Recent developments in beam-foil spectroscopy

NUCLEAR

INSTRUMENTS

AND

METHODS

IIO

0973) I-9;

©

NORTH-HOLLAND

PUBLISHING

CO.

Part L Optical spectra 1 - 78

RECENT D E V E L O P M E N T S IN BEAM-FOIL SPECTROSCOPY* INDREK

MARTINSON

Research Institute for Physics, 104 05 Stockholm 50, Sweden T h e developments in beam-foil spectroscopy since 1970 will be discussed. Special e m p h a s i s will be placed on the studies o f atomic spectra a n d transition probabilities.

I. Introduction

In this talk I shall try to summarize the progress in beam-foil spectroscopy (BFS) which has followed the Second International Conference, held at Lysekil in June 1970. Because of the time limitations only a fairly sketchy review will be possible, and I shall also place the main emphasis on already published results the most recent discoveries will be more expertly presented by the authors themselves. A study of the program for the present conference clearly shows that the progress in BFS since 1970 has been quite substantial and we can safely expect a most stimulating and instructive week. We are greatly indebted to Prof. Bashkin and his colleagues for having undertaken the arrangements for the Third International Conference. The beam-foil technique is entering its second decade. Already in the very first years a number of exciting and challenging results were reported. Nevertheless the First International Conference, held here in Tucson five years ago 1) marked a certain breakthrough for this atomic physics technique. The 1967 conference served as a thorough presentation of BFS and outlined future possibilities, founded on the already available experimental results. As a consequence several laboratories, both in the U.S. and Europe, added BFS to their research program, and the 1970 conference2) showed the results of the increased efforts, particularly in the field of atomic lifetime measurements. Furthermore, the extension of BFS to atomic fine structure studies - dating back to 1965 - began to crystallize and produced some beautiful results. Simultaneously, several possible systematic errors were also being scrutinized and remedies were suggested. In this presentation 1 shall discuss the latest results in BFS with respect to l) atomic spectra and energy * S u p p o r t e d by the Swedish N a t u r a l Science Research Council (NFR).

levels, 2) atomic lifetimes and transition probabilities, 3) astrophysical consequences of lifetime measurements, and 4) atomic fine-structure. 2. Atomic spectra and energy levels

Already in the early beam-foil literature evidence was found for a considerable number of previously unreported radiative transitions, even for comparatively simple elements, such as C, N and O (c.f., e.g. ref. 3). In 1967 Brown et al. 4) and Whaling et al. 5) also reported a wealth of unclassified spectral lines in the beam-foil spectra of sodium and iron, respectively. In the following years additional information has been obtained, not only in generating new spectral lines, but also in explaining their origin and thus determining new energy levels in atoms and ions. Although beam-foil researchers still have to be content with less than perfect line shapes and widths, the situation has greatly improved in recent years, largely thanks to the methodic experimental and theoretical studies of Stoner and Leavitt6), Kay7), and others. It is needless to say that good lineshapes facilitate spectral classification work. The determination o1 charge states for lines in beam-foil spectra, often the first step towards a complete classification, has for years been a fairly difficult task, and perhaps a controversial one. Since the thorough discussion, presented in 1970 by Dufay8), additional progress has been made, for example for the technique based on Dopplershifting the lines in strong electrostatic fields9). After the charge-state determination the tasks of line classification and energy-level deduction largely remain, but in this respect well-known spectroscopic techniques are available [Edl6nl°)]. It is worth mentioning, however, that BFS possesses an extra asset, viz. the possibility of combining spectral and lifetime data. A recent paper by Kernahan et al. ~1) illustrates this point very nicely. In their neon spectra the authors observed a line at 554 A which they tentatively ascribed

JULY 1973

I. O P T I C A L

SPECTRA

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INDREK MARTINSON

to the Ne VI 2s2p 2 2D-2p3 ZDU combination. Since the energy of the upper term, 2p 3 2D°, was not previously known for Ne VI, additional studies were needed. Kernahan et al. also found the 2s2p 2 2p_ 2p 3 2D° branch at 914 ~, however, and confirmed their assignments by lifetime measurements which yielded r(554 ,~)=0.35+0.04 nsand z(914 A ) = 0 . 3 3 + 0 . 0 3 ns. I might add that several similar analyses can be found in the beam-foil literature. As recent examples of fairly extensive classifications in light atoms, using BFS, we might mention the studies of carbon [Poulizac et a1.12)], neon [Denis et al.13)] and sodium [Dufay et a1.14)]. The beam-foil method is also very effective in producing hydrogenlike transitions in several times ionized atoms. It is interesting to note that such transitions can be observed even at relatively modest accelerator energies. Fig. 1 shows one such example, originating from a study of C1 spectra (500-2800/~)

E , (kK)

ns

np

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n,,q

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9OO

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80C

.

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+

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with a 2 MV Van de GraaffJs). This term diagram displays all the CI VII transitions which appeared in beam-foil spectra. Of these only the 3s-3p and 3p-3d combinations had been reported earlier. The polarization formula ~°) is easy to employ for CI VII, which has one electron outside the n = 2 core. However, also for other and more complex ions much information about hydrogen like transitions has been obtained from recent beam-foil studies. Dr. Bromander a6) will give a more detailed discussion of these results. The beam-foil technique has yielded a wealth of spectroscopic data for multiply-excited configurations in light atoms and ions. The doubly excited levels, e.g. 2p 2 3 p in He I, ls2p3d4D ° in Be 1I, etc., are frequently also called inner-shell excited states. At Lysekil, Holoien aT) recommended beam-foil studies of the doubly-excited He I levels, which lie more than 30 eV above the He II ground state. Because of parity and angular-momentum requirements, many doublyexcited levels are metastable against autoionization. Soon after the 1970 conference the first beam-foil results were reported ~s) and they have recently been extended19). Between 280 and 3500 A the beam-foil spectra of helium show a substantial number of lines which are either very weak or absent when other light sources are used. The assignments of these lines to the He 1 doubly-excited system are largely based on recent, accurate theoretical calculations2°). Two early beam-foil studies of Li spectra z~'22) showed that radiative transitions between the doublyexcited Li I terms of the type ls2snl 4L and I s2pnl 4L, 2sns

4S

eV I

2pnp ~p

2pns

2snp

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4D

5

66

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30(

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VII

3

3 ~%~q

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i

62

i

i

i

i

Fig. 1. Energy level diagram for C1 VII, according to ref. 15. All the transitions observed in the beam-foil spectra (500-2800A) are indicated. A n extension o f this work will be discussed by J. Bromander (this conference).

58

[quartets

2

Fig. 2. Energy level diagram for doubly-excited quartet terms o f Li I, (ref. 23).

RECENT DEVELOPMENTS

which lie more than 50 eV above the Li II ground state, are quite prominent in beam-foil spectra. Several additional investigations of the Li I quartet states have followed, most recently by Berry et al.23). Fig. 2 displays an energy level diagram for the Li I quartet system, based on beam-foil work and theoretical calculations24'25). In addition to these quartet levels, Berry et al. 23) also identified transitions from a number of doubly-excited doublet terms. Similar levels have also recently been found for Be I I. Using an 80 kV isotope separator Hontzeas et al. 16) identified several doubly-excited quartet transitions, as can be seen from fig. 3. While a few of the strongest quartet transitions in Li I also have been found with other light sources/7), none of the lines indicated in fig. 3 seems to have appeared in the spark spectra of Be. I should add that the Be II term diagram (fig. 3) should be regarded as a first attempt; more extensive studies are planned in Stockholm using a new 400 kV ion accelerator. A few of the doubly-excited quartet transitions have also been observed for B 1II and C IV. There is further a close link with the results of Sellin and co-workers/s) who studied Li-like spectra in higher degrees of ioni-

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135

......

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3

IN B E A M - F O I L S P E C T R O S C O P Y

zation, e.g. O VI, F V I I C1XV and A r X V I . The highly stripped ions were produced with a Tandem Van de Graaff or an isochronous cyclotron. As mentioned before, the doubly-excited quartet configurations, e.g. ls2s2p4P ° and ls2p24p, are stable against electron emission via the electrostatic interaction, but they can autoionize through the spin-orbit or the spin-spin interaction. By analyzing the autoionization electrons with an electrostatic spectrometer, the authors were able to determine the appropriate level energies and to measure the autoionization probabilities. Dr. Sellin29) will give a review of these experiments. It is quite evident that significant information about energy levels and transition rates in highly ionized atoms can be obtained from beam-foil experiments using Tandem Van de Graaffs or linear heavy-ion accelerators, and here many new results have been reported since 1970. At this conference we will hear detailed accounts of the work at Uppsala16), Orsay3°), Oak Ridge29'31), Manhattan, Kansas 32) and Berkeley33). These experiments have already revealed a wealth of new spectroscopic material for highly ionized atoms. The results obtained in Berkeley have probably attracted the most wide-spread interest. Using 412 MeV Ar ions from the heavy-ion linear accelerator (HILAC), Marrus and Schmieder 33'34) observed transitions in Ar XVII and ArXVIII, i.e. heliumlike and hydrogenlike argon, and they also measured the decay rates for magnetic dipole (M1), magnetic (M2), and electric quadrupole (E2) processes, as well as decays by two-quantum (2 El) emission. Fig. 4 shows the Ar XVII levels of interest, and their

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1:=1.7± 0.3 nsec 2 ls 2p 3pO// 1

/

0 E1

125

5

ls 2s

2

~=172±30nsec

120

ls21s/ ~ 0 115

Fig. 3. Energy level diagram for doubly-excited quartet terms o f Be II, (ref. 26).

ArXVII

Fig. 4. Energy level diagram for heliumlike argon (Ar XVII). level lifetimes measured by Marrus and Schmieder z4) are played. The excitation energies are: 3.1244 keV (2s zS0), 3.104 (2s 3Sz), 3.123 keV (2p 3Po), 3.1233 keV (2p 3Pz) and 3.1262 (2p 3P2). I. O P T I C A L

The diskeV keV

SPECTRA

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I N D R E K MARTINSON

experimental lifetimes. These latter serve as important experimental tests of the predictions of relativistic quantum mechanics and quantum electrodynamics. For example, the experimental 2s2S1/2 lifetime in hydrogenlike A r X V I I I yielded an upper limit of 6 x 10 - 4 for the amplitude of the 2p 2P1/2 a d m i x t u r e (parity impurity) - caused by possible P or PT violating interactions - into the 2s 2S1/2 state. The observations of forbidden transitions and higher multipole radiation and the search for parity mixing remind us of nuclear structure studies, where higher multipolarities are quite common and also parity impurities, as a result of weak interaction between nucleons, have been extensively studied in recent years 35). 3. Atomic lifetimes and transition probabilities Already in Lysekil a considerable amount of lifetime data were presented. Most of the results were for light atoms, such as C, N, O and Ne, in various degrees of ionization. For these systems additional measurements have been made since, and in many cases the experimental picture is fairly complete. For example, in the spectra of C III, C IV, and C V, beam-foil work has yielded decay times for most n = 2, 3, 4 states and several higher terms, whereas not a single experimental value was available in 1966, when the first volume of the "Atomic Transition Probabilities ''36) appeared. A study of the second part of this monograph 37) also shows that as late as 1968 there were no beam-foil results available for Na-Ar, but even here the situation has drastically changed. In the experimental studies of the third row atoms and heavier atoms Drs Andersen and Sorensen and their co-workers at Aarhus have been particularly productive. The present experimental results permit a number of interesting comparisons with other techniques and theoretical calculations. As an example of the quantitative increase in lifetime data, we can e.g. establish that the probability for the 3s-3p resonance transition in the Na I sequence now has been measured for N a I - ArVIII. Not surprisingly there exists good agreement between theory and beam-foil experiments in this case, but for several other transitions marked differences can be noted. The presence of configuration mixing may introduce large uncertainties in the theoretical calculations, and here lifetime measurements - as tests of the various theoretical models - are particularly valuable. Configuration mixing and cancellation effects may be prominent already in the Mg I isoelectronic sequence, where we e.g. have the interaction between the 3snd 1D (n = 3, 4, 5...) Rydberg series and the 3p 2 ID term

and that between the 3snf3F ° (n = 4, 5, 6...) series and the 3p3d 3F° term. The radiative lifetimes are very sensitive to such interactions, and beam-foil measurements have played an important role in verifying recent configuration-interaction calculations. A good example is the study of the AI II 3F° terms of Andersen et al. 38) which nicely confirmed Weiss's 39) calculations. Another example is given in fig. 5, which shows the oscillator strengths for the 3s23p2p°-3s3p 2 2D transition in the A I I sequence. The upper term interacts strongly with the 3s2nd2D series. Except for Si II all experimental /-values originate from beam-foil measurements, while the theoretical values are based on the configuration mixing calculations of FroeseFischer 4°) and the many-electron approach of Beck and Sinano~lu41). The experimental f-values are consistently larger than the theoretical ones, but they follow the same trend, showing that the mixing between 2D states is indeed very pronounced, especially for low Z. It is important to point out that the experimental f-values are typically 10-20 times smaller than the results of single-particle calculations.

Ar C[ S

078

P

Si

At

At I sequence 3s2 3p 2P°- 3s3p 2 2D

007

0.o6 0.05

• Hofmann (emission) I I C u r t i s et at. ( B F S ) A B e r r y et at. (BFS) t B a s h k i n and M a r t i n s o n (BF$) x L i v i n g s t o n et at. (BFS) e F r o e s e Fischer (theory] o B e c k and Sinano~tu (theory]

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+

o

003

t

002

O O

001

o o

0

t

0.04

i

,I

0.06

m

I

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Fig. 5. Theoretical and experimental oscillator strengths for the 3s~3p ~P°-3s3pg 2D transition in the A1 I isoelectronic sequence. Experiments: W. Hofmann, Z. Naturforsch. 24A (1969) 990; L. J. Curtis et al., Phys. Scripta 3 (1971) 197; H. G. Berry et al., J. Opt. Soc. Am. 60 (1970) 335; S. Bashkin and I. Martinson, re/. 15; A. E. Livingston et al., J. Opt. Soc. Am. 62 (1972) 1303. Theory: C. Froese-Fischer, re/. 40; D. R. Beck and O. Sinano~lu, re/. 41.

RECENT D E V E L O P M E N T S IN B E A M - F O I L S P E C T R O S C O P Y

Also for the Si I and P I sequences a considerable amount of experimental f-value material has been gained recently. With the exception of ref. 41 there hardly exist any modern f-value calculations for these sequences. Fig. 6 shows the present situation for the 3p3 4S0_3p4 4p resonance multiplet in the P I sequence. Even here the experimental f-values are typically 20 times smaller than the theoretical values 37) which have not considered configuration interaction. In 1970 systematic studies of lifetimes for homologous systems, e.g. the second spectra of the noble gases (Ne 11, Ar II, Kr i1 and Xe I1) and the spectra of neutral AI, Ga, In and T1 were discussed4Z). Additional systematic studies of this kind have been performed more recently. An example is given in fig. 7 which displays the f-values for the np 1P°-(n+ 1)s 1S transitions in A1 II (n = 3), Ga II (n = 4), In II (n = 5) and Tl II (n = 6). The experimental points are from the beam-foil experiment of Andersen and Sorensen 4a) whereas the theoretical f-values were calculated by Helliwell4a). Beam-foil studies of lifetimes in heavier atoms are complicated because of problems with the energy loss and energy spread in the foil as well as the beam divergence after the foil. Most previous work has indicated that in neutral, heavy atoms it is difficult for BFS to compete with other techniques, such as the Hanle effect. However, recent work has shown subAr Cl. £ P

f i

L P [ - sequence

0.15 i

3p 3 ~S- 3p z' ~P

!

! • Savage and Lawrence i ~8ashkinand Martinson

i

x Lawrence 010 -- •Pinningt°n eta[,

1

5

stantial improvements of the situation. For Sn I and Bi I Andersen et al. 44) thus measured lifetimes with only 10% uncertainties, and their results were in excellent agreement with accurate level-crossing studies45). Another example of the application of BFS to heavy atoms is shown in fig. 8 which displays a partial beam-foil spectrum of lead46). Decay times for several of the strongest Pb I lines were measured and here, too, good agreement exists between the preliminary beam-foil data and the results of level-crossing studies47). In discussing atomic lifetime measurements it is worth quoting a statement of Feneuille48): "For theorists a single very precise measurement is often more useful than a hundred uncertain experimental values." Traditionally the most serious limitation to f-value measurements using BFS has been caused by cascades from higher levels into the state under observation. This problem is of course not a new one. The formalism was already available before the Rutherford and Soddy days 49) and the appropriate relations in connection with atomic lifetime measurements appeared in 1927, in Wien's review article on canal raysS°). At Lysekil, 43 years later, certain feelings of despair about the cascade situation in beam-foil lifetimes measurements were expressed. Those discussions have been of lasting value, however, and they have stimulated efforts toward better understanding of the cascade situation. In particular, the work of Dr Curtis 51) has been quite successful in this respect. In these analyses, graphical and computer-fits to decay curves are complemented by, e.g., numerical integrations and differentations of the decay curves. Also a method of incorporating decay curves of the cascades through undetermined multipliers (ANDC) • Andersen and S~rensen (beam-foR) o Hettiwett (theory) 0.10

005 0.08 •

o

o

006 o

0

i

002

i__

004

~

L

006

008

Fig. 6. Experimental oscillator strengths for the 3s23pa4S ° 3s3p44p transition in the P I sequence. Experiments: B. D. Savage and G. M. Lawrence, Astrophys. J. 146 (1966) 940, phase shift; S. Bashkin and I. Martinson, ref. 15, beam-foil; G. M. Lawrence, Phys. Rev. 179 (1969) 134, pulsed-electron technique; E. H. Pinnington et al., J. Opt. Soc. Am. 61 (1971) 978, beam-foil.

0.04 0D2 0

L

I

I

I

AL1T

GaIT

ln][I

Tilt

3p- 4s

Zp.Ss

5p-6s

6p-Ts

Fig. 7. Experimental and theoretical oscillator strengths for the n p t P ° - ( n + l ) s l S transition in A1 II ( n = 3 ) , Ga II ( n = 4 ) , In II (n = 5) and Tl II (n = 6), (ref. 43). I. O P T I C A L SPECTRA

6

1NDREK MARTINSON

200 keY Pb"

cO c~

u'b c"3

-,a

¢xa c-a i

7-

//

¢

//

Fig. 8. Composite beam-foil spectrum o f lead, taken with the Stockholm 400 kV accelerator, (ref. 46).

has proven very valuable in extracting more reliable lifetimes from the observed primary data. With further improvements of the BFS accuracy it would be instructive to perform very precise measurements in cases for which present sophisticated atomic theories yield somewhat diverse results. An example of such a case is the 2s2p 1P°-2p2 1D combination in Be I for which the theoretical oscillator strengths are f = 0.001 [Weiss, superposition ofconfigurations25)],f= 0.020 [Nicolaides et al., non-closed shell many-electron theory52)]. However, both for theorists and experimentalists this Be I transition is a difficult one - the interaction between the 2snd 1D (n = 3, 4, 5...) series and the 2p 2 1D term is very strong and the resulting small f-value hardly enables lifetime studies. So far only an upper limit of 0.035 has been experimentally obtained38). Precise lifetime measurements for levels in heavy atoms are often of considerable theoretical interest because here comparisons between experiment and theory may yield information about relativistic effects on atomic transition probabilities53). 4. Astrophysical consequences of lifetime measurements

Several beam-foil experiments have aimed at obtaining reliable J-values for astrophysically significant atomic transitions. We are familiar with the results for Fe I and Fe 1I levels, obtained by Whaling and coworkers54). Their experiments confirmed previous doubts about many oscillator strengths, extracted from emission measurements, and - as a consequence - also supported substantial revisions of previously assumed

Fe abundances in the solar photosphere. These investigations have been followed by beam-foil studies of other 3d transition elements, and lifetime data for Sc, Ti, V and Cr have already appeared in the literature. The general trend of the new material is not too different from the iron case, viz. the directly measured lifetimes (BFS) are usually considerably longer than the results of e.g. Corliss and Bozman's emission experiments55). (In the ab;ence of more accurate oscillator strengths these and other emission f-values have often been used by astronomers for element abundance determinations.) In a recent beam-foil study of Cr I, Cocke et al. s6) found deviations by an average factor of 4.9 from the Corliss and Bozman ./-values, and the new data suggested an upward revision of the photospheric Cr abundance by perhaps a factor of four. As in the Fe case this will result in a better agreement between the photospheric and coronal abundances. Also for Ti and V significant revisions of previously adopted photospheric abundances may be necessary. Here in Tucson we will hear about the latest beam-foil results for the iron-group elements. Two years ago Engvold and Hauge 57) reviewed the solar abundances of chemical elements and also emphasized the astrophysical need for experimental transition probabilities in rare-earth spectra. For several of these elements spectral lines have been observed in the photospheric spectra, but in a number of cases the absence of reliable f-values has ruled out abundance determinations. As a first attempt toward beam-foil measurements, Dr. Curtis and myself recorded Tm spectra and measured a few Tm I and Tm II lifetimes. One of the spectra is shown in fig. 9.

R E C E N T D E V E L O P M E N T S IN B E A M - F O I L S P E C T R O S C O P Y

2,',9 keY

Tm +÷÷

Fig. 9. Beam-foil spectrum of thulium (L. J. Curtis, I. Martinson and R. Buchta, this conference).

The lines at 3700, 3701, 3462 and 3362 A, all of which combine with Tm II ground term, have been observed in the solar photosphere, and their equivalent widths have been measured by Grevesse and Btanquet 5s) who obtained a solar Tm abundance of log NT,,= 0.43_+ 0.20 (on the log NH= 12.00 scale). Since this value deviates from the more accurately determined meteoritic abundance of log NTm = 0.09, and even larger discrepancies in this direction can be noted for other 4f elements, Grevesse and Blanquet suggested that the available f-value scale [Corliss and Bozman55)] is too low for transitions in singly-ionized rare-earth spectra. The results of the preliminary beam-foil measurements seem to substantiate this suggestion, since the new oscillator strengths are 1.5-3 times larger than the Corliss-Bozman ones. Very introductory decay-time measurements for Tb I and Tb i l levels have also been made in Stockholm, but there is clearly much more work needed for both Tm and Tb, as well as for other rare-earth elements. It is not possible to list here all the numerous beamfoil papers that have been motivated by astrophysical problems. A good example of such work is an article by Pinnington e t a [ . 59) who made systematic f-value determinations for a large number of O I I and O lIl lines found in the spectra of B-type, O-type and Wolf-Rayet stars. 5. Atomic fine structure

Already at Lysekil impressive results of atomic finestructure studies, using BFS were presented. This work included measurements of fine- and hyperfine-structure, using the alignment condition, level-mixing studies in electrostatic fields, and preliminary determination of the n - - 3 Lamb shift in hydrogen. Progress has been impressive in these fields since 1970, as can be seen

7

from the present conference program. The zero-field quantum beat technique 6°'61) has been successfully extended to ions, c.f., e.g. the short preliminary results of Berry and Subti162). Several authors have also made extended studies for neutral hydrogen63'64). Also the measurements of atomic and ionic Land6 y-factors 65) belong to the most important advances of the beamfoil method. These studies have already provided g-factors for excited states in Ne I - Ne II1 and Ar I Ar 1II. The present experimental accuracy is quite promising (typical uncertainties are 1%) and with future refinements we may expect quantitative checks of the validity of various coupling schemes for several times ionized atoms. For years ion accelerators have been successfully used for Lamb shift measurements and the latest results include some very precise studies for the n = 3 state in hydrogen 66) and the first experimental determinations of the n---2 shift in hydrogenlike oxygen67'68). For the 2Sx/z-2pl/2 Lamb shift in O VIII Leventhal et al. 67) and Lawrence et al. 68) obtained the values of 2202.7-1-11.0 GHz and 2215.6+7.5 GHz, respectively, in good agreement with the most recent theoretical value, 2205.17 + 1.51 GHz69). In addition to the above-mentioned developments and recent results there have appeared several other interesting aspects which may lead to new fields of research. I refer e.g. to the investigations of the particlefoil interaction, performed by Bickel and co-workers7°), X-ray studies in BFS 71) and the Hanle effect experiments with ion beamsV2). A few years ago a sophist might have remarked, with a touch of irony, that, "beam-foil spectroscopy exists partly because there is not much else you can do with old, obsolete Van de Graaffs". As a contrast to this we now all know that BFS is one important motivation for constructing new, powerful heavy ion accelerators. We acknowledge permission from the Opt. Soc. Am. to reproduce figs. 1 and 2, and from Phys. Rev. for permission to reproduce fig. 4. References 1) S. Bashkin, ed., Beam-foil spectroscopy (Gordon and Breach, New York, 1968). "~) I. Martinson, J. Bromander and H. G. Berry, eds., Beam-foil spectroscopy (North-Holland Publ. Co., Amsterdam, 1970) [Nucl. Instr. and Meth. 90 (1970)]. 3) S. Bashkin, D. Fink, P. R. Malmberg, A. B. Meinel and S. G. Tilford, J. Opt. Soc. Am. 56 (1966) 1064. 4) L. Brown, W. K. Ford, Jr., V. Rubin and W. Tr~.chslin, ref. 1, p. 45. I. O P T I C A L S P E C T R A

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as) T. Andersen, J. R. Roberts and G. Sorensen, Phys. Scripta 4 (1971) 52. 39) A. W. Weiss, ref. 2, p. 121. 4o) C. Froese-Fischer, J. Quant. Spectrosc. Radiative Transfer 8 (1968) 755. 41) D. R. Beck and O. Sinano~lu, Phys. Rev. Letters 28 (1972) 945. 42) S. Bashkin, ref. 2, p. 3; T. Andersen, K. A. Jessen and G. Sorensen, ref. 2, p. 35. 43) T. Andersen and G. Sorensen, Phys. Rev. A5 (1972) 2447; T. M. Helliwell, Phys. Rev. 135 (1964) A325. 44) T. Andersen, O. H. Madsen and G. Sorensen, J. Opt. Soc. Am. 62 (1972) 1118. 45) S. Svanberg, Phys. Scripta 5 (1972) 73; L. Holmgren and S. Svanberg, Phys. Scripta 5 (1972) 135. 46) S. Bashkin, I. Bergstr6m, H. G. Berry, J. Bromander, R. Buchta, J. Hilke, L. Lundin and I. Martinson, to be published. ,t7) S. Garpman, G. LidO, S. Rydberg and S. Svanberg, Z. Physik 241 (1971) 217. 48) S. Feneuille, in Proc. 2nd European Conf. Beam-foilspectroscopy (ed. M. Dufay; Lyon, July 1971). 49) E. Rutherford and F. Soddy, Phil. Mag. 4 (1902) 370; Phil. Mag. 5 (1903) 576. 50) W. Wien, in Handbuch der Experimentalphysik, vol. 14 (eds. W. Wien and F. Harms; Akad. Verlagsges., Leipzig, 1927) p. 435. 51) L. J. Curtis, in Proc. 2nd European Conf. Beam-foil spectroscopy (ed. M. Dufay; Lyon, July 1971); see also L. J. Curtis, H. G. Berry and J. Bromander, Phys. Scripta 2 (1970) 216; H. G. Berry, J. Bromander, L. J. Curtis and R. Buchta, Phys. Scripta 3 (1971) 125. 52) C.A. Nicolaides, D. R. Beck and O. Sinano~lu, J. Phys. B6 (1973) 62. 53) C. P. Bhalla, ref. 2, p. 149; and this conference. 54) W. Whaling, R. B. King and M. Martinez-Garcia, Astrophys. J. 158 (1969) 389; W. Whaling, M. Martinez-Garcia, D. L. Mickey and G. M. Lawrence, ref. 2, p. 363; P. L. Smith, W. Whaling and D. L. Mickey, ref. 2, p. 47; M. Martinez-Garcia, W. Whaling and D, L. Mickey, Astrophys. J. 165 (1971) 213. 55) C. H. Corliss and W. R. Bozman, Experimental transition probabilities for spectral lines o f seventy elements, Nat. Bur. Std. Monograph 53 (U.S. Govt. Printing Office, Washington, D.C., 1962). 56) C. H. Cocke, B. Curnutte and J. H. Brand, Astron. Astrophys. 15 (1971) 299. 57) O. Engvold and O. Hauge, ref. 2, p. 351. 58) N. Grevesse and G. Blanquet, Solar. Phys. 8 (1969) 5. 59) E. H. Pinnington, J. A. Kernahan and C. C. Lin, Astrophys. J. 161 (1970) 339. 6o) H. J. Andr~i, Phys. Rev. Letters 25 (1970) 325; see also ref. 2, p. 343. 61) j. Macek, Phys. Rev. A1 (1970) 618. 62) H. G. Berry and J. L. Subtil, Phys. Rev. Letters 27 (1971) 1103. 63) D. J. Burns and W. H. Hancock, Phys. Rev. Letters 27 (1971) 370. 64) D. J. Lynch, C. W. Drake, M. J. Alguard and C. E. Fairchild, Phys. Rev. Letters 26 (1971) 1211. 65) C. H. Liu, S. Bashkin, W. S. Bickel and T. Hadeishi, Phys. Rev. Letters 26 (1971) 222; C. H. Liu and D. A. Church, Phys. Letters 35A (1971) 407; C. H. Liu, M. Druetta and D. A.

RECENT D E V E L O P M E N T S IN B E A M - F O I L S P E C T R O S C O P Y Church, Phys. Letters 39A (1972) 49; D. A. Church and C. H. Liu, Phys, Rev. A5 (1971) 1031. 66) C. W. Fabjan and F. M. Pipkin, Phys. Rev. A6 (1972) 556, and previous references quoted therein. 67) M. Leventhal, D. E. Murnick and H. W. Kugel, Phys. Rev. Letters 28 (1972) 1609. Gs) G. P. Lawrence, C. Y. Fan and S. Bashkin, Phys. Rev. Letters 28 (1972) 1612.

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69) G. W. Erickson, Phys. Rev. Letters 27 (1971) 780. 70) W. S. Bickel, E. Veje, G. Carriveau and N. Andersen, Phys. Scripta 4 (1971) 115; N. Andersen, W. S. Bickel, R. Boleu, K. Jensen and E. Veje, Phys. Scripta 3 (1971) 255, 71) C. L. Cocke, B. Curnutte and J. R. MacDonald, Phys. Rev. Letters 28 (1972) 1233. 72) D. A. Church, M. Druetta and C. H. Liu, Phys. Rev. Letters 27 (1971) 1763; M. Carr6, J. Desesquelles, M. Dufay and M. L. Gaillard, Phys. Rev. Letters 27 (1971) 1407.

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