VI Beam-Foil Spectroscopy

E. WOLF, PROGRESS I N OPTICS XI1 Q NORTH-HOLLAND 1974

VI

BEAM-FOIL SPECTROSCOPY BY

STANLEY BASHKIN Deparrnrent o/’ Physics, Unicersity of Arizona, Tucson, Arizona 8572/, USA

CONTENTS

PAGF

INTRODUCTION . . . . . . . . . . . . . . . . . . . 289 SPECTRAL LINE SHAPES . . . . . . . . . . . . . . .

290

WAVELENGTH STUDIES AND ENERGY-LEVEL SCHEMES . . . . . . . . . . . . . . . . . . . . . . .

292

DOUBLY-EXCITED LEVELS . . . . . . . . . . . . . .

304

METASTABLE ONE-ELECTRON LEVELS . . . . . . . .

310

. . . . . . . . . . . .

312

APPLICATIONS OF LIFETIME DATA . . . . . . . . .

323

COHERENCE AND ALIGNMENT . . . . . . . . . . .

325

CHARGE-STATE IDENTIFICATION . . . . . . . . . .

336

CONCLUSION . . . . . . . . . . . . . . . . . . . . .

339

MEAN-LIFE MEASUREMENTS

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . 339 REFERENCES . . . . . . . . . . . . . . . . . . . . . . .

340

5

1. Introduction

The fundamental observation which is made in beam-foil spectroscopy (BFS) is of the intensity of radiation as a function of some parameter such as time, wavelength, external field, etc. With the important exception of electrons, the observed iadiation is in the form of light (20 A < 2 < 8000 A), and the spectral purity of the detected spectral lines is often a matter of concern. Thus, much attention has been devoted in recent years to making improvements in the shape of the spectral lines. The need for improvement and the achievements to date are reviewed. Since the beam-foil source allows one to excite levels which are generally inaccessible in other light sources, the studies of spectral lines are immediately applicable to extending our knowledge of level term schemes, especially since one is not restricted to resonance transitions. The opportunity afforded by the beam-foil light source of studying the structures of many different elements in many different stages of ionization permits one to follow hitherto-unknown level schemes over a number of members of an isoelectronic sequence. Two areas are of special interest: levels in multiplyionized atoms, and levels due to the simultaneous excitation of two or more electrons. We describe this work. In treating beam-foil spectroscopy, it is necessary, but awkward, to make frequent reference to atoms and to ions of various charges. We attempt to simplify the language by introducing the word, i-ion, which we define to mean a monatomic particle of net charge 5. The measurement of spectral line intensity as a function of time after excitation is particularly simple with the beam-foil source, since the velocity of the emitters transforms the time-coordinate into a space-coordinate which is measurable directly. This, of course, leads to level mean lives. As of this writing, several hundred mean lives have been published. They have had application to problems of astrophysics and to the refinement of theoretical calculations of transition probabilities. Unfortunately, thc mean-life data are not always satisfactory; there are cases where differences of a factor of two or more distinguish several reports on a given level. We consider the possible 2R9

290

B E A M - F O I L SPECTROSCOPY

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s2

origins of such discrepancies. We also discuss the complications caused by cascades into the level under sudy. An interesting feature of the beam-foil light source is that the excited levels appear to be aligned for all cases for which J > 3. Coherent excitation also occurs. By alignment, we mean that the level population for a given J > 3 is a function of lm,l. (The term “oriented” is sometimes used as we use “alignment”, and “alignment” is elsewhere taken to mean that the population of level m, is not equal to that of -m,.) By coherence, we mean that the phase factors in the wave functions which describe the m, sublevels for a given spectroscopic term are fixed in a given experiment. The existence of alignment is indisputable, but its precise origin is not known; in particular, one cannot predict what the population imbalance will be for an arbitrary experiment. The origin of coherence is better understood: it has to do with the short impact time during which excitation occuts. When alignment and coherence are present simultaneously, one finds “quantum beats”, which can be used to measure Land6 g-factors, fine structure and hyperfine-structure separations, and, also, level lifetimes without the complication of cascade repopulation of the level of interest. Work using the coherence and alignment features is reviewed. In a source where many different stages of ionization are produced simultaneously, it is not always easy to associate a spectral line with the spectral order to which it properly belongs. Methods have been developed to make the charge assignment; we treat them briefly.

Q 2. Spectral Line Shapes The contributions to line broadening which are peculiar to the beam-foil light source come entirely from the Doppler effect. Figure 1 illustrates several of the ways in which the Doppler effect manifests itself. The wavelength, A, which is detected when a photon of wavelength A, is emitted from a moving source whose velocity is at angle 6 relative to the direction of observation, is given by

A

=

A,(1

-p

4-

cos 0)

’

where p is the ratio of the speed of the emitter to the speed of light. It therefore follows that any detector, even if it has an infinitesimal acceptance angle, will respond to a range in wavelengths because (a) there is an intrinsic velocity spread in the beam, (b) there is an intrinsic angular divergence of the beam, and (c) there is scattering in the foil. If one takes account of the

VI,

s 21

SPECTRAL LINE SHAPES

SLIT-

291

v

-

Fig. I . Arrangements for observing the 5-ions in beam-foil experiments. The points A and B define a beam segment, 0 is a representative angle between the c-ion velocity and the light which is accepted by a spectrometer, F is a (shielded) Faraday cup, L, and L2 are field lenses, and the slits indicate entrances into spectrometers. Lenses are not always used. The Doppler effect arises because of the finite size of the aperture which collects the light and because of the change in 0 between points A and B.

finite acceptance angles of real detectors, two other factors enter: (d) from a given point on the beam, 8 is not constant over the acceptance aperture, and (e) if light is collected over the beam segment from A to B (Fig. l), there is, again, a variation in 8 for the photons which reach the slit. Nobody has yet made a complete analysis of the above factors, although different parts have been treated by JORDAN [1968], STONER and RADZIEMSKI [1970, 19731, STONERand LEAVITT[1971a, b], and LEAVITT,ROBSONand STONER[1973]. One cannot write a simple expression which describes the situation accurately for the ranges of [-ions, [-ion energies, foils, etc., which are used in beam-foil experiments. However, some representative numbers can be given. Thus, lines at 5000 A from nitrogen at 1 MeV could easily have widths of 5-10 A (BASHKIN, FINK,MALMBERG, MEINEL and TILFORD [1966]); such widths are intolerable if serious spectroscopy is to be done. A great improvement can be made by recognizing that the principal contributor to the line width is apt to be the finite acceptance angle of the and LEAVITT[1971b]), in spectrometer. The refocusing method (STONER which the position of the grating or exit slit is adjusted to compensate for the variation of I over the length of the observed beam segment, permits one to reduce the line width to 5 1.0A. It has also been shown (STONER and LEAVITT [1971a]) that, where lenses may be used, the finite width of the entrance slit need not broaden the lines to any significant degree. Thus, at the cost of increasing a line width from 1.1 to 1.2 A, the detected intensity was raised by a factor of 20. The influence of scattering in the foil may be gauged from a comparison of the above with the line width obtained for the case of 200-keV Ar par-

-

292

BEAM-FOIL SPECTROSCOPY

[VI,

$3

ticles excited by collisions with CO, vapor (STONER and RADZIEMSKI [1972]). These particles are moving only one-fourth as fast as 1-MeV nitrogen atoms, so that the Doppler effect is substantially reduced by that factor alone. However, the scattering rises sharply because of the larger charges in Ar and CO, than in N + C . It rises also because scattering varies roughly as I/,?,, but is reduced because of the smaller energy loss in CO, relative to the carbon foil. (Unfortunately, one cannot circumvent these complications.) The empirical finding (STONERand RADZIEMSKI [1972]) is that line widths of 0.1 A at 5000 A can be obtained. Aside from refocusing, efforts to reduce the finite-aperture effect have been made by JORDAN[I968], BAKKEN and JORDAN119701, and by DUFAY, GAILLARD and CARRE[1971], who employ field lens L, (see Fig. I ) , or an equivalent mirror, which gives a large Doppler shift to each line but minimizes ;i./iXl and dA/l;p; by KAY and LIGHTFOOT [1970], who choose L, to have a short focal length and place L, close to the beam, so that the beam velocity of significance to the spectrometer is reduced by the demagnification of the optics; and by CARRIVEAU, DOOBOV, HAYand SOFIELI) [1972], who place the field lens L , one focal length in front of the entrancz slit, thercby ensuring that the principal illumination of the grating comes from light which leaves the beam at 90" to the particle velocity. The use of a lens precludes using these last mcthods in the vacuum ultraviolet; in some instances, a mirror may be used in place of a lens so as to permit work in the vacuum ultraviolet. In addition, observations at 0" are experimentally more awkward than those at 90" because the beam stop gets in the way. As a practical matter, most beam-foil experiments view the beam at 90". T o secure small line widths remains an important goal. At the present time, line-blending interferes with the proper identification of the parent levels, which in turn renders suspect a number of measurements of level lifetimes. For elements like the rare earths, where the level density is high, the prospect of using the beam-foil source is not attractive simply because of the line-width difficulty. The ultimate limit on linewidth will be set by the scattering in the foil. One of the reasons for using carbon is to keep the scattering small. The use of beryllium would reduce the scattering by a factor of two, but the health hazard has been a serious deterrent. There's no point in trying boron because boron foils are hard to prepare and have little mechanical strength or life under the beam as compared with carbon.

-

9 3. Wavelength Studies and Energy-Level Schemes The principal function of the wavelength, for our purposes, is to identify

ij

1 5 MeV

Oi

i

t

-

t-

cn

Z W I-

Z -

900

800

700 WAVELENGTH

(A)

600

Fig. 2. Part of the vacuum U.V. beam-foil spectrum of chlorine. Reproduced from BASHKIN and MARTINSON [1971] by kind permission of the authors and the journal.

294

BEAM-FOIL SPECTROSCOPY

IVI,

§3

the level, and the characteristics thereof, from which the light comes. This is especially interesting because beam-foil spectra frequently include spectral lines not previously reported. To date, these lines have been identified as having either of two origins, namely, C-ions whose structures had been incompletely explored in prior work, and multi-electron levels the radiative decay of which cannot be seen in other kinds of spectral sources. An example of the former is given by the beam-foil studies of C1 (BASHKIN and MARTINSON [ 19711, MARTINSON, BASHKIN, BROMANDER and LEAVITT [1973]). One of the spectra is illustrated in Fig. 2 (BASHKIN and MARTINSON [1971]),while Fig. 3 (MARTINSON, BASHKIN, BROMANDER and LEAVITT [1973]) gives the level structure of CI VII as deduced from the data. Of the lines shown in Fig. 3, only the two resonance transitions were known (BOWEN and MILLIKAN [1925], PHILLIPS [1938]) prior to the beam-foil work, although [1938]) via resonance transitions of levels up to 6f had been seen (PHILLIPS shorter wavelength.

ns

I 4001

--

nD

nd

nf

na

nh

ni

nk

nl

nm

i1

Fig. 3. Energy-level diagram for C1 VII. Wavelengths are given in Angstroms and level positions are in kilokaysers or cm- ’. Reproduced from MARTINSON, BASHKIN, BROMANDER and LEAVITT 119731 by kind permission of the authors and the journal.

o

VI, 31

NAVELENGTH S T U D I E S A N D ENERGY-LEVEL SCHEMES

,

1

2700

1

1

1

1

1

2600 WAVELENGTH

1

(A)

1

1

1

295

1

2500

Fig. 4. Part of the U.V. beam-foil spectrum of Mn. The incident 5-ion beam was M n + with an energy of 249 keV. Reproduced from CURTIS,MARTINSON and BUCHTA[I9731 by kind permission of the authors and the journal. + +

Fig. 5. Part of the beam-foil spectrum of Tm. The incident 5-ion beam was T m + + +with [I9731 by kind permission of the an energy of 249 keV. Reproduced from MARTINSON author and the journal.

296

B E A M - F O I L SPECTROSCOPY

[v, 0 3

Given the limited resolving power of BFS, the fine-structure of the higher n-levels cannot be detected by ordinary spectral analysis. Many of the transitions associated with large n-values can be treated as hydrogenic (BASHKIN and MARTINSON[1971], MARTINSON, BASHKIN,BROMANDER and LEAVITT [1973], LENNARD, SILLSand WHALING[1972], BROMANDER [ 19731, LENNARD and COCKE[1973]). The versatility of the beam-foil source is demonstrated by Figs. 4-6 which illustrate spectra of three different elements. The data on Mn (CURTIS, MARTINSON and BUCHTA[1973]) and Tm (MARTINSON [1973]) were taken in Stockholm, and the P spectrum (MAIOand BICKEL[1973]) was obtained at Arizona. These results also show that high-energy accelerators are not necessary. Even such systems as Si IV (BERRY,BICKEL,BASHKIN,DESESQUELLES and SCHECTMAN [1971a]), P V (CURTIS,MARTINSON and BUCHTA [1971]), G a 111, Ge IV, HS V, and Se VI (SPIRENSEN [1973]), Br VII (ANDERSEN, NIELSEN and SPIRENSEN [1973b]), Pb I v and Bi v (ANDERSEN, NIELSEN arid SPIRENSEN [ 19721) have been studied successfully with particle

450 -

400 350

Phosphorus (Moss 311 E = 5 MeV loop Slits i=5pA

-

300 -

I-

z

"z v,

2501

200

d) Fig. 6(a).

VI,

I 31

297

W A V E L E N G T H STUDIES A N D ENERGY-LEVEL SCHEMES

500

-

r

I

I

n

I

I

I

I

I

I

!

Phosphorus (Mass 31)

I

!

450 -

i

400 -

-

0

n

N I

0

N0

350 -

4 N

M a

cn 300I-

ln

2

3

"

:k

250200

-

50

I

700

750

I

800

1

850

1

900

I

950

1

1000

I

1

1100

1150

I

A(%

Fig. 6(b). Fig. 6. Part of the beam-foil spectrum of phosphorus as obtained by MAIOand BICKEL [1973] with a bombarding energy of 5 MeV. Tentative identifications are given for a few of the lines in (b), but it is clear that many prominent lines are unidentified. The slit widths refer to the entrance slit of a 1-meter normal-incidence McPherson vacuum spectrometer. Permission from the authors and the journal to reproduce these results is gratefully acknowledged.

energies below 500 keV or so. On the other hand, high-energy machines are useful for BFS. Tandem Van de Graaffs have been used to generate optica or electron spectra up to Ar XVI (BROMANDER [1973], SELLIN, PEGG,BROWN, [1971], SELLIN,PEGG,GRIFFINand SMITH[1972], SMITHand DONNALLY SELLIN[1973], DONNALLY, SMITH,BROWN,PEGGand SELLIN[1971], PEGG, SELLIN,GRIFFINand SMITH[19721, COCKE,CURNUTTE and MACDONALD [ 1973]), while linear accelerators operating at 1 MeV/nucleon (DUFAY, DENISand DESESQUELLES [ 19701, BUCHET, BUCHET-POULIZAC, Do CAOand DESESQUELLES [1973]), or I0 MeV/nucleon have produced levels in [-ions

298

[VI, 0 3

BEAM-FOIL SPECTROSCOPY

with [ as large as (2-1) for (C, N, 0, Ne) (DUFAY, DENIS and DESES[19701, BUCHET,BUCHET-POULIZAC, DOCAO and DESESQUELLES [1973]), and (Si, S, and Ar) (SCHMIEDER and MARRUS[1970a, b], MARRUS and SCHMIEDER [1970, 19721, MARRUS[1973]).

QUELLES

- 30MeV -

-

7u

0

I

l

m I

-

I

0

m I

s

a

-

m

VI,

B 31

WAVELENGTH STUDIES A N D ENERGY-LEVEL

U

12 MeV

SCHEMES

299

c

i

) I

I

j

i

I I 1 I

2000

I

m

I

I

I I I 3000

I I I I

1 I

I

I I I I

I

I I I 1 1 1 1 I;;$&

4000

Fig. 7(b). Fig. 7. The energy-dependence of spectral line intensity is clearly displayed in these beamfoil spectra of oxygen. Note the hydrogenic identification given to many of the lines. These data are from a paper by LINDSKOG, MARELIUS,HALLIN, PIHL,SJODINand BROMMANDER [1973]. We acknowledge the authors’ kind permission to use this figure.

As the particle energy is raised, there is a general tendency towards c-ions of increasing 5. There are three general consequences. The first, which is illustrated in Fig. 7, is that the relative intensities of spectral lines from

300

BEAM-FOIL SPECTROSCOPY

[VI, 8 3

various stages of ionization are altered. Secondly, the wavelengths of the transitions move towards the soft X-ray region, so that the techniques of detection and analysis of the radiations differ from the conventional optical ones. Thus, in the studies of transitions in He-like or Li-like C1 (COCKE, CURNUTTE and MACDONALD [1972, 19731, and of H-like and He-like Si, S and C1 (SCHMIEDER and MARRUS[1970a, b], MARRUS and SCHMIEDER [1970, 19721, MARRUS[1973]), a solid-state Si(Li) crystal was employed, the photons having energies of 1-3 keV. Thirdly, the character of the transitions changes in that the familiar electric dipole decays which dominate the spectra of [-ions of small [ become relatively less probable, while “forbidden” magnetic or two-photon radiations occur with appreciable rates (SCHMIEDER and MARRUS[1970a, b], MARRUSand SCHMIEDER [1970, 19721, MARRUS [1973]), and multi-electron levels with highly forbidden decay modes also [1971], become common (SELLIN,PEGG,BROWN,SMITHand DONNALLY SELLIN, PEGG,GRIFFIN and SMITH[1972], SELUN[1973], DONNALLY, SMITH, BROWN,PEGGand SELLIN [1971], PEGG,SELLIN,GRIFFIN and SMITH[1972], COCKE.CURNUTTE and MACDONALD [1972, 19731).

Fig. 8(a). Fig. 8. Beam-foil spectra of carbon, nitrogen, and oxygen, illustrating the similar spectral features in a given isoelectronic sequence. The results are reproduced from BUCHET, BUCHET-POULIZAC, DO CAOand DESESQUELLES [1973]with the kind permission of the authors and the journal.

W A V E L E N G T H S T U D I E S A N D ENERGY-LEVEL SCHEMES

Fig. 8(b).

30 1

302

B E A M - F O I L SPECTROSCOPY

tVI, 5 3

This is a good place in which to mention that the determination of line intensity as a function of [-ion energy is complicated by the need to normalize to some quantity which is either independent of energy or whose variation with energy is well known. There is no such quantity, although the mean charge, 5, of a beam transmitted through carbon has been reasonably well measured for a wide range of (-ions and particle energies (WITTKOWER and BETZ [1973]). Hence, by collecting the beam in a Faraday cup and making suitable corrections for ( ( E ) one can normalize with an uncertainty of perhaps a few percent. Other factors, such as the energy-dependent change in light collection efficiency or the appearance and disappearance of blending lines must also be considered. It is a curious fact that some lines persist over a broad energy range while others, presumably from the same stage of ionization and even nearby energy levels, wax and wane rather sensitively with energy. ANDERSEN, BICKEL,BOLEU,JESSEN and VEJE[1971a], in studying He and Li, show that excitation cross sections may bear little resemblance to charge-state distributions and that the energy dependence of spectral lines from a given element depends on both the charge state and on whether one-electron or multi-electron levels are involved. Because much of the light in the beam-foil source comes from [-ions of large 5, it is often difficult to identify the connecting levels. Representative examples are found in the cases of Na (BROWN,FORDJr., RUBINand TRACHSLIN [1968]) and P (MAIOand BICKEL[1973]), where numerous lines remain unclassified. The difficulty is worsened by the poor wavelength determinations (+ 1-3 A being usual), but lessened by recourse to studies of neighboring (-ions. The use of isoelectronic sequences in the analysis of spectra dates to the very earliest times in classical spectroscopy (for example, see E D L ~ [1964]), N and assumes an important role in beam-foil spectroscopy. We see an illustrative case in Fig. 8, where BUCHET,BUCHET-POULIZAC, Do CAOand DESESQUELLES [I9731 have compared the spectral patterns from C , N, and 0. The spectra show three prominent lines of C V and N VI (Fig. 8b) and 0 VII (Fig. 8a). Some of the other lines from N are also mirrored in the oxygen data. Thus it seems likely that the comparable lines correspond to the same transitions in (-ions of the same 5. In Fig. 9, we see another kind of analysis (BUCHET,BUCHET-POULIZAC, Do CAOand DESESQUELLES [1973]), according to which lines of the same wavelength should appear in [-ions which have lost the same number of electrons, as, for example, C VI, N VI, 0 VI and Ne V1. Figure 9 shows several such correlations. There is a problem in applying the above methods for assigning lines to transitions. In principle, the relative intensities of the corresponding lines

Nitrogen

Fig. 9. Beam-foil spectra of carbon, nitrogen, oxygen, and neon, illustrating the similarity of spectral features in emitters which have lost the same number of electrons. These results are reproduced from BUCHET,BUCHET-POULIZAC, D o CAO and DESESQUELLES [I5731 with the kind permission of the authors and the journal.

304

BEAM-FOIL SPECTROSCOPY

[VI,

04

should be similar. Look, however, at Fig. 9, where lines at 535 A appear in N VII and 0 VII. The corresponding line in Ne VLI is missing. A possible source of this vacancy is that the accelerator in use had a fixed energylamu and did not lend itself to the excitation of Ne’6 ions. You will note, also, that 1727 8, is assigned to Ne VIII, whereas the lines at 1729 8, are attributed to C VI, N VI and 0 VI. Presumably the general sparsity of Ne VII lines led the authors to conclude that 1727 A had to originate in a different ionization stage. A similar remark applies to the failure to see an 0 VIII line at 1727 8,; 0 VIII was not produced efficiently and only the relatively strong transition at 1633 8, was seen. Thus the line identifications are often complicated. One might remark that a good theory of the beam-foil interaction would allow us to understand the circumstances under which some levels are highly populated and others not. The identification of transitions is aided by compilations such as we see in Fig. 10, where there is a plot (MARTINSON, private communication) of the term value, E, per “effective charge” ([+0.4) versus 2 for several spectroscopic terms. Any line which is believed to involve one of the levels must place that level on the pertinent smooth curve.

35

il--

=

=

-

-

3pp ID 2

o

i

Fig. 10. Energy per “effective charge” versus 2 for several spectroscopic terms. The ordinate is in kilokaysers or cm-’. These data were kindly provided by I. Martinson.

5 4. Doubly-Excited Levels Doubly-excited levels seem to be created in profusion in the beam-foil source; we restrict our discussion of such levels to beam-foil work. Those levels, which may be arranged in a spectroscopic hierarchy of their own,

VI,

5 41

DOUBLY-EXCITED

305

LEVELS

have a term of lowest energy which lies well above the ionization energy, at least for the [-ion of smallest 5. (As one proceeds along an isoelectronic sequence in the direction of larger (, the energies of the multi-electron levels become lower relative to the ionization energy, and ultimately become negative.) Thus autoionization is the expected mode of decay, with level lifetimes of lo-'' sec or less. However, the selection rules for autoionization (AJ = 0, An = 0 and Table 1) sometimes lead to metastability because the continuum does not contain states to which transitions can occur with TABLE 1 Autoionization selection rules for LS coupling. AS

AL Coulomb Spin-orbit Spin-spin

0 0,

0, & I , * 2

0

0, 3 1

0, & I , &2

appreciable probability. For example, the continuum of 1-electron levels coupled to a singlet ground term (e.g., Li I 1s 2s('S,)nZ 2L) does not include quartets. Consequently,radiative decays of levels such as Li I Is 2s np 4P0lead to the lowest such term, whence electron emission or forbidden radiative transitions must occur. Both the radiative and autoionization processes have been studied with the beam-foil source. Consider, first, the radiative work, CURTISand LUNDIN which has been reported for He (BERRY,MARTINSON, [1971d], BERRY,DESESQUELLES and DUFAY[1972, 19731, KNYSTAUTAS and DROUIN[1973]), Li (MARTINSON[1970, 19731, BERRY,DESESQUELLES and DUFAY[1971, 19731, BICKEL,BERGSTROM, BUCHTA,LUNDINand MARTINSON [1969a1, BICKEL,MARTINSON,LUNDIN,BUCHTA,BROMANDER and BERGSTROM [1969b], BUCHET, DENIS,DESESQUELLES and DUFAY [1969], GAILLARD, DESESQUELLES and DUFAY[1969], BERRY,BROMANDER and BUCHTA[1970], ANDERSEN, BICKEL,CARRIVEAU, JENSEN and VEJE[1971b], ANDERSEN, BOLEU, JENSEN and VEJE [1971c], BERRY,BROMANDER, MARTINSON and BUCHTA [1971b], BERRY,PINNINGTON and SUBTIL[1972]), Be (MARTINSON [1970], BERGSTROM, BROMANDER, BUCHTA,LUNDINand MARTINSON [1969], BERRY, BROMANDER, MARTINSONand BUCHTA [1971b], ANDERSEN,JESSEN and S0RENSEN [ 1969a1, HONTZEAS, MARTINSON,ERMANand BUCHTA[1972, 19731, MCCAVERT and RUDGE[1972]), B (MARTINSON[1970], BERGSTROM, [19691, MARTINSON, BICKEL BROMANDER, BUCHTA,LUNDINand MARTINSON and ~ L M E[1970]), C (MARTINSON [19701, BERGSTROM, BROMANDER, BUCHTA, [1969]), N (BERRY,BICKEL,BASHKIN,DESESQUELLUNDINand MARTINSON

306

BEAM-FOIL SPECTROSCOPY

[VI, B 4

and SCHECTMAN [1971a]), and CI (COCKE, CURNUTTE and MACDONALD [1972, 19731). These experiments were stimulated by the attempts to classify beam-foil lines which do not fit into the ordinaiy energy-level schemes, and by previous experimental and theoretical work which, dating back as far as 1928 (COMPTON and BOYCE[1928], Wu [1934], FENDER and VINTI[1934]), suggested the occurrence of discrete multi-electron, autoionizing levels.

LES

I

I I

I

I

I

I

I

I I

I

I

I

I

I

I

I

I

I

I

I

I

W

ml

tn

I

0

m

0 1

.

M I40

WAVELENGTH (%)

290

Fig. l l a . Beam-foil spectra of He (bottom) and Li (top), reproduced with the kind permission of BERRY,DESESQUELLES and DUFAY119731.

VI, 0 41

D O U B L Y - E X C I T E D LEVELS

I

201

100 keV

He'

-+

307

C

*

V

0

'=,

101

c

c

0

V

Y

Fig. 11b. Beam-foil spectrum of He in the same wavelength range as in Fig. 1l a (bottom). and DROUIN [1973]. Reproduced with the kind permission of KNYSTAUTAS

Typical spectra for He (see Fig. 11) show numerous lines which cannot be fitted into the normal level diagrams for He I and He 11. Unfortunately, different assignments have been proposed by the two reporting groups. This illustrates the problem which results from relatively low resolving power, since these may be as many as ten lines within 1 A (MCCAVERT and RUDGE [1972]). Another example is given in Fig. 12, where we show the level scheme (HONTZEAS, MARTINSON, ERMAN and BUCHTA [ 19731) for two-electron terms in Be 11. Figure 12 shows a satisfying internal consistency, and the assignment of the levels is strengthened by the report (HONTZEAS, MARTINSON, ERMAN and BUCHTA[1973]) of lines which connect to bound systems. The fact that some levels have been identified in four or more members of an isoelectronic sequence gives further corroboration to the level schemes. However, the analysis of the spectrum is made awkward by the simple experimental facts that (1) a variety of spectrometers is needed to cover the entire spectral range, (2) the detection efficiency for a given spectrometer arrangement may be strongly dependent on wavelength, (3) lifetime effects

308

BEAM-FOIL SPECTROSCOPY

[VI,

Q4

A

ev l&O-

2sns

LS

2pns

w

2snp

2;np

2snd

/.Po

P w

'D

2pnd

w

135-

130-

125-

120-

115-

Fig. 12. Quartet system of autoionizing two-electron levels in Be. Reproduced from HONTZEAS, MARTINSON, ERMANand BUCHTA[1973] with the kind permission of the authors and the journal.

enter into the picture, and (4) there are ever-present limitations imposed by resolving power. The discrepancy noted above in the helium assignments illustrate the need for caution in dealing with the multi-electron levels. There are, of course, similar problems for ordinary levels. We have mentioned that the beam-foil source liberates electrons as well as light. These electrons, many of which have discrete energies, have been PEGG,GRIFFIN and SMITH[1972], DONNALLY, studied for 0 and F (SELLIN, SMITH,BROWN,PECGand SELLIN[1971], BERRY[1972]) and C1 (PEW, GRIFFIN, SELLIN and SMITH[1973]). They have paid particular attention to C-ions of Li-like and Na-like character, for example, Cl14+ and C16+.The experimental method is to direct a beam of foil-transmitted [-ions down the axis of a cylindrical electrostatic analyzer. Electrons ejected from the beam

DOUBLY-EXCITED

309

L EV ELS

8 - c m FOIL POSITION

ELECTRON ENERGY SPECTRA 70-220 eV 5 MeV CHLORINE BEAM

3-crn FOIL POSITION

70

90

110 130 150 170 ELECTRON ENERGY ( e V )

190

210

Fig. 13. Beam-foil electron spectra of chlorine at two different distances from the foil. Reproduced from PEGG,GRIFFIN, SELLINand SMITH [1973] with the kind permission of the authors and the journal.

in a small solid angle are energy-analyzed. A spectrum so obtained is illustrated in Fig. 13. As discussed by DONNALLY, SMITH, BROWN,PEGGand SELLIN[1971], an experimental problem in measuring the electron energies is that they vary over the finite width of the entrance aperture, quite analogous to'the Doppler broadening for the light. A significant energy spread is also contributed by scattering. Total spreads are a few eV per keV. Despite these difficulties, the electron energies have been well-enough determined to associate them with autoionizing, but metastable, levels in [-ions of three or eleven charges. The metastability arises from the large spin of the electronic arrangements such as 1s 2s 2p "P+ in Cl'"' or perhaps 1s' 2s' 2p5 (nZ)(n'Z')and 1s' 2s 2p6 (nl)(n'Z'), with n, n' 5 3, for C16+.What is surprising is that there appear to be many metastable, autoionizing levels in a great variety of [-ions, and they are populated prolifically in the beam-foil source,

310

BEAM-FOIL SPECTROSCOPY

IVI,

I5

0 5. Metastable One-Electron Levels The transitions which are most commonly observed in spectroscopy satisfy the selection rules AL = & 1, AJ = 0, 5 1, An = 1, with 0 4 0 transitions forbidden and, in L-S coupling, AS = 0. The selection rule for AS arises because the electric-dipole operator commutes with the spin and thus cannot connect levels of different spin. In point of fact, L-S coupling is not perfect, and so-called "intercombination lines", for which AS = & 1, do occur, especially in heavy elements; for example, there is the strong resonance line 12537 A in Hg (6s' IS, - 6s 6p 'P;). The selection rules characterize electric dipole radiation, in which the photon carries away one unit of angular momentum and a unit of parity. Thus, in the cases of hydrogen and helium, for which some of the low-lying levels are drawn in Fig. 14, we see that some direct decays to the ground state are forbidden.

2 'P

? ' S O T

I I

1

I

I I

I I

H

/

I

I

I

/ I

I

He

Fig. 14. Low-lying energy levels of hydrogen and helium. For He-like C-ions with 5 > 2, the 'P levels are inverted. Allowed transitions are indicsted by solid arrows, forbidden ones by dashed arrows.

VI,

o 51

METASTABLE ONE-ELECTRON

LEVELS

311

If one considers transitions of higher order, such as magnetic dipole, electric or magnetic quadrupole, or double electric dipole, one finds that they occur with rates which are strongly increasing functions of Z . Thus, in DONNALLY and FAN [1968], a beam-foil study of He-like oxygen, SELLIN, SELLIN, BROWN,SMITH and DONNALLY [19701, observed the intercombination line 1s’ ‘So-ls 2p 3P, (see Fig. 14); they also measured the mean life of the upper level. Using the heavy-ion linear accelerator at Berkeley, MARRUS and SCHMIEDER [1970,1972], SCHMIEDER and MARRUS [1970b], MARRUS [1973] showed that the “forbidden” decays illustrated as dashed lines in Fig. 14 actually occur with substantial rates in Si, S, and Ar. Indeed, the Z dependence of the forbidden transitions may be greater than that of allowed electIic-dipole transitions. At Z 18, for example, the M2 decay 2 3P2 -+ 1 ’ S o dominates the El decay 2 3P, + 2 %, (see Fig. 15). It is worth mentioning that

-

FORBIDDEN DECAYS IN He

FORBIDDEN DECAYS IN H

z=I T ~ ~ = ~ XZ I O3 ’ e TZEl=

o 12~

c

3 e c

rMI=45x1O5 Z-”sec

5~10’sec

Z=18 14x10-’sec

012 sec

353x 10-’sec

4 5 ~ 1 sec 0~

126xIO-’sec

I

Is,

rZE,(He)=O5 ti)

Fig. 15. Illustration of forbidden decays in hydrogen and helium. The lifetimes are taken from MARRUS[1973].

GABRIEL and JORDAN [1969a], well before the experiments of Marrus and Schmieder, proposed to account for certain solar coronal lines in terms of just such forbidden transitions in [-ions of high [, and used the line intensities to deduce the electron density in the solar corona (GABRIEL and JORDAN [1969a, b, c]). These experiments on H-like and He-like [-ions show generally good agreement with calculations of the level positions and decay rates. An interesting problem is to measure the Lamb shift for one-electron [-ions of high (; so far, such data have been published for systems up to hydrogenic

312

BEAM-FOIL SPECTROSCOPY

IVI, S 6

oxygen (LEVENTHAL, MURNICK and KUGEL[1972], LAWRENCE, FANand BASHKIN [1972], LEVENTHAL [1973]), but they aren't quite good enough to test the predictions of quantum electrodynamics.

6 6. Mean-Life Measurements Probably the most important achievement of BFS is its making possible the measurement of the mean lives of excited levels in (-ions with arbitrary values of [. Moreover, BFS is not restricted to resonance terms or to those which can be reached by optical pumping. The early experiments were, naturally, devoted to the light elements, and especially to elements which make gaseous compounds. More recently, attention has been devoted to the metals and rare earths. Of the first 37 elements in the periodic table, only Co and Zn have so far escaped study in BFS, while Cd, In, Sn, Sb, Pd,Te, Xe, Hg, T1, Pb, Bi, Gd, Tb, Dy, Tm, and U are other elements for which some work has been reported. Needless to say, no one has made a thorough study of all the levels of any [-ion. However, a given level has often been studied for many members of an isoelectronic sequence. Thus, MARTINSON [1973] notes that the 3s-3p resonance transition has been measured in eight [-ions, from Na I to Ar VIII. Such measurements provide a valuable check on theoretical calculations of transition probabilities and on level assignments. Recent developments on the theoretical side have taken ever more detailed account of configuration mixing, and the lifetime data are a particularly sensitive test of the validity of the theory. In Fig. 16 we see a comparison (MARTINSON [1973]) of the experimental and theoretical results forthe 3s' 3p 'P0-3s 3p2 3 D transition in the A1 I sequence. The importance of the lifetime experiments is such that a great deal of effort has gone into methods of reducing the uncertainties in the measurements. Three main problems can be treated separately. First of all, the reciprocity between distance and time obviously involves the particle speed. More exactly, it involves the speed of the particles after their penetration through the foil. The best way of finding that velocity is, naturally, by making a direct measurement. In practice, that is virtually never done, but it sometimes is (BICKEL,BERGSTROM, BUCHTA,LUNDIN and MARTINSON [ 1969a1, ANDERSEN, M0LHARE and SBRENSEN[ 19721). Rather, one usually calculates the energy loss experienced by the particle as it goes through the foil. This leads to serious problems, especially for medium-weight and heavy elements at low energy, partly because foil thickness is usually not well known, and largely because the calculations are not always satisfactory.

VI,

0 61

MEAN-LIFE

Ar C l S

f

0.08

A1

313

MEASUREMENT

P

Si

A1

I sequence

3 s2 3p 2Po-3s 3p2 2D

0.07 0.06 0.05

Hofmann (emission 1 .Curtis et a1 ( B F S ) A B e r r y et a l ( B F S ) r B a s h k i n and M a r t i n s o n (BFS) x L i v i n g s t o n e t a1 (BFS) o F r o e s e Ftscher (theory1 oBeck and Sinanog'Lu (theory)

0.04 0.03

O

0

+

0.02

t 0

0

0.01

0

0

0

0

0.04

0.06

0.081/z

Fig. 16. Oscillator strength versus Z - ' for a transition in the Al I sequence. The open symbols are from theory, the others from experiment. Reproduced from MARTINSON [1973] with the kind permission of the author and the journal.

Foil thicknesses are sometimes measured in terms of the energy loss sustained by alpha particles, and sometimes by an optical transmission method which is based on an absolute determination of the carbon content of a foil (STONER [19691). Most often, however, only the manufacturer's estimate is available and this may be grossly uncertain. (Many laboratories make their own foils; they rarely describe how they determine foil thicknesses.) Even if the foil thickness is well known, the translation into an energy loss depends SCHARFF and SCHIOTT [1963]. As pointed out, on the theory by LINDHARD, for example, by ANDERSEN [19731, the calculations overestimate the energy loss, especially for heavy C-ions at low energy. CARRIVEAU (private communication) and his associates have found that the actual energy loss by Kr at 200 keV is less than half that calculated from Lindhard's theory. Thus if one uses calculated energy losses, the effect is to make the beam-foil mean lives appear longer than they are. The other two main complications in the lifetime work are line blending and cascades. We will see later that these effects can be reduced or even

314

[VI,§ 6

BEAM-FOIL SPECTROSCOPY

eliminated in some cases; however, the requisite method is not yet in general use. The most common treatment of lifetime data is to fit the observed decay curve by a sum of exponentials. A recent example (ROBERTS, ANDERSEN and SBRENSEN [1973b]) appears in Fig. 17, where the data and the decomposition into two exponential decays are given.

i

2945.5A T i U e4G 300 keV

\

T,,, = 3.0 ns

\ ,

I

1

10 20 30 40 DISTANCE FROM FOIL ( m m )

Fig. 17. A decay curve for 12945.5A from 4Gin Ti 11. Note the decomposition into a cascade contribution and the main decay. Reproduced from ROBERTS, ANDERSEN and S0RENSEN [1973b] with the kind permission of the authors and the journal.

In Fig. 17, we see that the decay curve was followed over a factor of 30 in intensity. However, one sees from Fig. 17 that there is still appreciable slope to the curve at the longest observed times. It would be better practice to extend the region of observation to the place where the signal is lost in background plus noise. This is often hard to do, since the lifetimes may be long, necessitating movement of the foil over awkward distances. For instance, a medium-weight (-ion (say 20) with a moderate energy (say 1.5 MeV) moves 3.8 mm per nanosec. For a mean life of 15 nsec, this gives a mean decay distance of 5.7 cm, so to follow a decay curve over even 3 mean decay lengths requires moving the foil over a straight track 17 cm long. Not only is such a length hard to incorporate into a target chamber, but there

VI, 3 61

MEAN-LIFE MEASUREMENTS

315

is an associated difficulty not yet discussed. In order for the signals from different points to have any physical significance, they must be normalized to some common denominator. The usual practice is to normalize to the charge which is collected in a Faraday cup (see Fig. 1). The big problem is that the beam is scattered by the foil so that the cup collects a decreasing fraction of the 6-ions as the foil-to-cup distance increases. Generally speaking, one cannot move the cup with the foil, for one quickly obscures the spectrometer’s view of the light. The best one can do, other than going to the limit of measuring the scattering and correcting for it directly, is to make the cup large in diameter. Often this dictates the minimum distance from the beam to the entrance slit of the spectrometer, especially for work in the vacuum u.v., where lenses cannot be used. An alternative normalization is to use the intensity of some spectral line or wavelength band as the common denominator. A filter-photo-multiplier combination which sees the light from some point close to the foil is relatively simple to arrange. Of course, this apparatus must be moved with the foil. However, one needs a window as long as the distance over which the foil is to be translated, and the whole must be in a light-tight enclosure. This method is not in general use. Two other problems are present for either of the above normalizations. One is that scattering at the foil affects the fraction of the beam which the spectrometer sees. Of course, one tries to use a long slit so that particles, even though scattered, can still emit their light into the spectrometer, but it is easy to see that the efficiency of colIection of light is degraded when the foil is far from the point of observation. The other problem is that foil characteristics change under bombardment. They may thicken or become thinner. They may develop pinholes, or disintegrate. All of these changes affect the relative amount of a given kind of light that is generated at the foil, and also the amount of scattering. If one is using charge normalization, the foils (pinholes and breakage not considered) may produce charge equilibrium so that thickness changes don’t alter the common denominator, but the likelihood is that the light output is not constant, so that the numerator suffers. The result of all this is that one must make a value judgment about the quality of the lifetime data and analysis. This, of course, comes down to a matter of opinion; quantitative assessments can be made only by recourse to laborious studies. Every measurement includes a contribution from background and noise. In addition, the level of interest may be populated by cascades as well as by the direct interaction at the foil. If we have a single cascade, we may write

316

s

N

Iv1, $ 6

BEAM-FOIL SPECTROSCOPY

s0+2u- " 5 2 -71

N;exp

(-) :

u52

x exp

where,

(- 5)sinh A 72-71

-,

(6.1)

V 71

S = signal; So = background plus noise; u = beam speed; z1 = lifetime of level of interest; z2 = lifetime of higher level which cascades into level of interest; d = distance downstream from foil at which S is detected; 24 = observed length of beam; NP, N i = initial populations of levels 1 and 2. So great a variety occurs of relative values of z1 and T ~ and , of So, N;/rl, and N ~ / that T ~no simple rules can be given to relate the quality of the data to the parameters in eq. (6.1). Note, however, from Fig. 18 that 24, the observed length of the beam, depends on the distance between the beam and the entrance slit, assuming that no field lens is used. That distance is determined by the need to collect the beam in a shielded Faraday cup, and possibly also by physical interference from the detector. In one fairly typical case, that distance is 6.6 cm, and 24 is 6.6 mm.

Fig. 18. Arrangement for measuring lifetimes. The foil is mounted on a movable frame, driven either manually or with a stepping motor. The spectrometer views the finite beam segment of length 24.

Now consider a beam with a speed of 3 x lo8 cmjsec, and a level with a mean life of sec. The mean decay distance is 3 mm. However, the smallest value d can have is 3.3 mm, for otherwise one is looking at the foil.

VI,

8 61

MEAN-LIFE MEASUREMENTS

317

Thus the level population has declined to 33 % of its initial value before the first measurement has been made. Suppose, further, that there is a cascade from a level with 7 = 10 nsec. At the first observation point, this level population is still 90 % of its initial value. If, then, the upper level has an initial population equal to that of the level of interest, the cascade intensity is 25 % of the total, and it grows rapidly for successive points downstream. From Fig. 18, one sees also, that the bulk of the desired information is contained in that edge of 24 which is closer to the foil, and the light from that edge illuminates only a small part of the grating. The rest of the grating is illuminated by light from the cascading level and by the background. Therefore the quality of the data is reduced by using the entire grating, and a mask should be employed (LIVINGSTON, IRWINand PINNINGTON [1972]). Unfortunately, a mask reduces the resolving power of the grating. Consequently, when spectral lines are close together, masking the grating may cause them to overlap, which again causes the lifetime data to be unsatisfactory. Only for the cases of isolated lines, low background and noise, insignificant cascading, and lifetimes 2 5 nsec can the customary measurements be considered satisfactory. We feel that lifetimes less than 1 nsec should be treated with reserve unless an especially good argument is presented to show the 201

I

I

I

I

1

-

'50

10 20 30 40 DISTANCE DOWNSTREAM FROM EXCITER FOIL (rnrn)

Fig. 19. Decay curve for 13714 from a doubly-excited level in Li. Reproduction from

BICKEL, BERGSTROM, BUCHTA,LUNDINand MARTINSON [1969a] with the kind permission of the authors and the journal.

318

BEAM-FOIL SPECTROSCOPY

[VI,

B6

correctness of the experiment. Merely following the customary method and extracting a decay constant is inadequate. Differing experimental arrangements can easily cause substantial discrepancies in lifetimes. Consider the data of Fig. 19, from BICKEL, BERGSTROM, BUCHTA,LUNDIN and MARTINSON [1969a]. They follow an unmistakable exponential decay,

J

Fig. 20. Level diagram for multi-electron levels in Li. Reproduced from BERRY, DESESQUELLES and DUFAY 119731 with the kind permission of the authors and the journal.

VI, § 61

MEAN-LIFE MEASUREMENTS

319

from which a mean life of 6.4 nsec was deduced for the doubly-excited level 1s 2p2 4P of Li I. However, now examine Fig. 20, where we show the corresponding energy level diagram (BERRY,DESESQUELLES and DUFAY[19731). It is seen that the level in question is populated by no fewer than eight cascades! How then, can the decay be characterized by a single exponential? This kind of apparent inconsistency can be very frustrating, especially since the lifetime and energy level determinations often appear in separate publications from separate laboratories. We do not know how to account for the cited results, which are not merely an isolated case for which some fortuitous values of lifetimes and initial populations could lead to a strictly exponential decay despite the numerous cascades. This type of peculiarity occurs fairly frequently. The cascade situation would be materially simplified if the cascade lines were themselves specifically identified in the papers which more-or-less casually invoke cascades in explanation of the lifetime curves. This, again, is rarely done, partly because the cascade lines are in so different a wavelength region from the main line under investigation that a single spectrometer is not suitable for the work. Moreover, the judgment that one line is the precursor of another, even when both are seen, is based only on inference from an energy-level diagram, whereas what is really needed is a coincidence measurement. Delayed-coincidence experiments have been reported (MASTERSON and STONER [1973]), but the technique seems hard to use, requiring very long running times even where both members of a known simple cascade appear with high intensity. For the general case, where the participating transitions may have quite different wavelengths and relative intensities, and where the sequence of related transitions is not known, the time-coincidence method will not permit an easy deciphering of the cascade scheme. One can measure level lifetimes by several other methods. One, which is applicable when the lower state is so short-lived that it has appreciable width, is based on the fact that the non-instrumental part of the width of a spectral line comes from the combined natural widths of the initial and final levels. This approach has been used (BERRY, DESESQUELLES and DUFAY[1971,1972, 1973]), in studies of autoionizing levels. Unfortunately, there are no independent experimental verifications of the lifetimes so reported, and calculated values are generally inapplicable because the experiments cited above could not resolve closely-spaced levels of widely different theoretical lifetimes. The trouble one has in making a realistic assessment of lifetimes measured with the foregoing methods may be appreciated as follows. From the work of BERRY,SCHECTMAN, MARTINSON, BICKELand BASHKIN[1970b], we de-

320

BEAM-FOIL SPECTROSCOPY

[VI,4 6

duce anf-value of 0.38 for the (multiplet) transition 3s %-3p 'P in S VI, whereas SBRENSEN [1973] quotes unpublished work by himself and Andersen as giving 0.53. Since f i k = 1.5 x

,Iz (gk/gi)Aki>

wherefik is the absorption oscillator strength, I is the wavelength (in Angstroms) of the transition, g is a statistical weight, and A k i is the transition probability, the discrepancy reduces to one of lifetime. BERRY,SCHECTMAN, MARTINSON, BICKELand BASHKIN[1970b] resolved the two components of the transition array and made separate lifetime measurements using each line, obtaining 1.05 and 1.07 nsec for the P, and P, levels, respectively. The details of the Serrensen-Andersen measurement are not available. We believe that this particular problem may be related to the short mean life and the corresponding experimental difficulty in observing over several mean decay lengths. A different situation is found in oxygen, where the mean life of 0 111 3d 5 D is reported as 1.44nsec, 2.12nsec, and 2.84 nsec (DRUETTA and POULIZAC [1969]); as 25.2 nsec (LEWIS,ZIMNOCH and WARES[1969]); as 15 nsec (PINNINGTON [1970]); and as 7.0 and 8.6 nsec (DRUETTA, POULIZAC and DUFAY[1971]). The three numbers given by DRUETTA and POULIZAC [1969] were based on three separate lines in the transition array 3p 5D0-3d 5D;a cascade correction was included in the treatment of the 2.84 number. DRUETTA and POULIZAC [1969] and PINNINGTON [1970] used a line from 3p 5P0-3d 5D, since they were unable to detect the lines from 3p 5D0-3d 5D. DRUETTA, POULIZAC and DUFAY[1971] use both transition arrays, but report that the line from 3p 5P0-3d 5 D was blended with a line from 0 I1 or 0 IV. No indication is given as to why the value given by DRUETTA, POULIZAC and DUFAY[1971] is so different from those of DRUETTA and POULIZAC [1969], nor does the latter paper account for the spread of a factor of 2 in its listings. Unfortunately, the confusion which is generated by these conflicting ieports is widespread, and the reader can only occasionally make a value judgment as to which, if any, of the lifetimes approximates the truth. When different particle energies are employed, relative line intensities are apt to differ. Blends are an ever-present possibility. The common suggestion that cascades occur is rarely substantiated by anything other than the shape of the decay curve, and that could be severely influenced by, for example, normalization procedures. This last could also be affected by foil thickness, because of scattering, and, as we have noted previously, foil thickness is notoriously uncertain. Further on the matter of cascades, we have already

VI.

5 61

MEAN-LIFE MEASUREMENTS

32 1

commented that there is no clear understanding as to when a line will or won't exhibit a cascade contribution, and it would be most helpful if authors would address themselves to the question of whether it is sensible to invoke the cascade mechanism. To be specific, the 0 111 3d 5D term referred to above lies 398000 cm-' above the ground state. The ionization level is only slightly higher, namely, at 443000 cm-l. MOORE[I9491 lists but two terms (4p 5D0at 438000 cm-' and 4p 'Po at 439000 cm-') which could decay by fully allowed transitions to 3d 5D, and the oscillator strengths for those transitions are almost certainly vanishingly small (they are not listed in WIESE,SMITHand GLENNON [1966]). Thus the present author finds it perplexing that cascades, emphasized by LEWIS,ZIMNOCH and WARES[1969] and DRUETTA, POULIZAC and DUFAY[1971], could play a significant role in the decay of 0 I11 3d 5D.It is our belief that authors would perform an important service were they to give some physical argument to buttress the claim of cascade influence. The striking discrepancies we have cited can, we believe, scarcely originate in cascades. It is far more likely that the problems are (a) line blending, (b) improper normalization, and/or (c) poor signalto-background ratio; these factors should be given a thorough analysis in every lifetime paper. 33L9.L A T i I1 Z4G'

1 0 0 ~ ''

'

' 1" 0 " " 20 ' " 30 ' ' ' ',40 DISTANCE FROM FOIL (mm) "

Fig. 21. Decay curves for A3349.4A from 2 4G" in Ti 11, taken at two different bombarding energies. There is no evidence of cascades over the wide range in intensities. Reproduced from ROBERTS, ANDERSEN and SBRENSEN [1973a] with the kind permission of the authors, Astrophysical Journal, and the University of Chicago Press. "Copyright 1973 by the American Astronomical Society. All rights reserved".

322

BEAM-FOIL SPECTROSCOPY

[VI,

06

Although we have stressed the uncertainty that sometimes makes lifetime data difficult to interpret, one must recognize that, overall, the lifetime experiments have contributed a wealth of information which is quantitatively satisfying. We have already cited the work by ROBERTS,ANDERSEN and SORENSEN [1973a], from which we reproduce our Fig. 21, showing intensity data for a line in Ti 11. Note particularly that the intensity was followed over a range of 100 or so, that the error bars indicate reasonable attention was paid to the physical significance of the experimental details, and that, from the size of the error bars at the largest distance, one can conclude that the line was followed well into the noise. Moreover, branching ratios were also measured. ROBERTS,ANDERSEN and S~RENSEN [1973a] yielded some 350 absolute oscillator strengths for transitions in Ti 11, along with others for T I I, 11, and IV. It is instructive to compare the results with those of a shock-tube experiment by WOLNIKand BERTHEL[1973], which appeared at about the same time. Luckily both groups examined many of the same transitions; the common transitions are listed in Table 2. The agreement between these entirely independent measurements is gratifying. TABLE 2 Absolute values of log (gf) for levels in Ti I1 Multipleta

4'Q

Beam-foilb

Shock-tubec

~~

20 32 34 39 49 50 51 60 61 70 82 86 87 87 92 93 I04 113 I14

4344 4341 3932 4583 4709 4590 4408 458 1 439 1 5227 4530 5129 4028 4054 4780 4375 4387 5027 4874

MOORE[1949]. ROBERTS, ANDERSEN and SQRENSEN [1973a]. ' WOLNIKand BERTHEL[1973]. a

-2.03 -2.22 -1.90 - 2.73 -2.63 -1.73 -2.14 -2.73 -2.79 - 1.24 -2.15 -1.51 -1.12 -1.33 - 1.37 -1.62 -1.41 -1.23 -1.01

-2.01 -2.10 -1.77 -2.74 -2.40 -1.85 -2.55 -2.89 -2.33 - I .44 -1.82 - 1.49 -1.26 - 1.38 - 1.42 - 1.60 -1.06 -1.12 -0.96

VI,

8 71

A P P L I C A T I O N S OF L I F E T I M E D A T A

323

0 7. Applications of Lifetime Data The lifetime data have had two principal applications, namely to astrophysics and atomic theory. The connection with astrophysics stems from the fact that determinations of relative element abundances in astronomical sources depend directly on the oscillator strength for the observed transition. The mean life of level k may be related to the total decay probability by

r;' = CA,.. ick

From eqs. (6.2) and (7.1), we see that a measurement of z, gives an upper limit to the oscillator strength for a particular transition. If one couples the measurement of z with another of the branching ratio of the transition of interest to the total transition intensity, one can find the oscillator strength itself, rather than just an upper limit thereto. Moreover, for cases where a single transition is dominant, the measurement of z is adequate to determine f. Of all the elements whose abundance one might wish to know, iron is outstanding in its significance for astrophysics. The reason is that there appears to be (CAMERON [1968]) a strong local maximum in the abundances of elements in the immediate neighborhood of iron, with iron itself at the peak. This apparently universal feature of the element abundances has given rise to extensive calculations (TRURON[1972]) on, for example, the mechanism whereby such a distribution could have been produced. Since the death throes of stars are involved (BURBIDGE, BURBRIDGE, FOWLER and HOYLE[1957]), the subject has singular fascination for the inquiring mind, and an enormous effort has been exerted on the problem. The several beam-foil measurements (WHALING, KINGand MARTINEZGARCIA[ 19691, WHALING,MARTINEZ-GARCIA, MICKEYand LAWRENCE [19701, ANDERSEN and S0RENSEN [19711, LENNARD and COCKE [19731, LENNARD, WAHLING, SILLSand ZAJC[1973]) of lifetimes in Fe I and Fe 11, along with numerous independent investigations (HUBERand TOBEY [1968], GARZand KOCK[1969], SEASDOLEN, HUBERand PARKINSON [1969], BRIDGES and WIESE[1970], WOLNIK, BERTHEL and WARES [1970, 19711, WIESE[1970], BELLand UPSON[1971], KLOSE[1971], HUBER and PARKINSON [1972], ASSOUSA and SMITH[1972]) have shown that oscillator strengths derived from earlier work (CORLISSand BOZMAN[1962], CORLISSand WARNER [1964, 19661, CORLISS and TECH[1968]) were seriously in error. On the basis of the more recent studies, the photospheric solar abundance of iron has been revised upwards (GARZ,KOCK,RICHTER,BOSCHEK, HOLMEYER and KOCKand RICHTER[1969b1, GARZ, UNSOLD[1969a1, GARZ,HOLMEYER,

324

BEAM-FOIL SPECTROSCOPY

[VI, I 7

RICHTER, HOLMEYER and UNSOLD[1970], BOSCHEK, GARZ,RICHTER and HOLMEYER [1970], COWLEY [1970], NUSBAUMER and SWINGS[1970], GREVESSE, NUSSBAUMER and SWINGS[1971], FOY [1972], Ross [1973]) by approximately a factor of ten, with a possible uncertainty of a factor of two (FOY [1972]). In the absence of mechanisms which cause alteiations in the surface abundances, one assumes that photospheric abundances are representative of the interior constituents of the sun. Thus the enhancement of the iron abundance is taken to indicate the iron complement of all of solar matter. The immediate consequence of the new iron abundance is to raise the opacity (BAHCALL [1964]), which, in turn, demands an increase in the central temperature so as to account for the observed radiant flux from the sun. The effect of the increased temperature on the thermonuclear events which presumably generate a star’s luminous power output has been studied by Bahcall and his associates (BAHCALL [1966], BAHCALL, BAHCALL and ULRICH [1969], BAHCALL and ULRICH [1971]). The result is that the calculated neutrino flux expected at the earth is 5 or more timesegreater than the experimental upper limit (DAVIS[1964], DAVIS,HARMER and HOFFMAN [1968], DAVIS,RADEKAand ROGERS[1971]), giving rise to a variety of speculations (BAHCALL, CABIBOand YAHIL[1972], BAHCALL [1973]) concerning such things as the particle stability of the neutrino, the existence of additional resonances in thermonuclear reactions, the long-term stability of the sun, and so forth. One can summarize this extensive activity on the nature of the sun, and, presumably, on all stars, by saying that reliable lifetime data have strengthened the idea that iron-group elements are more abundant than their neighbors and have raised serious questions as to how to interpret this abundance. Measurements on lifetimes of other elements in the iron group such as nickel (BRAND,COCKE and CURNUTTE [1973]), chromium (COCKE, CURNUTTE and BRAND[1971]), and manganese (CURTIS, MARTINSON and BUCHTA [1973]) also cause a revision upwards in their solar abundances. On the other hand, the abundance of thulium must apparently be reduced (CURTIS, MARTINSON and BUCHTA[1973]). Thus one sees that beam-foil lifetime data are critically important to the fundamental problem of ascertaining the relative abundance of the elements. Another use of lifetime data has been to assist in the refinement of calculations of transition probabilities and oscillator strengths. DALGARNO I19731, SINANO~LU [1969, 19731, WESTHAUS and SINANO~LU [I9691 have recently summarized the theoretical advances made by themselves and others in calculating oscillator strengths. The Z-expansion method treated by Dal-

VI, 0 81

325

COHERENCE A N D ALIGNMENT

garno shows that the regularities which others had discovered (WIESE[1968a, b, 19701, WIESEand WEISS[19681, SMITHand WIESE[19711, SMITH,MARTIN and WIESE[1973]) infversus 2 have a good theoretical basis. At the same time, the refinements of Sinanoglu's non-closed shell, many-electron theory, in which electron correlation is specifically included for both spectroscopic terms linked in a transition, have given oscillator strengths with uncertainties of a few percent. Since beam-foil experiments can also be that good, the comparison between theory and experiment becomes significant. An example appears in Fig. 22. I

I

I I I

I

I

I

I

I

I

)

BORON SEQUENCE 2s' 2 p 2po- 2s 2p' 'D A

o

0

0

NCMET

A PHASE

1

A

SHIFT

HANLE EFFECT

NBS

0.05

0.10

0.15

0.20

112-

Fig. 22. Comparison of theoretical and experimental values of oscillator strength vs. Z-' for a transition in the B I isoelectronic sequence. Reproduced from SINANO~LU [1973] with the kind permission of the author and the journal.

Many other transitions remain to be studied. Sinanoglu has called attention to the failure of certain critical experiments to give consistent values and to the need for further experimental work on doubly-excited systems, metastable states, and transitions in (-ions of large (-

5 8. Coherence and Alignment 8.1. COHERENCE

If levels of the same n, Z, s are collisionally populated in a time At << hjAE,

326

PI,8 8

B E A M - F O I L SPECTROSCOPY

where AE is the level separation, the wave function for the system is a superposition of the individual level wave functions, with a fixed phase difference from one to another. This is called coherent excitation. We write Y(t) =

1a j u j exp [- ;(

+i?)

1 1 .

j

Thus

there is a damped oscillatory time-dependence of the probability density. Since parity is a good quantum number, Y has a definite parity, which means that coherence, as treated for the moment, docs not mix levels of different parity. We will later consider cases where such mixing can occur. Of course, one does not directly observe the population of a level. Instead, one sees a transition between levels. MACEK[1969] has shown that the total intensity is unmodulated in an electric-dipole transition. To observe the modulations, we must have another factor. 8.2. ALIGNMENT

By alignment, we mean that the magnetic substates for a given J > Jj-are not equally populated, although the rate of production of MJ is the same as that of - M J . When there is alignment, the light emitted in a given direction is polarized; then there are coherence-generated oscillations, called quantum beats. 8.3. QUANTUM BEATS

-

When the beam-foil light source is used, At is certainly no longer than the 3 x lo-'' sec. transit time of the c-ions through the foil, a matter of Hence levels with energy separations of an electron volt or so may be coherently excited. The time-dependence of the level population is transformed into a spatial dependence, so one looks for the quantum beats in the variation of the intensity of a given kind of polarization as a function of distance between the foil and the point of observation. Although a number of experimental papers have been published (BASHKINand BEAUCHEMIN [1966], ANDRA[1970a1, LYNCH,DRAKE,ALGUARD and FAIRCHILD [19711, BURNS and HANCOCK [1971]) on this phenomenon, the first full study of coherent excitation with the beam-foil method was made by WITTMAN,TILLMANN and ANDRX[1973], who studied n = 3,4 in hydrogen and the 3 3P term of He I. Consider the latter case (see Fig. 23).

COHERENCE A N D ALIGNMENT

3p

2s a s ,

327

‘P, 185564.9466cm-’

’ y 185564.6760 % ’ 185564.6540

-$

159850.38

Fig. 23. Part of the triplet levels of He I and the geometry used in observing quantum beats.

For our purposes, the three components of A3889 A are indistinguishable. Let the direction of the beam be z and the direction of observation y . The intensity of the light which can be detected is then

I = I,+I,.

(8.3)

The relative magnitudes of these polarized components depend on time because of the oscillatory nature of the probability density of the 3P term. Suppose the situation at some time were such that I, = 0. We would then detect I,. Sometime later, the system would emit part of its light as I, and some as Iy , the latter being unobservable. The result is that the total detected intensity would fluctuate in time with a frequency, or set of frequencies, characteristic of the energy intervals in the upper term. Analysis of the frequency pattern can then give those intervals. Andrii’s first work (ANDRL[1970a]) was necessarily crude; the observed beam length was 1 mm (0.25 nsec), and the total observation time was only 6 nsec. Nonetheless the quantum beats were clearly displayed, as well for n = 3 and 4 in H as for the 3 3Pterm in He. In a later experiment (WITTMA”, TILLMANN and ANDRA [1973]), a striking improvement had been achieved; the results for He 1 3 3P are reproduced in Fig. 24. While Fig. 24 (top) shows the beat pattern for a time of 65 nsec, Fig. 24 (middle) illustrates the detailed features of a single period. In Fig. 24 (bottom), we see a similar study, but for 3He. (Note the different time scales for the three curves). It is thus clear that this quantum-beat technique is suitable for the determination of the energy separations of fine and hyperfine terms. WITTMAN, TILLMANN and ANDRA[1973], BERRYand SUBTIL[1973], and BERRY,SUBTIL,PINNINGTON, ANDRA,WITTMANN and GAUPP[1973a] have also applied the method to several terms in 6”Li. 8.4. ALIGNMENT AND A N EXTERNAL NON-OSCILLATORY MAGNETIC

FIELD

The alignment means that the excited system behaves Iike a magnetic dipole which can be coupled to an external magnetic field, H . This coupling

328

BEAM-FOIL SPECTROSCOPY

3 37-3p2 BEATS 658 MHZ

HELIUM-4

10

I

I

I

10

QUANTUM-BEATS

20

I I

I

J F 0 112-

2

I

L

0

I

L

I

2

3

4

A

1

3

I 30

OF THE 33P STATE OF 4He

0

la

I

4

5

6 (nsec)

I - I . ,

7

6 (nsec)

1

(ns)

VI, §

81

COHERENCE AND ALIGNMENT

329

creates new MJ levels out of the initial configurations, so one may consider that the field generates coherence among the Zeeman levels. Coupling between states of different parity does not occur. Let the geometry be as in Fig. 23 with a variable magnetic field in the x-direction. A short segment of the beam is observed at a distance d from the foil. The dipole precesses in the y-z plane, so that the intensity detected in the y-direction is a function of H, . If H, is itself varied linearly in time,

I,(H,) = A(I + B cos 20.1, t)e-" = A(I

+B cos 201, d/~)e-~'"

(8.4a) (8.4b)

where oLis the Larmor (circular) frequency,

thus

B is a measure of the alignment, and the other symbols are familiar. From the period of the sinusoidal intensity variation, one can determine the Land6 g,-factor (LIu, BASHKIN, BICKELand HADEISHI [1971], LIU and CHURCH [1971], CHURCH, DRUETTA and LIU [1971], CHURCH and LIU [1972, 1973b], GAILLARD, CARRE,BERRYand LOMBARDI [1973]). The attractive feature is that those numbers can be obtained for levels in [-ions of a wide range of 5, and for levels which do not connect to the ground term by allowed decays. The general result is that G S coupling is a good approximation in nearly all cases studied. A few exceptions have been found, especially for the n 3P term of Li I1 (GAILLARD, CARRE,BERRYand LOMBARDI [1973]). Furthermore, if the c-beam includes a level of known g, any unknown g; can be and LIU obtained in terms of the ratio (LIU and CHURCH[1971], CHURCH [1973bl) g; = g p / R ' , (8.7) Fig. 24. Quantum beats in He 1V and He 111. The top figure shows data extending over a time of 65 nsec. The middle figure shows the detailed structure of one of the periods in the top figure. The bottom figure shows the particulars for the same transition but in He 111. The arrows in part a of the bottom figure illustrate the transitions and their amplitudes which are contributors to the pattern of part c. Part b is a computer fit to the data using the frequency distributions of part a. These figures are reproduced from WITTMANN, TILLMANN and ANDRA[1973] with the kind permission of the authors and the journal.

330

BEAM-FOIL SPECTROSCOPY

[VL

88

where R and R’ are, respectively, the mean changes in magnetic field to produce one oscillation for the known and unknown values of gJ. An important application of this method is to check on the validity of the transition assigned for a given spectral line. For example, LIUand CHURCH [1971] note that 12778A, ascribed to Ne I11 3s’ 3D:-3p’ 3D3 (STRIGANOV and SVENTITSKII [1968]), shows no oscillations, a condition generally expected only for J = 0 or 4.Hence it is suggested that the line in question be reexamined. Several variations of the above technique have appeared. In one variation (LIu, BASHKIN, BICKEL and HADEISHI [1971], CHURCH,DRUETTA and LIU [1971], CHURCHand LIU [1972]), a long beam segment is observed. This gives an experiment similar to a Hanle-effect study in which, however, the finite mean life of a level under study may require a modification of the appropriate equation. One finds (CHURCH,DRUETTA and LIU [1971])

where z is the mean life of the level and oL = g J ( p B / h ) His the Larmor precessional frequency. If the g-value is known, perhaps from quantum-beats work, this method enables one to find z, about which more is said later on. Results for g-values have been given for levels in Ne I, 11,111 (LIu, BASHKIN, BICKEL and HADEISHI [1971], LIU and CHURCH[1971]), 0 11, TI1 (CHURCH and LIU [1973b]), and Ar I, 11, I11 (CHURCH,DRUETTA and LIU [1971], CHURCH and LIU [1972]). From eqs. (8.6) and (8.8), it is seen that N and d play the same role as regards the oscillatory behavior of I. Advantage has been taken of this fact in another variation of the basic method (LIUand CHURCH[1972], CHURCH and LIU [1973c], LIU, DRUETTA and CHURCH[1972]). In this, the magnetic field is held constant, and the foil is moved backwards and forwards. This v)

L

C

0

V

a

I Chonnel number

7

Fig. 25. Quantum-beat data from which lifetimes can be determined without the influence of cascades. Reproduced from CHURCH and LIU 11973~1with the kind permission of the authors and the journal.

VI, 8 81

COHERENCE A N D ALIGNMENT

33 1

gives the exponential-type decay, on which is superimposed the oscillatory pattern. If, now, one sweep of the foil (with field on) is followed by a sweep with the field off, and the two signals added with opposite signs, the exponential behavior is eliminated and the oscillatory function is clearly displayed. One such result is shown in Fig. 25, the level in question being 0 I1 3p' 'F;. The advantage of this work is explained by the following equations (LIU and CHURCH [ 19721, CHURCH and LIU [ 1973~1).We represent the intensity, in the absence of a magnetic field, as

I(t)

+ ~ ( to)+D, ,

Ae-r/r

(8.9) where D is the background and C arises from cascades. When the magnetic field is on, we have whence

I'(t) 1'-I

=

=

=

e-'lr(A+B cos 2m,t)+~(t, H,)+D,

(8.10)

B~-"'(COS~~,~-~)+C(~,H)-C(~,O). (8.11)

If, as will now be argued, C(t, H )

= C(t, 01,

(8.12)

it follows that z can be determined independent of cascades. It is immediately obvious that the equality implied in eq. (8.12) holds when the cascading levels have J < 5, for such levels cannot exhibit alignment effects. Moreover an extensive study was made (LIu, DRUETTA and CHURCH[1972], LIU, GARDINER and CHURCH [1973], CHURCH and LIU [1973a]) on levels which are known to be subject to strong cascades from others with J > +, but no cascade influence was found. In Table 3 we list results (CHURCH and LIU [1973c]) obtained by this and the standard beam-foil method for lifetimes of levels in 0 11. The variety of numbers from a given reference is due to the use of several different transitions from the upper term. Since the lifetime is the same for all members of a multiplet, the spread illustrates that the standard method is subject to difficulties.What is more, note that the cascade lifetime, which, in the standard method affects the decay curve for 3p' 'F;, is deduced by DRUETTA, and DUFAY[1971] to be 4.0 nsec. However, the direct measurePOULIZAC ments on the upper level of prime importance (3d' 'G,) are 5.1 to 9.5 nsec. This illustrates the difficulty of ascertaining a cascade mean life from a standard decay curve. It appears that these problems are largely avoided by the method of LIU and CHURCH [1972], CHURCH and LIU [1973a, cl LIU, DRUETTA and CHURCH [1972], LIU,GARDINER and CHURCH[19731, and that the important matter of level lifetimes is perhaps best investigated in this manner.

332

PI, § 8

BEAM-FOIL SPECTROSCOPY

TABLE3 Lifetimes of some 0 I1 levels by two methods t

Transition

(upper level) (nsec)

T

(cascade) (nsec)

CHURCH and LIU [1973c]

Other

CHURCH and LIU [1973c]

Other

13.7h0.4

14.0b 12.8' 9.9 10.7d 12.0d 14.0d 8.7"

None

4.0b

3p"Fo4-3d"G3

6.8*0.2

9.P 6.1b 5.1"

None

2Sb 20b

3s 2P3-3p 'P"+

6.8hO.I

7.1b 6.0'

None

None

~

3s' 'D3-3p'

a

'Fa%

PINNINGTON and LIN [1969b]. DRUETTA, POULIZAC and DUFAY[1971]. DRUETTA and POULIZAC [1969]. KERNAHAN, LIN and PINNINGTON [1970a].

8.5. COHERENCE WITH A NON-OSCILLATORY ELECTRIC FIELD

In the previous examples of coherence, only levels of the same parity were connected. However, when an electric field is applied, either directly or by sending the c-ions through a transverse magnetic field, there is Stark coupling of levels of opposite parity. This coupling manifests itself as time- (or space-) dependent oscillations in the intensity of a spectral line. Measurements have been reported on several Lyman and Balmer lines in H and He 11. The early experiments on the visible lines in H (BASHKIN, BICKEL,FINK and WANGSNESS [1965], SELLIN, MOAK,GRIFFINand BIGGERSTAFF [1969a]), and He I1 (BICKELand BASHKIN[1967]) clearly established that the rate of radiation was an oscillatory function of time when the field was applied but the use of photographic recording precluded precise determinations of the intensity patterns. Later work, using photomultipliers (BICKEL[1968], ANDRA[1970b], ALGUARD and DRAKE[1973], PINNINGTON, BERRY, DESESQUELLES and SUBTIL[1973]) or a Geiger counter (SELLIN, MOAK,GRIFFIN and BIGGERSTAFF [1969b] for Ly a), was more satisfactory in that such intensity variations as occurred were properly recorded. Despite this improvement, certain confusions were introduced as a consequence of the several field geometries which were employed. We believe these confusions

VI, 8 81

C O H E R E N C E A N D ALIGNMENT

333

can be eliminated, essentially on the basis of AndrP’s work (ANDRA[1970b]) as follows. What Andra showed is that the oscillations can be seen only if the electric field is parallel to the beam. Most of the experiments used fields normal to the beam, but still generated oscillations; AndrP argued that only the fringing part of the field, which contained a component parallel to the beam, was effective. Experimental corroboration was provided by PINNINGTON, BERRY, DESESQUELLES and SUBTIL[I9731 in a study of Stark modulations in He I1 and Li 111. They used geometries as illustrated in Fig. 26b, c, while Fig. 26a F i N K and WANGSNESS [1965], shows the geometry used by BASHKIN, BICKEL, BICKELand BASHKIN[1967], and BICKEL[1968]. Geometry 26a gave oscillations but 26b did not. The reason seems to be that 26a has a significant longitudinal field, while 26b doesn’t. Again, 26c produces oscillations, as does the case where foils perpendicular to the beam serve as the field plates.

(a 1

(b)

(C)

Fig. 26. Various geometries used in investigating the effect of small external electric fields on emissions from hydrogen and He 11.

The observed patterns are Fourier-analyzed so as to deduce the component frequencies, these being related in turn to the energy separations between the levels the interaction of which generates the oscillations. For a simple model, consider the n = 2 term in H. The 2s level cannot decay to the ground state, whereas the 2p levels can. If, then, the external field causes a periodic transformation between the 2s and 2p level systems, the intensity of the radiated light (Ly a) will be high when the 2P character dominates the excited system, low when 2s is dominant, and, generally, oscillatory with a period dependent on the 2S-2P energy spacing. Other levels can be expected to give more complicated patterns because of the greater number of interfering states. One of the peculiarities is that only certain frequencies, none predicted in advance of the experiments, seem to occur. Consider the results of PINNINGTON, BERRY,DESESQUELLES and SUBTIL[1973]. The n = 6 term in He I1 was observed by means of the decay to n = 3. Figure 27 illustrates the level scheme and the dominant frequency which was detected. PINNINGTON, BERRY,DESESQUELLES and SUBTIL[1973] attribute their result to the requirement that, as described in our model, one interacting level should be

334

[VI,

BEAM-FOIL SPECTROSCOPY

08

long-lived, and the other short-lived, a condition which, they say, is best met by the f;-gg pair. They particularly note that the g-state cannot decay t o n = 3. 8.206

h"2/-

8.192

9%-

8.1704,

f,

f2

6, If2

Fig. 27. Levels for n

d5,

=

b

/2

8.170 8.134

a2 dJ+8.062 ~

426697.862 ~

8.134

8.192

h9/2-

"2

~

7.845

6 in He 11. The level positions are given in cm-'. The arrow indicates the pair which beat together.

We are not convinced that the argument is valid. In the first place, the g-h combination better satisfies the above condition than f-g, but the corresponding frequency was not seen. Secondly, the f+--g; pair is the same as the f,-g, pair as regards relative lifetimes, but the former set seems not to contribute to the pattern. Thirdly, PINNINGTON, BERRY,DESESQUELLES and SUBTIL[1973] stress that the g-states cannot decay to n = 3. While that is true, it seems to us that what really counts is the fact that the constituents of n = 6 are interacting with each other. Whether a particular state participates directly in the transition one chooses to detect should not be important. Thus, in the present instance, the instantaneous populations of the 6g-states should be affected by the decays to n = 4 and 5, and those of the 6f-states by the decays to n = 3, 4, and 5, as well as by mixing with all the other Mates. The effects of these several interactions should show up in every transition from n = 6 downward, but the corresponding frequencies are apparently not present. Our conclusion is that the phenomenon of Starkmixing of the hydrogenic levels is not yet adequately explained. 8.6. OSCILLATING EXTERNAL FIELDS

Two different kinds of experiments have been done with oscillating fields applied to the (-ion beam. In one kind (FABJAN and PIPKIN[1972], LUNDEEN, YUNGand PIPKIN[1973]), a foil-excited beam of 20-30 keV H-atoms was sent through an rf cavity, and the long-lived 3S, state was quenched by tuning the rf to match the S,-P, level separation. Such work has given the n = 3 Lamb shift to -0.015 % (FABJAN and PIPKIN[1972]). In a second type of work, the rf was generated by electrodes which, connected to d.c. power supplies, were constructed with a periodic geometry.

VI,

5 81

COHERENCE A N D ALIGNMENT

335

Thus, HADEISHI, BICKEL,GARCIAand BERRY[1969] used the arrangement of Fig. 28 to induce transitions between the 3S, and 3P, levels in hydrogen. The magnetic field separated the Zeeman studies to the value appropriate to the rf seen by the beam. This experiment demonstrated that a periodic potential barrier could be used in the study of fine-structure. MAGNETIC FIELD

*

Recorder

Fig. 28. Arrangement used in the application of rf to a beam of hydrogen. A variable d.c. potential difference is applied to the electrodes; the c-ions see this as rf with a frequency dependent on the C-ion speed and the spacing of the “teeth”. The magnetic field introduces a Zeeman splitting of the levels. Reproduced from HADEISHI, BICKEL,GARCIA and BERRY[I9691 with the kind permission of the authors and the journal.

AND^ [197Oc] sent a beam of H-atoms down the common axis of two helices which were connected to a d.c. power supply. An axial magnetic field was also applied. To the H-atoms, it appeared as though they were being irradiated with circularly-polarized light with a frequency dependent on the beam speed and the pitch of the helices. Andra observed the resonant decay of Ly cx as a function of the magnetic field. and BERRY[I9691 and ANDRA[197Oc] dealt HADEISHI, BICKEL,GARCIA with attempts to measure the Lamb shift in hydrogen, and they achieved a modest success. A somewhat different problem was studied by LIU, BASHKIN, BICKEL and HADEISHI[1971]. They sent Ne’ ions through a foil and then down the axis of a row of copper rings so arranged that direct current circulated circumferentially,but in opposite directions, in successive rings. This produced an oscillating axial magnetic field, H, with an intensity proportional to the current through the rings. By adjusting H, resonance transitions were induced between Zeeman sublevels of the 2p, level of Ne I. These resonance transitions affected the intensity with which light, polarized either parallel or normal to the magnetic field, was radiated in a given direction. Thus detection of that light which was transmitted through a linear polarizer

336

BEAM-FOIL S P E C T R O S C O P Y

[VI,

I9

indicated the resonance condition. If the polarizer is normal to the magnetic field, the appropriate expression, at resonance, reduces to (LIu, BASHKIN, [19711) BICKELand HADEISHI

I

-

(y~)~/[4y~~~+r~],

(8.13)

where y is the gyromagnetic ratio and r the decay constant for the level. Thus we see that this application of rf to the [-ion beam leads to the determination of y and r.

Q 9. Charge-State Identification One of the fortunate features of the beam-foil light source is that C-ions with a wide range of [-values can be excited. One of the unfortunate features is that three or four different values of [ appear in the same foil-transmitted beam. Thus it is a bit of a problem to decide to which particular %-iona given observed spectral line actually belongs. Of the methods in use, two derive from the particular properties of the beam-foil source. These are: 1. Measuring the line intensity as a function of [-ion energy and associating the line with that value of C which exhibits a similar dependence on [-ion energy (BASHKIN and MARTINSON [19711, WITTK~WER and BETZ[19731, ANDERSEN, DESESQUELLES, JESSEN and S0RENSEN [19701, ANDERSEN, BICKEL, BOLEU,JESSEN and VEJE [1971a], ANDERSEN, BICKEL,CARRIVEAU, JESSEN and VEJE[1970b], BERRY,DESESQUELLES and DUFAY[ 19711, ANDERSEN, JESSEN and S0RENSEN [1969a, b], MARTINSON, BICKELand ULME [1970], BERRY,MARTINSON, SCHECTMAN and BICKEL[1970a1, BERRY,SCHECTMAN, MARTINSON, BICKEL and BASHKIN [1970b1, BERRY, BICKEL, BASHKIN, DESESQ U E L L E ~and SCHECTMAN [1971a], KERNAHAN, LINand PINNINGTON [1970b1, KAY[1965], BASHKIN and MALMBERG [1966], DENIS,DESESQUELLES, DUFAY and POULIZAC [1968], DENIS,DESESQUELLES and DUFAY [1969], DENIS[1969], DENISand DUFAY[1969], DENIS,CEYZERIAT and DUFAY[1970], DRUETTA, POULIZAC and DESESQUELLES [19701, POULIZAC, DRUETTA and CEYZERIAT [ 19711, MARTINSON, BERRY,BICKELand OONA[19711, PINNINGTON and DUFAY[19711, ANDERSEN, ROBERTS and S0RENSEN [197I 1, POULIZAC and BUCHET[1971], BUCHET,POULIZAC and CARRE[1972], BERRY,BUCHETPOULIZAC and BUCHET [1973b]). 2. Deffecting the [-ions in an external field and carrying out a spectral BICKELand analysis on each of field-separated particle beams (MARTINSON, ~ L M E[1970], MALMBERG, BASHKIN and TILFORD [1965], FINK [1968a, b], BROWN,FORD Jr., RUBINand TRACHSLIN [1968], CARRIVEAU and BASHKIN [ 19701, BASHKIN, CARRIVEAU and HAY[19711.

o

VI, 91

337

CHARGE-STATE IDENTIFICATION

Each method has favorable and unfavorable aspects; the former, as one might guess from the relative bibliographies, is the easier to use. Its great virtue is experimental simplicity; all one need to do is observe the intensity of a line from some point along the beam and vary the [-ion energy. In general, what is observed is that the line intensity grows with energy until a rather broad maximum is reached, after which a monotonic decline occurs. If several lines exhibit a similar energy dependence which differs from that of another group of lines, it is natural to attribute the groups to different stages of ionization. There are two main problems with such an approach, namely, not all lines from the same stage of ionization behave the same way with C-ion energy and it is often impossible to be sure of the effect of line blends on the energydependence. Sometimes blends ate suspected as the cause of the former problem, but not always. For example, ANDERSEN, BICKEL,BOLEU,JESSEN and VEJE[1971a] obtained data some of which are reproduced in Fig. 29. The top curve originates from the transition Li I 2p 'P0-ls 2s 3s 4S and the middle one from a transition from an autoionizing level in Li I. Thus they both come from Li I, but their energy dependencies are quite different. In

X - 413.3nm Li Ia

z

I

'

1

I I I I 1 1 10 20 30 40 50 60 70 80 keV BEAM ENERGY IN THE LABORATORY SYSTEM

Fig. 29. Intensity variations of three different spectral lines as a function of particle energy. The two top curves are for transitions in Li 1, the bottom from a transition in Li 11. Adapted from ANDERSEN, BICKEL,BOLEU,JESSENand VEJE[I971 a] with the kind permission of the authors and the journal.

338

BEAM-FOIL SPECTROSCOPY

[VI, 0

9

fact, the bottom curve, from Li I1 3d 3 D 4 f 3P0,looks rather like the middle curve, although the charge states of the parent [-ions differ by one. In the above case, one can argue that the similarity between the two lower curves is to be expected because the metastable levels involved in Li I 1s 2s 2p 4P0-ls 2s 3s 4S are well above the ionization limit for Li I so that Li 11-like behavior is not unlikely. However, the argument is ad hoc: the force of the charge-state identification rests on the spectroscopic analysis of the source of A2934, and is both independent and contradictory of the association with the energy variation of charge states. This situation is not restricted to lines from autoionizing levels. Thus LIVINGSTON, IRWIN and PINNINGTON [1972], in a study of argon beam-foil spectra, assert that there are several intense lines from Ar IX or higher although, at the [-energy of 1.4 MeV which they used, less than 10 % of the beam has a net charge of 6 and higher. ANDERSEN, ROBERTS and SBRENSEN [I9711report strong differences in the energy-dependenceof A1 I1 lines from 3s nf 3F levels. The problem of line blending seems extremely hard to solve as regards charge identification. Numerous papers, among them those by LIVINGSTON, IRWIN and PINNINGTON [1972] and POULIZAC, DRUETTA and CEYZERIAT [1971], claim that the failure of certain lines to follow patterns established for others is rooted in line blends from transitions in two or more charge states, and this could well be the case. However, it does not result in confidence in charge assignments. It is our feeling that the correlation of line intensity with charge fraction is merely suggestive of the charge of the emitting [-ion, that it always depends on some quite independent information for calibration of the set of charges to be assigned, and that it is apt to be misleading if complete reliance is placed on it, particularly if there is any suspicion that blends are present. The second method has involved static electric fields which are applied transverse to the I-ion beam. Observations may be made normal to the plane of the split beams (MALMBERG, BASHKIN and TILFORD [1965], FINK[1968a]), in which situation a spectral decomposition is carried out on each of the separated (-ion beams, or in that plane (BROWN,FORDJr., RUBINand [19681, CARRIVEAU and BASHKIN[19701, BASHKIN, CARRIVEAU TRACHSLIN and HAY [1971]), in which case one makes use of the fact that there is a Doppler shift which differs with the charge of the emitter. The former approach gives completely unambiguous - and correct results. Unfortunately, the parabolic beam paths tend to produce rather poor images in the focal plane of the spectrometer. The latter has the draw-

VI,

B 101

CONCLUSION

339

back that transition arrays from different charge states move through one another, making it difficult to decipher the patterns. Both ways of examining the beams fail for short-lived emitters since decay then occurs before adequate spatial movement or Doppler shift has developed. If 7 = 3 x lo-’ sec for a level in N3+,the transverse displacement is 0.5 mm for a 1-MeV beam passing through a field of 50 kV/cm. The Doppler shift at the end of that time is only 4 A (at 4000 A) and of course, the line intensity has fallen by e-l. One gains by using the highest possible deflecting field. A practical upper limit is in the neighborhood of 75 kV/cm. The [-ions, on reaching a collector, release electrons which can give rise to electrical discharges in the target chamber. The discharge problem can be reduced by maintaining a pressure 5 torr and by slotting the electrodes so that ions (and electrons) are not collected in the region of high field. A word of caution might be in order. The energetic electrons do generate X-rays and care should be exercised to prevent their causing unnecessary irradiation of laboratory personnel.

-

0 10. Conclusion We have omitted a number of interesting topics. These include the question, What is the relative population of the levels of a given n and also of the magnetic substates of a given I? The literature contains quite a few quite different answers to these questions. Closely related is the fundamental problem of determining precisely what happens when the [-ions pass through the foil. Whether volume or surface effects are dominant has been much debated, but no one has yet presented a detailed theory of the beam-foil interaction. Still other matters untouched in the present review are prospective developments, such as laser stimulation of the foil-excited [-ions or the application of pulse techniques to the beam of [-ions. In this review, we have adopted a critical attitude towards beam-foil spectroscopy. The reason is simply that the successes in this field are well known, while some of the handicaps often go unrecognized. It is our hope that calling attention to the present drawbacks will lead to their early elimination.

Acknowledgments It is a pleasure to record my thanks to my colleagues for their critical comments, and to many people who have permitted me to reproduce figures from their papers. Preparation of this paper was supported by NSF, ONR and NASA.

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