Drake G.W.F. (editor) Handbook of Atomic, Molecular, and Optical Physics

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Precision Oscillator Strength and Lifetime Measurements 17.2 Lifetimes 265

Fabry–Perot spectrometry at very low temperatures and

pressures, and in beam–foil studies of radiative transi-

tions in which the lower level decays very rapidly via

autoionization. The linewidth can also be determined

through the use of the phase shift method. Here modu-

lated excitation is applied to the source, thus producing

similarly modulated emitted radiation, and the width

can be speciﬁed from the phase shift between the two

signals. Other methods involve resonance ﬂuorescence

techniques, where sub-Doppler widths are obtained be-

cause the width of the exciting radiation selects a subset

of particle motions within the sample. Resonance ﬂu-

orescence techniques that can be used to determine

level widths include zero-ﬁeld level crossing (the Hanle

effect), high-ﬁeld level crossing, and double optical

resonance methods, but the Hanle effect is the most

common.

17.2.1 The Hanle Effect

In its most commonly used form, the Hanle effect makes

use of polarized resonance radiation to excite atoms in

the presence of a known variable magnetic ﬁeld. The

magnetic substates of the sample are anisotropically ex-

cited, and the subsequent radiation possesses a preferred

angular distribution. By applying the magnetic ﬁeld in

a direction perpendicular to the anisotropy, the angular

distribution is made to precess, producing oscillations in

the radiation observed at a ﬁxed angle. At inﬁnite pre-

cessional frequency the intensity would be proportional

to the instantaneous average angular intensity, but at ﬁ-

nite precessional frequency it depends upon the decay

that has occurred during each quarter rotation. Measured

as a function of magnetic ﬁeld, the emitted intensity

has a Lorentzian shape centered about zero ﬁeld with

a width that depends on the lifetime and g-factor of the

level [17.2].

17.2.2 Time-Resolved Decay Measurements

The most direct method for the experimental determi-

nation of level lifetimes is through the time-resolved

measurement of the free decay of the ﬂuorescence

radiation following a cutoff of the source of ex-

citation. An important factor limiting the accuracy

is the repopulation of the level of interest by cas-

cade transitions from higher-lying levels. For this

reason, decay curve measurements fall into two

classes: those that involve selective excitation of

the level of interest, thus eliminating cascading al-

together; and those that use correlations between

cascade connected decays to account for the effects of

cascades.

Selective Excitation

Lifetime measurements accurate to within a few parts

in 10

have been obtained through selective excitation

produced when appropriately tuned laser light is inci-

dent on a gas cell or a thermal beam, or on a fast ion

beam (Sect. 18.1). With a gas cell or thermal beam, the

timing is obtained by a pulsed laser and delayed coin-

cidence detection. With a fast ion beam, time-of-ﬂight

methods are used. In either case, after removal of the

background, the decay curve of intensity vs. time is

a single exponential, and the lifetime is obtained from

its semilogarithmic slope. Laser-excited time-of-ﬂight

studies were ﬁrst carried out by observing the optical de-

cay of the ion in ﬂight following excitation using a laser

beam which crossed the ion beam. In these studies, the

laser light was tuned to the frequency of the desired

absorption transition either through the use of a tun-

able dye laser, or by varying the angle of intersection to

exploit the Doppler effect. Recent measurements have

utilized diode laser excitation in this geometry [17.11].

A number of adaptations of this technique have been

developed in which the laser and ion beams are made

to be collinear, and are switched into and out of res-

onance within a segment of the beam by use of the

Doppler effect [17.12]. The collinear geometry can pro-

vide a longer excitation region and less scattering of

laser light into the detector than occurs in the crossed

beam geometry. In one adaptation [17.13], excitation oc-

curs within an electrostatic velocity switch, and the time

resolution is obtained by physically moving the velocity

switch. In another adaptation [17.12], the ion beam is

accelerated with a spatially varying voltage ramp. The

resonance region is moved relative to a ﬁxed detector

by time-sweeping either the laser tuning or the ramp

voltage.

While these selective excitation methods totally

eliminate the effects of cascade repopulation, they are

generally limited to levels in neutral and singly ion-

ized atoms that can be accessed from the ground

state by strongly absorptive E1 transitions, and the

selectivity itself is a limitation. Many very precise

measurements have been made by these techniques,

but they have primarily involved ∆n = 0reso-

nance transitions in neutral alkali atoms and singly

ionized alkali-like ions. A summary of these meas-

urements is given in Table 17.1, and a comparison

of these values with theoretical calculations is given

in [17.14].

Part B 17.2

266 Part B Atoms

Table 17.1 Measured np

lifetimes

Atom n J τ(ns)

Li 2 1/2 27.20(20)

,27.29(4)

Na 3 1/2 16.38(8)

,16.40(3)

,16.30(2)

3 3/2 16.36(2)

,16.25(2)

3 1/2 3.854(30)

3 3/2 3.810(40)

4 1/2 7.07(7)

,7.098(20)

4 3/2 6.87(6)

,6.924(19)

Cu 4 1/2 7.27(6)

4 3/2 7.17(6)

5 1/2 7.47(7)

5 3/2 6.69(7)

Ag 5 1/2 7.408(32)

5 3/2 6.791(19)

5 1/2 3.11(3)

5 3/2 2.77(6)

Cs 6 3/2 30.55(27)

6 1/2 7.92(8)

6 3/2 6.312(16)

[17.17]

[17.18]

[17.19]

[17.20]

[17.21]

[17.22]

[17.23]

[17.24]

[17.25]

[17.26]

[17.27]

[17.11]

[17.28]

Advances have recently been made in the measure-

ment of transition probabilities of long-lived metastable

levels. Through a laser probing technique [17.15]us-

ing an ion storage ring, an extremely long lifetime (28 s)

has been measured [17.16]. The metastable level is pop-

ulated in the ion source and preserved in the storage

ring until it is destructively probed at variable times

after excitation. The laser light is collinearly merged

with the beam and tuned to a transition that promotes

the population of the metastable level to a higher un-

stable level. The ﬂuorescence subsequently emitted by

this unstable level gives a relative measure of the pop-

ulation of the metastable level. Thus, by varying the

delay time between the excitation and the laser prob-

ing, a decay curve of the population remaining is

obtained.

Nonselective Excitation

Much more general access can be obtained by non-

selective excitation methods, such as pulsed electron

beam bombardment of a gas cell or gas jet, or in-

ﬂight excitation of a fast ion beam by a thin foil.

Pulsed electron beam excitation can be achieved ei-

ther through use of a suppressor grid, or by repetitive

high frequency deﬂection of the beam across a slit

so as to chop the beam. Particularly in the case of

weak lines, the high frequency deﬂection technique

offers the advantages of high current and sharp cut-

off times. The high currents yield high light levels,

so that high resolution spectroscopic methods can be

used to eliminate the effects of line blending. Pulsed

electron excitation methods are well suited to measure-

ments in neutral and near neutral ions (although for very

long lifetimes in ionized species, the decay curves can

be distorted if particles escape from the viewing vol-

ume through the Coulomb explosion effect [17.29]).

However, for highly ionized atoms, the only gener-

ally applicable method is thin foil excitation of a fast

ion beam. Nonselective excitation techniques can also

be applied to measurements such as the phase shift

method [17.30] and the Hanle effect [17.31], in which

case cascade repopulation also can become a serious

problem. However, most of the attempts to eliminate or

account for cascade effects have occurred in decay curve

studies.

In beam–foil studies, the excitation is created in

the dense solid environment of the foil, after which

the ions emerge into a ﬁeld free, collision free, high

vacuum region downstream from the foil. A time-

resolved decay curve is obtained by translating the foil

upstream or downstream relative to the detection ap-

paratus. The beam is a very tenuous plasma, which

has both advantages and disadvantages. The low den-

sity avoids the effects of collisional de-excitation and

radiation trapping, but also produces relatively low

light levels. This requires fast optical systems with

a corresponding reduction in wavelength dispersion,

and care must be taken to avoid blending of these

Doppler broadened lines. Methods have been developed

by which grating monochromators can be refocussed to

a moving light source, thus utilizing the angular depen-

dence of the Doppler effect to narrow and enhance the

lines.

In these nonselective excitation methods, the decay

curve involves a sum of many exponentials, one cor-

responding to the primary level, and one to each level

that cascades (either directly or indirectly) into it. De-

cay exponentials do not comprise an orthogonal set of

functions, and the representation of an inﬁnite sum by

a ﬁnite sum through curve ﬁtting methods (Sect. 8.1.2)

can lead to large errors. Fortunately, alternative methods

to exponential curve ﬁtting exist, which permit the ac-

curate extraction of lifetimes to be made from correlated

sets of nonselectively populated decay curves.

Part B 17.2

Precision Oscillator Strength and Lifetime Measurements 17.2 Lifetimes 267

ANDC Method

Precision lifetime values have been extracted from

cascade-affected decay curves by a technique known as

the arbitrarily normalized decay curve (ANDC) method

(Sect. 18.1.1, [17.32]), which exploits dynamical corre-

lations among the cascade-related decay curves. These

correlations arise from the rate equation that connects

the population of a given level to those of the levels that

cascade directly into it. The instantaneous population

of each level n is, to within constant factors ξ

involv-

ing the transition probabilities and detection efﬁciencies,

proportional to the intensity of radiation I

(t) emitted in

any convenient decay branch. In terms of these inten-

sities, the population equation for the level n can be

written in terms of its direct cascades from levels i as

) =







− I





/τ

. (17.5)

Thus, if all decay curves are measured at the same

discrete intervals of time t

, the population equation pro-

vides a separate independent linear relationship among

these measured decay curves for each value of t

, with

common constant coefﬁcients given by the lifetime τ

and the normalization parameters ξ

. Although the sum

over cascades is formally unbounded, the dominant ef-

fects of cascading from highly excited states are often

accounted for by indirect cascading through the lower

states, in which case the sum can be truncated after

only a few terms. ANDC analysis consists of using this

equation to relate the measured I

) (using numerical

differentiation or integration) to determine τ

and the ξ

through a linear regression. If all signiﬁcant direct cas-

cades have been included, the goodness-of-ﬁt will be

uniform for all time subregions, indicating reliability.

If important cascades have been omitted or blends are

present, the ﬁt will vary over time subregions, indicating

a failure of the analysis. Very rugged algorithms have

been developed [17.33] that permit accurate lifetimes to

be extracted even in cases where statistical ﬂuctuations

are substantial, and studies of the propagation and cor-

relation of errors have been made. Clearly the ANDC

method is most easily applied to systems for which re-

population effects are dominated by a small number of

cascade channels. Further applications are discussed in

Sect. 18.1.1.

17.2.3 Other Methods

Coincidence measurements provide another method

for elimination of cascade effects. While the low

count rates and correspondingly high accidental rates

make the application of these methods difﬁcult for

optical spectra, the use of Si(Li) detectors for the

very short wavelength emission in very highly ion-

ized systems offers new possibilities [17.34]forthese

measurements.

Another method of accounting for cascading in-

volves the combined use of a laser and beam–foil

excitation [17.35, 36]. The beam–foil excitation pro-

vides a source of ions in excited states, and a chopped

laser is used to stimulate transitions between two ex-

cited states. By subtracting the decay curves obtained

with laser on and with laser off, the cascade-

free, laser-produced portion of the decay curve is

obtained.

17.2.4 Multiplexed Detection

Recently, the detection efﬁciency and reliability of

beam–foil measurements have been improved through

the use of position sensitive detectors (PSD), which

permits measurement of decay curves as a function

both of wavelength and of time since excitation. The

PSD is mounted at the exit focus of the analyz-

ing monochromator, where it records all lines within

a given wavelength interval simultaneously, including

reference lines with the same Doppler shifts. De-

cay curves can be constructed by integrating over

a line proﬁle, and that proﬁle can be examined

for exponential content to eliminate blending. The

time dependent backgrounds underlying the decay

curves are directly available from the neighboring

channels.

The use of multiplexed detection greatly en-

hances the data collection efﬁciency, and causes many

possible systematic errors to cancel in dif ferential

measurements. Effects such as ﬂuctuations in the

beam current, degradation of the foil, divergence of

the beam, etc., affect all decay curves in the same

way.

The most accurate measurement [17.37]made

by beam–foil excitation (± 0.26%) used a type of

multiplexed detection in which two spectrometers si-

multaneously viewed the decays of the

and

levels of the 1s3p conﬁguration in neutral helium. The

emission exhibited the desired multi-exponential de-

cay curve (with only weak cascading), whereas the

emission exhibited a zero ﬁeld quantum beat pattern

superimposed on its decay because of the anisotropic

excitation of that level. The quantum beats provided an

in-beam time base calibration which permitted this high

precision.

Part B 17.2

268 Part B Atoms

References

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17.2 L. J. Curtis: Atomic Structure and Lifetimes: A Con-

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17.4 J. E. Lawler, S. D. Bergeson, J. A. Feldchak,

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17.5 J. E. Lawler, S. D. Bergeson, R. C. Wamsley: Phys.

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17.7 S. Cheng, H. G. Berry, R. W. Dunford, D. S. Gem-

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17.10 L. J. Curtis: J. Phys. B 33, L259 (2000)

17.11 C. E. Tanner, A. E. Livingston, R. J. Rafac, F. G. Serpa,

K. W. Kukla, H. G. Berry, L. Young, C. A. Kurtz: Phys.

Rev. Lett. 69, 2765 (1992)

17.12 J. Jin, D. A. Church: Phys. Rev. 47, 132 (1993)

17.13 H. Winter, M. L. Gaillard: Z. Phys. A281, 311 (1977)

17.14 L. J. Curtis: Phys. Scr. 48, 599 (1992)

17.15 J. Lidberg, A. Al-Kahlili, L. O. Norlin, P. Royen,

X. Tordoir, S. Mannervik: Nucl. Instrum. Meth. Phys.

Res. B 152, 157 (1999)

17.16 H. Hartman, D. Rostohar, A. Derkatch, P. Lundin,

P. Schef, S. Johansson, H. Lundberg, S. Mannervik,

L.-O. Norlin, P. Royan: J. Phys. B 36, L197 (2003)

17.17 J. Carlsson, L. Sturesson: Z. Phys. D14, 281 (1989)

17.18 A. Gaupp, P. Kuske, H. J. Andrä: Phys. Rev. A 26,

3351 (1982)

17.19 J. Carlsson: Z. Phys. D9, 147 (1988)

17.20 U. Volz, M. Majerus, H. Liebel, A. Schmitt,

H. Schmoranzer: Phys. Rev. Lett. 76, 2862 (1996)

17.21 W. Ansbacher, Y. Li, E. H. Pinnington: Phys. Lett. A

139, 165 (1989)

17.22 R. N. Gosselin, E. H. Pinnington, W. Ansbacher:

Nucl. Instrum. Meth. Phys. Res. B31, 305 (1988)

17.23 J. Jin, D. A. Church: Phys. Rev. Lett. 70, 3213 (1993)

17.24 J. Carlsson, L. Sturesson, S. Svanberg: Z. Phys. D11,

287 (1989)

17.25 P. Kuske, N. Kirchner, W. Wittmann, H. J. Andrä,

D. Kaiser: Phys. Lett. A 64, 377 (1978)

17.26 J. Carlsson, P. Jönsson, L. Sturesson: Z. Phys. D16,

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17.27 E. H. Pinnington, J. J. van Hunen, R. N. Gosselin,

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17.28 H. J. Andrä: Beam–Foil Spectroscopy,Vol.2,ed.

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17.31 M. Dufay: Nucl. Instrum. Meth. 110, 79 (1973)

17.32 L. J. Curtis: Beam–Foil Spectroscopy,ed.by

S. Bashkin (Springer, Berlin, Heidelberg 1976)

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17.34 R. W. Dunford, H. G. Berry, S. Cheng, E. P. Kanter,

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Phys. Rev. A 48, 1929 (1993)

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Part B 17

269

Spectroscopy o

18. Spectroscopy of Ions Using Fast Beams

and Ion Traps

A knowledge of the spectra of ionized

atomsisofimportanceinmanyﬁelds.

A wide variety of light sources are avail-

able for the study of such spectra. In

recent years, techniques coming under the

broad headings of fast beams and ion

traps have been used extensively for such

studies. This chapter will consider the ad-

vantages each technique has for particular

applications.

18.1 Spectroscopy Using Fast Ion Beams ....... 269

18.1.1 Beam–Foil Spectroscopy............. 269

18.1.2 Beam-Gas Spectroscopy ............. 270

18.1.3 Beam-Laser Spectroscopy........... 271

18.1.4 Other Techniques

of Ion-Beam Spectroscopy.......... 272

18.2 Spectroscopy Using Ion Traps ................ 272

18.2.1 Electron Beam Ion Traps............. 273

18.2.2 Heavy-Ion Storage Rings ............ 275

References .................................................. 277

18.1 Spectroscopy Using Fast Ion Beams

A beam of ionized atoms has several advantages as

a spectroscopic source. Unlike arcs, sparks, and high

temperature plasmas, the ions can be studied in an envi-

ronment that is free of electric and magnetic ﬁelds and

relatively free of interparticle collisions [18.1]. Standard

accelerator techniques can be used to produce a well-

collimated, mass-analyzed beam of ions having a low

velocity spread. In principle, virtually any charge state

of any element, isotopically pure if required, can be

obtained. Finally, the well-deﬁned velocity of the ions

permits the study of processes evolving in time in terms

of their spatial evolution along the beam. This is partic-

ularly important in the case of lifetime measurements.

18.1.1 Beam–Foil Spectroscopy

A beam of ions passing through a thin (50–200 nm) foil

emerges in a range of ionization states, with the mean

charge state increasing with the incident energy [18.2].

Thin foils made from a light element, usually carbon, are

used to minimize particle scattering and energy strag-

gling. Thus, a F

beam of 0.5 MeV that enters a carbon

foil emerges with a mean charge of about +2e, while

a Xe ion beam at 180 MeV emerges with a mean charge

of about +29e. The outer electrons are distributed over

many different states, most of which then decay to lower

states by photon emission as the ions move away from

the foil. The beam-foil interaction is a highly nonse-

lective excitation process, which is an advantage for

spectroscopic studies but causes a problem for lifetime

measurements. (Methods for tackling this problem are

discussed in Sect. 17.2.2.) A major disadvantage of the

beam-foil light source is its low intensity; consequently,

scanning spectrometers have usually been equipped with

photon-counting detectors. In recent years, however, po-

sition sensitive detectors have become available, which

permit the simultaneous recording of information over

a wide spectral range, resulting in a greatly improved

detection efﬁciency (Sect. 44.4).

The intrinsic properties of the beam-foil interaction

are important in understanding its usefulness for spec-

troscopic studies. The electrons of the moving ion are

shielded from the travelling ion core as the ion passes

through the foil and are then recaptured into a statisti-

cal distribution of outer states. The probability that more

than one electron in a given ion will be captured in an

excited state is high relative to other light sources, and

hence the technique has been used extensively to study

doubly- and multiply-excited states [18.3] (Sect. 64.1).

The interaction also favours the production of high-L

Rydberg states [18.4](Chapt.14). At low incident ion

energies, electron capture can give a downstream beam

containing neutral and even negative ions. The ﬁrst ob-

servation of photon emission between bound states in

a negative ion was achieved using beam-foil excita-

tion [18.5]. A more recent example of multiple excitation

in a negative ion is the identiﬁcation in lithium-like He

−

of the 2p

state in which all three electrons are ex-

cited [18.6,7]. The observation of the same triply excited

level in neutral Li has resulted in one of the most pre-

Part B 18

270 Part B Atoms

cise (40 ppm) wavelength measurements in beam-foil

spectroscopy [18.8]. The time-resolution inherent in the

beam-foil source can also be used to aid in the iden-

tiﬁcation of transitions from long-lived states, such as

intercombination transitions [18.9] (Sect. 10.16). Here

the beam foil spectrum is ﬁrst recorded close to the

foil and then far downstream (a few mm to a few cm);

“far” in this context means that the short-lived states

have had time to decay. The intercombination (or other

long-lived) transitions are then easily identiﬁed by their

relatively strong intensity in the (overall much weaker)

downstream spectrum. This has been a decisive step

in identifying laboratory lines with lines in the so-

lar corona [18.10, 11]. A recent example of beam-foil

spectroscopic analysis is given in [18.12].

One problem with using fast ions as a light source

for precision wavelength measurements is the inevitable

Doppler broadening of the spectral lines. However, this

can be removed by appropriately refocusing the spec-

trometer [18.13, 14]. Furthermore, since the Doppler

width varies with the wavelength, and the line width

of a given grating spectrometer used on a fast ion beam

usually is dominated by spectrometer geometry, not by

diffraction, Doppler broadening often becomes less im-

portant in measurements at shorter wavelengths, as in

the UV or EUV. This is the primary range of emission

from the more highly-ionized atoms, and that is where

beam-foil spectroscopy really comes into its own. For

example, the leading terms omitted in calculations of

the wavelength of the 1s2s

S − 1s2p

transition in

He-like ions [18.15] scale as Z

, with the result that

measurements made with higher-Z ions need not have

as high a precision for a meaningful test of the calcula-

tion as would be required for a low-Z ion. The beam-foil

measurement for the leading (J = 1toJ = 2) com-

ponent in Ni

26+

[18.16] has an uncertainty of 0.02%,

which is about equal to that in the calculation. The two

values agree well within this limit. (Naturally, measure-

ments made using the beam-laser techniques discussed

in Sect. 18.1.3 yield results with a much higher pre-

cision, but such measurements are restricted to low-Z

ions because of the excitation energy steps and transi-

tion wavelengths involved; the theoretical uncertainties

in this case are also much smaller.)

Turning now to beam-foil lifetime measurements,

here the intensity of a given transition is studied as

a function of the time that has elapsed since excita-

tion, usually by stepping the foil upstream. Because

of the nonselective nature of the excitation, the possi-

bility exists that the state being studied is itself being

repopulated by higher-lying states, resulting in a de-

cay curve that consists of the sum of exponential terms,

one term corresponding to the primary level being stud-

ied and the other terms to higher-lying levels involved

in repopulating that level. The analysis of such decay

curves can be problematic. Several computer routines

have been developed to tackle this problem, such as

Discrete [18.17]andHomer [18.18]. One useful trick

here is to record the decay curve for each of the ma-

jor transitions repopulating a given primary level and

then include the lifetimes obtained for those transi-

tions as ﬁxed parameters in ﬁtting the decay curves

for that primary level. A more rigorous method to in-

clude the decay data from the repopulating transitions

in the analysis of the primary lifetime is the ANDC

technique described in detail in Sect. 17.2.2. An addi-

tional problem may arise in the measurement of very

short lifetimes, which tend to be associated with short-

wavelength transitions for which no lenses are available

to focus the beam at the spectrometer entrance slit. The

observation region is then deﬁned by the spectrome-

ter aperture and extends for a ﬁnite length along the

beam that can be comparable to, or even greater than,

the decay length for that transition. Here it is nec-

essary to ﬁt the decay curve including the vignetted

region around the foil [18.19, 20]. Lifetimes in the

picosecond regime have been successfully measured

in this way.

18.1.2 Beam-Gas Spectroscopy

While the use of a gas target in place of a foil has

the obvious advantage that it cannot break, the loss

of a tightly-localized excitation region means that the

ﬁne time-resolution of the beam-foil light source is

largely lost. The beam-gas source, however, has two

main advantages. First, the passage of a beam of fast,

highly-stripped ions through a neutral gas results in the

production of recoil ions (Sect. 65.2) that are moving

very slowly relative to the beam ions, thus reducing the

Doppler broadening problem mentioned earlier. Sec-

ondly, it is possible to study details of the interaction

between the gas and beam ions, such as charge-exchange

reactions, as they occur, rather than merely observing

their consequences. Such experiments have experi-

enced a resurgence with the advent of the ECR ion

source [18.21, 22]. A recent example of such work is

given in [18.23].

When a fast beam of highly-charged ions passes

through a neutral gas, it leaves a trail of ionized gas atoms

in its wake. These ions recoil from the interaction re-

gion with relatively low velocities (v/c = 10

−4

–10

−5

Part B 18.1

Spectroscopy of Ions Using Fast Beams and Ion Traps 18.1 Spectroscopy Using Fast Ion Beams 271

Furthermore, the recoil velocities tend to be restricted

to a narrow range of angles approximately perpendic-

ular to the beam direction. Hence, observation of the

radiation emitted by the recoil ions transverse to their

motion, i. e., along a direction parallel to the beam,

gives a very low Doppler width, ∆λ

/λ being typi-

cally 10

−6

, the limit imposed by the thermal motion

of the target gas atoms. Recoil ion spectroscopy is

therefore a useful procedure for precision wavelength

measurements for highly-stripped ions, such as He-

like Ar

16+

recoil ions produced by a beam of 2 GeV

70+

ions [18.24]. The energies and charge states of the

recoil ions may be determined using standard time-of-

ﬂight techniques [18.25], and detecting the recoil ions

in coincidence with their progenitor ions yields infor-

mation on the dependence of the recoil energy on the

details of the ionizing collision [18.26]. In later de-

velopments, the differentially pumped gas target has

ﬁrst been replaced by a supersonic jet target which re-

duces the thermal motion of the target particles, and

then by a cold atom sample in an atom trap; replac-

ing optical detection by position-sensitive fast-timing

detectors for all collision products, the technique of

COLTRIMS (cold target recoil ion momentum spec-

troscopy) can now be employed to study the momentum

distribution of the collision partners (developed largely

by the groups of H. Schmidt-Böcking (Frankfurt) and

C. L. Cocke (Manhattan, Kansas)).

Measurements made on the projectile ions them-

selves also yield useful information about electron-

capture processes. The strength of such a process is

described in terms of its cross section (Sect. 63.1.2).

Recent work has shifted from measurements of the to-

tal cross section for electron capture to more detailed

studies of the individual capture channels [18.27]. Such

studies provide much more stringent tests of theoreti-

cal models of ion–atom charge transfer processes. They

often involve such techniques as spectroscopy of the op-

tical radiation or of the Auger electrons (Sect. 25.1.1)

emitted by the ions after electron exchange. This topic

is covered in Chaps. 51, 64,and65. A further example

is the study by Prior et al. [18.28] of the angular dis-

tribution of Auger electrons emitted by doubly-excited

states formed in hydrogen-like projectile ions with an en-

ergy of 40 keV, following double-electron capture from

target helium atoms. They found that signiﬁcant align-

ment of the magnetic substates of the projectile ions can

result from electron capture. Such anisotropies in the

Auger electron emission demonstrate the danger of using

single-angle measurements to determine cross sections.

18.1.3 Beam-Laser Spectroscopy

As for the beam-foil source, excitation of a beam of

fast ions by a transverse tuneable laser produces the

localized excitation required for high temporal resolu-

tion. Now, however, the excitation is highly selective,

permitting the population of just a single level. The

laser-induced-ﬂuorescence (LIF) signal as a function

of the distance along the beam from the excitation

region is therefore described by a single exponential

decay, for which an exact analysis with rigorous er-

ror bounds is possible. The restriction to levels that

can be accessed by electric dipole (E1) transitions from

the ground and metastable levels may be overcome by

combining laser excitation with a nonselective mode of

excitation, as in beam-gas-laser [18.29,30] or beam-foil-

laser [18.31] measurements. A discussion of precision

lifetime measurements using laser excitation of a fast

beam is given in Sect. 17.2.2. Here the discussion will

be limited to precision optical spectroscopy. Exam-

ples of precision beam-laser wavelength measurements

may be found in [18.32, 33]. A further example is the

measurement of the spin-forbidden 1s2s

–1s2p

interval in N

[18.34], where the experimental value,

986.321 (7) cm

−1

is in agreement with the calculated

value, 986.58 (30) cm

−1

[18.34]. An example of a sim-

ilar measurement in a molecular ion is given in [18.35],

while a recent study of the hyperﬁne structure in a rare-

earth ion is given in [18.36].

A major aim in beam-laser spectroscopy is to min-

imize the width of the LIF signal. The instrumental

linewidth of the laser itself can be reduced to below

1 kHz, so that the width of the LIF signal is usually

dominated by the velocity spread of the ions and by the

divergences of the ion and laser beams. The effects of

beam divergence can be minimized by using a collinear

geometry, in which the ion and laser beams are parallel.

If the angle between the ion and laser beams is θ,the

Doppler-shifted laser frequency, as measured in the ion’s

rest frame, is f

(1 − β cos θ), where f

is the laser fre-

quency and β = v/c and is much less than unity. Hence

the range in frequency resulting from a beam divergence

∆θ is given by f

β sin θ∆θ, which tends to zero as θ

tends to zero. One disadvantage of the collinear geome-

try is that, if the laser is brought into resonance with an

atomic transition by adjusting the ion velocity and/or the

laser frequency, the LIF signal is produced over the entire

overlap region between the ion and laser beams. The res-

onance can be restricted to a desired region by setting the

ion velocity to be slightly off resonance. The velocity can

Part B 18.1

272 Part B Atoms

then be adjusted locally for resonance with the laser by

passing the ion beam through a Faraday cage electrode

to which an adjustable voltage is applied [18.37, 38].

The width of the resonance signal here is usually dom-

inated by the spread in the ion velocity, c∆β, usually

arising in the ion source being used. The width result-

ing from a given ∆β can therefore be reduced by using

a higher ion energy. This is known as kinematic com-

pression. In terms of the ion energy E, the range in the

ion energy ∆E andtheionmassM, the Doppler width

of the LIF signal is given by f

∆E/(2Mc

1/2

, and

thus decreases as E is increased.

A more signiﬁcant improvement in frequency res-

olution is made possible by including rf resonance in

a laser double-resonance experiment. Here the ions are

brought into resonance with an off resonance laser using

two separate Faraday cage electrodes. The ﬁrst reso-

nance depletes the population in the ion state from which

excitation occurs, thus weakening the second resonance

signal. An rf ﬁeld is then applied to the ions between

the two electrodes. Tuning the frequency of this ﬁeld

over the region that corresponds to ﬁne- or hyperﬁne-

structure intervals in the ion can then repopulate the state

from which laser excitation occurs, thus re-establishing

the second laser LIF resonance signal. The width of

the resonance signal is now determined by the transit-

time broadening that results from the ﬁnite time spent

by the ions in the rf ﬁeld. For example, in the experi-

ments by Sen et al. [18.38] with a beam of

131

ions

at 1.35 keV, the width of the laser-rf double-resonance

signal was 59 kHz, compared with a width of 45 MHz

obtained using a single LIF resonance.

18.1.4 Other Techniques

of Ion-Beam Spectroscopy

Ion beams ﬁnd uses in many other applications, three

of the main areas involving storage rings (discussed

in Sect. 18.2.2), merged beams, and studies of the

ion-surface interaction at grazing incidence. Merged

beam experiments usually study recombination pro-

cesses involving electrons and atomic or molecular ions

(Sect. 54.1 regarding recombination processes). The

advantage of using merged beams is that the time devel-

opment of the processes may be studied spatially, while

maintaining a low relative velocity between the ions

and the electrons. This permits measurements at the low

energies of importance in studies of Rydberg state for-

mation and in some astrophysical applications. A very

different type of experiment studies the ion-surface in-

teraction using a well-collimated ion beam at grazing

incidence on a clean, ﬂat surface. Such experiments have

revealed very large atomic orientations [18.39]. This ori-

entation can be passed on to the nuclei of the atoms

via the hyperﬁne interaction, thus providing a source of

oriented nuclei.

18.2 Spectroscopy Using Ion Traps

A basic purpose of ion traps is to conﬁne ions to the ﬁeld

of view of detectors for time intervals that are longer

than the radiative lifetimes of long-lived atomic levels

of possible interest. At thermal energies, the ion veloc-

ities are large enough to leave a typical detection zone

within microseconds. Electrostatic (Kingdon), magnetic

(Penning), and radiofrequency (Paul) traps have served

for this task for decades (Chapt. 75), with recent addi-

tions to the armory by electrostatic mirrors of various

shapes [18.40,41]. Two trap varieties of particular inter-

est for spectroscopy, the electron beam ion trap and the

heavy-ion storage ring, will be treated in Sects. 18.2.1

and 18.2.2, respectively.

Collisions with the neutral atoms and molecules of

the residual gas cause charge exchange, and thus loss of

the ion species. Therefore, an ultrahigh vacuum is of pri-

mary importance. Over the last three decades the ﬁgure

of merit has moved from pressures of about 10

−8

mbar

to about 10

−11

mbar. Further improvements can be ex-

pected from working with traps at liquid helium temper-

ature; in fact, even ion traps as large as an ion storage ring

at Aarhus (Sect. 18.2.1) have been cooled considerably

to vary both the vacuum and the amount of blackbody

radiation experienced by ions in weakly bound states.

The energy steps in multiply charged ions are regu-

larly larger than what is available from lasers, at least for

excitation from the ground state. Hence, single-ion trap-

ping and laser spectroscopic investigation are rarely an

option for these ions; many ions are needed to provide

a sufﬁciently strong emission signal. The production of

quantities of multiply charged ions used to be achieved

by electron bombardment of a dilute gas inside the trap

volume, or by ablation from a surface. Evidently, this is

detrimental to any subsequent measurements, since the

residual gas is still present. Precision work like mass

spectrometry that exploits the ion cyclotron motion of

stored ions, or detailed studies of the radiative processes

(including the effects of the interrogating laser ﬁeld)

Part B 18.2

Spectroscopy of Ions Using Fast Beams and Ion Traps 18.2 Spectroscopy Using Ion Traps 273

in ions nowadays employ a sequence of ion traps. In

a ﬁrst trap, the ions of interest are produced and pos-

sibly cooled by laser light or other mechanisms, and

then, by applying electric ﬁelds, the ions of interest

are moved to a second trap that works under better

vacuum conditions or that can be more ﬁnely tuned.

In the same sense, a heavy-ion storage ring is being

fed by an isotopically pure, charge-state selected ion

beam. Any loss of ions, measured by whatever means,

is thus proportional to the loss of the ion species of

interest.

18.2.1 Electron Beam Ion Traps

Electron beam ion traps (EBIT) make use of the attrac-

tive potential of a high-density electron beam, as well

as of the space charge compensation that is provided

by the electron beam to any ion cloud already trapped.

Most electron beam ion traps generate the high-current

density electron beam by feeding the beam from an elec-

tron gun into a magnetic ﬁeld that then compresses and

guides the beam. In most cases, superconducting mag-

nets with ﬁelds of 3 to 8 T are being used, and current

densities of the order of 10

A/cm

are reached. This

high current density corresponds to an electron density

of the order of 10

/cm

. This low-density environment,

roughly comparable to tokamak discharges, is one of the

factors that renders the electron beam ion trap a very

interesting device for laboratory astrophysics. The mag-

netic ﬁeld helps to conﬁne any ion cloud that is produced

from the residual gas (or gas bled in) or from injected

low charge ions. However, the ions could move away

along the ﬁeld lines, if they were not stopped by poten-

tial barriers provided by electrically charged drift tubes.

Obviously, the basic design is the same as that of a Pen-

ning trap, with the permanent electron beam added. In

fact, EBIT with the electron beam on has been said to

operate in electronic trapping mode [18.42]; while the

same device with the electron beam off (“magnetic trap-

ping mode”) still works as a Penning trap. This option of

producing an ion cloud with intense electron bombard-

ment and then studying the ions without the electron

beam present is the basis for a variety of experiments on

charge exchange (CX) reactions and long-lived excited

levels [18.43](seebelow).

The ﬁrst working electron beam ion trap, EBIT-I,

has been set up at Livermore [18.44,45]. The successful

operation instigated an upgrade to SuperEBIT, the ﬁrst

such machine that was able to completely ionize all

naturally occurring elements [18.46]. Based mostly on

the Livermore design, some 8 to 10 EBITsarenow

either running or under construction around the world.

The EBIT operating principles have, for example, been

described by Currell [18.47].

Ionization of ions trapped in the combination of

electrical ﬁelds proceeds as long as the electron beam

energy is high enough to overcome the ionization poten-

tial. Thus, the highest charge state can be pre-selected

by the appropriate choice of the electron beam energy.

The technical effort required to reach, for example, bare

uranium in SuperEBIT is much smaller than in an ion

accelerator. In both cases the ionization is achieved by

frequent energetic collisions of ions with electrons. In

SuperEBIT, the ions are (practically) stationary, and the

design energy of SuperEBIT, 250 keV, is enough to re-

move even the last electron of uranium. At a heavy-ion

accelerator, the electrons are stationary (in a foil tar-

get), and the ions are fast. Consequently an ion energy

per nucleon that is higher by the proton/electron mass

ratio is required – some 500 MeV/amu. Such energetic

ion beams are only available in a few large accelera-

tor laboratories, whereas an electron beam ion trap with

its auxiliary equipment ﬁts into an ofﬁce-sized labora-

tory space. Of course, there are experiments that need

speciﬁc properties of either fast ion beams or station-

ary ions, so both types of devices have their speciﬁc

merit.

The ions in an EBIT are not only stationary in

the sense that they are localized in a cloud, and mov-

ing either way along the magnetic ﬁeld with the same

probability, but their energy (temperature) can also be

controlled by the height of the potential barriers. The

voltages on the conﬁning drift tubes are usually cho-

sen to be few hundred volts. This makes for barrier

potentials +qeU (charge state q, elementary charge

e, voltage U) that are higher for highly charged ions

than for low-charge state ions. This not only bene-

ﬁts the conﬁnement of highly charged ions directly;

light ions (residual gas or purposely bled in gases)

may become fully ionized by the collisions with the

electron beam and by charge exchange, but they still

have a larger chance to evaporate from the trap and

thus they cool the remaining ion cloud. Under typical

conditions, the ion cloud may have a temperature of

a few keV. This can be lowered by introducing a cool-

ing gas and by lowering the potential barriers. With

45+

in the trap, this has been demonstrated by re-

ducing the (thermal) Doppler spread of X-ray emission

lines until it was smaller than the natural line width

of the emitter, thus yielding a measurement of fem-

tosecond level lifetimes from highly resolved X-ray

spectra [18.48].

Part B 18.2

274 Part B Atoms

The other good level lifetime range of an EBIT

reaches from a few microseconds (limited by practical

switching issues) to many milliseconds. Under direct

optical (X-ray, EUV, visible) observation of a spectral

feature, the electron beam is used to produce an ion

cloud with ions of a desired charge state. When the elec-

tron beam is stopped, all direct excitation and prompt

emission ceases. Any later photon signal relates to de-

layed emission from long-lived levels, or from excitation

by charge transfer collisions (highly charged ions cap-

turing electrons from the residual gas atoms). CX is

an important loss mechanism, and the CX signal also

serves as a monitor of the number of ions remaining

in the trap. Owing to the excellent vacuum in cryo-

genic EBITs, trapping times of many seconds, if not

minutes have been observed [18.43]. The ion loss rate

is the major correction to the apparent decay time of

the delayed photon signal. For atomic level lifetimes

of a few milliseconds and less, this correction is small

(a few percent or less). EBIT lifetime measurements

that take this correction into account yield results that

agree with those from heavy-ion storage rings [18.49]

and that are, at uncertainties of 0.5% and less, remark-

–10

–20

–30

0 102030405060

He sequence M1 transition rate

Deviation from theory (percent)

Atomic number

TSR

EBIT

Slow

ion

beam

Fast ion beam

Fig. 18.1 The lifetime of the 1s2s

level in the He iso-

electronic sequence varies by 15 orders of magnitude from

He (about 6000 s) to Xe

52+

(a few picoseconds). The ﬁgure

shows the deviation of selected experimental results from

calculations, and indicates the dominant experimental tech-

niques for the various lifetime ranges. The consistency of

experimental results from a heavy-ion storage ring (TSR

Heidelberg) and an electron beam ion trap (Livermore

EBIT-II) with theory in the low-Z range is impressive.

(After [18.50]).

ably consistent with theory in a case for which the

theory can do very well (see Fig. 18.1). This observation

can be turned around and interpreted as a demonstra-

tion of the reliability of the experimental techniques

that then can be applied to more complex cases in

which theory evidently has problems (for examples,

see [18.50, 51]).

An EBIT is an excellent light source for precision

spectroscopy of highly charged ions because it not only

gives access to all charge states of all elements, but it

does so at low particle densities. Of particular inter-

est to precision spectroscopy have been the ions with

a single valence electron (Li, Na, Cu isoelectronic se-

quences) that are rather amenable to calculation. Such

spectra of ions up to Z = 60 or 70 have been meas-

ured at low-density plasmas like the tokamak, and they

have been found to agree well with theory. Higher

charge states were then reached in laser-produced plas-

mas (Sect. 44.1.2), but the wavelength results seemed

to deviate from the theoretical trend that had sup-

ported the tokamak results. There also were (very few)

high-nuclear charge Z data from fast ion beams. Elec-

tron beam ion trap data have now conﬁrmed that the

trend of the tokamak data was correct and that the-

ory [including second-order quantum electrodynamics

(QED) contributions] provides a good description of the

n = 3 (Na sequence) [18.52]andn = 4levels(Cuse-

quence) [18.53]uptoZ = 92, within the 40 ppm error

margin of the EBIT results for the heaviest Cu-like ions.

The agreement with theory for the Zn-like ions of the

same elements is much poorer. As the QED contribu-

tions are rather similar, this is a problem of theory with

the computational treatment of two (and more) valence

electrons in the same shell.

The atomic systems purportedly under best theo-

retical control are H-like ions, with only one electron

in total. In high-Z H-like ions, the lines of high-

est interest are in the hard X-ray range (n = 1−2),

or are severely lifetime-broadened (2s–2p) and in the

EUV. One line is in the visible (for a number of

ions), where it is accessible to high-resolution spec-

troscopy, and not even notably broadened, because its

upper level has a millisecond-range lifetime: the M1

transition between the hyperﬁne levels of the ground

state. For two isotopes (of Bi and Pb), this transition

has been induced by laser radiation in a heavy-ion

storage ring ([18.54], see below), and for 5 isotopes

(of Re, Ho, and Tl) emission spectroscopy at the Su-

perEBIT electron beam ion trap [18.55] was successful.

Using the ion cloud (with its cross section largely

determined by the electron beam diameter of about

Part B 18.2