ON THE PROBLEM OF SHORTWAVE LASERS

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ON THE PROBLEM OF SHORTWAVE LASERS

A. Vinogradov, I. Sobelman, E. Yukov

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C4, suppliment au no 7 , Tome 39, Juillet 1978, page C4-61

ON THE PROBLEM OF SHORTWAVE LASERS

A. V. VINOGRADOV, I. I. SOBELMAN and E. A. YUKOV P. N. Lebedev Physical Institute, The Academy of Sciences of the USSR.

Leninsky prospect 53, Moscow. U.S.S.R.

RCsumk. - Les investigations actuelles sur les lasers UVL utilisant les transitions dans les ions multicharges font l'objet de cette synthese. Les parametres physiques et optiques necessaires, a la creation du plasma en etat d'equilibre et a I'obtention de cavite sont discutCs en detail.

Abstract.

-

A review of present investigations towards vacuum UV laser action utilizing transition in multicharged ions is given. The necessary plasma parameters together with existing reflecting materials are discussed. The emphasis is made on steady-state methods of inversion production.

1. Introduction.

-

In the present paper some possible ways for producing lasers in far U V and soft X-ray region are treated. We are mostly concerned with aspects of the problem which are being developed in the Lebedev Physical Institute. A detailed survey of works on the shortwave lasers with a large biblio- graphy was published recently by Elton and Way- nant [l].

2. Conditions necessary for existence of the popu- lation inversion. - We shall discuss possible methods of obtaining the inversion in a hot plasma in steady- state or quasi-steady-state conditions. In plasma devices of different kind, in particular, in laser heated plasma both the temperature in the 100-1 000 eV region, and the ions with the charge Zi

-

10-15 are easily obtained. The transitions between excited levels of such ions correspond to wavelengths from several tens to several hundreds of angstroms. This spectral range should be divided into two groups. In the 300-700

A

region a number of heavy metals (OS, Ru, Pt, Au) have a reflection coefficient equal to 10-20

%.

With the gain factor g equal to several inverse cms, this offers the possibility to use a tradi- tional scheme of laser with an usual optical resonator. In the region of tens of angstroms there are no reflecting materials and it is then impossible to use actually classical resonator.

A considerable part of the stored inversion can be used in the condition :

where I is the length of the active region, R is the mirror reflection coefficient, n = zc/2 L is the number of passes of photon inside the cavity, z is the lifetime of the inversion, L is the length of the cavity. Plasma

at the temperature of some millions of degrees occurs usually during the time z z 10-S S. Taking the resonator length - - . L = 10 cm and R = 0.OlrOLI one can

satisfy the condition (l), if

g2

-

4-8. By focusing the. pulsed laser radiation with the energy of several tens of joules, it is possible to obtain a plasma cylinder (spur) at the temperature T equal to 100-300 eV, and the length f = 1 cm. Thus, if /l

2

300

A,

then a value of g

-

10 is quite sufficient for the generation. In the region of shorter wavelengths (l) the reflection is negligibly small, hence the amplification requir- ed per pass should be larger than g1 > 30.

To produce the radiation with good angular properties, the unstable resonator may be found useful in spite of smallness of the reflection coefficient. The multilayer mirrors discussed recently [41-441 can, in principle, produce the reflection up to 40

%

[42, 441 in extreme ultraviolet region. A lot of techno- logy and radiation damage problems must be solved before the realization of these mirrors in practice. However, the results of calculations of the reflection coefficient based on recent experimental data on the optical constants are quite promising (see Table I). Now let us define the temperature, the density, and the configuration of the active medium which are needed. Consider, at first, the three-level scheme (see Fig. 1) in which the upper laser level 2 is populated due to collisions with electrons, and the lower level 1 is depleted due to a rapid radiative decay. Here and further we use a spectroscopic symbol for the ion

z = z i

+

1.

Along the isoelectronic series the ionization potential increases proportionally to Z2. The temperature, at which the ion Z has a maximum concentration,

( l ) The division of the spectral range into two parts is of course,

rather arbitrary.

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A. V. VINOGRADOV, I. I. SOBELMAN AND E. A. YUKOV

The reflection coefficient, RC-,,

(X),

for the mul- tilayer structure composed of N pairs of layers made of carbon andgold. The periodand the relative thickness of layers, P, are optimized according to [42, 441, R,

(X)

and RA,

(X)

are the reflection coefficients from carbon and gold bulks measured by Hagemann, Gudat and Kunz (Preprint DES Y , SR-7417, 1974).

inversion

/-72

co!!isiona!

excitation

spontaneous decay

U

FIG. I .

increases also proportionally to Z 2 . The rates of excitation by electron impact ( vo ) decrease as 2 - 3. The probabilities of the radiative decay of the reso- nance levels A

--

Z4. The populations of the excited levels N j may be expressed in terms of the density of ions in the ground state No :

Thus, the excited level populations relative to the ground state for ions with different Z are approxima- tely similar, provided that

It can be easily shown that in this density and temperature scale at the Doppler line broadening mechanism, the gain is directly proportional to Z3.5. In the litera- ture the recombination mechanism of the inversion formation in a supercooled plasma is widely discussed [2, 3, 4, 51. The time of cooling needed in this case falls drastically as Z - and, for kxample, for ion C V1 is, in accordance with estimations [4, 51, equal to 10-l2 S. So we shall restrict ourselves by the energy

schemes, for which the steady-state inversion may be achieved.

Strict limitations on the shape of an active region is imposed by the radiation trapping at the resonance 0-1 transition (see Fig. 1). Existence of the inversion is provided by a rapid radiative decay of the level 1 in the case of the 2-1 transition, and hence the radiation at the frequency of the 0-1 transition should freely escape an active volume, i.e. plasma must be optically thin in this line, at least, in one dimension. The transverse dimension of a plasma active volume should be much smaller than its length l. Calculations for several schemes given in [10, 151 show that it is necessary to have 911

-

10-2-10-3. The quantity 9 should be, in this case, no more than 100-200 p. In a number of cases the limitation on the transversal dimension 9 appears to be more severe and eliminates

practically the possibility of using the inversion. 3. The population inversion in ions of different isoelectronic sequences. - 3.1 H-LIKE IONS. - The calculations of the level population of H-like ions made by Bates, Kingston, and McWhirter [6], by McWhirter and Hearn [7] and also in later papers [8, 91 showed that in a steady-state plasma there is no inversion between levels with different principal quantum numbers averaged over orbital momentum. An analysis of data obtained from the calculations of the excitation cross-section implies that the steady- state inversion may occur between separate levels with different values of the orbital momenta. This is possible, however, only in an extremely rare plasma, and hence the corresponding gain value is very small g

--

10-4 cm-'.

3 . 2 He-L.IKE IONS. - In He-like ions the steady-

state population inversion occurs at the intercombination 33L-21P and 43L-31P transitions [10]. The spectrum of these ions is very simple, the excitation cross- sections are known with a good accuracy, and the population kinetics can be calculated quite reliably. The level scheme is illustrated in figure 2.

cascade

excitatron

l

IsZ

' S

I

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O N THE PROBLEM O F SHORTWAVE LASERS C4-63

The radiative lifetime of the triplet level for ions with the charge Z

-

10-15 is 2-3 orders of magnitude larger, than the lifetime of the singlet level 2lP. In the case of He-like ion Mg XI the radiative probabilities are

and

On the other hand, as was shown by Vainshtein [l l] the cross-section of the excitation of the 2'P level near the threshold is practically equal to the excitation cross-section of the 23P term. Therefore, at low plasma density, when the populations of the levels N j are defined by the balance of the rates of the pumping and the radiative decay (2) :

the population of the triplet n = 2 levels is the same 2-3 orders of magnitude larger, than the population of the singlet levels.

Collisional desexcitation arising at higher densities affects at first, the triplet levels having long radiative lifetime. In figure 3 one can see the rates of the transi- tions beginning from the 23 levels.

FIG. 3. - Energy dependence of the rates for different transitions from the triplet n = 2 level of He-like ion Mg XI.

As is seen from figure 3, at not too low temperatures, the rates of the intercombination Z3 -+ 2' transitions

are considerably lower, than the rates of the transitions without spin change. That is why, the singlet and triplet level systems are practically independent. At a sufficiently high electron density, Ne, the effective cascade excitation of the triplet levels with principal quantum numbers n = 3, and n = 4 occurs. In the same time the population of the singlet 2lP, 3lP levels is still rather small because of a great rate of the radiative decay. This mechanism accounts for the population inversion at the 33 -+ 2lP and

43 -+ 3lP transitions. The relative inversion per

non-degenerated state may be rather large (see Fig. 4). The wavelengths of the inverted 33 -+ 2lP, 43 -+ 3 'P

transitions and the density and temperature values, for which the maximum gain occurs, are given in table 11. The characteristic density and temperature ranges are N,

-

1021-1022 Te 300-700 eV. Presented in figure 4 and in table I1 results are based on a numerical solution of the rate equations, taking into account the radiative and collisional transitions among all levels with principal quantum numbers

n = 4. The inversion value depends most strongly on the ratio of the rate of the 23 + i ionization to the rate of the 23 -+ 33 excitation. In figure 4 the dashed

curve shows the inversion calculated with this ratio multiplied by a factor of 2. As is seen from figure 4 the value of the inversion does not change considerably even if such an uncertainty in the collisional rates is assumed.

Optical plasma parameters and the gain at intercombination transitions of He-like ions

Ion Transition 1 (A) g (cm- l) N, (cm 3, T, (eV)

- - - - 33-2LP 58 0.4 1.3 X 10'' 350 Mg XI 43-31 160 2 1.3 X 10'' 350 33-21P 34 2 1 . 1 x 1 O Z 2 500 P 43-31 ₉₃ ₈ _{1 . 1 x l O Z Z 500} 33-21P 26 4 2.9 X 10'' 700 c1 XVI 43-31 75 24 4.5 X 10'' 700

( 2 ) In equation (2) q, is the rate of the population of the level j

to which, at low densities, the processes of the electron impact, 10 20 102' f0 22 N e photo- and dielectronic recombination contribute; A, is the total FIG. 4. - Rehtivg inversion between the trQlet n = 4 and singlet radiative decay probability. Usually, under steady-state conditions n = 3 levels of He-like ion P XIV. Dashed curve -the pame obtained the main contribution to the pumping rates qjof the lowlying discrete ( eu(2' -+ i) )

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C4-64 A. V. VINOGRADOV, I. I. SOBELMAN AND E. A. YUKOV

The results given in table I1 exhibit that the inversion occurs at the transitions of He-like ions in the wavelength 30-150

A

region, but in this case the gain, g

--

1-20 cm-', is not sufficiently high. If there is the radiation trapping of the resonance l l S -+ 2'P and

1's -+ 3'P transitions, then the population inversion

vanishes. To avoid this, the transverse dimension of the plasma layer should not exceed 1-10 p at the parameters listed in table 11. Under these conditions it is quite unreal to use the inversion.

3.3 Ne-LIKE IONS. - In the spectral region of 300-700

A

where one can hope to have a normal- incidence resonator, the population inversion can be obtained at the 3p -+ 3s transitions of ions with the ground 2~~ configuration, k = 1, 2,

...,

6. The idea

of using the mechanisms of gas-discharge ion lasers in short wavelength range was discussed in the lite- rature earlier [12]. The gain evaluations and the necessary plasma parameters for ions with the 2p2 and 2p6 configurations are reported in the papers [13,14]. Among all the ions with ground 2pk configuration the Ne-like ions having the 2p6 configuration seem to be most perspective. There is a drastic jump of the ionization potential from Na-like to Ne-like ion, similar to that taking place between Li-like and He-like ions. Therefore, there exists a rather large temperature range, in which Ne-like ions dominate. The level scheme of Ne-like ion Ca XI is shown in figure 5. The mechanism of inversion at the 3p -t 3s

transitions is rather simple. It corresponds to the mechanism of the scheme in figure 1. The radiative decay of the 3p levels to the ground state is forbidden, while the two levels with the 3s configuration decay quite rapidly. The cross-section of the excitation of

the 3p configuratiorb is several times larger, than that of the 3s configuration.

Unlike He-like ions, there is, in this case, considerably less information on the cross-sections and the probabilities, and their accuracy is quite poor. There- fore, we have confined ourselves, at first, to an analysis of the elementary processes and populations in frame of LS-coupling scheme [15]. We have used the cross- sections calculated in the Born-Coulomb approximation without taking into account the exchange. Such a calculation gives a rather high gain

--

100 cm-

'

for the 2p5 3p' So -+ 2p5 3s' P, transition. The gain

as a function of the density N, in optically thin plasma is shown in figure 6.

FIG. 6. - Density dependence of the gain for the 3p + 3s transition in Ne-like ion Ca XI at different values of the optical thickness, s,

in the 2p -t 3d line. In the resonance 2p + 3s line the plasma is

opticalIy thin. Solid curve is obtained at T, = 150 eV, and dashed curve at T, = 100 eV.

Under real conditions it is practically impossible to avoid the trapping of radiation at the 2p6 + 2p5 3s

transition. This fact results in a sharp decrease in the decay probability of the 3s levels in optically thick plasma, while the density region with asgreat gain is getting narrower. In figure 7 the density dependence of the gain is given for the case when the transverse

FIG. 7. - Density dependence of the gain for the 3p + 3s transition at fixed transverse plasma dimension. At low densities the plasma

is optically thin in the 2p + 3s line and the gain increases with the

ZP6

'S,,

0

nlasma dimension due to the trapping of the 3d + 2p radiation, whereas at higher densities the 3d + 2p radiation is trapped and

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ON THE PROBLEM O F SHORTWAVE LASERS C4-65 dimension of the plasma is fixed and equals 50-200 p.

On the other hand, if the density is fixed, there arises a distinct maximum of the gain as a function of charge of the ion Z (see Fig. 8). The temperature range also turns out to get rather narrow (see Fig. 9). In the limit of 1 0 ~ temperatures the population of excited levels become extremely small, whereas at high temperatures the ionization equilibrium shifts towards a greater ionization degree, and the total concentration of the Ne-like ions drops down.

FIG. 8. - The 3p + 3s gain for Ne-like ions of different elements a t a given transverse plasma dimension d = 100 p.

FIG. 9. - Temperature dependence of the gain for the 3p + 3s

transitions of Ne-like ion Ca XI.

If LS-coupling scheme is accepted for the energy levels, and if the exchange scattering is neglected, the only one level of ten belonging to the 2ps 3p configuration is effectively excited by electron impact, namely, the singlet 'So level with the total angular momentum 3 = 0. The transition to this level is due to a monopole term in the potential expansion over multipoles (3). Since the ground state 2p6 IS, is

(3) If the jl-coupling scheme is accepted, and the exchange is not taken into account, the only levels with 3 = 0 will be effectively excited, namely, the two levels 'S, and 3P,. The excitation cross- section of the 3p 'S, level is high enough in both types of the coupl-

ings.

spherically symmetric, the quadrupole potential gives the excitation cross-sections of the 3p levels different from zero only for the levels with the total momentum 3 = 2. The calculation in the Born-Coulomb approximation shows, that the cross-section for the monopole transition is considerably larger, than that for the quadrupole transitions. Excitation of the levels with the 2ps 3p configuration and the angular momentum

3 = 1, 3 is possible only due to the exchange interaction. As results from the calculations, a total purely exchange cross-section for the 2ps 3p configuration is only just a little smaller, than that calculated on the basis of Born-Coulomb approximation without exchange. Thus, the exchange interaction is of great importance for all levels with 3 # 0. As for the levels with 3 = 0, the account of exchange interaction appears to be unable to change the cross-section value substantially. So, the analysis of excitation rates shows that, at least, two levels of the 2ps 3p configuration have sufficiently high excitation rates from the ground state. Available information on the effective cross sections is not enough yet for detailed calculation of population of all levels with principale quan- tum number n = 3. Thus, the accuracy of results presented in figures 6-9 is not very high.

Up to the date there were neither experimental nor theoretical data on the wavelengths and oscillator strengths of the 3p ,+ 3s and 3d + 3p transitions.

Some calculations have been made recently by Vainstein et al. [16]. These results for several transitions are given in table 111.

TABLE I11

The wavelengths for the 3p 'So-3s 'P1

and 3p 3P0-3s

??,

transitions in Ne-like ions

A(3p 'So-3s 'P,) A(3p 3p0-3s 3 ~ , )

Ion

(A>

(4

- -

-

S V11 604 8 12 C1 V111 526 707 Ar IX 465 624 K X 418 557 Ca XI 380 50 1 Sc XI1 349 458 Ti XI11 323 412 V XIV 30 1 377 Fe XVII 252 294

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A. V. VINOGRADOV, I. I. SOBELMAN AND E. A. YUKOV Emitting ion

-

Na X (2'P + 1's) Si XI11 (2'P l's) K XIX (2~1,2 -+ Is1,2) Ni XIX (3d -+ 2p) Cr XV (3d + 2p) CO XVIII (3d + 2p)

Resonance pairs of ions

Resonance Absorbing transition defect (eV)

- - Ne IX (1's -+ 4'P) 0.45 A1 XI1 (1's -+ 3'P) 3.9 C1 XVII (Is -+ 4p) 1

.o

F IX (Is -t 3p) 0.2 V XIV (2s2 2p6-2s 2p6 3p) 0.03 Cr XV (2p + 5d) 0.1 Lasing transitior 4-3 3-2 4-3 3-2 2p -t 2s 5-4 Wavelength

(4

230 46 65 8 1 120 150 nism - a selective pumping of a given level by linear

/Ve

dense

radiating

(ayer

radiation. This may be done when the wavelength of intensive line of one ion Z , coincides with that of the other ion within its width accuracy, as is shown in figure 10 [17, 18, 191. Some pairs of ions with a relatively small resonance defect are given in table IV. In a homogeneous, optically thin plasma the density of photons (number of quanta per field oscillator), corresponding to the spectral line, is defined by the excitation rate, and absorption of radiation emitted by ion 2, does not affect greately the level population of ion Z,. There are two methods to

provide higher density of photons at the frequency :

r

(see Fig' 1°) and thereby a larger rate

FIG. l l . - Selective pumping in nonhomogeneous plasma.

inversion

4

- -

Ion Z,

Ion

Z,

FIG. 10. - Selective pumplng in two-component plasma. to the level 2 of ion Z,, namely : (1) in non-homogeneous plasma and (2) in an homogeneous plasma which is optically thick at the frequency W, in the 0-1 line of ion Z,, but thin in the 0-1 line of ion Z,.

In the first case emitting ions Z, should be located in a more dense layer with the density N;", and absorbing ions Z, - in a less dense layer with the

density N:,)

<

N:'), as, for instance, is shown in figure 11. It is desirable to have the density N i l ) so high, that levels of ion 2, has the Boltzmann equilibrium, and spectral radiation intensity at the frequency W, were as close to a blackbody intensity

radiation as possible. For He-like ion Si XI11 the Boltzmann distribution takes place at

Nil)

2

lOZ4 cm-3

.

may be rather high

2

100 cm-' (4). In the region of tens of angstroms the gain may be written as :

The second mechanism based on trapping of radiation of the frequency o, in homogeneous plasma also enables to provide the selective pumping. In the case of Doppler broadening (specific mechanism of resonance lines of multicharged ions, even in a rather dense plasma), the radiation density at the frequency

o, increases proportionally to z

f i

z [20-231, where z = k,, 3 is the optical thickness in the center of the line. In this case, plasma should be optically thin in the 0-1 line of ion Z,, i.e. ion Z2 should be a small admixture. A rough estimate of the gain, at reasonable volumes of plasma, leads also to a relationship of the type (3).

Thus, all considered methods of pumping for the region of tens angstroms require to produce a plasma with the density of N,

-

1022-1023 cmp3, that sug- gests a very high rate of energy deposition into cubic centimeter ( 5 ) . At the present time a hot plasma with

the temperature of 0.5-1 keV has been obtained only at the density N,

-

10,' cm-3 [25, 261. One may

(4) In the case when NA') 2 1OZ2

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ON THE PROBLEM OF SHORTWAVE LASERS C4-67

expect that it would be possible to advance with a success into a region of higher densities with the help of the eximer lasers [27], with the critical density 1-2 X 1022 Just now there are neither the

necessary plasma parameters, nor resonator.

5. Present status and perspectives. - A lot of different methods of generating a coherent radiation in the wavelength region

A

< 1 000

A

have been suggested. Since 1971 a series of experimental papers has been published, for example [28-401. A successful advancement has been attained in a shortwave length region with the aid of methods of nonlinear optics [3 1- 341. In the 1000-1 100 1$ a coherent radiation was achieved in the presence of two-photon resonance by summing three waves [31, 321. The radiation with a wavelength of 520 1$ - the twentieth harmonic of Nd-laser radiation - was obtained by generating

the fifth harmonic at 2 661

A

[33]. In the work [34] the authors succeeded to obtain the radiation with

A = 380

A

using the generation of the seventh harmonic of the radiation with wavelength at 2 661

A.

The number of photons per pulse obtained in these experiments was equal to 107-10'.

A number of experiments had a purpose to observe the population inversion and the gain. In the paper [28] the intensities of 2p5 4d[3P,, 3D1, 'Pl] 2p6['S0] lines of the Ne-like ion AI IV were studied in a laser plasma. The line 2p5 4d3 P, + 2p6 'S, (A = 1 17.41

A)

having the smallest oscillator strength appeared to be the most intensive. This effect was interpreted by the authors [28] as the induced radiation from the dense region of laser plasma. They investigated also the time structure [29] of the spectrum and carried out measurements on the gain, the value of which was found to be 2-20 cm-' [30].

In the paper [24] it was shown that a high gain can be obtained by using the process of charge transfer in plasma expansion into neutral gas. Experimental approach to this problem is reported in [35, 361. In the work [37] the inversion was observed between the levels with principal quantum number n = 5, 4, 3 of H-like ion C V1 and He-like ion C V.

In a series of experiments a non-steady-state mecha-

nism of the inversion were studied [37-391. The population inversion between levels with n = 4, 3, 2 was discovered in measurements of intensities of Lyman series for ion C V1 in an expanding and decay-

ing laser plasma [37]. According to the authors' estimations this inversion occurs at N,

-

1017 cm-3 with a very small gain

-

10-5 cm-'. A similar method was used to obtain the inversion at the 3 -t 2

transition for the same ion C V1 in a laser evaporation

of carbon filament at N,

-

3 X 1019 cmp3. The

gain of

-

2 X 1 0 - ~ per pass has been estimated [38].

Radiation spectrum of the plasma spur along and across its axis was investigated in the work [39]. The KC1 target was heated by two consecutive ultra- short pulses of Nd laser. In the spectral region 58-75 1$

some increase in relative intensities of several lines of Na-like ion C1 V11 was observed. This effect may be connected with an induced radiation.

Some experiments using the resonator were directed to laser action at 3p -P 3s transitions of Ne-like ion

Ca XI [40]. The normal-incidence resonator with a grating as beam-splitter was used. The scheme of such cavity is given in figure 12. The results of this experiment are promising, but it is still early to speak about of a laser device.

FIG. 12. - Arrangement of the experiment by A. A. Iluchin et al.

(1977).

In our view one can hope that in the 300-700

A

range, where it is not complicated to provide the necessary plasma parameters, and to use the resonator, a stable laser generation might be obtained in the nearest future.

References [l] WAYNANT, R., ELTON, R. C., Proc. IEEE 64 (1976) 1059.

[2] GORDIETS, B. F., GUDZENKO, L. I. and SHELEPIN, L. A., PMTF (in Russian) 5 (1 968) 1 16.

[3] GUDZENKO, L. I., EVSTIGNEEV, V. V. and YAKOVLENKO, S. I.,

Kvantovaya Elektron. (in Russian) l (1974) 2061. [4] BOHN, W. L., Appl. Phys. Lett. 24 (1974) 15.

[5] JONES, W. W., ALI, A. W., Appl. Phys. Lett. 26 (1975) 450. [6] BATES, D. R., KINGSTON, A. E. and MCWHIRTER, R. W. P.,

in Atomic and Molecular Processes, edited b y D. R. Bates (N.Y.) 1962.

171 MCWHIRTER, R. W. P., HEARN, A. G., PYOC. Phys. Soc. London

82 (1963) 641.

[S] GORDIETS, B. F., GUDZENKO, L. I. and SHELEPIN, L. A., J.

Quant. Spectrosc. Radiat. Transfer 8 (1968) 791.

[g] JOHNSON, L. S., HINNOV, E., J. Quant. Spectrosc. Radiat.

Transfer 13 (1973) 333.

[l01 VINOGRADOV, A. V., SKOBELEV, I. Yu., SOBELMAN, I. I. and YUKOV, E. A., Kvantovaya Elektron. (in Russian) 2 (1975)

2100, ibid. 3 (1976) 981.

[l l] VAINSTEIN, L. A., Zh. Eksp. Theor. FIZ. (in Russian) 67 (1974) 63.

[l21 MOLCHANOV, A. G., UFN (in Russian) 106 (1972) 165. 1131 ELTON, R. C., Appl O p t 14 (1975) 97.

1141 ZHERIKHIN, A. N., KOSHELEV, K. N. and LETOKHOV, V. S.,

Kvantovaya Elektron. (in Russian) 3 (1976) 152. [IS] VINOGRADOV, A. V., SOBELMAN, I. I. and Y u ~ o v , E. A.,

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C4-68 A. V. VINOGRADOV, I. I. SOBELMAN AND E. A. YUKOV

[l61 VAINSTEIN, L. A., VINOGRADOV, A. V., SAFRONOVA, U. I. and SKOBELEV. I. Yu., Kvantovaya Elektron. 5 (1978) 417. [l71 VINOGRADOV, A. V., SOBELMAN, I. I. and YUKOV, E. A..

Kvantovaya Elektron. (in Russian) 2 (1975) 105.

1181 NORTON, B. A., PEACOCK, N. J., J. Phys. B 8 (1975) 989. 1191 BHAGAVATULA, V. A., Preprint LLE, 41, Rochester, May, 1976. [20] HOLSTEIN, T., Phys. Rev. 72 (1947) 1212; ibid. 83 (1951) 1159. [21] BIBERMAN, L. M., Zh. Eksp. Teor. Fiz. (in Russian) 17 (1947)

416 ; ibid. 19 (1949) 584.

[22] IVANOV, V. V., V SBORN., Teoriya zvezdnych spektrov (in Russian) ((( Nauka D, Moskva), 1966.

1231 NAGIRNER, D. I., Astrofiz. (in Russian) 5 (1969) 507. [24] VINOGRADOV, A. V., SOBELMAN, I. I., Zh. Eksp. Teor; Fiz.

(in Russian) 63 (1972) 21 13.

[25] BAYANOV, V. I., GULIDOV, S. S., MAK, A. A., PEREGUDOV, G. V., SOBELMAN, I. I., STARIKOV, A. D. and CHIRKOV, V. A.,

Pis'ma Zh. Eksp. Teor. Fiz. (in Russian) 23 (1976) 206;

Kvantovaya Elektron. (in Russian) 3 (1978) 2253. [26] BOIKO, V. A.. PIKUZ, S. A. and FAENOV, A. Ya., Preprint

FIAN (in Russian) 1977.

[27] HOFFMAN, J. M., HAYS, A. K. and TISON, G. C., Appl. Phys.

Lett. 28 (1976) 538.

1281 CARILLON. A., JAEGLE. P,. JAMELOT, G., SUREAU, A., DHEZ, P. and CUKIER, M,, Phys. Lett. 36A (1971) 167.

1291 JAMELOT, G., CARILLON, A., JAEGLE, P. and SUREAU, A., Paper presented at the Int. Con$ on the Physics of X-ray

Spectra, N.B.S., Gaithersburg, Maryland, USA, 1976.

[31] KUNG, A. H., YOUNG, J. F. and HARRIS, S. E., Appl. Phys.

Lett. 22 (1973) 301.

[32] ARMSTRONG, J. A., SOROKIN, P. P. and WYNNE, d. J., Phys.

Rev. Lett. 32 (1974) 343.

[33] REINTJES, J., ECKARDT, R. C., SHE, G. Y., KARANGELEN, N. E., ELTON, R. C. and ANDREWS, R. A., Phys. Rev. Lett. 37 (1976) 1540.

[34] REINTJES, J., SHE, C. Y., ECKARDT, R. C., KARANGELEN, N. E., ANDREWS, R. A. and ELTON, R. C., Appl. Phys. Lett. 30

(1977) 480.

[35] ANDERSON, D., MCCULLEN, J., SCULLY, M. and SEELY, J.,

Opt. Commun. 17 (1976) 226.

[36] DIXON, R. H., ELTON, R. C., Phys. Rev. Lett. 38 (1977) 1072. [37] JRONS, F. E., PEACOCK, N. J., J. Phys. B 7 (1974) 1109. [38] DEWHURST, R. J., JACOBY, D., PERT, G. J. and RAMSDEN, S. A.,

Phys. Rev. Lett. 37 (1976) 1265.

[39] ZHERICHIN, A. N., KOSHELEV, K. N., KRUKOV, P. G., LETO- C H ~ V , V. S. and CHEKALIN, S. V., Pis'ma Zh. Eksp. Teor.

Fiz. (in Russian) 25 (1977) 235.

1401 ILUCHIN, A.. A.. PEREGUDOV, G. V., RAGOZIN, V. N., SOBEL- MAN, I. I. and CHIRKOV, V. A., Pis'ma Zh. Eksp. Teor.

Fiz. (in Russian) 25 (1977) 569.

[41] SPILLER, E., Appl. Phys. Lett. 20 (1972) 365, Appl. Opt. 15

(1976) 2333.

[42] VINOGRADOV, A. V., ZELDOVICH, B. Ya., Appl. Opt. 16 (1977) 89; Preprint P. N. Lebedev Physical Institute, NO 185, Moscow, 1976.

[43] HAELBICH, R. P., KUNZ, H. J., Opt. Commun. 17 (1976) 287. 1301 JAEGLE, P., JAMELOT, G., CARILLON, A., SUREAU, A. and DHEZ, I441 VINOGRADOV, A. V., ZELDOVIC~, B. Ya., Opt. Spektrosk.