1078 J. Opt. Soc. Am. B/Vol. 2, No. 7/July 1985 Jannitti et al.

Photoabsorption spectrum of Be+

E. Jannitti

Istituto Gas Ionizzati, Consiglio Nazionale delle Ricerche, Padova, Italy

M. Mazzoni

Istituto di Astronomia, Universit) di Firenze, Firenze, Italy

P. Nicolosi, G. Tondello, and Wang Yongchang

Istituto di Elettrotecnica ed Elettronica, Universitd di Padova, Podova, Italy

Received August 1, 1984; accepted February 12, 1985

The absorption spectrum of the ion Be+ has been recorded in the vacuum ultraviolet by utilizing the method of twolaser-produced plasmas. The photoionization cross sections of the outer electron for transitions of the type 2s-epand 2p-ed have been measured at threshold; the values are = (1.5 0.1) X 10-18 cm2 and = (2.5 + 0.5) X 10-18cm2 , respectively. The inner-shell transitions lying in the region 90-105 A have been measured and completelyidentified.

INTRODUCTION

Although a great deal of information on the atomic structurecould be derived from absorption spectroscopy, such a tech-nique is difficult to implement for ionic species, and only fewexperiments have been made up to now. So far, the mostfrequently used techniques for producing the absorbing ionshave been resonant laser absorption' of tunable light andlaser-produced plasmas.2 We have applied the method oflaser-produced plasmas to the study of the absorption spec-trum of Be+ (Be II) both in the normal-incidence region, i.e.,from 600 to 1000 A, and in the grazing-incidence region from90 to 110 A. In the former region lies the absorption that isdue to the external optical electron, whereas in the latter theabsorption that is due to the inner electron is present.

The photoionization cross section of Be+ has been deter-mined by following the same method that was proved suc-cessful in the study of the spectrum of Be2+.3 The wave-lengths of the inner-shell transitions of the same ion have beencarefully measured in the grazing-incidence region. Somepreliminary observations and measurements of such transi-tions have already been reported.2 Most of these transitionshave been identified as corresponding to single-electron ex-citations and just a few to double-electron excitations.

EXPERIMENT

The experimental setup is shown in Fig. 1 and refers to themounting used in the normal-incidence region, whereas theone used in the grazing-incidence region has already beendescribed together with the general characteristics of the ex-periment.3 Briefly, a laser beam of 10-J energy and 15-nsec(FWHM) duration is split into two parts and generates twoplasmas. One, on a copper target T, is used as a backgroundcontinuum-emitting source, and the other one, on target A,is used for producing the absorbing species, which is to bestudied. The latter is focused with particular care. A

spherocylindrical lens is used for producing a focal spot,typically 100 gtm wide and up to 10 mm long. In this way thespreading of velocities of the streaming plasma along the lineof sight is minimized, and the absorbing length is maximized.The distance from the target at which the measurement iscarried out can be varied (0.5-3 mm), as can the delay betweenthe two plasmas (20-100 nsec). The plasma emitting thecontinuum is produced on a target tilted about 450 with re-spect to both the incoming laser beam and the axis of obser-vation, in order to collect the radiation from the densest partof the plasma itself. The radiation is collected by a toroidalmirror whose radii of curvature, R = 640 mm in the plane ofincidence and p = 530 mm in the plane perpendicular to theformer, are such as to compensate the astigmatism of thespherical grating used in the 2-m-radius normal-incidencespectrograph.4

On the focal surface of the normal-incidence spectrograph,a movable trolley carries a plate, coated with 1 mg/cm2

scintillator (therphenil-butadiene). The latter is imagedoutside the vacuum with two high-speed objectives (N.A. =0.75) on an intensified photodiode array (512 elements) con-nected with an optical multichannel analyzer (OMA). A filterset between the objectives selects only the radiation emittedby the scintillator (peak wavelength at 4200 A). The ad-vantages of using such a technique have already been proved,particularly as regards photometric accuracy, linearity, anddynamic range.3 The output of the OMA is sent to a PDP 11computer for further data processing.

The absorption coefficient is given by

k(X) = ln IO(X) Iso(X)IN - I -Is W ) (1)

where the spectrum of the background continuum source Io(X)and the absorption spectrum I(X) are corrected by the con-tributions of the stray light Io(X) and I (X) and those of theemission Ie (X) from the absorbing plasma. The amount of

0740-3224/85/071078-06$02.00 © 9185 Optical Society of America

Vol. 2, No. 7/July 1985/J. Opt. Soc. Am. B 1079

n = 5-8, are broadened when compared with the instrumentalfunction. The latter is shown in the inset of Fig. 2 (solid line),and it is fitted with a Voigt profile (dashed line) of FWHM-1.2 A and parameter t = (AXL)/(AXG), i.e., a ratio of theLorentian to the Gaussian component of 6. Some absorptionis also present in the discrete region of the spectrum in be-tween the lines. It may be due to the scattering of the con-tinuum radiation from the quite dense and inhomogeneousabsorbing plasma, to the absorption from the 1s22p 2

p0 state

(see below), or to some impurity, such as carbon, in the ab-

TO O MA sorbing path. Indeed, some weak absorption lines of C I and

C II are observed.The true absorption coefficient of the series of lines, as is

shown in Fig. 3 (solid line), has been obtained by the methodexplained in Refs. 3 and 6. Briefly, a synthetic spectrumconsisting of a series of Voigt profiles simulating the true ab-sorption spectrum is created. The latter is convoluted withthe instrumental function, yielding a modeled absorption

LIFig. 1. Experimental setup used in the normal incidence. L andL2, laser beams; T, target for the background-continuum source; M,toroidal mirror; A, target for the absorbing plasma; S, entrance slitof the spectrograph; G, grating; P, Rowland surface; H, scintillator-coated plate; 01 and 02, high-luminosity objectives; PDA, photodiodearray.

stray light, i.e., the light entering the spectrograph and thenrandomly diffused (e.g., by the grating and the zero-orderstop), is obtained by observing a zone of the scintillator closeto the one where the spectrum is focused. The emission Ie(X)

is determined by observing only the absorbing plasma. Tento thirty exposures were acquired for any spectral portionabout 100 A wide. Several of such portions were later accu-mulated together, and partial smoothing was applied to somedata.

The inner-shell spectrum was recorded photographicallywith a 2-m-radius grazing-incidence spectrograph fitted witha 2400-line/mm grating. The wavelength determination wasmade by using Ti lines as standards, emitted by the ions Tix-Ti xI-Ti XII and reported by Kelly and Palumbo.5 Thiselement was chosen in order to minimize some broadening and

shift effects that could be present in laser-produced plasmas.For the same reason, a convenient amount of power densitywas focused onto the target. The Ti targets were mountedwith the Be targets on the same target holder in front of theentrance slit of the grazing-incidence spectrograph. Conse-quently, the resulting spectrum was totally astigmatic. Theexposure of the standard lines was taken before and after theabsorption spectrum in order to consider possible thermaldrifts of the equipment. The measurements have been av-eraged among several exposures, and their standard deviationis reported.

SPECTRUM OF THE OPTICAL ELECTRON

The absorption spectrum in the region 680-790 A, i.e., nearthe ionization limit of Be+, is shown by a solid line in Fig. 2.It was recorded by producing the continuum-emitting plasma-70 nsec later than the absorbing one, the latter being irra-diated by the continuum at 0.6 mm above the target. In Fig.2, the photoionization jump near the series limit is clearlyvisible; it also appears that the lines 1S22S 2

S-ls2

np 2Po,

2.40

2.00

1.60

1.20-

0.80k

0.40

n.n

K

-_- _- - - - --

n=9 8 7 6 5

680 712 744 776 AFig. 2. Solid curve, experimental absorption coefficient of the res-onance series 1s22s

2S-ls

2np

2po with n = 5-8 of Be+ versus wave-length at 0.6-mm distance from the target. Dashed curve, convolutionof the computed coefficient with the instrumental function. In theinset, the best fit of the instrumental function (solid curve) with aVoigt profile (dashed curve) is shown.

9.60K

8.00

6.40

4.80

3.20

1 .60-

0.00t680 712 744 776 A

Fig. 3. Computed absorption coefficient of the resonance series ls 2282

S-1s2

np 2po with n = 5-8 of Be+ versus wavelength before (solid

curve) and after (dashed curve) convolution with the instrumentalfunction.

PDA

Jannitti et al.

1080 J. Opt. Soc. Am. B/Vol. 2, No. 7/July 1985

spectrum that is compared with the experimental one. Thebest-fit process is carried on with free parameters: the nor-malized Voigt profiles i (A) (which affect mainly the widthof the lines) and the column density (f ngdl, where ng is theground-state density and the integral is taken along theplasma length 1), which determines the peak value of the ab-sorption coefficient k (A0) at the center of the line profile X0.As in all convolution processes, the accuracy of the results islimited by the noise present in the original data and by thewidth ratio between the recorded lines and the instrumentalfunction. 7 In our case a good fit is obtained, as is shown bythe dashed line in Fig. 2. Here, the modeled spectrum hasbeen offset by a constant absorption kc = +0.35 to take intoaccount the residual absorption, and one more line, n = 9, hasbeen added for smoothing the jump between discrete andcontinuous transitions.

The comparison between the true (solid line) and modeled(dashed line) absorption coefficients is shown in Fig. 3. Eventhough the difference between the true and the modeledcoefficients is very large, particularly for n = 5, 6, where theoptical depth at line center is quite large, the true absorptioncoefficient can be determined with an uncertainty lower than10%. From the true absorption coefficient, the column den-sity f ngdl can be derived if the oscillator strengths of the linesare known.6 For the latter, we have taken the values reportedby Lindgdrd and Nielsen.8 After having determined thecolumn density, the photoionization cross section can be de-rived by measuring the jump of the absorption coefficient atthe limit. Table 1 reports the various atomic data and theresults. The value of the cross section at threshold a = (1.5i 0.1) X 10-18 cm 2 should be compared with the calculationsof Reilman and Manson 9 giving 1.4 X 10-18 cm 2 at 20 eV abovethe ground state (620 A). The agreement is extremelygood.

In a similar way, the true absorption coefficient was derivedfrom the observed one, for the series is2 2p 2Po1s 2 nd 2D, n= 6-8, starting from the first excited state of Be+, which isshown in Fig. 4 by a solid line. Here the quality of the ex-perimental data is lower than before, mainly owing to themuch lower value of the absorption coefficient. However, thend lines are considerably more broadened than the np lines,and so the fitting is again quite good. In Fig. 5 the comparisonbetween the modeled and the true absorption coefficients(dashed and solid lines, respectively) indeed shows that thedistortion introduced by the finite resolution of the spectro-graph in this case is quite low, the optical depth being small.The atomic data and the results referring to the 2p-nd seriesare reported in Table 1.

The photoionization cross section at the threshold relativeto the 2O state is a = (2.5 0.5) X 10-18 cm2. It includes theed and Es channels of ionization, although the former is ex-pected to dominate. No comparison is available here withtheoretical calculations, but the ratio between the two crosssections, one out of the 2S state and the other out of the 2o

state, closely follows the ratio of the oscillator strengths of thediscrete series 2s-np and 2p-nd, well known from theory. 8

The column density and consequently the population of the2po level is about four times less than the population of theground state. If we assume local thermodynamic equilibrium(LTE) conditions between the states 2S and 2pO, we derivea temperature of -1.6 eV from the ratio of populations. LocalLTE conditions are not unreasonable here. The electron

+a)

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a,0

a

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BE4

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cs o

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ma+

0 b

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In CD C 0

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Jannitti et al.

0)

Vol. 2, No. 7/July 1985/J. Opt. Soc. Am. B 1081

0.8

0.6

0.4

0.2 -

0.0

n=8 7 6

I I I I I

888 920 952 984 A

Fig. 4. Solid curve, experimental absorption coefficient of the series1s2 2p 2 Po-ls 2 nd 2D with n = 6-8 of Be+ versus wavelength at

0.6-mm distance from the target. Dashed curve, convolution of thecomputed coefficient with the instrumental function.

0.9

0.64

0.481

K

density can be assumed, neglecting double ionization, to beat least equal to the Be+ density. A lower limit to the latteris given by the density in the 2 S + 2P0 states. The absorbinglength of the plasma was -1 cm. We get ne > 2.7 X 1017 cm- 3.

The criterion given by McWhirterl for LTE conditions isamply fulfilled here, although we do not consider the timeevolution of the plasma.

The plasma broadening present in the lines is particularlyinteresting; for instance the 2p-6d transition is considerablybroader than the 2s-6p one. In a laser-produced plasma twomain broadening mechanisms are involved: the Dopplerbroadening resulting from the streaming motion out of theplane target and the Stark broadening.11 An indication of theDoppler broadening can be obtained by going far from thetarget, where the density is sufficiently small. Figure 6 showsthe 2s-np series recorded at 2.3-mm distance from the target.Comparison with Fig. 2 reveals much narrower lines. In fact,three more components of the series appear, two of which, n= 10 and n = 11, are new. Their wavelengths are reported inTable 1. The width of the lines in Fig. 6 is practically equalto the instrumental width (Fig. 2), which proves that theDoppler broadening at this distance from the target is smaller

than 0.3 A. Similarly, the 2p-nd series shows one morecomponent with respect to n = 9 in Fig. 4, whose wavelength

is given in Table 1.The Stark broadening can be roughly estimated for hy-

drogenic levels in the quasi-static approximation as'2

Ax(A, FWHM) = KZPA 1/3/ 2(n. 2- n 2) 2/3

J(2)

0.32

0.16

0.888 920 952 984 A

Fig. 5. Computed absorption coefficient of the series 1s22p 2p0-

Is 2 nd 2D, n = 6-8, of Be+ versus wavelength before (solid curve) and

after (dashed curve) convolution with the instrumental function.

0.48

0.40

0.16

0.

7

8

9

where K is a constant, Zp is the average charge of the per-turbers, A is the wavelength (in centimeters) of the transition,nu and nj are the principal quantum numbers of the upper and

the lower levels of the transition, and J is the net charge of the

nucleus. An application of the formula gives AX = 0.7 A,corresponding to -130 cm-1 for the 2s-6p line, and AX = 1.3A, corresponding to -133 cm-' for the 2p-6d line.

The previous formula is an approximation that is expectedto work best under the hydrogenic condition of n degeneracy.The calculated Stark perturbation in the case of the 6p levelis considerably smaller than the distance of -220 cm-' be-tween the 6p level itself and the level nearest to it, i.e., 6d,whereas it is much larger than the distance of -8 cm-' be-tween the 6d and the 6f levels. Consequently, in the case ofthe 2s-np series, perhaps with the exception of the 8p level,hydrogenic conditions are not fulfilled for our value of per-turbation (the weak-field approximation), whereas they arefulfilled for all the members of the 2p-nd series (even 4ddiffers from 4f by only -25 cm-', i.e., the strong-field ap-proximation).' 3 Therefore we expect a large broadening for

the nd levels and only a moderate one for the np levels, as has

been observed.Finally, we point out that the present technique is well

suited for measurements of the profiles of (Stark-) broadenedlines and is not affected by the complications of opticalreabsorption, such as, most often, the profiles recorded inemission. 11

SPECTRUM OF THE INNER ELECTRON

The absorption spectrum resulting from excitation of an innerelectron has been observed in the region 90-105 A. It consists

672 704 736 768 A

Fig. 6. Absorption coefficient of the resonance series 1s22S 2 S-ls 2 np2PO, n = 5-11, of Be+ versus wavelength at 2.3-mm distance from thetarget.

Jannitti et al.

1082 J. Opt. Soc. Am. B/Vol. 2, No. 7/July 1985

Table 2. Inner-Shell Transitions Observed and Calculated in the Spectrum of Be+

ObservedTransition X (A) Observed X (A) Calculated Rel. Intensity

1S22p 2po _ ls2p 2

2 104.68 + 0.02 3.51s2

2S 2

S - ls(2s2p 3)22PO 104.42 + 0.03 41S22p 2po - 12p2 2p 104.05 + 0.02 2.21s2 2S 2S - ls(2s2p lp)2po 102.51 0.01 2.11S2

2p 2 - 1s2p 2 2S 101.76 + 0.01 1.2

1S23p 2O - ls2p('P)3p 2 100.949 + 0.006 101.01 1.31S2

3p 2O - s2p(lP)3p 2 100.778 0.002 100.75 0.81S2 3p 2O - 1s2p(1P)3p 2S 100.576 + 0.008 100.51 1.0ls2 2p 2o - ls2s( 3S)3d 2 97.88 + 0.04 98.28 0.71S

22p 2po - ls2p( 3P)3p 2 96.27 1 0.04 96.63 1.5

1S22p 2po - 1s2p(3P)3p 2 96.02 1 0.07 95.91 0.5

is 22S 2- ls2s(3S)3p 2po 95.78 A: 0.01 95.78 2.01S22p 2O - ls2p(3P)3p 2

S 95.734 + 0.005 95.61 2.51s22p 2po - ls2s('S)3d 2 95.34 + 0.04 95.53 0.81S22p 2o - ls2p('P)3p 2 94.79 + 0.01 94.82 2.11S2

2p 2o - ls2p(lP)3p 2 94.56 + 0.04 94.60 0.8ls2 2p 2po - s2p(3p)4p 2 93.93 0.02 93.89 0.21s

2 2p 2o - ls2p(3P)4p 2D 93.71 0.04 93.64 0.71s2 2p 2po - ls2p(3p)4p 2S, 93.57 4 0.04 93.49 1.11s 221 - 1s2s4(1 + 1) 93.43 k 0.01 93.39 1.11s2

2s 2S - s2s(1S)3p 2P? 93.17 : 0.02 93.23 1.1

92.62 0.01 1.092.53 + 0.06 0.4

1s2 21- ls21nl'n > 4 92.6-91.091.36 + 0.04 0.391.06 + 0.04 0.2

of the satellite transitions to the resonances ls 2 -lsnp of Be2 +.Absolute-wavelength measurements, corresponding theo-retical values, observed intensities, and proposed identifica-tions, are reported in Table 2. On the whole, twenty-five lineshave been attributed, six of which were never previously ob-served, and thirteen were published without identifica-tion.2

The five strong lines at lower energy are already well knownboth experimentally and theoretically.14-19 They are thetransitions s2 2s-ls2s2p and 1s 22p-1s2p 2 , whose identifi-cation has also been confirmed on the basis of isoelectronicinterpolations by the double-difference method.'4 Predictedwavelengths are not reported for these, inasmuch as the in-volved levels underwent a configuration interaction that wecould not account for.

Besides the above-mentioned lines, little was known so farabout the transitions for the doublets requiring higher energy.The identifications given here are based on the analysis oftransitions resulting from single-electron and two-electronexcitation, whose wavelengths are within the range of 85-110A. The core-excited levels were obtained through Hartree-Fock computations carried out with the Cowan-Zealotsuite,20'2' whereas all the other levels were taken from Moore'stables.22 We could then ascertain that they are single-elec-tron transitions, starting from configurations with core 1s2 andouter electron 2s, 2p, or 3p, except for two weak two-electrontransitions.

The analysis of the spectrum was accomplished by firstconsidering the lines slightly above 100 A. The only suitabletransitions are 1s2 n1-ls2p('P)nl, with n 3 and 1 p, d, i.e.,satellites to Be I 1s2 -ls2p measured at 100.255 A.14 Morespecifically, the computed values for the case n = 3p are in

agreement with the experimental ones within 0.1 A (1% inenergy). Unfortunately we could not observe those valuesrelative to parent 3P, since their wavelengths are expected tobe between 102 and 103 A, and they are probably merged withother strong lines. A recent theoretical work by Davis andChung2 3 on doublet states of Be+ confirms our identificationfor the line corresponding to the 2D term at 100.949 A, whereaswe think that the line observed at 100.576 A should be at-tributed to the 2S term of the considered multiplet. Fur-thermore, the present identification of the ls2p3p levels isconfirmed by the fact that the corresponding transitionsstarting from s22p are also visible in the spectrum. Actually,as for the parent P, the lines are observed in exactly thepredicted positions. We have to mention that the line at 94.79A was identified in a different way by Mehlman and Esteva.24

In the case with parent 3P, there is a good agreement with

previous work. The 2P were already both calculated and

measured,'5 and the line at 95.73 A (also reported by Kennedyand Carroll'4 ) in our opinion originates from 2S.

The other lines have been attributed to the members of thetwo series: 1s22s 2 S-ls2snp 2Po and 1S22p 2P0-ls2pnp 2pboth extended up to n = 4. As for the four shorter wave-lengths, there are many different possible transitions, whoseenergies differ little from one another. Such differences aresmaller than the uncertainty of measurement and the com-putational approximation. This justifies the chosen assign-ments.

As for the transitions from the ground state to ls2s3p, thereare two possible parents, namely, S and 3S. Both terms havebeen already calculated, 1 ad a full agreement i8 found for3S, whereas according to our computations the singlet tran-sition lies at 93.23 A, and it is referred to a line observed at

Jannitti et al.

Vol. 2, No. 7/July 1985/J. Opt. Soc. Am. B 1083

93.17 A. However, the calculations performed for the iso-

electronic sequence Li to C indicate that the predicted singletenergy is always rather higher than the observed one. In-terpolation for Z - 4 suggests a wavelength X _ 93.6.Therefore, at this stage, we are still uncertain about thisidentification.

The two weak lines around 98 and 95 A did not correspondto any predicted one-electron transitions but matched thetwo-electron transition s22p 2 -ls2s3d 2D fairly well.Although in this case the agreement is somewhat less than the

average for single-inner-electron transitions, the attributionsseem correct. Moreover, for one of these, we found confir-mation in a previous observation performed with Augerspectroscopy.'6 Further transitions with higher values of theprincipal quantum number are not clearly visible. They al-most coincide with other lines; the intensity, however, is al-ready very low for n = 3.

CONCLUSIONS

An investigation of the absorption spectrum of Be+ in theregions where the absorption of the outer and the inner elec-tron lies has been performed. The values of the photoion-ization cross sections corresponding to transitions of the type

2s-Ep and 2p-Ed is in good agreement with theoretical pre-dictions.

The measurement and the analysis of the inner-shellspectrum in the grazing-incidence region are quite completefor the permitted transitions arising from the 1s22s, 1s2 2p,

and 1s23p states.

ACKNOWLEDGMENTS

The authors wish to thank N. Spector (Soreq Nuclear Re-search Center, Israel) for helpful discussions on the spectrumof the inner electron. Mrs. V. Pearce's kind help in the revi-sion of the manuscript has been greatly appreciated.

Wang Yongchang was on leave from Northwest NormalCollege, Lanzhou, China.

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