Physica Scripta. Vol. 64, 237^244, 2001
Experimental Investigation of Radiative Decay Rates of Metastable
Levels in Eu II
D. Rostohar1, K. Andersson2, A. Derkatch3, H. Hartman4, S. Mannervik1, L.-O. Norlin5, P. Royen3, A. Schmitt6 and
X. Tordoir7
1
Atomic Physics, Stockholm University, S-104 05 Stockholm, Sweden
Department of Physics, Chalmers University of Technology and GÎteborg University, S-412 96 GÎteborg, Sweden
3
Physics Department, Stockholm University, PO Box 6730, S-113 85 Stockholm, Sweden
4
Atomic Spectroscopy, Department of Physics, Box 118, S-221 00 Lund, Sweden
5
Physics Department in Frescati, Royal Institute of Technology, S-104 05 Stockholm, Sweden
6
Fachbereich Physik, UniversitÌt Kaiserslautern, D-67663 Kaiserslautern, Germany
7
Physique Nuclëaire Experimentale, Universitë Lie©ge, B-4000 Lie©ge, Belgium
2
Received April 20, 2001; accepted May 23, 2001
pacs ref: 32.50.Cs
Abstract
9
The radiative lifetimes of the metastable a DJ (J ˆ 2^5) levels in Eu II have
been measured by laser probing of a stored ion beam. The lifetimes of all
four J levels are slightly above 1 s. A deviation from the expected energy
dependence of the decay rates for electric quadrupole transitions is observed
and discussed.
1. Introduction
The rare earth elements have very complex atomic structure
due to the open f-shell. The density of levels is very high
and the optical spectra are crowded with lines. Detailed
knowledge of the atomic structure and the spectra is still
limited for most rare earths due to the complexity. Di¤culties are present for theory as well as for experiments.
For theory the vast number of con¢gurations and mixing
between them require large-size calculations. In experiments, very high spectral resolution is needed to resolve different spectral structures.
Due to the dense optical spectra, rare earth elements are
presently often used for improving the light emission of
lamps and the understanding of the emission spectra is
consequently of great interest for application within the
lighting industry [1]. In astrophysics rare earth elements
are also of great interest. This is partly connected to the
e¡orts to understand the creation of heavy elements in different objects. Europium is mainly formed by rapid neutron
capture (r-process) and it is hence a valuable tracer for this
nucleosynthesis process in the chemical evolution of the
universe, see e.g. Refs [2^4]. In our laboratory, we previously
performed a study of isotope shift in Eu II [5] on request of
astrophysicists. In this case, the issue was related to an idea
to determine the age of the Galaxy from determination
of Th/Eu spectral line ratios (where Th is radioactive with
a half-life of 14 Gyr). This required detailed knowledge
of the hyper¢ne structure and isotope shift in an unresolved
Eu II line at 4129.7 Ð.
For many applications, not only the wavelength and the
assignment of transitions are needed, but also the transition
rate. In recent years, time-resolved laser spectroscopy has
been used to obtain lifetimes of levels in singly charged rare
earth elements (for Eu II see Refs [6^8]) (and also very
recently in doubly charged ions [8]). The lifetime of a level
# Physica Scripta 2001
is the inverse of the sum of the transition probabilities
for all possible decay channels. In order to determine
transition probabilities for individual transitions, the lifetime measurement has to be complemented by a measurement of relative intensities of all di¡erent decay channels.
This is a di¤cult task since it requires intensity-calibrated
equipment, often for large wavelength ranges. In combination with theoretical calculations, however, lifetime
measurements have turned out to be very valuable. A comprehensive compilation of lifetimes of levels in neutral
and singly ionized lanthanides has been given by Blagoev
and Komarovskii [9].
In recent years there has been experimental work devoted
to studies of metastable levels. Here, devices like ion traps
and ion storage rings have played a key role. The 3d 2D5/2
level in Ca II is one example of a level for which many different measurements have been performed (see Refs [10^12]
and references therein). This atomic system is ideal for
studies in traps, since it has very few low-lying levels and
laser cooling can be applied. Recent experiments show,
however, that also for a simple system like Ca II there
are systematic e¡ects that were originally not considered
[11,12].
It is well known that experiments where fast ion beams are
excited by collinear laser light can give very high spectral
resolution [13]. This is due to an e¡ect called kinematic compression [14] which reduces the Doppler width by orders of
magnitude. Thus, collinear laser spectroscopy has frequently
been used for measurements of hyper¢ne structure and isotope shifts. We have recently developed a laser probing technique for a stored ion beam that takes advantage of the
kinematic compression at the same time as lifetimes in
the millisecond to second range can be measured [15,16].
The laser probing technique in an ion storage ring has
the advantage of high e¤ciency, high selectivity and high
resolution, which make it possible to utilise the technique
for studies of ions with complex atomic structure. We have
recently used this method to determine lifetimes of metastable levels in Fe II [17]. Here, two of 62 metastable levels
were selected and their lifetimes of 0.23 and 0.53 s,
respectively, were determined. The success of the laser probing method for attacking complex structures has inspired
us to apply the technique to the rare earth elements. Here
Physica Scripta 64
238
D. Rostohar et al.
we enter an area of almost complete lack of information as
regards the lifetimes of metastable levels. To the best of
our knowledge, there are neither theoretical nor experimental determinations of lifetimes of metastable states in
rare earth elements except for Yb‡ [18,19]. This ion has been
studied in traps in relation to search for new frequency standards [19,20]. On the other hand, metastable levels in rare
earth elements have frequently been used in laser experiments in order to reach more high-lying levels.
Already a long time ago it was realised that forbidden
transitions could be used for diagnostics of low-density
plasmas. In astrophysics such transitions are frequently used
for determination of properties of astrophysical objects (see
e.g. Refs [21,22]). The forbidden lines in Fe II, which govern
the decay of the metastable levels mentioned above, have for
instance been observed as prominent emission lines in
spectra from astrophysical objects (see e.g. [23]).
The present experiment deals with the metastable a 9 DoJ
(spectroscopically denoted 4f7(8So)5d 9 DoJ ) levels in Eu II.
It has previously been found that these levels could be
populated directly in the ion source and that these levels
could be used for laser-induced £uorescence experiments
in order to determine atomic lifetimes [7] and hyper¢ne
structure [24^26]. In this experiment we have used the laser
probing technique to determine the lifetime of the a 9 DoJ
levels for J ˆ 2^5. Some of the most low-lying levels in
Eu II are shown in Fig. 1.
2. Experiment
Lifetime measurements by laser probing of a stored ion
beam were introduced on Xe‡ . Here hyper¢ne selective
measurements were performed in 129Xe‡ [27]. For the 5d
4
D7/2 level, a very strong hyper¢ne e¡ect on the lifetime
was found. Also other levels (not showing hyper¢ne dependent lifetimes) were measured [28]. The probing technique
was developed further with inclusion of di¡erent normalisation curves for treatment of systematic e¡ects. The technique was applied to the 3d 2D3/2,5/2 levels in Ca II [10]
Fig. 1. Schematic ¢gure showing the levels and transitions that are involved in
the present experimental study. The 9So4 level is the ground state of Eu‡ .
Note that every ¢ne structure level (J) is split
Wavelengths are given in A.
into a number of hyper¢ne levels not indicated in this ¢gure but partly
resolved in the experiment.
Physica Scripta 64
and it was found that the laser probing technique in a storage
ring was competitive with what could be achieved in ion
traps. The laser probing technique has been described in
detail in Ref. [15]. The accuracy of 5% obtained for the
Ca levels was limited by the uncertainty in the correction
for collisional destruction of the metastable ions, due to
interaction with the residual gas in the ring. This accuracy
is equal to what was obtained in traps for the 3d 2D3/2 level
for which laser cooling can not be applied, but lower than
for 2D5/2 for which cooling can be used. On the other hand,
the laser probing technique in the ring does not su¡er from
the systematic e¡ect present in laser cooling schemes, which
was originally overseen in the trap measurements [11,12].
For the corresponding levels in the homologous ion Sr II,
our measurements in the ion storage ring are the most accurate measurements presented so far [29,30].
The present experiment was performed at the CRYRING
facility of the Manne Siegbahn Laboratory in Stockholm
[31]. Solid europium was introduced in an oven of a
low-voltage electron impact ion source (of Nielsen type).
Argon was used as support gas in order to stabilise the discharge. Ions were extracted from the ion source, which is
placed on a 40 kV platform. The europium isotope with mass
151 was selected in a 90 bending magnet and this isotope
was injected into the ring. The stored ion beam current
was typically 1 mA. Since the ring has a circumference of
about 51.6 m and the revolution time for one turn is
0:23 ms, this beam current corresponds to slightly more
than 109 stored Eu‡ ions.
Laser light was obtained from a ring dye laser (Coherent
699-29, Autoscan) operated with the dye Rhodamine 6G
and pumped by an argon ion laser (Innova 400-25). The
cw laser light was focussed by a telescope and transported
by mirrors to one of the twelve straight sections of the ring,
where it was introduced into the ring and merged with
the ion beam. A small fraction of the ions produced in
the ion source were in the metastable a 9DJ levels. They
could be detected in the ring by laser probing utilising
laser-induced £uorescence. The metastable ions were
laser-excited from the metastable levels to the z 7PJ levels
(or, as given by the NIST data base [32], in jj-coupling:
4f7(8So7=2 )6p3/2 (7/2,3/2);J) and £uorescence at 3700^4000 Ð
was observed from the decay to the a 9S and a 7S levels
(Fig. 1). Fluorescence was collected perpendicularly by a
lens (f/1) and was detected by a Peltier-cooled photomultiplier (EMI 9789 QA) equipped with a coloured glass
¢lter that blocked scattered laser light. Local Doppler tuning
was used to localise the laser excitation in front of the
PM-tube [15]. This was achieved by letting the ion beam pass
axially through a cylindrical electrode, which was held at
2 kV, causing an additional Doppler shift of 10 GHz
at the present laser frequency. The laser power was
100^500 mW (depending on the wavelength). Highest £uorescence signal was obtained for a laser beam spot size of
about 10 mm in the interaction region. The magni¢cation
of the imaging lens system is close to 1:1, implying that
the optimal laser beam size matches the size of the
photocathode of the PM tube.
In the ion beam injection line, the ions have to pass
through the radio frequency quadrupole (RFQ), which
normally is used for acceleration. For 40 keV heavy ions
the beam velocity is relatively low and the RFQ can not
# Physica Scripta 2001
Experimental Investigation of Radiative Decay Rates of Metastable Levels in Eu II
be used for acceleration, but it is needed in a passive
o¡-resonance mode for focussing of the ion beam. We have
observed that the RFQ introduces a velocity spread, the size
of which is dependent on the power applied to the RFQ. The
Doppler Tuning Device (DTD) has a large diameter
(80 mm), which extends ¢eld gradient in the device compared
to the single pass experiments [36]. This gradient as well as
the RFQ e¡ect will limit the line width in the laser-induced
£uorescence spectra to about 300 MHz (which is still far
below the Doppler limit for a thermal light source).
A measurement always has to be started by ¢nding the
laser frequency, at which the desired transition occurs. This
is done by scanning the laser and search for £uorescence.
Due to the operation of the storage ring, this has to be done
in a special way (to avoid that the resonance frequency does
not coincide with the time when the ion beam is to be injected
or during beam dump). A special routine and tailored electronics have been developed to synchronise the scanning system of the laser to the ring operation.
With the laser set at resonance, lifetime measurements can
be performed by applying the laser light at di¡erent delay
times after injection of ions into the ring. The ions in the
metastable state are created in the ion source. The control
system of the ring governs the ring cycle, i.e. injection of
ions into the ring, storage in the ring and closing the ring
cycle by dumping the ion beam. The control system may also
be used to control the measurements. We let beam injection
de¢ne time zero. This event is used to trigger an electronic
delay unit (CAEN N938) or a VME-based data acquisition
and control system. These two alternative systems are used
to open a mechanical shutter to expose the ion beam for laser
light at a speci¢c time and duration [15].
The probing of the metastable level is destructive in the
sense that the laser will optically pump out the metastable
population and transfer the ions to the ground state. We
have chosen long exposure times in order to pump out
the metastable almost completely. In this way the measurement would not be sensitive to variations in the pulse length
(a jitter of about 0.1 ms in the pulse length of the mechanical
shutter has been observed). The £uorescence signal from the
PM-tube has been fed into a multichannel scaler (MCS) to
determine the time needed to pump out at least 99% of
the initial population. For Eu II a pulse length of 100 ms
was used for the probing.
A decay curve is obtained by a sequential variation of
delay times. Since every di¡erent point on the decay curve
corresponds to di¡erent ring cycles, the injected intensity
of ions in every cycle has to be monitored to permit
normalisation to intensity variations that may occur. After
another straight section in the ring a BaF2 scintillator detector has been mounted. This detector counts neutralised ions
[33] that will travel straight out of the magnet since the
charge has been lost. The intensity of neutralised ions is
proportional to the beam intensity. The signal from this
detector is used for two purposes. Firstly, the number of
counts within a ¢xed time interval gives a relative measure
of the injected beam intensity. This is the method used
for monitoring the number of ions injected in every cycle.
Secondly, the signal from the particle detector can be connected to a multichannel scaler (MCS) recording system.
From the decay curve of the ion beam intensity, the lifetime
of the stored ion beam can be determined. The ion beam
# Physica Scripta 2001
239
lifetime in the present experiment (40 keV Eu‡ ) was approximately 18 s. The pressure in the ring was about 10 pTorr.
It is not su¤cient to control the number of injected ions,
but of crucial importance is also to know that the relative
fraction of metastable ions keeps constant. For this purpose,
the £uorescence in every fourth (could be chosen freely) cycle
was recorded at a ¢xed delay time and stored separately
[15,30]. With constant beam current and constant metastable fraction, this signal should stay constant. If not,
the measured variations could be used for normalisation
of the decay curve. In the present experiment, these curves
were used for normalisation of raw data. The variations
were, however, found to be small, less than 5%.
In the early experiments on Xe [34] and Ca [10], it was
found that although the pressure in the ring is very low, there
was a substantial excitation to the metastable states by
collisions with the rest gas, thus giving rise to repopulation
of these states. A method for measuring such repopulation
curves was developed. Since the decay of the metastable ions
created in the ion source is to be studied, the metastable ions
excited in the ring have to be subtracted. In previous experiments on Ca II [10] and Sr II [30], such corrections turned
out to be important. If this e¡ect had been ignored in these
cases, the measured lifetime would have di¡ered by almost
10%. In the recent experiment on Fe II [17], repopulation
was found to be negligible. It was suggested that this could
be due to the large number of metastable levels present
in this ion, and that the repopulation was spread out on
all these levels and consequently only caused a minor,
not observable, relative population increase in a speci¢c
level. The same phenomenon was found in the present experiment on Eu II. An alternative explanation would be that the
collisional excitation cross section for Fe‡ and Eu‡ is much
lower, than for the elements studied previously. Only at
raised ring pressure, repopulation could be observed, and
in this case extremely weak.
Besides the radiative decay, the metastable states could
also be depopulated in collisions with atoms and molecules
in the residual gas in the ring. This e¡ect can be selectively
studied by variation of the rest gas pressure. Such pressure
variations are not easily performed in an ultra high vacuum
(UHV) system like the storage ring, in particular since
the relative rest gas composition should be maintained.
We have utilised a method where we heat one of the
NEG (non-evaporative getter) pumps. The NEG pumps
are the main pumps on the ring that keeps the UHV conditions. If such a pump is heated, the rest gas absorbed
in the getter material will be released and the pressure is
raised. Since only one NEG pump out of 50 is heated, pressure will only increase locally in one part of the ring. The
lifetime of the ion beam as well as the lifetime of the metastable state corresponds to very many turns of the beam
in the ring, and the locally raised pressure will correspond
to an average increase of the pressure in the whole ring. This
average pressure increase could be determined from the
shortening of the lifetime of the ion beam current intensity.
From a Stern-Vollmer plot, in which decay rate of the metastable state is plotted versus pressure, the pure radiative
decay rate could be deduced (as the extrapolated rate at zero
pressure). This was clearly demonstrated in Sr‡ for optical
pumping [29,30]. Here the collisional destruction was found
to contribute by 5% to the decay of the metastable level.
Physica Scripta 64
240
D. Rostohar et al.
Fig. 2. An experimental spectrum of the 4f7(8So)5d 9Do2 ^4f7(8So7=2 )6p3/2; J ˆ 4 transitions at 5818 A recorded in a separate single-pass experiment at a small
isotope separator as described in Ref. [34]. The spectrum contains 14 line [23], but the weakest cannot be observed due to low intensity and limited resolution.
Of importance in the present experiment is that the lines are grouped in a way that allows the lower levels to be measured separately.
For laser probing experiments on very small metastable
fractions in the ion beam, it is more di¤cult to obtain conclusive results from pressure variations. This is due to the
fact that raised pressure does not only decrease the decay
rate of the metastable state but it also increases the
repopulation rate. Because of these two counteracting processes it is more di¤cult to obtain very conclusive results.
For Ca‡ an indirect method [10,15] was used to deduce
an 8% contribution from collisional destruction. In the present experiment on Eu‡ , just as for Fe‡ , it was not possible,
within the statistical error, to determine any signi¢cant contribution from collisional destruction. The uncertainty in
this respect is included the uncertainty of the ¢nal result.
3. Measurements
Four (J ˆ 2 ^5) of the ¢ve ¢ne structure levels of the a 9D
term were investigated in the present experiment. To study
the ¢fth J ˆ 6 level it would have been necessary to change
dye in the laser, which was not possible in the present
experiment. Europium has two stable isotopes with mass
151 and 153, respectively, having about the same natural
abundance. Both isotopes has nuclear spin I ˆ 5=2, implying
that the spectra of both isotopes will exhibit hyper¢ne
structure. The lighter europium isotope, however, has a
magnetic dipole moment that is more than twice that of
the other [35]. Consequently, the hyper¢ne splitting for 151Eu
is larger than for the other isotope. The collinear laser probing technique has the potential of hyper¢ne selective
measurements as was demonstrated for 129Xe‡ [27]. If different J levels have di¡erent lifetimes (for instance due to
LS-mixing, J selection rules, . . .), the hyper¢ne interaction
may mix di¡erent J levels resulting in F-dependent lifetimes.
For the low-lying metastable levels in Eu II such hyper¢ne
e¡ects were not expected but nevertheless it was considered
essential to check this experimentally. Consequently, we
chose the lighter isotope for our lifetime studies, since it
was easier to perform hyper¢ne selective measurements in
151
Eu due to the larger hyper¢ne splitting.
Physica Scripta 64
The transitions investigated here, have been studied by
collinear fast ion beam laser spectroscopy by Arnesen et
al. [24]. With nuclear spin I ˆ 5=2 many hyper¢ne transitions will appear. For the multiplets studied here 14^16
components will be present. The line width of 100^150
MHz achieved by Arnesen et al. was not su¤cient to resolve
every single component in the multiplet. In the present
experiment it is only the lower metastable states that are
of interest. Since the hyper¢ne splitting of the lower metastable a 9DJ levels are larger than for the upper levels,
the multiplet will exhibit a gross structure with groups of
lines. Within each of these groups all lines have a common
lower level. This is illustrated in Fig. 2 showing results from
a separate measurement, which was performed at an isotope
separator (INIS) [36] at the Manne Siegbahn Laboratory in
advance of the ring experiment. In CRYRING the line width
of the laser resonances is presently limited to about 300 MHz
partly due to broadening of the velocity distribution in the
RFQ (see discussion above) and partly due to the big open
DTD used for local Doppler tuning. This resolution is,
however, su¤cient to resolve the hyper¢ne states of the
lower level.
Search for di¡erential hyper¢ne lifetimes was performed
by scanning the hyper¢ne multiplet at di¡erent delay times.
As mentioned above, special electronics has been developed
to synchronise the PC that controls the scanning of the laser
with the control system of the ring. Thus, laser exposure of
the stored ions can be delayed by a variable time from injection implying that the spectrum can be scanned at a variable
delay time. By comparing the relative intensities of di¡erent
hyper¢ne components for di¡erent delay times, di¡erential
hyper¢ne lifetimes would be detected. Spectral scans
recorded at di¡erent delay times for the transition at 5818 Ð
are shown in Fig. 3. No indication of variations in lifetimes
with hyper¢ne quantum number F could be detected and
therefore no hyper¢ne selective lifetime curves were
recorded. For lifetime measurement of the di¡erent J levels,
the laser frequency was set at a frequency within the
hyper¢ne multiplet that yielded highest £uorescence intensity.
# Physica Scripta 2001
Experimental Investigation of Radiative Decay Rates of Metastable Levels in Eu II
Fig. 3. Study of the hyper¢ne multiplet at 5818 A recorded in the storage ring
at di¡erent delay times after injection into the ring. The line width (FWHM)
at injection is slightly above 300 MHz, which is more than twice the line width
obtained for single pass (Fig. 2). This is due to the special conditions in the
ring measurements as discussed in the text. As the beam is stored in the ring,
collisions with the rest gas molecules will gradually broaden the ion beam
velocity distribution as seen in the ¢gure. Would hyper¢ne induced e¡ects
be present in the decay of the metastable levels, the relative intensities between
the peaks from di¡erent lower levels would change as the delay time is varied.
No such e¡ect was observed.
For the lifetime measurement the machine cycle was set to
6.4 s with ion beam dump after 6.0 s. The decay curve was
obtained by increasing the delay time by 100 ms for each
cycle. Every data set stored in the data acquisition system
contained 5 curves: the lifetime curve, the ion beam intensity
in the corresponding time interval, the integrated ion beam
intensity in a ¢xed interval, the £uorescence at a ¢xed delay
time every fourth cycle (for normalisation of metastable
fraction from the ion source) and the corresponding ion
beam intensity normalisation curve. An example of such
a data set is given in Fig. 4. Note that while the two upper
curves give the time dependence of the intensity, the three
lower ones give intensities in a ¢xed time window as a function of the ring cycle number. The part of the lifetime curves
recorded after beam dump is important since it make possible to distinguish between beam-dependent and beamindependent background.
The complete decay curve of the beam current intensity is
also simultaneously recorded separately for every cycle
# Physica Scripta 2001
241
Fig. 4. A typical data set obtained by the data acquisition system. On top the
raw data of the lifetime measurement of the metastable level by the probing
technique. Below is the beam current in the corresponding time window
(re£ecting the decay of the stored ion beam current). Next is a measurement
of the number of injected ions recorded during a ¢xed time interval (implying
that here, as well as for the curves below, the abscissa should just be interpreted as the cycle number). Finally the measurement of the injected metastable fraction is given and the corresponding particle normalisation.
Normalisation to the metastable fraction was obtained probing the £uorescence intensity at a ¢xed delay time every forth ring cycle.
by a multichannel scaler (MCS). The lifetime of the ion beam
in the ring was much longer than 6 s and in order to determine this lifetime, the cycle time was prolonged to permit
a separate measurement of this quantity. The beam lifetime
was found to be about 18 s. For every transition used for
lifetime measurement, we have also separately recorded
repopulation curves. Such curves are recorded exactly as
the lifetime curves except that an extra laser pulse is applied
immediately after injection in order to quench all metastable
ions produced in the ion source. This procedure is described
in detail in Ref. [15]. In the present experiment repopulation
was very weak and only for measurements at raised pressure
a signi¢cant contribution was observed.
4. Data analysis
The data analysis had to be performed in a number of steps
in order to take all normalisation curves into account.
Physica Scripta 64
242
D. Rostohar et al.
For measurements with signi¢cant repopulation (in the present experiment, only for raised pressure), these curves
had to be analysed ¢rst. This was done by ¢rst normalising
the curve to the number of ions injected in each cycle in
the ¢rst step. Since the ion beam was very stable, this
was only a minor correction. Then the repopulation curve
was ¢tted to two exponential functions (one growing and
one decaying). The ¢tted function was scaled by a factor
(usually very close to 1, if the same number of scans were
used) to let the tail of this curve coincide with the tail of
the decay curve. Then the scaled repopulation curve was
subtracted from the decay curve and a single exponential
was obtained (re£ecting the decay of the metastable states
created in the ion source). The £uorescence normalisation
curve was then ¢tted to a polynomial. Since the ion source
delivered a stable beam, this curve was essentially £at
and it was ¢tted to a linear function. This ¢tted function
was used to normalise the decay curve to the minor drift
in the ion beam intensity. Finally, a constant was added
to the normalised decay curve in order to restore the statistics of the initial curve.
The description above describes the general procedure for
how to compensate for repopulation and variations in beam
current. There are, however, two remaining problems to
treat. It has been found that there is an initial loss of ions
in the ring, which is much faster than the loss later in the
cycle where ions are lost according to a single exponential
decay (re£ecting the neutralisation rate) [10,30]. The amplitude of this initial transient loss has been found to depend
on the ion beam intensity and the ring parameters set. It
could be due to intra-beam scattering or some beam optical
e¡ects in the storage ring. This loss of particles also has
to be considered, when the radiative decay rate of the metastable state should be extracted. In principle, the contribution from this transient behaviour could be avoided by
starting the lifetime analysis later down on the decay curve
when this e¡ect has died out. That would, however, mean
that the part in the decay curve with good statistics would
be lost. Instead we have certi¢ed that the slope of the particle
curve in the part where the lifetime curve is recorded is much
steeper than in the tail (where the slope is determined by the
neutralisation rate). If we assume that the additional slope
in the beginning is of instrumental origin, it will be independent of the electronic state of the ion. Consequently, the loss
e¡ect could be compensated for by dividing the £uorescence
decay curve with the ion beam current decay curve. This procedure has been utilised here and resulted in an increase of
the lifetime with about 20%. In the data analysis also systematic studies of the extracted lifetime were performed
as a function of the start point for the ¢tting. This was done
both for normalised data and raw data. As expected,
normalised data showed a stable lifetime result, while the
lifetime becomes systematically longer for raw data as
the ¢tting started later down on the curve.
The other remaining problem to deal with is to distinguish
the natural radiative decay from collisional destruction
(deexcitation and neutralisation) of the metastable state.
As mentioned in the previous section, we were not able
to observe any signi¢cant change in the decay rate as the
pressure in the ring was increased to the extent that it
corresponded to an average increase of 60%. The uncertainty
in estimating this collisional loss is included in the estimated
Physica Scripta 64
uncertainty. Error bars should be considered as one standard
deviation and include statistical as well as estimated systematical errors as discussed in the next section.
5. Results and discussion
Some of the most low-lying levels in Eu II are shown in
Fig. 1. According to, for instance, Ref. [32], the lowest levels
are well described by LS-coupling. Among the ¢ve a 9 DoJ
levels, three are described as purely due to the given
LS-symmetry, while the two remaining (J ˆ 4 and 5) have
a 1% admixture by the a 7DoJ levels of corresponding J [32].
From the basic selection rules (see e.g. [37]), we see that electric dipole transitions (E1) from the a 9 DoJ to the ground
levels are strictly forbidden (no parity change). Within
LS-coupling, magnetic dipole transitions (M1) to the ground
state are forbidden as well. Electric quadrupole transitions
(E2) are, however, allowed to the ground level a 9So4 within
LS-coupling (D !S, spin conserved). Deviations from
LS-coupling may also open for E2 transitions to the a
7 o
S3 level. We conclude that the main decay mode for the
a 9 DoJ levels is by E2 transitions.
King published an extensive experimental study of arc and
spark spectra of europium in 1939 [38]. This spectrum
covered the region from 2100 to 10165 Ð and contained 3950
lines. The spectrum was analysed by Russell et al. [39] and a
large number of transitions were assigned in Eu II. The
transitions utilised in the present experiment, which are
given in Fig. 1, are among the strongest lines in King's
spectrum. The E2 transitions responsible for the decay of
the a 9 DoJ levels should appear in the near infrared wavelength region. From the a 9 DoJ level energies we calculate
the wavelengths down to the a 9So4 level to be: 8983.7, 9392.8,
9694.0, 9916.3 and 10075 Ð, respectively, for upper levels
J ˆ 6; . . . ; 2. King reported no lines at these wavelengths
(which could hardly be expected).
Since europium is almost exclusively created by rapid
neutron capture (r-process), astrophysicists have found
Eu II to be a very useful indicator for r-process sites [40,41].
Many stellar spectra exhibit Eu II absorption lines from
the a 9S4 and a 9DJ levels. In particular, the lines at 4129.7 Ð
(a 9S4^4f7(8So7=2 )6p3/2 (7/2,3/2); J ˆ 4) and 6645.1 (a 9D6^
4f7(8So7=2 )6p3/2 (7/2,3/2); J ˆ 5) are studied in relation to
spectral lines from other elements [42,43] that are created
by other processes. A number of allowed transitions between
the low-lying levels discussed in the present work have also
been observed in the solar spectrum (see e.g. Ref. [44]).
However, to the best of our knowledge, forbidden transitions in Eu II have never been reported, neither from astronomical observations nor from laboratory experiments.
In addition to the radiative decay of the a 9DJ levels to a
9 o
S4 by E2 transitions, there could be M1 transitions between
the J-levels within the a 9D term. In the non-relativistic limit,
in pure LS-coupling, the M1 transition probability will only
depend on the angular momentum quantum numbers and
the transition energy (to the third power) and the selection
rule is DJ ˆ 1. For splittings between adjacent J-levels
as large as corresponding to transition energies in the optical
wavelength region, such M1 transitions could have
probabilities of 1^100 s^1. In the present case of the a
9
DJ levels in Eu II, the splittings are only a few hundred
cm^1 (Table I) and the transition probabilities will be small.
# Physica Scripta 2001
Experimental Investigation of Radiative Decay Rates of Metastable Levels in Eu II
Table I. Experimental lifetimes and corresponding decay
rates for the a 9DJ metastable levels in Eu II.
J
Level energy [cm^1]
Lifetime [s]
Decay rate [s^1]
2
3
4
5
9923
10082
10313
10643
1.130.18
1.020.14
1.180.12
1.160.16
0.880.14
0.980.14
0.850.09
0.860.12
Fig. 5. Radiative lifetimes of the four di¡erent ¢ne structure levels measured in
the present work.
If we use the expression given by Curtis [45] (for nonrelativistic LS-coupling) we obtain the following rates:
410^3 s^1 (J ˆ 6), 210^3 s^1 (J ˆ 5), 0.910^3 s^1 (J ˆ 4)
and 0.310^3 s^1 (J ˆ 3). This rate is about three orders of
magnitude lower than the measured decay rate. Hence,
we do not expect a strong e¡ect from the M1 transitions
on the lifetimes of the di¡erent J levels.
Our results are given in Table I and in Fig. 5. All four
levels have lifetimes slightly above 1 s. There are neither
other experimental results nor theoretical values to compare
with. The conditions in the present experiment were more
demanding than in the previous experiment on Ca II [10]
and Sr II [30]. Thus, it is more di¤cult to perform a strict
error estimate in the present case. Instead we have to make
plausible assumption based on our experience in earlier
experiments as well as in the present. We consider the error
estimate described here to be conservative. The ¢rst contribution to the uncertainty is the statistical error, which is
obtained directly from the curve-¢tting program. The
magnitude of this error is about 5%. The normalisation procedure using the beam current decay curve (in the transient
part) described above, introduces an uncertainty that is hard
to estimate quantitatively. We consider that allowance for
25% uncertainty in this correction should make the procedure ``safe''. Since the correction itself is about 20%, the
uncertainty due to the correction contributes with about
5%. Finally, the uncertainty concerning contributions from
collisional destruction of the state has to be included.
The experimental investigation of this e¡ect was not very
conclusive in the present experiment. Low statistics in the
decay curve and repopulation make the error bars large
for the lifetimes here. In addition, it was hard to get an accurate measure of the relative pressure change. No signi¢cant
increase in the decay rate could be observed as the pressure
# Physica Scripta 2001
243
was raised by about 60%. Consequently, no correction
for collisional destruction was made but we include an
uncertainty due to this collisional e¡ect. Considering the
quality of our present results for base pressure and raised
pressure we assign an uncertainty of 5% of the ¢nal value
to this uncertainty. The magnitude of this error is also
reasonable in relation to the correction for collisional
destruction in Ca II [10] and Sr II [30]. The di¡erent errors
are added in quadrature.
As seen in Fig. 5 the lifetime of all J levels is within error
bars the same. This result is somewhat surprising. The decay
rate caused by E2 transitions scales with the transition
energy (E) to the ¢fth power. With the energy di¡erence
between the J levels studied here, the lifetime of the
J ˆ 5 level should be 30% shorter than that of the J ˆ 2 level
provided that the electric quadrupole matrix elements are
the same. For the J ˆ 5 level there is also the M1 decay
mentioned above, which is not present for the J ˆ 2. The
calculated strength of the M1 for J ˆ 5 of 0.004 s^1 is,
however, negligible compared to the error bars. The NIST
database indicates that the a 9Do4 and the a 9Do5 levels are
mixed with the 7DoJ levels (of corresponding J) by 1%.
The a 7DoJ levels are based on the same con¢guration as
the a 9 DoJ levels (4f7(8So)5d) and we expect the electric
quadrupole matrix element of the radial part to be the same.
The energy of the septet levels is, however, much higher (at
about 17000 cm^1) and due to the energy factor to the ¢fth
power, which gives an enhancement by a factor of 7,
the expected decay rate should be much higher for the septets
than for the nonets. With a 1% admixture a lifetime
shortening should be just on the limit to be observable
on the present level of accuracy.
To enhance the manifestation of deviation from an E5
dependence of the decay rate, we have scaled the decay rates
with this factor in Fig. 6 (by dividing the rate by E5). For a
strict E5 dependence, the points should line up horizontally
in such a plot. If a level has additional decay channels,
the corresponding point would raise to a higher level.
The interesting phenomenon is that the J ˆ 4 and J ˆ 5
levels are below the level de¢ned by the other two points.
Fig. 6. The decay rates of the ¢ne structure levels normalized to the transition
energy of the E2 transition to the ¢fth power. Would the rate follow this
expected power law, the points should line up horizontally as indicated by
the line. Including additional decay modes for J ˆ 4 and 5 as discussed
in the text, these two points would be expected to lie slightly above the line.
Physica Scripta 64
244
D. Rostohar et al.
This is just the opposite of what could be expected due to the
extra decay channels expected for these levels. We conclude
that the explanation for this unexpected lifetime trend
between di¡erent J levels should probably be sought in a
re¢ned theoretical structural analysis that includes all decay
modes, mixing and con¢guration interaction.
6. Conclusion
We have presented the ¢rst measurements of decay rates of
metastable a 9DJ (J ˆ 2^5) levels in Eu II. The decay rates
correspond to lifetimes of about 1 s. No theoretical values
are presently available for comparison. It is believed that,
for every J level studied here, the natural radiative decay
should be due predominantly to an E2 transition. The
expected characteristic energy dependence for E2 transitions
was, however, not observed. A thorough theoretical treatment of the electronic structure and transition probability
would be helpful for elucidating this issue.
Acknowledgements
Excellent support from the sta¡ of the Manne Siegbahn Laboratory has been
most valuable. Discussions with Professor Sveneric Johansson are gratefully
acknowledged. This work was supported by the Swedish Natural Science
Research Council (NFR). XT acknowledges ¢nancial travel support from
the Belgian National Fund for Scienti¢c Research (FNRS).
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# Physica Scripta 2001