Let us examine in more detail the possible processes of populating of upper laser levels (see Table 5.3). The first models [19, 20] for NPLs operating on mixtures 3He-Xe and 3He-Ar were based on preferential populating of nd levels of Xe and Ar atoms as a result of the process of collisional-radiative recombination: B+ + e + e —— B*(nd) + e (B+ = Xe+, Ar+) (process (1)). Individual characteristics of lasers were calculated in [19, 20]; a detailed comparison with experimental results was not made. Process (1) was also included in kinetic models developed later for lasers

operating on the mixtures He-Xe [29, 30, 32] and He-Ar [31], the supposition was made that up to 60 % of the total reaction flux (1) may come to the nd levels. As is known (see [10], for example), process (1) is not selective, so as a result it is possible for atoms to appear in different excited states. In this regard, the assump­tion of a significant contribution of process (1) to populating of the nd levels of atoms Xe and Ar, advanced in studies [19, 20, 29—32], is doubtful. Moreover, the rate constant kcr of process (1) greatly depends on the temperature of the electrons (kcr ~ Te—4,s), so that He-Xe(Ar) lasers are hardly able to operate in a wide range of experimental conditions in the case of populating nd levels through this process.

In study [23], other populating mechanisms of upper laser levels were proposed for Ar-Xe NPLs: a) process (5), energy transfer in inelastic collisions Ar* + Xe —— Xe*(5d) + Ar; b) process (6), populating of 5d levels of the Xe atom by electron impact from states 6 s. Process (5) was also included in the kinetic models [25, 27—30, 32], and process (6) in models [28—30, 32]. Process (5) cannot provide efficient pumping of 5d levels, since as a result of this process, highly excited Xe levels are formed initially (states 7d, 8d, etc.), while populating of 5d levels is possible only as a result of subsequent radiative-collision processes with a proba­bility of a few percent [40]. In this regard, the assumption of [28—30, 32] regarding populating of 5d levels of the Xe atom through process (5) with a probability of 20­30 % is too optimistic. As for process (6), experimental studies [41, 42] show that there is no marked contribution of this process to populating of the nd levels.

The hypothesis regarding populating of nd levels of the Xe, Kr, and Ar atoms through dissociative recombination of heteronuclear molecular ions of ArXe+ or

HeB+ (B = Xe, Kr, Ar) with electrons is the most widespread. In a number of models (see [21, 22, 24], for example), this process is viewed as the only one, while in others [27—32] it is viewed as one of the main ones, with a populating probability of up to 40 % [28, 29]. In the majority of studies [22, 24, 27—32], it was proposed that populating of nd levels occurs directly as a result of process (3). Study [21] proposes for the Ar-Xe mixture a more complex two-stage mechanism of populat­ing of the 5d levels of the Xe atom—formation, in the process of recombination ArXe+ + e, of high states 7p, 7s of the Xe atom, with subsequent collisional transitions Xe*(7p,7 s) + Ar(Xe)! Xe*(5d) + Ar.

In binary A-B mixtures, heteronuclear molecular ions AB+ are formed in three — body collisions:

B++ B + A! B+ + A (5.3.a)

B++ B + A! AB+ + B; (5.3.b)

B++ A + A! AB+ + A. (5.4)

and are destroyed as a result of the processes:

AB+ + A! B++ 2A. (5.5)

AB+ + B! B+ + A. (5.6)

AB+ + ! B++ A + e. (5.7)

Information about rate constants of processes (5.3)-(5.7) is extremely limited. The rate constants for these ions used in various models (see, for example, information for the ArXe+ in Table 4.11) are estimates, sometimes quite rough, so that it is virtually impossible to predict the contribution of dissociative recombination of ions AB+ to population of nd levels. Unknown constants most often were estimated in the process of fitting the results of calculation of NPL characteristics to the experimental data.

The destruction of heteronuclear ions largely depends on their bond energy, which decreases with an increase in the difference in masses of the atoms making up the ion [43, 44], and equals 0.14, 0.050, 0.030, and 0.027 eV for ArXe+, HeXe+, HeKr+, and HeAr+, respectively [44]. The estimates cited in study [10] provide the following values for the rate constants of process (5.5): for ArXe+ ions, k55«5 x 10-11 cm3/s, while for the HeB+ ions (В = Xe, Kr, Ar), k55 > 10-10 cm3/s. Heteronuclear ions are also destroyed by plasma electrons as a result of process (5.7); moreover, the rate constants of such processes can reach 10~7-10~6 cm3/s [10].

The characteristic time of process (5.5), for example for HeXe+ ions when the atmospheric pressure of the He-Xe mixture is ~ 3 x 10~10 s, while the characteristic time of the process of dissociative recombination of this ion under the most favorable conditions (Te = 300 °K, ne < 1015 cm~3) will be > 10~7 s. Consequently, heteronuclear ions HeB+ are effectively destroyed as a result of collisional processes, so their recombination cannot make a marked contribution to formation of excited atoms. The latter circumstance is confirmed by the results of spectro­scopic research on dissociative recombination of heteronuclear ions in the after­glow of gas-discharge plasma, in which “despite the large number of studies of these particles, it has not yet been possible to discover the formation of excited atoms associated with their recombination” [10].

An additional argument against a significant contribution from dissociative recombination of heteronuclear ions to the population of the upper laser levels comes from the results of experiments studying the influence of the medium temperature on laser characteristics. It follows from Table 3.7 (see Chap. 3, Sect. 3.1) that the temperature at which the output laser power decreases by half differs insignificantly for the mixtures Ar-Xe, He-Xe, and He-Ar, and is 350-450 °K. If populating of the upper laser levels occurred with the participation of the heteronuclear ions ArXe+ (mixture Ar-Xe) or HeXe+, HeAr+ (mixtures He-Xe, He-Ar), for the mixtures He-Xe and He-Ar, the reduction in energy parameters would have to occur at substantially lower temperatures than for the mixture Ar-Xe, owing to the more efficient destruction of HeXe+ and HeAr+ ions as the temperature increases due to reaction (5.5). In addition, in experiments [45, 46] with mixtures He-Xe and He-Ar, the specific energy depositions were ~ 1 J/cm3 per pulse, and the temperature of the medium by the end of the pumping pulse reached 800-1,000 °K, but lasing occurred throughout the entire pulping pulse (see Fig. 2.10, for example).

Thus construction of the models [22, 24] based on the reaction of dissociative recombination of ions HeB+ with electrons, or its insertion in models [29—32], where the contribution of this reaction to populating of nd levels is estimated at 15­25 % [31], is invalid.

In the majority of kinetic models, the process of dissociative recombination of molecular ions B2+ with electrons was viewed as a loss channel, populating the lower laser (n +1) p levels. This assumption was initially based on the results of spectroscopic investigations (see review [10] and the literature cited there), which registered intensive radiation from (n +1)p levels. However, it should be noted that spectroscopic investigations were carried out in the spectral range of X < 1,000 nm using photoelectric multipliers for registration, so IR transitions nd-(n + 1) p could not be observed. Consequently, one can assume that the radiation from (n +1) p levels registered in these studies is the consequence of preliminary IR transitions nd-(n + 1) p.

In study [47], based on the measured intensities of spectral lines, a conclusion was drawn regarding preferential population as a result of the process Xe^ + e of level 6p[5/2]2 in comparison with level 5d[3/2]10 which are the lower and upper levels of the laser transition respectively, with X = 1.73 pm (see Fig. 3.1). The authors [47] drew this conclusion from calculation of the ratio of the recombination fluxes Г, populating these levels:

^ r5d I5dA6pA5dT6p (5 8)

Г6р 16pA5pA6pT5d

where hd and I6p are the intensities of the 1.73 ^m and 0.992 ^m spectral lines measured in [47] > A5d and A6p are the wavelengths of these lines, A5d and A6p are the probabilities of radiative transitions, and T5d and T6p are the lifetimes of the levels. In [47] it is assumed that т 5d is equal to the radiative lifetimes of the level 5d [3/2] 10, which is about 200 ns. With these assumptions, the authors of [47] obtained Y < 0.2 for PXe _ 5-10 Torr.

Study [48] reevaluated correlation (5.8), taking into account the processes of collisional quenching. From results of experiments [49], it follows that quenching of the level 5d [3/2]10 by Xe atoms in ground state already become noticeable at PXe ~ 0.1 Torr. This means that for PXe « 0.1 Torr, the radiative lifetimes of level 5d[3/2]10 are roughly equal to the lifetimes of this level through the process of collisional quenching. Hence, it follows that the rate constant of the quenching process is~2 x 10~10 cm3/s-1 (similar values of this constant were obtained in kinetic models [21, 25]). Therefore, for PXe _ 10 Torr, taking into account colli­sional quenching, T5d ~ 10 ns, and accordingly, the ratio у ~ 5. Thus if one allows for the reduction in the lifetimes of the level 5d[3/2]10, then based on the spectral lines measured in [47], one can infer the opposite to the conclusion drawn by the authors [47]: the level 5d[3/2]10 is populated primarily due to the dissociative recombina­tion Xe2 + e.

This inference is confirmed by the information of study [50], which concludes, based on experimental investigations of the process Xe^ + e, that there was prefer­ential populating of the 5d level of the Xe atom in comparison with the 6p levels. A significant role of the process Xe^ + e in populating levels 5d is also noted in study [51]. And finally, analysis [52] of the kinetics of an Ar-Xe laser (A_ 1.73 ^m) showed that the probability of populating of the level 5d [3/2] 10 through the process Xe)~ + e can reach 90 %.

In 1979, VNIIEF offered the hypothesis of selective populating of nd levels of Xe, Kr, and Ar atoms through dissociative recombination of molecular ions B2 + e! B *(nd) + B(B _ Xe, Kr, Ar), published later in [33]. Based on this hypothesis, kinetic models were developed for calculation of NPL characteristics [34—39]. Populating of nd levels of Xe and Ar atoms through the processes of dissociative recombination of molecular ions B2l with electrons was also taken into account (along with other processes) in kinetic models [27—32]. The efficiency of populating of nd levels was taken as equal to 15-20 % with regard to the total pumping flux.

A somewhat different lasing mechanism, proposed in the study [25] for Ar-Xe NPLs and later used in a kinetic model of a He-Xe NPL [26], was based also on preferential populating of the 5d levels of the Xe atom as a result of dissociative recombination of molecular ions Xe^. However, in this case dissociative recombi­nation of the ion (XeJ) * in an excited state (electronic or vibrational) was proposed as the basic populating channel. According to this model, the excited (XeJ) * ions are formed in the reaction ArXe+(HeXe+) + Xe! (Xe2) * + Ar(He), while the Xe2 in the ground state are a result of the reaction Xe+ + Xe + Ar(He)! Xe2 + Ar(He). Authors of [25, 26] proposed that recombination of the Xe2 ion in the ground state leads to populating of the levels 6p and 6p’. To test the reliability of this model, which contains a large number of unknown constants, additional research is nec­essary, particularly calculations of the characteristics of a Xe laser in various experimental conditions.

Thus the most efficient populating of the nd levels of Xe, Kr, and Ar atoms, which are the upper laser levels in rare gas mixture NPLs, most likely occurs through the processes of dissociative recombination B2 + e! B * (nd) + B (B = Xe, Kr, Ar). Unfortunately, direct experimental proof of such inference is still absent, except perhaps for the information contained in study [50]. To resolve this problem, spectral-luminescence studies are needed, analogous to those performed using the single-photon spectrometry method in the visible and UV spectral ranges [53, 54]. However, IR photodetectors of the same high sensitivity as photoelectronic multipliers are needed in order to carry out such investigations.