(GSI-Preprint-96-50

Oktober 1996

PHOTOELECTRIC EFFECT IN THE RELATIVISTIC DOMAIN REVEALED BY THE TIME-REVERSED PROCESS FOR HIGHLY CHARGED URANIUM IONS

Th. Stohlker, P.H. Mokler, C. Kozhuharov, A. Warczak

( submitted to Comments on Atomic and Molecular Physics)

Gesellschaft fur Schwerionenforschung mbHPlanckstraBel • D-64291 Darmstadt • GermanyPostfach 110552 • D-64220 Darmstadt • Germany

0E98FI1O6IX*

KS002112552 R: FIDE00945081X

Photoelectric Effect in the Relativistic Domain Revealed by the

Time-Reversed Process for Highly Charged Uranium Ions

Th. Stohlker1*

Institut fur Kernphysik, University of Frankfurt, August-Euler- Strafie 6, D 60486 Frankfurt

and GSI-Darmstadt, Darmstadt, Germany

P.H. Mokler and C. Kozhuharov

GSI-Darmstadt, Darmstadt, Germany

A. Warczak

Institute of Physics, Jagellonian University, Cracow, Poland

Key Words: radiative electron capture, photoionization, spin-flip transitions, retardation,

highly-charged ions

Abstract

The photoelectric effect in the near relativistic energy regime of 80 to 350 keV is studied

by the time-reversed process in ion-atom collisions, i.e. by the radiative capture of a quasi-

free target electron. We review shell and subshell differential photon-angular distribution

studies of radiative capture into highly-charged uranium ions. The experimental data are

compared with exact relativistic calculations and give detailed insight into both the atomic

structure of high-Z few-electron ions and into the fundamental electron-photon interaction

process involved. In particular it is shown that the angular-differential measurements provide

a unique method to study the magnetic interaction in relativistic electron-photon encoun-

" e-mail address: t.stoehlker@gsi.de

1

ters. Spin-flip contributions which are difficult to observe for the photoelectric effect can be

identified unambiguously by this method.

1 Introduction

The atomic photo effect, i.e. the interaction of a photon with an initially bound electron, can be

considered as one of the most fundamental quantum-mechanical processes and has been studied

continuously since its discovery. With the third generation of high-energy synchrotron radiation

facilities a detailed investigation of photo-ionization (PI) seems now feasible even close to the

near relativistic regime where photon energies around 100 keV and above are involved. Here,

photon-electron interactions beyond electric dipole contributions are of special interest [1, 2],

In the near relativistic regime and for heavy atomic systems the magnetic interaction gains

importance for the PI process which leads to the appearance of spin-flip transitions between

the initial bound state and the final continuum state [3, 4]. These contributions reveal the role

which the electron spin plays in the PI process in a unique way and they are unambiguously

visible in the angular distributions. As can be deduced from angular momentum conservation,

non-vanishing cross sections at 0° and 180° can only be caused by such magnetic transitions [5].

However, for the high-energy regime the photon fluxes at synchrotron facilities are small and

- even more significant - the relativistic kinematics forces the photo-electrons towards forward

emission angles thus masking the details of the structure there. This is depicted in Fig. 1 where

the angular distribution of a photo-electron produced by the interaction between a 279 keV

photon and the strongly bound K-shell electron of uranium is given as an example. The dotted

curve (bottom part) represents the fully relativistic calculation of Ailing and Johnson [6] which

is compared with the non-relativistic approach (solid line) which treats the electron as a spinless

particle, but takes into account already the retardation of the photon plane wave [7]. In the

polar diagram shown at the top of figure 1, for clarity, only the non-relativistic result is shown

due to the large overlap with the relativistic distribution in that representation. This figure

demonstrates the difficulty in measuring higher order contributions to the photo-effect.

2

The fundamental interaction mechanisms between a photon and an atomic electron can also

be studied in the two time reversed processes, Radiative Recombination (RR) and Radiative

Electron Capture (REC), where a free electron or a quasi-free target electron, respectively, is

transferred via the photon interaction to the final bound atomic state [3, 8, 9]. In both cases

the photon carries away the difference in energy and momentum between the initial and final

electron state. Fig. 2 demonstrates quite clearly the equivalence of PI and REC (or RR). In the

atomic reference system the energy of the photon, ftw, is given by energy conservation:

hu = Ekin + Ebin (1)

where E*,„ and Et,„ corresponds to the kinetic energy of the free electron and to the binding

energy in its final atomic state , respectively. For the near relativistic case, we have for RR and

REC a fast free electron with respect to the atomic center, which for REC is a highly-charged

and usually fast projectile. Also, for REC, the electron to be captured is loosely bound to the

target atom at rest. Within the impulse approximation - an excellent approach at high energies

- the electron in its initial state is considered as free, with the momentum distribution given

by the Compton profile of its initial bound state in the target. Due to the equivalence of both

radiative effects (REC and RR), in the following the abbreviation REC will refer to both of the

processes.

In contrast to PI, its time-reversed analogon, the REC process gives access to investigate the

dynamics of electron photon interaction in simple and clean atomic systems at strong central

fields, i.e. to highly-charged ions at high atomic numbers Z. In particular, the capture into

bare very heavy ions can be studied without any electron screening problems. PI usually deals

with many electron systems (in general neutral atoms) which complicates the comparison with

theory. Moreover, PI normally is restricted to initially non-excited electron bound states. For

PI in relativistic encounters, the angular distribution of the emitted electrons is strongly shifted

into the direction of the incoming photon momentum due to retardation. This is equivalent to

the case of REC where the photon distribution is shifted towards forward angles with respect

to the velocity of the quasifree electrons. However, as the initial electron velocity is inverted in

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the projectile frame, the angular distribution of the REC photons is directed backwards in the

projectile system. It is the relativistic transformation of the photon distribution from the moving

system to the observer in the laboratory system which shifts the distribution forwards. In a first

approximation it completely counterbalances the strong backward directed angular distribution

in the projectile frame. Hence, for REC - at least into s-levels of the projectile - we expect a

preferred photon emission perpendicular to the projectile direction [10]. The difference in the

photon-angular distributions between REC in the projectile frame and REC in the laboratory

system is demonstrated in Fig. 3 for the case of 295 MeV/u U92+ ions assuming pure electric

interaction (projectile system (top) and laboratory system (bottom)) [7]. This corresponds to

an electron impact leading to an emission of a 279 keV photon (compare with the time reversed

process in figure 1). As depicted in the figure, the advantage of using the REC process for

investigating PI arises from the combination of the following transformations one has to apply:

(a) The time reversal (p' —> -p') which describes REC as time reversal of PI in the projectile

frame

O' = 7T — 0pi (2)

where p' denotes the momentum of the free electron in the projectile frame, 0pi is the angle

between the electron momentum p' and the photon momentum k'.

(b) The relativistic angle and solid angle transformations from the projectile frame (primed

quantities) to the laboratory system (unprimed quantities)

U!

cos O'

■yu(l - 0 cos 0)

cos 6-0 1-0 cos 9' (3)

dO.' _ 1dSl 72(1 - 0cosd)2 (4)

4

By applying the given transformations the desired angle-differential cross section becomes

dvREcjO) ^REc(^) dfi!

dn dsi1 <m' (5)

Taking into account the retardation contained in the photon plane wave e ,kr we expect the

following angular distribution in the projectile frame [7] (Fig. 3, top):

daREcW a s^n2(^)(6)dtl " (1 + /3cos(6')4'

Applying now the given transformations of all quantities into the laboratory system one finds

the simple angular-differential cross-section dependence [10] (Fig. 3, bottom), i.e.:

« »;„>(*). (7)

The polar angle dependent differential cross-section corresponds exactly to that of the completely

non-relativistic dipole-approach which results from neglecting the photon momentum (kr < 1)

as well as the fast electron velocity (v < c) [11]. This complete cancellation of relativistic and

retardation effects, which occurs within the non-relativistic approach applied for capture into the

K-shell, was originally predicted by Spindler et al. [10]. In fact, these predictions were verified

experimentally for 197 MeV/u bare Xe54+ projectiles by Anholt et al. [12]. For heavier systems

and even higher energies and also for states with angular momentum l > 0 this cancellation is

no longer valid as will be discussed in this article.

We review in this article the photon/bound electron interaction in the near relativistic regime

based on the equivalence by time reversal between PI and REC. REC is investigated for highly-

charged uranium projectiles in the energy range between 80 and 350 MeV/u. REC into the

projectile K- and L-shell is studied for initially bare ions, L- and M- shell REC is investigated

for initially He-like projectiles. In the next section the general features of REC into the ls^

ground state is considered; total and angular differential aspects are discussed. Here, special

emphasis is given to the relevance of the electron spin for the PI process. The section on L-

REC elucidates the role of the orbital angular momentum of the final state for radiative capture

(initial state for PI). The angular distributions for the different L-substates 2s1/2+2pi/2 and

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2p3/2 manifest a complete break-down of the electric dipole-approximation for describing the

details of the PI process. For completeness, in an additional section, the total angular emission

characteristics for capture into the M-shell is discussed. Moreover, the possible relevance of RFC

investigations for QED studies is discussed before the summary.

2 REC into the K-shell

In Fig. 4 an x-ray spectrum is shown, recorded for initially bare uranium ions at 358 MeV/u

under single electron capture conditions. The spectrum was taken at the heavy ion storage ring

ESR at GSI in Darmstadt [13] (for a review see e.g. Mokler and Stohlker [14]). Stored U92+

ions, permanently cooled by electron cooling, and exactly fixed to a well known velocity, capture

one electron in a N2 gas target. The down-charged U91+ ions are detected behind the next down

stream dipole magnet by a particle counter in coincidence with x-rays emitted from the target

area. For this purpose an intrinsic Ge(i) x-ray detector was used, installed at a laboratory angle

of 132°. The energies in the x-ray spectrum shown are transformed into the emitter frame in

order to correct for the large Doppler shift (red shift) observed in the laboratory system. The

most prominent x-ray line, at a photon energy around 320 keV, is caused by radiative capture

into the ls1y2 ground state. The relatively broad width of the line is due to the momentum

distribution of the quasi-free electrons bound in the N2 molecule. The shape of the REC line

can be well described by theory [13]. The line width decreases with decreasing projectile velocity.

At around 220 keV we find the radiative capture transitions to the uranium L-shell, at 200 keV

into the M-shell and so on up to the series limit (marked in the figure). The capture into

excited levels leads via cascades to the ground-state transitions which are denoted in the figure

as Lyman lines. Obviously, these lines are narrow (as compared to the REC line). Transitions

from the L-shell split into two lines, the Lytti- transition (2p3/2->lsi/2) and the Lya3 transition

(2pi/2—>• lsi/2) which is additionally blended with the 2si/2—»lsi/2 Ml decay. The splitting of

the Lya components reflects the fine structure in the L-shell of H-like U91+.

Given the emission characteristics for the different REC lines, the total shell-differential cross­

6

sections for REC can be deduced from the spectra. As charge exchange for high-Z ions and low

Z-target atoms is entirely dominated by REC, the measurement of the total electron pick-up

cross-sections reduces almost completely to an integration over the whole x-ray spectrum of

REC into all the empty projectile shells. Such measurements have been reported by Stohlker et

al. [13, 15]. There, in some analogy to the Sommerfeld parameter v {y = Z/v), a general scaling

parameter (adiabaticity parameter, rj) was introduced in order to compare the experimental cross

section data gained for various bare, high-Z ions in a unified way.

By using this parameter 77, a general scaling law for the total K-REC cross-section was also

established which was found to be in agreement with the predictions of the non-relativistic

approximation [16]. For not too high energies this scaling holds true even for the heaviest

projectiles. All the experimental data fall onto one common curve as predicted by the non-

relativistic dipole approximation based on Stobbe’s [8] treatment of the photo-ionization process,

assuming non-relativistic hydrogen-like wave-functions for the Is ground-state. Deviations occur

only at high projectile energies [13]. This good agreement found between the non-relativistic

dipole approximation and the correct relativistic description, for not too high energies, appears

to be a general feature of all photon-electron interaction processes [17]. It can be explained in

terms of an approximate cancellation among relativistic, retardation, and multi pole effects [18]

which, however, only occurs for bound s-states and for total cross sections.

This fortuitous cancellation of the various effects does not hold true for the angular differ­

ential aspects of the REC (PI) process. Looking into details of the angular distribution for

the heaviest projectiles one should be able to detect clearly the non electric (i.e. magnetic)

multipole contributions to the interaction. This is true, in particular, for very small and very

large observation angles whereas the regime close to 90°, used for the measurement of the total

K-REC cross sections, appears to be quite insensitive to such effects. The magnetic transitions

should show up unambiguously at 0° or 180° in the x-ray spectra. Only by taking into ac­

count the interaction of the electron magnetic moment with the magnetic field of the photon

the calculation produces radiation into 0° or 180° in the laboratory system. Up to now, we have

disregarded the electron spin. Taking into account the electron spin, the conservation of angular

7

momentum does no longer prohibit photon emission at 0° or 180° as a spin-flip mediated by

magnetic interaction can compensate the angular momentum carried by a photon. Therefore,

non-vanishing cross sections at forward and backward angles allow for a unambiguous identifi­

cation of the occurrence of spin-flip transitions. The relevance of such studies has been outlined

in detail by Eichler et al. [5] (see also Meyerhof and Eichler [19]). It is shown there, that the use

of any approximate wave functions such as provided by any Born type approximation give rise

to spurious spin-flip contributions. Consequently, measurements of spin-flip transitions provide

an extremely sensitive test of the wave functions used.

In Fig. 5 the angular distribution for REC into 295 MeV/u bare uranium projectiles is plotted

[13]. The magnetic transitions, corresponding to a spin-flip of the electron during capture,

contribute significantly in the forward directions [3, 13]. The hatched area shows the spin-flip

contributions to the angular distribution (full line). The non-relativistic approach is given by the

dashed line for comparison. In the upper part of the figure, the REC emission characteristics,

as predicted by the rigorous relativistic theory [3], is displayed once more in a polar diagram.

It is instructive to compare Fig. 5 with Fig. 1, where the same interaction in the time inverted

process governs the angular distribution of the photoelectrons. Due to the relativistic solid

angle transformation, the spin-flip contributions are clearly visible in the REC case (Fig. 5).

It is obvious that only in the case of REC spin-flip contributions can be investigated easily in

experiments. We are currently preparing K-REC experiments aiming at the identification of

these magnetic contributions at the heavy ion storage ring ESR. Here, relativistic conditions are

provided for both the initial quasi-free electron states and for the final bound states.

3 REC into the L-shell sublevels

The width of the Compton profile for the REC x-ray lines decreases for lower projectile velocities

in proportion to the scalar product of the momentum distribution of the electron in the target

and of the momentum of the projectile. In Fig. 6 an x-ray spectrum associated with one-electron

capture into initially bare U92+ ions is shown for projectile energies of only 68 MeV/u [20]. This

8

relatively low projectile velocity (compared to the charge state of 92+) was achieved in the

storage ring ESR by an active deceleration of U92+ ions initially stored at 358 MeV/u. Before

switching on the N2 gas jet target at the low ion energy, the electron cooling at the lower velocity

was switched on again. The spectrum shown in the figure was taken at 132° in the laboratory

and the photon energies given are already transformed into the emitter system. Compared to the

spectrum shown in Fig. 4, taken at the high injection energy of 358 MeV/u, the RFC lines are

shifted to lower photon energies. The K-REC line appears at around 165 keV; the L-, M-, and

higher-shell RFC lines are found approximately at 70 keV, 50 keV, and 40 keV, respectively. The

Compton profiles are now so narrow that the energy distribution of the L-REC photons splits

clearly into the fine-structure components with j = 1/2 and j — 3/2 corresponding to the Lya%

- Ly«2 splitting. In addition to the RFC and Lyman lines, characteristic x-ray transitions from

cascades to the L-shell show up at around 20 - 30 keV. These Baimer transitions are not only

fed by RFC to excited states. Non-radiative capture to those states contributes considerably

to the population of these high-lying levels at the low ion velocity used. Because the spectrum

shown was recorded in an experiment dedicated to measure the ground state Lamb shift, where

only three observation angles were used, an angular differential L-REC measurement was not

possible within this experiment. However, the spectrum clearly demonstrates the potential of

the ESR storage ring for such studies.

The photon-angular distribution of the two fine-structure components for RFC into the L-

shell was studied in great detail at the heavy ion synchrotron SIS using 89 MeV/u He- like

U90+ projectiles colliding with C target atoms [21]. By stripping at this energy, He-like ions,

which have an initially empty L-shell, can be produced in abundant quantities. This experiment

represents the first subshell resolved L-REC photon-angular distribution study and in particular

the first investigation of the photon-angular distribution for capture into a pure p-state.

By fitting the Compton profile to the two L-REC fine-structure components in the spectra

taken simultaneously at different laboratory angles, we get the photon-angular distributions

displayed in Fig. 7. In the figure both a representation in Cartesian and in polar coordinates is

given. In the polar diagram, for graphical representation, the j = 3/2 component is multiplied

9

by a factor of two. All the measured data points were also multiplied by one common factor of

0.65 to adjust to the results of rigorous relativistic calculations [3]. This is still within the total

absolute normalization uncertainty of the measurement.

The j=1/2 fine-structure component is the dominant REC contribution. Here, the radiative

capture to the 2slevel contributes mostly to the observed line. As in the case of the ls^

ground state, the angular distribution of the 2%i/2 L-shell REC photons does not vanish for

zero emission angle and is, additionally, more forward directed (see dotted-line). From the

non-vanishing contribution at 0° one may once more infer spin-flip contributions in the photon-

electron interaction. In contrast to the j = 1/2 distribution the one for the j = 3/2 component

shows a slight enhancement at backwards angles. It is interesting to note, that the photon

emission from the Pi/2 and p3/2 contributions shows quite similar patterns and intensities. In

both cases, the p-character of the bound wave-functions seems to be the dominant feature and

not the individual j value. In contrast to radiative capture into the K-shell of medium Z

ions [12], no approximate cancellation of the effects of retardation and Lorentz transformation

occurs for the p-levels. The 2si/2 and 2pj/2 substates add up to the measured j = 1/2 L-shell

REC component. An excellent agreement between measurement and relativistic theory is found

for both the fine-structure components [21]. The use of a non-relativistic treatment for the

time reversed photo-effect would yield strong deviations especially in forward and backward

directions.

4 REC into the M shell

With the same experimental set-up as for the L-REC investigations [21], the angular-differential

studies have been extended to radiative capture into the M shell of He-like U90+ projectiles at

89, 110, 124, and 140 MeV/u colliding with C target atoms [22]. As can be read from the region

between 30 keV and 70 keV shown in Fig. 8, the M-shell REC components for the different

subshells cannot be disentangled - even for the lowest projectile energy of 89 MeV/u. The

complete spectral region is fitted by folding the Compton profile to the expected REC transition

10

energies (for the details of the analysis we refer to Ref. [22]). From those fits the intensity for

the total M-REC emission under each observation angle can be deduced. For a projectile energy

of 110 MeV/u the resulting total M-REC photon-angular distribution is presented in Fig. 9.

For an absolute normalization, the experimental cross-sections were adjusted at 90° observation

angle to the theoretical prediction which is shown by the full line. The experimental emission

pattern agrees well with this fully relativistic theory [3].

The basic feature of the angular distribution is a slight asymmetry between forward and

backward emission directions, where forward angles are slightly preferred. In contrast to the

L-REC studies, the M-REC photon spectrum does not allow to distinguish directly between the

different fine-structure levels of the uranium M-shell. Comparing the predicted contributions

for the individual sublevels, the slight shift of the emission pattern into forward directions is

mainly caused by the dominant capture into the 3st/2 shell (compare the total M-REC angular

distribution in Fig. 9). This forward shift can obviously not be compensated by radiative capture

into levels with higher angular momentum, l > 0. According to the theory the emission patterns

for capture into the 3pj levels follow closely the one discussed already for capture into the 2pj

states. For the 3d, states the emission pattern is distinctly shifted to backward directions.

However, the contribution of the latter to the total M-REC is almost negligible.

It is obvious that for all the considered cases, the capture into the lowest angular momentum

states - nsj/2 levels - is preferred for the strong central atomic fields at adiabaticity parameters

r) > 1. At these adiabaticities capture into the lowest n levels dominate the total REC cross

sections. For radiative capture into exited levels (n > 2) the cross section decreases rapidly with

increasing angular momentum / of the final state. This can also be read from the intensity ratio

of the two Lya components, see e.g. the spectrum at 358 MeV/u for initially bare U92+ in Fig. 4.

There, ground state transitions from the j — 3/2 levels (Lyaj line) are strongly suppressed; this

is true including also cascades to the L-shell levels from REC into the M and higher shells. For

the spectrum at the lower impact energy of 68 MeV/u (Fig. 6), the intensity ratio for the Lya

lines changes dramatically, which is partially caused by non-radiative capture preferring high l

states and higher n shells. This experimental observation is currently being analyzed. In the

11

unambiguous case of high ion energy, the Lyai emission should show also an anisotropic emission

pattern, if the magnetic substates of the 2p3/2 level are populated non-statistically. From the

angular emission patterns of the characteristic x-ray lines the magnetic subshell population for

the initial REC process may be deduced. First results point to an appreciable alignment of the

2p3/2 level caused by REC [23].

5 Radiative Corrections

The electrons captured into the K-shell of initially bare U92+ for instance, are exposed in the final

bound state to a strong average central electric field of almost 10+16 V/cm. Here, fluctuations of

the virtual photon field have to be considered in addition. So, beyond the relativistically correct

treatment of the electron in the initial (free or quasi-free) and final (bound) state, and beyond

the inclusion of all the possible multipoles (electric and magnetic), the importance of possible

radiative corrections to the photoelectric effect is more than a legitimate question.

A theoretical study of radiative corrections to the atomic photoeffect has been reported by

Botto and Gavrila [24] (see also McEnnan and Gavrila[25]). Here, the QED contributions are

considered by a corrective factor [1 + (a/7r)<5] multiplied by the angular differential cross-section

for the photoeffect. The quantity S was derived in considering the lowest order in a and aZ

and was found to be always negative. It increases with the photon energy and also slightly with

the electron ejection angle. As a result the correction amounts to 0.2% for 100 keV and is as

large as 5% for a photon energy of 5 MeV. For completeness, in Fig. 10, the lowest order QED

corrections [24] are depicted (dashed curve) for the case of the photoeffect induced by a 297 keV

photon impact on the K-shell electron of H-like uranium (full line).

Within this lowest order approach the QED corrections appear to be independent of the

nuclear charge Z of the atom, i.e. the binding energy of the electron can be neglected with

respect to the photon energy. As such an approximation is known to be meaningless for high-

Z systems, e.g. uranium, more complete calculations are urgently needed. Note, that as a

consequence of the strong fields in high-Z systems, QED corrections in such atomic systems are

12

strongly enhanced. Therefore, quite appreciable corrections can be expected for high photon

energies and heavy Z systems which appear to be accessible by REC angular distribution studies.

Such experiments would provide an alternative approach for the test of QED in the domain of

strong electric fields and would constitute a very first study of dynamic QED effects in ion-atom

reactions.

6 Summary

In the present review the fundamental interaction process between an electron and a photon in

the presence of a strong central atomic field was discussed from the point of view of radiative

electron capture into highly-charged uranium ions in the near relativistic regime. The REC

cases studied with fast bare U92+ and He-like U90+ ions provide simple and clean atomic sys­

tems where the interaction can be studied without the additional electron correlation present in

dressed atoms encountered in photoionization experiments. Due to the partial cancellation of

the retardation and relativistic transformations from the emitting fast ion system into the labo­

ratory frame, the angular distribution of the REC photons is not squeezed strongly into forward

directions, as it is the case for photo electrons in the near relativistic regime (Fig. 1). Thus,

REC emission patterns are a very sensitive probe for deviations from pure electric multipole

interaction and give, additionally, detailed information on the subtleties of the relativistic wave

functions in the final bound states.

The structure of the photon spectra allows to clearly differentiate between radiative capture

into the ground state and into higher shells. It corresponds to PI of high-Z one-electron atoms

from the ground or from the excited levels. For the L-shell even the fine-structure components

are resolved in the REC spectra, which provides an additional differentiation among the j values

of the L-levels and 2pi/2 as well as 2p3/2). On the other side, the emission patterns of

REC photons are sensitive to the angular momentum l of the final bound state allowing to

disentangle REC contributions to the 2sj/2 and 2p1/2 levels. Even for the M-REC photon

distribution, the influence of the different l levels turns out to be obvious. Here, however, the

13

fine-structure components cannot be resolved in the photon spectra by any means. REC into

excited states is necessarily followed by characteristic x-ray transitions in a heavy few-electron

atom. The emission pattern of these characteristic lines gives additional information on the

magnetic sublevels populated by REC. This point is presently under investigation. In total,

REC into highly-charged heavy projectiles provides a unique tool to study state and substate

selectively the electron-photon interaction even for excited bound states.

Within a rigorous fully relativistic treatment of the photon-electron interaction, by including

all the possible multipole transitions, both total and photon-angular differential emission cross

sections can be well described by theory. The former non-relativistic approach gives already

a reasonable estimate for the total K-REC cross sections. A general scaling is applicable in

this approach, where the K-shell cross section is a function of the adiabaticity factor 77 only.

There is no way to describe correctly the details of the measured emission patterns within the

non-relativistic calculations. In particular, for photon emission in REC into final ns^ states

a non-vanishing emission is found around 0° and 180° which is not allowed in any kind of

electric multipole transitions. Here, the magnetic dipole transitions contribute significantly to

the photon-electron interaction. For a ls-electron this, corresponds to a spin-flip transition

which is a pure relativistic effect. The importance of these spin-flip transitions can be seen

clearly in Fig. 11, where the relative contribution of the magnetic transitions to the K-REC

emission pattern is plotted as a function of the observation angle. Especially at forward angles

the K-REC distribution is completely governed by spin-flip transitions. Similar findings can be

stated for REC into the s^ levels of higher shells.

For higher angular momenta /, in particular also for the 2pj states, the l value and not the

total angular momentum j determines the general shape of the emission pattern. For REC into

higher projectile shells (L, M, ...) the emission for capture into s-states is more forward directed,

whereas for capture into the p levels the distribution is slightly bent to backwards directions. The

calculated emission characteristics for capture into d levels already shows a strong preference

of backwards angles [22]. The subshell differentiation between the j = 1/2 and j = 3/2 is

displayed once more in fig. 12. Here, the intensity ratio R for x-ray transitions into the j = l/2

14

and the j=3/2 L-shell sublevels is displayed. Also in this case, the fully relativistic treatment

is in concordance with the experimental findings, whereas the non-relativistic approach which

considers retardation to lowest order [26], fails completely.

We emphasize that REC into highly-charged, heavy projectiles is a unique way to study via

time reversal the photoelectric effect under clean conditions in the near relativistic regime. As

has been shown within this report, the heavy ion storage ring ESR appears as an ideal tool

for this fundamental research even when the powerful possibilities of the most modern third

generation synchrotron facilities are kept in mind

7 Acknowledgments

The experiments reported here were done in close collaboration with A. Galius, G. Menzel, H -

Th. Prinz, P. Rymuza, Z. Stachura, and P. Swiat and with the members of the ESR team under

the leadership of B. Franzke. The fruitful cooperation with the members of the FRS group,

in particular with H. Geissel and C. Scheidenberger, is gratefully acknowledged. The authors

would like to thank J. Eichler, A. Ichihara, and T. Shirai for interesting discussions and the

close collaboration. We are grateful to R.W. Dunford for stimulating suggestions and helpful

comments on the manuscript.

Dedication

This review is dedicated to Prof. Dr. Peter Armbruster on the occasion of his 651/l birthday.

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17

Figure 1: Angular distribution of a photo-electron produced by the interaction between a 279 keV

photon and a strongly bound K electron of uranium. Bottom: The dotted curve gives a fully

relativistic calculation of Ailing and Johnson [6]. The solid curve is based on the non-relativistic

approach which treats the electron as a spin-less particle, however considers the retardation of

the photon plane wave [7].

Figure 2: Schematic sketch of the time reversed processes: a) the photoeffect (PI) and b) the

radiative electron capture (RFC).

Figure 3: Photon-angular distribution for RFC into U92+ ions at 295 MeV/u calculated by

assuming only electric interaction (top: projectile frame; bottom: laboratory system).

Figure 4: An x-ray spectrum for 358 MeV/u U92+ on is shown following electron capture into

the projectile. The data were taken at the ESR storage ring at an observation angle of 9=132°

(not corrected for detection efficiency). The x-ray energies in the emitter frame are given.

Figure 5: Differential K-REC cross sections for U92+ —collisions at 295 MeV/u. The solid

line gives the relativistic angular-differential cross-section predictions [3], The full area gives

the spin-flip contributions to the total distribution. The dashed line was calculated using the

non-relativistic dipole approximation (see Eq. (3)). At the top, the emission characteristic as

predicted by the rigorous relativistic theory is displayed in a polar diagram.

Figure 6: X-ray spectrum associated with capture for 68 MeV/u U92+ on N%. The data were

taken at the ESR storage ring at an observation angle of 9=132° (not corrected for detection

efficiency). The x-ray energies in the emitter frame are given.

18

Figure 7: Experimental angular distribution of L-REC radiation (full points) for REC into the

j = I2 levels a) 2s1/2, 2p1/2 and b) into the 2p3/2 state. The solid lines give the results of exact

relativistic calculations. In addition, the theoretical results for 2si/2 [dotted line in (a)] and for

2pi/2 [dashed line in (a)] are presented. In the upper part of the figure, the various contributions

are displayed in a polar diagram, where the 2p1/2 contribution is displayed by the shaded area.

For visual reasons, the 2p3/2 component is enlarged by a factor of two.

Figure 8: X-ray spectrum associated with capture for 89 MeV/u U90+ on C2 collisions. The

spectrum was taken at an observation angle of 6=135° (not corrected for detection efficiency).

The x-ray energies in the laboratory frame are given.

Figure 9: Experimental angular distribution of M-REC radiation (full squares) measured for

U90+ —► C collisions [22]. The theoretical angular distributions for capture into the various

sublevels are given separately by the full line. In the upper part of the figure, the various

contributions are displayed once more in a polar representation. For visual reasons, the 3d3/2,5/2

components are summed up and are, in addition, multiplied by a factor of two. The total M-shell

emission pattern is shown in addition.

Figure 10: Electron angular distribution produced by the interaction of a 279 keV photon with

a strongly bound K electron of uranium. The dotted curve gives the fully relativistic calculation

of Ailing and Johnson [6] whereas the dashed line depicts the size of the QED contributions to

the differential cross section as predicted by [24]. The latter approach is only correct to first

order in aZ).

Figure 11: Relative contribution R of the magnetic transitions to the emission pattern for REC

into the K-shell of U92 at 295 MeV/u [13].

19

Figure 12: Intensity ratio (see full points) for capture into the p3/2 state relative to capture to

the j=l/2 levels (2s!/2, 2px/2) as a function of the observation angle, measured for U90+ —> C

collisions at 89 MeV/u. The full curve gives the result of the exact relativistic calculations [3],

and the dashed curve gives the predictions of the non-relativistic dipole-approximation including

lowest order retardation effects [26].

20

90

Fig. 1

180 150 120 90 60 30

Observation Angle 0 (deg)

do/d£2 (barn/ster)

a) PI b) REC

CO

E L

Fig. 2

Zq+ + e" => Z(q"1)+ + h<x>

a) projectile frame

b) laboratory frame

Lorentztransformation

Fig. 3

500-

400-O CC

300 -

200-

100-

Energy (keV)

Fig. 4

90

150

180 150 120 90 60 30 0

Observation Angle 0 (deg)

Fig. 5

LymanBalmer

C 400-K-RECL-REC

^ j=3/2j=1/2

Energy (keV)

Fig. 6

89 MeV/u J=1/2

J=3/2( x 2)

180 150 120 90

LABObservation Angle 6

da/dQ (barn/ster)

L-REC600 -

400 -

X-Ray Energy (keV)

110 MeV/u

U90+

'^3/2+'^5/2

(X 2)

M-REC

o

Fig. 9

do/d

£2 (b

arn/

ster

)

da/d

Q (b

arn/

ster

)

QED contribution

180 150 120 90

Electron Emission Angle 0 (deg)

Fig. 10

Spin-Flip Contribution

30 60 90 120 150 180

Observation Angle (deg)

Fig. 11

Rat

io 2p

/ (2p

+ 2s

Observation Angle 0 (deg)

Fig. 12