at low pressures, when use of the filter is not necessary. One can see in Figure 3a the 220-nm KrF (D-X), 248-nm KrF (B-X), and 275-nm emission bands. At higher pressures, the 220-nm band is much less intense with respect to the 248-nm band because of strong KrF (D-B) collisional quenching. In Ar/Kr/F₂ mixture, the 275-nm band is stronger with respect to Kr₂F* emission than in Kr/F₂ mixture and could be supposed to be a superposition of KrF (C-A) and Ar₂F (see Fig. 2a) emission bands. The absorption spectrum of Ar/Kr/F₂ mixture is shown in Figure 3b, which also presents absorption spectrum of Ar/Kr mixture. Like in the case of Rg/F₂ mixtures, adding fluorine to Ar/Kr leads to narrowing of absorption profile (~ 90 nm FWHM in Ar/Kr/F₂) because of reduction in the long-wavelength part though maximum at λ ~ 310 nm remains fairly unchanged. Line absorption gets significantly reduced. However, there is no direct evidence that recorded absorption continuum is related completely to Kr₂F* and in no way to Kr₂⁺. If one adds neon instead of argon as a buffer gas to Kr/F₂ mixture, then there will be no absorption caused by Ne₂⁺ and Kr₂⁺ (Levchenko et al., Reference Levchenko, Ustinovskii and Zvorykin2010a). Thus, absorption spectrum of Ne/Kr/F₂ mixture shown in Figure 4a is completely related to Kr₂F* absorber (spectrum of Ne/Kr mixture is also shown in Fig. 4a). Nevertheless, it is not possible to evaluate the magnitude of photoabsorption cross-section like it was done in Levchenko et al. (Reference Levchenko, Ustinovskii and Zvorykin2010a) for Rg₂⁺ absorber in pure rare gas: one has to know both absorber number density and absorption coefficient at some instant. In the case of Kr₂F* absorber, the difference between the measured integral absorption coefficient k _meas(λ) (Eq. (1)) and peak absorption coefficient k _max(λ) corresponding to the instant of maximum absorber number density is expected to be less than in pure rare gases (Levchenko et al., Reference Levchenko, Ustinovskii and Zvorykin2010a) because of longer lifetime of the absorber. However, to calculate it, as well as the peak absorber number density, one needs to develop a complicated kinetic code, which is not possible because of insufficient knowledge of the reaction rate constants in Ne/Kr/F₂ mixture (see, e.g., Section IIIC in Levchenko et al. (Reference Levchenko, Ustinovskii and Zvorykin2010a)). In Kr/F₂ and Ar/F₂ mixtures, where kinetics is simpler and more thoroughly studied, recorded absorption continuum may contain contribution from another broadband absorber. Besides, because of strong fluorescence in all the mixtures which is subtracted from the measured signal, accuracy in the present absorption measurements is lower than in Levchenko et al. (Reference Levchenko, Ustinovskii and Zvorykin2010a). Comparison of the absorption spectra in Figures 3b and 4a shows that the spectra are fairly similar though that of Ar/Kr/F₂ mixture seems to contain little bit of the absorption by Kr₂⁺. However, one can consider that dominant absorption in Ar/Kr/F₂ mixture is due to Kr₂F (9²Γ ← 4²Γ) transition.

Fig. 3. Spectra of (a) fluorescence from Ar/Kr/F₂ = 90.7/9/0.3 mixture at p = 0.2 (1), 0.4 (2), 0.8 (3), 1.05 (4), and 1.8 (5) atm (at p > 0.2 atm, the short-wavelength side is saturated and not shown) and (b) absorption in Ar/Kr = 91/9 (1) and Ar/Kr/F₂ (2) mixtures at p = 1.8 atm.

Fig. 4. Spectra of (a) absorption in Ne/Kr = 93.6/6.4 (1) and Ne/Kr/F₂ = 93.4/6.4/0.2 (2) mixtures and (b) fluorescence from Ne/Kr/F₂ (1) and Ne/Kr/NF₃ (2) 93.4/6.4/0.2 mixtures at p = 2.5 atm.

Figure 5 demonstrates virtually linear pressure dependence of the absorption maximum at p ≥ 0.6 atm. Pressure dependences of the fluorescence at different wavelengths are obtained using appropriate filter set in front of photodiode to select a wavelength of interest. It is seen that pressure dependence of Kr₂F emission is close to quadratic at low pressures, whereas at higher pressures it becomes linear (note that correcting for volumetric absorption hardly changes its slope) and very similar to that of the absorption maximum. Such similarity shows that both fluorescence and absorption maximums are related to the same Kr₂F (4²Γ) state. The intensity of KrF (B-X) emission band tends to saturate with pressure. The 275-nm emission band shows non-monotonic pressure dependence peaking at p ~ 0.8 atm and then significantly decreasing, with specific energy deposition being nearly constant in the pressure range 0.8–1.8 atm (because of backscattering reflector). Adding of Ne to Kr/F₂ mixture leads to great increase in the intensity of 275-nm KrF (C-A) fluorescence, with the latter becoming even more intense than 410-nm Kr₂F fluorescence (see Fig. 4b). In Ne/Kr/F₂ mixture, pressure dependence of KrF (C-A) emission intensity is similar to that of 275-nm band in Ar/Kr/F₂ mixture. In both cases, correcting for volumetric absorption (Eq. (2)) cannot change non-monotonic pressure behavior of the 275-nm fluorescence, unlike the case of Ar₂F fluorescence in Ar/F₂ mixture (see Section 3.1). It is thus likely that in Ar/Kr/F₂ (and obviously in Ne/Kr/F₂) mixture, the 275-nm fluorescence is related rather to KrF (C-A) then to Ar₂F.

Fig. 5. Absorption at λ ~ 310 nm (4, triangles) and fluorescence intensity at λ ~ 248 (1), 275 (2), and 410 nm (3) vs. total pressure of Ar/Kr/F₂ = 90.7/9/0.3 mixture.

Fig. 6. Fluorescence intensity at λ ~ 248, 275, and 410 nm, each normalized to its own maximum intensity at p = 1.8 atm, vs. partial pressure of helium added to Ar/Kr/F₂ = 90.7/9/0.3 mixture at p = 0.2 atm.

In Ar/Kr/F₂ mixture, buffer gas Ar, whose main action is to acquire e-beam energy, also participates as a third body in formation of KrF (via ion branch) and Kr₂F excimers. Another buffer gas can provide different ratio of the reaction rates for such formation. Figure 6 shows behavior of the emission band intensities in Ar/Kr/F₂ mixture at low pressure of 0.2 atm gradually diluted by helium up to the total pressure of 1.8 atm. Taking into account the difference in stopping power of He and Ar, one can see that intensity of the 248-nm emission band increases proportionally to the energy deposition into the (Ar + He)/Kr/F₂ mixture. The 275-nm emission (recall that the wavelength matches both Ar₂F and KrF (C-A) emission bands) intensity hardly changes with adding He, which can be regarded as an evidence, though indirect, that formation of KrF(C) via ion branch with He as a third body is inefficient: otherwise one has to assume, contrary to the above, that Ar₂F emission is mainly responsible for the 275-nm emission band in Ar/Kr/F₂ mixture. In contrast, Kr₂F emission intensity (410-nm band) increases greatly with adding helium, in direct proportion to the total pressure of the mixture, whatever the buffer gas.

3.3. Transformation of Fluorescence and Absorption Spectra of Ar/Kr/F₂ Mixture with Adding Nitrogen or Replacing F₂ by NF₃

3.3.1. Ar(Ne)/Kr/NF₃ Mixtures

Effect of replacement of F₂ by NF₃ in Ar/Kr/F₂ (as well as in Ne/Kr/F₂) mixture is illustrated in Figures 4b and 7. As a result, Kr₂F fluorescence intensity (λ ~ 410 nm) increases, whereas KrF emission decreases significantly, as is shown in Figure 4b by the example of fluorescence spectra of Ne/Kr/F₂(NF₃) mixtures. Both spectra in Figure 4b were recorded under exactly the same conditions. And, as KrF* is commonly believed to be a main direct precursor of Kr₂F* (see, e.g., Rokni & Jacob, Reference Rokni, Jacob, McDaniel and Nighan1982), it seems that 248-nm and 410-nm fluorescences should have changed in unison. Transient absorption within UV range hardly changes with replacing F₂ by NF₃. However, within the blue spectral range of λ ≥ 440 nm it decreases to such an extent that becomes negative (see Fig. 7) indicating an amplification of the probe signal. A negative absorption as high as −0.05 m⁻¹ has been recorded at λ ~ 460 nm range by optimizing Kr fraction in Ar/Kr/NF₃ mixture.

Fig. 7. Absorption spectra of Ar/Kr/NF₃(SF₆) = 90.7/9/0.3 mixtures at p = 1.8 atm.

Why do the mixtures with NF₃ and F₂ behave differently? It was believed for a long time that quenching rates of Kr₂F (4²Γ) by F₂ and NF₃ were approximately equal (Huestis et al., Reference Huestis, Marowsky, Tittel and Rhodes1984). More recent measurements (Xu et al., Reference Xu, Gadomski and Setser1993) show that the former is 14 times larger than the latter; moreover, NF₃ quenches KrF(B) 26 times faster than Kr₂F (4²Γ), whereas the rate constants for quenching those species by F₂ differ by only 2.5 times. However, this difference in the quenching rates cannot be an explanation (at least the only one) for increased Kr₂F fluorescence. We used another fluorine donor, SF₆, with the quenching rate constants even more favorable for Kr₂F emission (quenching rates of Kr₂F (4²Γ) by SF₆ and F₂ are as 1 to 250 (Xu et al., Reference Xu, Gadomski and Setser1993), but have not obtained the results comparable with NF₃. Fluorescence intensities of both KrF and Kr₂F in Ar/Kr/SF₆ mixture drastically decrease. Both line absorption and UV absorption continuum are lower compared with Ar/Kr/NF₃ mixture but the long-wavelength tail of the continuum does not become negative (see Fig. 7). The rate constant for electron attachment to SF₆ (and hence the production rate for F⁻ ions and the rate of ion channel in formation of KrF) is larger than to F₂. The same was considered to be true for the rate of electron attachment to NF₃ at electron temperatures of 1–2 eV (Chantry, Reference Chantry, McDaniel and Nighan1982) typical of e-beam-pumped KrF lasers (Brau, Reference Brau and Rhodes1984). Besides, in contrast to F₂, NF₃ does not absorb KrF 248-nm radiation. Nevertheless, NF₃ (and SF₆ all the more) is less efficient in KrF laser than F₂ (Rokni & Jacob, Reference Rokni, Jacob, McDaniel and Nighan1982), despite that ion channel in formation of KrF* is believed to be dominant under e-beam pumping.

In Brau (Reference Brau and Rhodes1984), poor efficiency of NF₃ in KrF laser was explained by decreased rate of neutral channel in production of KrF* since branching ratio towards KrF* in the harpoon reaction of Kr* with NF₃ is less than for F₂ (0.57 against 1.0, respectively). However, the neutral channel is not dominant under e-beam pumping. Another explanation for poor efficiency of NF₃ is ion-molecular charge transfer from Kr⁺ to NF₃ reducing the production rate for KrF* and producing positive molecular ions to which electrons may combine (Rokni & Jacob, Reference Rokni, Jacob, McDaniel and Nighan1982; Boichenko et al., Reference Boichenko, Tarasenko and Yakovlenko2000). Note that following the rate constants commonly accepted at that time (Chantry, Reference Chantry, McDaniel and Nighan1982; Shaw & Jones, Reference Shaw and Jones1977), the rate of such charge transfer was to be much smaller than the rate of electron attachment to NF₃. Later measurements (Miller et al., Reference Miller, Friedman, Miller and Paulson1995) that the rate constant for electron attachment to NF₃, (7 ± 4) 10⁻¹² cm³/s at 300 K, is one and a half orders of magnitude less than that in Chantry (Reference Chantry, McDaniel and Nighan1982) indicate worse efficiency of NF₃ as fluorine donor and support the assumption about relative significance of charge transfer from Kr⁺ to NF₃.

3.3.1.1. Discussion on feasible cause for blue radiation alternative to Kr₂F

Chemistry of the reaction between Kr⁺(Kr*) and NF₃ is complicated and gives rise to various species. One can assume existence in the mixtures with NF₃ of another precursor for Kr₂F (4²Γ) alternative to KrF*, which is particularly evident in the case of Ne/Kr/NF₃ mixture. Indeed, of all the four possible immediate precursors for Kr₂F* in Ar/Kr/F₂ mixture (KrF*, ArKrF*, Kr₂⁺, and Kr₂* (Boichenko et al., Reference Boichenko, Tarasenko and Yakovlenko2000), in order of decreasing importance), only two (KrF* and Kr₂*) are present in Ne/Kr/NF₃ mixture: NeKrF* complex is not known to exist, whereas Kr₂⁺ is absent (see Fig. 4a and Levchenko et al. (Reference Levchenko, Ustinovskii and Zvorykin2010a)). It is known that NF₃-containing mixtures do not recycle (e.g., in XeF laser), which is related to irreversible decomposition of NF₃ in reaction 2NF₃ → N₂ + 3F₂ resulting in formation of some amount of nitrogen (Mandl & Hyman, Reference Mandl and Hyman1986). Then, e.g., an N₂KrF* excimer (formed via three-body reaction of KrF(B) with nitrogen) can be assumed as one of direct precursors to Kr₂F. In Basov et al. (Reference Basov, Zuev, Kanaev, Mikheev and Stavrovskii1980) and Zuev et al. (Reference Zuev, Kanaev, Mikheev and Stavrovskii1981), N₂KrF* was supposed to be an intermediate stage in formation of Kr₂F and was reported responsible for emission in the range around λ ~ 450 nm. It is thus possible that increased fluorescence in the blue region could be related not only to Kr₂F. The features discussed seem to be a reason why a gain medium of Kr₂F laser, which operates at λ ~ 435 nm (Tittel et al., Reference Tittel, Smayling and Wilson1980), is Ar/Kr/NF₃ but not Ar/Kr/F₂ mixture. In light of above discussion, it is of necessity to study the effect of adding nitrogen to Ar/Kr/F₂ mixture.

3.3.2. Ar/Kr/F₂/N₂ Mixture

Adding nitrogen to Ar/Kr/F₂ mixture is found to reduce transient absorption, although unequally throughout the spectral range under study. Within quite a broad interval in the range from 410 to 500 nm, it is reduced to a negative value. Figure 8 shows a part of the absorption spectrum of Ar/Kr/F₂ = 90.7/9/0.3 mixture at pressure of 1.7 atm to which 0.08 atm of nitrogen is added. Weak negative absorption (in other words, amplification) is seen to occur; there are a lot of absorption lines that “notch” and even break the amplification region, especially at the short-wavelength side. The lines are mainly related to Kr I spectral lines but there are also those related to Kr₂* and even to Ar I (e.g., 420.1-nm line) (Levchenko et al., Reference Levchenko, Ustinovskii and Zvorykin2010a). The most broad “amplification band” is centered at about 460 nm being red-shifted with respect to the maximum of Kr₂F (4²Γ → 1,2²Γ) fluorescence band. The result of optimization of the amplification magnitude at λ ~ 460 nm by varying pressure of N₂ additive is shown in Figure 9a. Nitrogen is added to Ar/Kr/F₂ = 90.7/9/0.3 mixture at p = 1.7 atm. Particular symbols are related to different measurement runs, which may differ in some experimental features, such as scheme alignment, different optics, etc. Two dashed curves are related to the “most different” data sets. However, all the recorded dependences are “smooth” and show weak amplification in all the measurement runs, so the averaged curve (the solid curve) is expected to reflect the true behavior. The optical gain can be assumed to lie in the range from 0.05 m⁻¹ to 0.15 m⁻¹. Evolution of the 310-nm absorption maximum with adding nitrogen is also shown in Figure 9a. Added nitrogen slightly reduces the width of absorption profile in Ar/Kr/F₂ mixture because of shortening the long-wavelength tail: small additions of nitrogen reduce the long-wavelength 460-nm absorption but hardly affect the absorption maximum, which might be even somewhat increased. The effect of nitrogen upon fluorescence from Ar/Kr/F₂ mixture is illustrated in Figure 9b. Fluorescence intensities at λ ~ 248 nm (KrF (B-X)) and λ ~ 460 nm behave quite differently. The 460-nm fluorescence shows local maximum for small nitrogen additive, whereas 248-nm fluorescence monotonically drops with increasing nitrogen pressure.

Fig. 8. Part of the absorption spectrum of Ar/Kr/F₂/N₂ mixture at p ≈ 1.78 atm with N₂ partial pressure of 0.08 atm.

Fig. 9. Absorption (a) and fluorescence (b) in Ar/Kr/F₂ = 90.7/9/0.3 mixture at p = 1.7 atm at wavelengths of (a) 310 and 460 nm and (b) 248 and 460 nm vs. pressure of nitrogen added to the mixture. Different symbols correspond to different measurement runs.

It is seen from above that both replacing F₂ by NF₃ in and adding small amount of nitrogen to Ar/Kr/F₂ mixture affect the fluorescence and absorption spectra in a similar manner. However, as further increase in the pressure of nitrogen additive leads for a while to increase in the magnitude of negative absorption, 460-nm fluorescence intensity begins to decrease, and maximum amplification in the blue spectral range is reached when fluorescence has already dropped below initial level. Hence, there has to be another reason for increasing negative absorption in the blue range different from hypothetical amplification by N₂KrF* or some other nitrogen-containing species. Note also that 410-nm fluorescence related only to Kr₂F (4²Γ → 1,2²Γ) transition behaves with adding nitrogen similarly to 460-nm fluorescence. There are some obvious effects of adding nitrogen to Ar/Kr/F₂ mixture related to that nitrogen is efficient vibrational relaxant. First, it is significant decrease in electron temperature in the course of electron-impact vibrational excitation of N₂ molecule, to the value of a few tenths of an eV (Sauerbrey et al., Reference Sauerbrey, Tittel, Wilson and Nighan1982). Since the dependence of the rate constant for electron attachment to F₂ on electron temperature is monotonically declining (Chantry, Reference Chantry, McDaniel and Nighan1982), there is to occur an increase in the electron attachment rate constant. However, like in the case of replacing F₂ by NF₃, such increase is followed by decrease in KrF* number density. Apparently, electron attachment to F₂ is a dominant process of electron loss both with and without N₂ additive. Irrelevance of the increased rate of electron attachment for enhanced formation of Kr₂F has also been demonstrated above by the example of SF₆-containing mixtures. Another effect of adding nitrogen is efficient vibrational-vibrational (VV) relaxation of excited molecules, particularly Kr₂F, in the collisions with nitrogen. Both fluorescence and absorption at λ ~ 460 nm are related to Kr₂F (4²Γ) but to different v levels. Taking into account that absorption peak is much farther from 460 nm than fluorescence maximum, it is reasonable to assume that, in the case of absorption, v is higher. Vibrational relaxation will then reduce absorption rather than fluorescence, and the gain can exceed the absorption loss at λ ~ 460 nm.

3.3.2.1. Comparison with literature data on Ar/Xe/CCl₄/N₂ mixture

Somewhat similar situation was observed for e-beam-excited Ar/Xe/CCl₄ high-pressure mixture (Sauerbrey et al., Reference Sauerbrey, Tittel, Wilson and Nighan1982) where adding nitrogen led to increase in the output energy of Xe₂Cl laser (λ ~ 515 nm). Like in our case of Ar/Kr/F₂ mixture, the rate constant for electron attachment to CCl₄ halogen donor greatly increased with adding nitrogen though fluorescence of XeCl* (a precursor to Xe₂Cl*) decreased. However, the intensity of Xe₂Cl* fluorescence was relatively insensitive to addition of nitrogen over a broad range of N₂ partial pressure. It was said (Sauerbrey et al., Reference Sauerbrey, Tittel, Wilson and Nighan1982) that production rate of Xe₂Cl* is not affected by N₂ but modeling showed that number densities of the absorbing species Xe*, Xe₂⁺ and presumably Xe₂* (the latter is misprinted in Sauerbrey et al. (Reference Sauerbrey, Tittel, Wilson and Nighan1982)) decrease with nitrogen. This reduced absorption was assumed to be responsible for increasing output of Xe₂Cl laser. Let us note that, in the case of Xe₂Cl*, self-absorption seems to be insignificant: the absorption and emission profiles related to Xe₂Cl(4 ²Γ) are more separated than those of Kr₂F (4 ²Γ). The reason is that Xe₂Cl* absorption is significantly blue-shifted with respect to Xe₂⁺ 1(1/2)_u → 2(1/2)g UV absorption (McCown et al., Reference McCown, Ediger, Geohegan and Eden1985), whereas absorption profiles of Rg₂F* species are similar to those of Rg₂⁺ (see, e.g., Section 3.1).

Taking into account complicated kinetics in Ar/Kr/F₂/N₂ gas mixture, it seems to be of interest to examine transient absorption in the mixtures of argon and krypton with nitrogen.

3.4. Ar/N₂, Kr/N₂ and Ar/Kr/N₂ Mixtures

In the spectral range under study, no measurable fluorescence was observed in e-beam excited Ar, Kr, and Ar/Kr gas mixture (Levchenko et al., Reference Levchenko, Ustinovskii and Zvorykin2010a). However, even small additive of nitrogen to argon leads to origin of strong well-known fluorescence corresponding to (0 → 0), (0 → 1), and (0 → 2) v′→ v″ transitions of the second positive band system С³П_u → В³П_g of molecular nitrogen (Pressley, Reference Pressley1971; Ernst et al., Reference Ernst, Tittel, Wilson and Marowsky1979) centered at 337.1, 357.7, and 380.5 nm, respectively. In our experiments, the 357.7-nm emission line is much stronger than the others, which disagrees with early observations of the spontaneous emission from e-beam-excited Ar/N₂ mixtures that intensities of 337.1-nm and 357.7-nm emission lines are nearly equal (Ernst et al., Reference Ernst, Tittel, Wilson and Marowsky1979). The energy is known to be transferred from metastable Ar atoms to N₂ via resonant reaction

(3)

When nitrogen is added to pure Kr or Ar/Kr mixture, no fluorescence is detected (more exactly, it is within the noise level, if any). Indeed, it is known from the literature (Levchenko et al., 2010a; Brau, Reference Brau and Rhodes1984) that, in Ar/Kr mixture with minor additive of Kr, excitation is efficiently transferred from argon (mainly from atomic and molecular ions) to krypton with subsequent production of Kr* (5s). The energy of Kr*(5s) levels is lower than that of Ar*(4s) levels, and energy transfer to nitrogen in reaction of type (3) becomes impossible.

Absorption spectra of the mixtures with nitrogen show some interesting features (see Fig. 10). Already small addition of nitrogen (in amount of about 3%) to argon leads to significant decrease in the absorption maximum at 295 nm (related to Ar₂⁺ (Levchenko et al., Reference Levchenko, Ustinovskii and Zvorykin2010a)). That is surprising taking into account that the energy transfer is believed to go via reaction (3) and Ar*(4s) is produced after dissociative recombination of Ar₂⁺. In other words, loss of Ar*(4s) is not to affect the number density of higher-energy Ar₂⁺. Unfortunately, the spectra have been recorded using a Cu target and thus the absorption peak at 325 nm related to Ar₂* is not seen in pure Ar (Fig. 10a). Because strong 357.7-nm emission saturates the CCD, absorption around 357.7 nm in Ar/N₂ mixture is not as well represented in Figure 10a. Note that 325-nm peak is to be decreased with nitrogen because reaction (3) reduces number density of the atomic precursor for Ar₂*. Contrary to the case of argon, even rather significant addition of nitrogen (in amount of about 10%) to krypton does not affect the absorption maximum although somewhat reduces its long-wavelength fraction (Fig. 10b). Similarity (both in the shape and magnitude), between the absorption spectra of pure Kr and Ar/Kr mixture was discussed in detail in (Levchenko et al., Reference Levchenko, Ustinovskii and Zvorykin2010a): in both cases, absorption is caused by Kr₂⁺ ions. It is however seen in Figure 10c that even small (~ 3%) addition of nitrogen to Ar/Kr mixture significantly reduces (approximately halves) the absorption. Further increase in nitrogen number density (up to about 17% of the total pressure) does not significantly affect the absorption. On comparing Figures 10a, 10b, and 10c, one has to assume that, besides well-known reaction (3), nitrogen “captures” excitation from high-lying energy states of argon. We may suggest it occurs via reaction (Smith et al., Reference Smith, Adams, Alge, Villinger and Lindinger1980)

(4)

in which nitrogen “seizes” all the charge from doubly charged Ar²⁺ ions, which are produced in e-beam-excited argon in a noticeable amount (Langhoff, Reference Langhoff1994). Such ions finally convert into Ar₂⁺ and Ar⁺ ions (Wieser et al., Reference Wieser, Ulrich, Fedenev and Salvermoser2000) with the latter, in turn, converting into Ar₂⁺ ions. The rate of the energy transfer to nitrogen seems to be high enough for nitrogen added in amount of about 3% apparently depletes high-lying energy reservoir (Ar²⁺(³P) in (4)) as further increase in nitrogen pressure causes only slight effect. Contrary to the case of Ar/N₂ mixture, reaction of less energetic Kr²⁺ ions with nitrogen is known to proceed exclusively via single charge (electron) transfer (Smith et al., Reference Smith, Adams, Alge, Villinger and Lindinger1980)

(5)

and thus does not lead to equally drastic reduction in Kr₂⁺ number density; however, it should be somewhat decreased. Nitrogen is known to reduce the intensity of the second emission continuum (145 nm) related to Kr₂* (Kanaev et al., Reference Kanaev, Zafiropulos, Ait-Kaci, Museur, Nkwawo and Castex1993): then, one could have supposed that the long-wavelength fraction of the absorption continuum decreasing with nitrogen was related to Kr₂*. However, in Ne/Kr mixtures, there is no continuous absorption at all whereas absorption related to Kr*(5s) is definitely present (see Fig. 4a and Levchenko et al. (Reference Levchenko, Ustinovskii and Zvorykin2010a)). Absolute concentration of Kr is not small, and as long as there are Kr*(5s) atoms, there also have to be Kr₂* dimers responsible for the emission in the second continuum. Hence, whole 320-nm absorption continuum is caused by only Kr₂⁺; its absorption maximum and long-wavelength fraction are related, respectively, to low-v and high-v states of Kr₂⁺ (see Levchenko et al. (Reference Levchenko, Ustinovskii and Zvorykin2010a)) with the latter being collisionally quenched by N₂. Such collisional quenching enlarges population of low-v levels and increases 320-nm absorption, which might compensate the reduction in the production rate of Kr₂⁺ due to reaction (5). As a result, there is no noticeable decrease in the maximum of continuum absorption with adding nitrogen to Kr. Similarly, observed reduction in the absorption at λ ~ 460 nm in Ar/Kr/F₂/N₂ mixture can be caused by enhanced vibrational relaxation of Kr₂F (4²Γ, v > >0). In the light of above, one can expect that, after adding nitrogen to Kr/F₂ mixture, spurious transfer of energy to nitrogen reducing excitation rate will be minimal whereas collisional quenching of vibrationally excited Kr₂F is to proceed.

Fig. 10. Absorption spectra in (a) pure Ar and Ar/N₂ = 1.75/0.05 mixture at p = 1.8 atm, (b) pure Kr and Kr/N₂ = 0.95/0.1 mixture at p = 1.05 atm, and (c) Ar/Кr = 1.64/0.16 and Ar/Кr/N₂ = 1.6/0.16/0.05 mixtures at p = 1.8 atm.