i. e., j3 cannot be the smallest positive zero of U0(a).
Because S[P0ol is the maximum value of S[P] in theclass of pupil functions that satisfy (3), it is certainly anupper bound for S[P] in the class of pupil functions thathave ( as the Rayleigh limit. We shall next show thatS[P0 ] is the least upper bound for s[P] in the latter classwhen l?'< Pf.
Consider the complex-valued pupil function P2(p)= Po(p) co sy+ iP, (p) siny, where v is a constant and P,(p)is defined so that P, (p) = + l when 0 < p < pm, =i/ll, andP,(p)= 0 when Pm< p< 1. We observe that
| p 2(p) 1 2 = pg(p) cOs%1+ P (p) sin 2 y,
1
f P, (p) Jo(atp)p dp = J, (apm)pm a"
It follows that P2(p) satisfies (2) and (3) because Po(p)and Pl(p) do. If U2(a) is the phase and amplitude distri-bution corresponding to P2(p), then U2(a) does not vanishwhen 0< a< 3, because its imaginary part is positive.Therefore, 13 is the Rayleigh limit for P2(p). Moreover,P2 converges uniformly to P0 as y approaches zero. Itthen follows that S[P2) is arbitrarily close to S[PO3 if yis sufficiently close to zero, i. e., S[PO] is the leastupper bound.
The analysis in Ref. 3 showed that S[P]< S[P0 ] for
every pupil function P(p) that satisfies (3) and is not aconstant multiple of PO(p). Because S[PO] is the leastupper bound, it follows when '> 3* that there is no pupilfunction that maximizes the Strehl ratio S[P] in the classof complex-valued pupil functions that have (3as the Ray-leigh limit.
* Work performed under the auspices of the U. S. Energy Re-search and Development Administration.Present address: EG and G Idaho, Inc., P. 0. Box 1625,Idaho Falls, Ida. 83401.
'R. K. Luneburg, Mathematical Theory of Optics (Universityof California, Berkeley, 1964), pp. 349-351.
2R. Barakat, "Solution of the Luneberg apodization problems,"J. Opt. Soc. Am. 52, 264-275 (1962).
3J. E. Wilkins, "Luneberg apodization problems," J. Opt.Soc. Am. 53, 420-424 (1963).
4P. Jacquinot and B. Roizen-Dossier, "Apodization," in Pro-gress in Optics, Vol. III, edited by E. Wolf (North-Holland,Amsterdam, 1964), Chap. 2.
5H. Osterberg and J. E Wilkins, "The resolving power of acoated objective," J. Opt. Soc. Am. 39, 553-557 (1949).6P. M. Morse and H. Feshbach, Methods of Theoretical Phys-
ics (McGraw-Hill, New York, 1953), p. 436.70. Sz~sz, "Inequalities concerning ultraspherical polynomials
and Bessel functions, " Proc. Am. Math. Soc. 1, 256-267(1950).
Observations of Lii and Liii absorption spectra in the grazing incidence region*A. M. Cantfi
Osservatorio Astrofisico di Arcetri, Unitd di Ricerca del Consiglio Nazionale delle Ricerche, Florence, Italy
W. H. ParkinsonCenter for Astrophysics, Harvard College Observatory, 60 Garden Street, Cambridge, Massachusetts 02138
G. TondelloCentro Gas lonizzati, Consiglio Nazionale delle Ricerche, Universitd di Padova, Italy
G. P. TozziOsservatorio Astrofisico di Arcetri, Instituto di Astronomia dell'Universita, Florence, Italy
(Received 12 November 1976)
The atomic spectra of LiU and Lini have been observed in the region 215-160 A. The flash-pyrolysistechnique has been used to produce the atomic vapor. A toroidal focusing mirror has been used which allowsthe background continuum from the BRV source to be photographed with a single shot. Thirteen lines of theprincipal series of singly ionized lithium and the continuous absorption at the limit of the series have beenobserved. Absorption lines from inner-shell excitation of neutral lithium have also been observed andtentatively identified.
The flash-pyrolysis technique has been used success-fully to produce sufficient vapor density for absorptionspectroscopy of atoms'-5 and more recently of singlyionized barium. "' Roig, 8 in evaluating the flash-py-rolysis technique, has confirmed that photoionization isthe dominant mode of ionization. In the present workwve have applied the technique to obtain in absorption theprincipal series of Liii and to extend the inner-shellspectrum of Li i. In the earlier work of Ederer, Lu-
1030 J. Opt. Soc. Am., Vol. 67, No. 8, August 1977
catorto, and Madden, 9 the inner-shell spectrum of Li iwas observed in absorption by using the National Bu-reau of Standards 180 MeV synchrotron as a continuumbackground source and a heat-pipe furnace to produceand contain the lithium vapor. Recently, Lucatorto andMcIlrathl° have developed a new approach which uses apulsed dye laser to produce ionized sodium and a BRV-type" source as background continuum. They have mea-sured the photoionization cross sections of Naii and ob-
BRV Source TABLE II. Lines of Lii (from ground level ls2 2s2S except
FIG. 1. Schematic of the experiment showing the BRV source,the flash-pyrolysis tube, the focusing mirror M, and the graz-ing-incidence spectrograph, Cs and C2 are the condensers, T1and T2 the trigger generation units, and D the variable delaydevice. S is the entrance slit of the spectrograph, G is thegrat ing.
served the neonlike series 2s 22p6- 2s2 2p5ns and nd andautoionization resonances of the type 2s?2p-'- 2s2p6 np.This new method is also successful in studies of Liiil2
and Ca ii. 3
In the present work, using the flash-pyrolysis tech-nique, finely divided Li3N, Li20, or LiH was placed ina 25-cm-long quartz or glass absorption tube surround-ed by a helical flash lamp. The schematic of the ex-periment is reported in Fig. 1.
The material inside the tube is heated and vaporizedby the strong luminous flux emitted by the flash lamp(maximum energy density about 50 J/cm2 ) in times ofabout 10 jis. 8 After a suitable delay the backgroundcontinuum source is fired and the absorption spectrumis photographically recorded with a grazing-incidencespectrograph. The flash lamps employed are of theanti-inductive type, working with a voltage up to 10 kVand are used with a spark gap in series. They are sup-plied with two condensers Cl of 60 . F capacity each.
The continuum source is a BRV'1 source connectedto a fast discharge condenser C2 of 2. 5 p.F capacityand charged up to 25 kV. A polyethylene capillary witha hole of 0. 7 mm diam was fitted over the end of theuranium anode to fix the location of the discharge. Thecontinuum source too is in series with a spark gap in
TABLE I. Lines of Li ii 1S2 t S-isnp 1PJ.
Wavelength (A)±0. 01 A exceptwhere stated Intensity n n*
bsorption also by Ederer et al. (Ref. 9).bObserved in emission also by Buchet et al. (Ref. 18).0Theoretical position also by Cooper et al. (Ref. 17).
order to provide a reproducible start, delayed with re-spect to the flash lamp firing and independent of thepressure existing inside the tube. The delay between thecontinuum source and the flash lamp is continuouslyvariable from 50 to 500 ps in order to optimize the con-ditions for the absorption. The maximum of the inten-sity of the Liii lines with respect to the Lii ones isreached for a value of the delay between 80 and 120 pis,i. e., very near the peak of intensity of the flash lamp.For longer delays there is a decrease of the intensityof the Liii lines that disappear at all for delays longerthan 350 pUs. For the Liz lines there is no apparent dif-ference in intensity during such interval.
Because the threshold for photoionization of Li I is at2300 A, the substitution of a quartz absorption tube fora glass one proved useful to discriminate between theproduction of Lii and Liii spectra. When glass absorp-
Cantu et aL 1031
blend with emissionline
blend with emissionline
0-
10VI
0V
CVI
¶0 170 10 10 200 O A
1_S' Op II I I I [SP 14P 3 I 12p Lt l Isp 'P
U I ls 12v 'p %os S p 1 I N I* 1 13P 1.Op
L.1 %2pSl *P is P 4 H I 20 14s '3s '2l
- 3s 'S 1 0 3 12p LIT 1,3s,, 'PI I I II I II II I
FIG. 2. Microphotogram of the spectral region 160-215 A showing the principal features of the recorded spectra. In the lower
part are shown the Liii and the Lii identified series. On the bottom are the remaining Lii unidentified lines. Also indicated inthe trace are some impurity lines appearing in emission in the BRV source, and on the left-hand side the dashed line shows the
lowering of continuum due to the absorption at the limit of the Liii resonance series.
tion tubes were used, only one Li II line (199. 28 A) wasrecorded very weak. Helium or argon buffer gas at apressure of 10 to 150 mTorr was usedtoreducethemeanfree path of the lithium ions and consequently the re-combination at the walls of the tube.
The spectra were photographed with a 2 m grazing-incidence spectrograph equipped with a platinum coated,600 lines/mm Bausch and Lomb grating blazed at 3031'and used at an angle of incidence of 86°. Eastman Ko-dak 101-05 plates were used. A toroidal focusing mir-ror14 was used between the 10 Aim entrance slit and ab-sorption tube. The mirror has radii of curvature of416 and 77 mm, respectively, in the plane of incidenceand in the plane perpendicular to it and was used at anangle of incidence of 80°. With this arrangement, theaperture of the spectrograph is filled and the spectraare nearly stigmatic at 100 A. By using the improvedBRV source and the toroidal mirror, only one shot wasneeded for an exposure. The wavelengths were mea-sured in first and second order using emission lines ofOV, OVI, SiVI,, 15 and uranium' 6 that appeared in thespectrum of the BRV source. In addition, absorptionspectra of helium have been recorded in order to evalu-ate a possible Doppler shift of the emission lines of theBRV source due to plasma motion. The latter effect, ifpresent, is below our stated precision and is also inagreement with the fact that no apparent relative shiftwas found between lines of oxygen and uranium.
In Fig. 2 a microphotogram trace of the 160-215 Aregion is reported; absorption lines of Li II, Li I, and someemission lines of the BRV source are visible. In Ta-ble I are reported the observed Li II lines, due to tran-sition from ground state s2 'S to the lsnp 'Po, 2•n c 14states. The first three lines have been previously ob-served in emission. 1
5 The microphotogram trace alsoshows the photoionization absorption of the LiII begin-ning at the Is 2S limit: on the left side of Fig. 2 the
dashed line shows the lowering of continuum due to suchabsorption. The behavior of the effective quantum num-ber n* and the absence of such lines and the continuum
1032 J. Opt. Soc. Am., Vol. 67, No. 8, August 1977
absorption at 163. 9 A when using a glass absorption tubeleaves little doubt about this identification. In Fig. 2are also present several lines of Li I due to the K shellelectron or the simultaneous excitation of two electrons,one of the K shell and the other of the L shell. The ob-served lines with relative intensity are listed in TableE. These lines are common to all spectra obtained withLiH and with Li 3N and on this basis are assigned to thelithium atom. The possibility of the weakest ones aris-ing from some common impurity or from molecular ex-citation cannot, however, be ruled out at the presentstage. Together with the classification of Ederer et al., 9in Table II are reported tentative classifications of otherlines based essentially on the behavior of f*;. the(ls3s 'S)np 2Po series, three terms of which have beenclassified and whose profiles are similar and character-istic of autoionization, has the highest degree of cer-tainty. The position of five resonances, (is 2s 1S)3p 2PO,(ls2p '1P)3s 2 Po, (ls2p 3 P)3d 2P0 (ls2p 3P)4s 2PO, and(ls2p 3 P)4d 2
pO reported by Cooper et al. 17 have been con-firmed only for the second one and with some uncertaintyfor the fourth.
We plan to continue in the study of the Li II spectrumextending the spectral region below 100 A in order toobserve the absorption spectrum due to the simultaneousexcitation of two electrons.
ACKNOWLEDGMENTS
The authors are indebted to Professor G. Righiniand Professor G. Tagliaferri for encouragement andhelp received. The technical help of P. Stefanini andthe support of Dr. M. Mazzoni and T. Grisendi aregratefully acknowledged.
*This research was supported by Consiglio Nazionale delleRicerche with a grant to Osservatorio Astrofisico di Arcetri,Italy.
'L. S. Nelson, "Intense rapid heating with flash dischargelamps," Science 136, 296-303 (1962).
Canti) et al. 1032
0
2G. Tondello, "The absorption spectrum of Si in the vacuumultraviolet," Astrophys. J. 172, 771-783 (1972).
3G. Tondello, "Absorption spectrum of Cui in the vacuum ul-traviolet, " J. Opt. Soc. Am. 63, 346-352 (1973).
4R. A. Roig, "The photoionization spectrum of neutral alumi-num Ali, " J. Phys. B 8, 2939-2947 (1975).
5R . A. Roig and G. Tondello, "The absorption spectrum ofneutral boron, BI, " J. Phys. B 9, 2373-2378 (1976).
6R. A. Roig and G. Tondello, "Extensions to the spectrum ofsingly ionized barium (Bari), " J. Opt. Soc. Am. 65, 829-830 (1975).
TR. A. Roig, "Absorption spectrum of BaIi in the vacuum ul-traviolet, " J. Opt. Soc. Am. 66, 1400-1405 (1976).
8R. A. Roig, "The photoionization spectra of Ali, Bi andBaii," Ph.D. thesis, Physics Dept., Harvard University(1975) (unpublished).
9 D. L. Ederer, T. Lucatorto, and B. P. Madden, "Autoioniza-tion spectra of lithium, "' Phys. Rev. Lett. 25, 1537-1540(1970).
10T. B. Lucatorto and T. J. McIlrath, "Efficient laser pro--duction of a Nab ground-state plasma column: Absorptionspectroscopy and photoionization measurement of Na', "
Phys. Rev. Lett. 37, 428-431 (1976)."G. Balloffet, J. Romand, and B. Vodar, "An emission source
of continuous spectrum extending from the visible to the ex-treme ultraviolet, " C. B. Acad. Sci. Paris 252, 4139-4151(1961).
12T. Lucatorto and T. J. McIlrath (private communication).t 3W. H. Parkinson, C. Skinner, and P. Smith (private communi-
cation).14A. M. Canta and G. Tondello, "Improvements to a continuum
source and a focussing technique for the 80-500 A range,"Appl. Opt. 14, 996-998 (1975).
16T. H. Newsom, "Wavelength standards for use with a BRVsource, " Appl. Opt. 13, 2712-2715 (1974).
17 J. W. Cooper, M. J. Conneely, K. Smith, and S. Ormonde,"Resonant structure of lithium between the 23S and 21Pthresholds, " Phys. Rev. Lett. 25, 1540-1543 (1970).
18 J. P. Buchet, M. C. Buchet-Poulizac, and H. G. Berry,"Classifications of some transitions in doubly excited Liiand Liii, " Phys. Rev. A 7, 922-924 (1973).
Satellite spectra from laser-produced plasmas of Be, B, C, N, and 0 inHe-like and Li-like configurations
Piergiorgio Nicolosi and Giuseppe TondelloCentro Gas Ionizzati, Consiglio Nazionale delle Ricerche, Universitd di Padova, Italy
(Received 3 January 1977)
Satellite lines near the resonance lines in He-like and Li-like configurations have been observed in laser-produced plasmas of Be, B, C, N, and 0. The observations have been made with a grazing incidencespectrograph with spatial resolution. These lines have been identified and compared with the existingtheoretical predictions. Their intensities have been measured relative to the accompanying resonance lines.
INTRODUCTION
Satellite lines located at wavelengths slightly longer thanthe resonance lines of H-like and He-like ions were ob-served long ago.", 2
Such satellite lines arise, respectively, from transi-tions of the type lsnl-2pn1, satellite to the Lyman lineLca, ls-2p of a H-like ion, and from transitions likels'nl-1s2pnl, satellite to the first resonance line is 2
_
ls2p of a He-like ion. An additional electron nW actsas a perturbing element with respect to the transition ofthe ion of charge Z+I. The configurations correspond-ing to the upper states of such satellites correspond tothe simultaneous excitation of two electrons. Recentlythere has been some interest in these configurations.
In the case of He-like configurations sophisticatedquantum mechanics calculations developed mainly byDoyle, Oppenheimer, and Drake, 3 Drake and Dalgarno 4
have predicted wavelengths and intensities of severalsatellite lines.
In the case of Li-like configurations, Gabriel 5 andGabriel and Paget6 have extensively developed the anal-ysis taking particularly into account the populatingmechanism of the upper level of the satellites. The
1033 J. Opt. Soc. Am., Vol. 67, No. 8, August 1977
diagnostic relevance of such satellite lines, particularlyfor ions with relatively high nuclear charge Z and ofastrophysical significance, has been demonstrated. 7,8
Recently, observations involving transitions to doublyexcited states have been performed in Hei 9 and Liu10' 11
in absorption, whereas for higher values of Z, satellitelines have been recorded in emission from both the so-lar corona'2 -
16 and from laboratory sources like thetapinches6 and low-inductance sparks.' 7"8 A sourcestrongly emitting satellite lines is the plasma producedby laser focusing: observations have been reported forC,' 9 F,'9' 20 Na,2' Mg, Al,' 9'2 1' 22 and Si.21
In this paper we report observations of several satel-lites for He-like ions Be iii, B iv, C v, N vi, and 0 viiand for Li-like ions Be II, B III, Civ, Nv, and Ovi. Themeasurements have been made with a laser-producedplasma, and comparison of the results for both wave-length and intensity of the satellite lines with existingtheory gives quite good agreement.
EXPERIMENT
The plasma was produced by focusing a Q-switched10 J, 10 ns ruby laser with an aspherical lens of 50 mm
