Picosecond lifetime measurements in 109Cd and 110Cd

Nuclear Physics A 683 (2001) 157–181
www.elsevier.nl/locate/npe
Picosecond lifetime measurements in 109 Cd
and 110 Cd
S. Harissopulos a,∗ , A.Dewald b ,A.Gelberg b ,K.O.Zell b ,
P. von Brentano b ,J.Kern c
a Institute of Nuclear Physics, N.C.S.R. “Demokritos”, POB 60228, GR-15310 Aghia Paraskevi, Athens, Greece
b Institut für Kernphysik, Universität zu Köln, D-50937 Cologne, Germany
c Physics Department, University, CH-1700 Fribourg, Switzerland
Received 30 May 2000; revised 13 September 2000; accepted 26 September 2000
Abstract
Mean lifetimes of the lowest 6 yrast band members in 110 Cd and of 9 excited states in 109 Cd,
populated via the 100 Mo( 13 C, 3n/4n) reactions, have been measured using the Recoil Distance
Doppler Shift technique (RDDS). The data have been analyzed using the Differential Decay Curve
Method (DDCM). The E2 transition probabilities deduced from the data for the ground band of
110 Cd are in rather good agreement with the predictions of the U(5)-limit of the Interacting Boson
Model-1 (IBM-1). © 2001 Elsevier Science B.V. All rights reserved.
PACS: 27.60.+j; 21.10.Tg; 21.60.Ev
Keywords: NUCLEAR REACTIONS 100 Mo( 13 C, 3n/4n), E( 13 C) = 50 MeV, measured I γ , 109,110 Cd levels
deduced mean lifetimes τ and B(E2) values; Enriched target, Ge detectors, differential decay-curve analysis,
recoil distance Doppler-shift method; Comparison to theoretical predictions of intraband E2 transition strengths
1. Introduction
Gamma-ray spectroscopic studies have established for many cadmium nuclei spectra of
excited levels with very interesting features. These features can be summarized mainly in
two points.
Firstly, in almost every even even cadmium nucleus, a two-phonon triplet of states
with spin J = 0, 2, 4 has been found in the lowest part of their level scheme. These
findings have been the main argument for assigning a vibrational character to these
nuclei. Among them the nucleus 110 Cd has been characterized by Arima and Iachello [1],
as one of the best examples of nuclei resembling the U(5) symmetry of IBA-1. This
∗ Corresponding author. Tel.: +3016503493, Fax: +3016511215.
E-mail address: sharisop@mail.demokritos.gr (S. Harissopulos).
0375-9474/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved.
PII: S0375-9474(00)00473-5

158 S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181
assignment was based mainly on the excitation energies and branching ratios of the lowlying
collective states of 110 Cd. The U(5) properties of 110 Cd have been further discussed
by Kern et al. [2]. The “good” vibrational character of the even even cadmium nuclei has
been additionally supported by previous Coulomb excitation measurements [3–5]. Recent
studies in 108,110,112 Cd nuclei [6–9], in which the respective level schemes have been
extended to higher energies, have shown that their level spectra exhibit properties not only
of a quadrupole vibrator but also of a rotating deformed nucleus since sharp backbending
patterns have been observed to occur in some of their excited bands. These backbendings
indicate drastic structural changes along the yrast line of these nuclei, which could be
elucidated via lifetime measurements.
Secondly, in the odd-neutron 105,107,109 Cd isotopes Stromswold et al. [10] have observed
a strongly populated band consisting of I = 2 transitions built upon a 11/2 − state. Such
a band has been identified also in 111 Cd by Juutinen et al. [11]. Via the latter work the
level scheme of 109 Cd has been considerably improved. By extending the band built upon
the considered 11/2 − state to higher energies a sharp backbend has been revealed. The
members of the considered bands in 105,107,109 Cd have been interpreted in [10] to arise
from rotation–alignment coupling (RAC) [12] of one-quasiparticle to the even rotating
core states. However, Häusser et al. [13] have measured the mean lifetime of the respective
15/2 − state in 107 Cd and the resulting reduced transition probability B(E2; 15/2 − →
11/2 − ) has been found to deviate from the corresponding RAC value, being further
in very good agreement with the predictions of the so-called PVC model [14], i.e. the
model describing the coupling of quasineutron states to an anharmonically vibrating core.
Hereby, it has to be pointed out that the latter predictions-check is based on a single
experimental value. Hence, it would be very useful to measure the B(E2) values of the
rest of the I = 2 γ -transitions of the band in consideration and further derive systematic
information concerning the mean lifetimes of the similar excited states identified in other
odd-neutron isotopes such as 109 Cd.
The above mentioned features of the cadmium nuclei have motivated us to carry out
the present lifetime measurements in 109 Cd and 110 Cd nuclei, using the Recoil Distance
Doppler-shift method (RDDS) [15]. In 109 Cd the main goal was to measure mean lifetimes
in the band built upon the first 11/2 − state, whereas our aim in choosing 110 Cd is to follow
the evolution of the B(E2) values along its yrast line in order to test further the predictions
of the U(5) limit of IBA-1 in terms of transition probabilities.
2. Experiments
In the present work two independent experiments, namely a lifetime measurement
(RDDS) and an “intensity measurement”, have been carried out at the FN Van de Graaff
Tandem accelerator at the University of Cologne. In both measurements the respective
targets have been bombarded by a 13 C beam having an incident energy of 50 MeV. At
this energy, excited states in 110 Cd as well as in 109 Cd nucleus have been populated via
the 100 Mo( 13 C, 3n) and 100 Mo( 13 C, 4n) reactions, respectively. The intensity ratio of the

S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181 159
204 keV γ -ray (5/2 + → 3/2 + )of 109 Cd to the 658 keV γ -transition (2 + 1 → 0+ 1 )of110 Cd
was found equal to 4.2(2), i.e. the 4n-channel was the dominating reaction channel.
In the RDDS experiment, γ -singles spectra have been measured at different target-tostopper
distances by means of three Ge detectors, each having a relative efficiency of
about 18%. The detectors were positioned at angles of 0 ◦ ,55 ◦ and 160 ◦ with respect
to the beam axis. The distance between target and each detector was about 15 cm. The
energy resolution of the detectors was about 2 keV for the 1408 keV γ -rays of an
152 Eu-source. The counting rate was about 5, 7 and 8 kHz for the detector at 160 ◦ ,0 ◦
and 55 ◦ , respectively. The plunger apparatus used in the RDDS measurements is described
in [16]. In order to determine the absolute values of the target-to-stopper distances, and
further monitor their stability, the capacitance method [17] was used during the experiment.
Gamma-ray singles spectra were taken at 24 target-to-stopper distances d in the range
2.9 µm-8 mm. Fig. 1 shows three different γ -singles spectra taken with the detector
positioned at 0 ◦ at distances of (a) d = 6.1 µm, (b) d = 73.9 µmand(c)d = 8 mm. Hereby,
the Doppler-shifted and unshifted components of γ -transitions in the yrast line of 110 Cd
are labeled with the letters s and u, respectively. Numbers in parenthesis indicate the energy
in keV of the Doppler unshifted components of some γ -rays depopulating excited states
in 109 Cd nucleus, whereas the numbers 633 and 876 are the energies in keV of the 2 + 1 →
0 + 1 and 4+ 1 → 2+ 1 γ -transitions of 108 Cd nucleus which is also produced due to a small
admixture of 98 Mo in the target. Peaks indicated as [x] are mainly γ -rays due to activation.
Fig. 1. Gamma-singles spectra measured at different plunger distances d with the Ge detector placed
at 0 ◦ with respect to the beam axis (see text).

160 S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181
Table 1
Experimental details of the present RDDS and intensity measurements
Experiments Target Backing Stopper Beam stopper
RDDS 0.6 mg/cm 2 thick 2 mg/cm 2 thick 40 mg/cm 2 thick
self supporting Ta foil Ta foil
100 Mo foil
Enrichment: 98%
Intensity 0.6 mg/cm 2 thick 4.3 mg/cm 2 thick 93 mg/cm 2 thick
measurement 100 Mo foil rolled on Au foil Bi foil
Au backing
Enrichment: 98%
In the “intensity measurement”, γ -singles spectra were taken by means of one Ge
detector placed at 55 ◦ with respect to the beam axis, in order to determine the relative
intensities of the γ -rays deexciting the levels of interest. Details on the targets, stoppers
and beam stoppers used in both experiments are given in Table 1.
3. Data analysis
The data have been analysed according to the so-called Differential Decay-Curve
Method (DDCM), which has been proposed [18] for determining mean lifetimes from
plunger data. DDCM has been further extended in [19] so as to be applicable also
to Doppler-Shift Attenuation Method (DSAM) [15] measurements. Hence, DDCM has
been proved to be a general and a reliable method of analysis of Doppler-shift timing
experiments. As DDCM is discussed in details elsewhere [18,19], in the present paper
only the last step of this method is outlined.
According to DDCM, one can determine at every target-to-stopper distance x a mean
lifetime τ for the excited state of interest, by using the following equation:
[
( ∑
τ(x)=− Q ij (x) − b ij
h
(
Ihi
I ij
)
Q hi (x)
)]/[
v · dQ ij (x)
dx
]
. (1)
In order to understand the quantities used in Eq. (1), the schematic decay pattern shown
in Fig. 2 is necessary. Hereby, a level L i is fed from levels L h by γ -transitions noted here
as (L h → L i ). Level L i is further deexcited to levels L j via the γ -transitions (L i → L j ).
Hence, Q ij (x) and Q hi (x) are the experimental decay curves of the depopulating
transitions (L i → L j ) and the populating transitions (L h → L i ), respectively. The quantity
b ij is the branching ratio of the transition (L i → L j ) in consideration and v is the mean
velocity of the recoiling nuclei. Furthermore, I hi and I ij are the intensities measured at 55 ◦ ,
i.e. in an intensity measurement, for the respective γ -rays (L h → L i )and(L i → L j ). The
quantity dQ ij (x)/dx is the first derivative of the experimental decay curve Q ij (x).Eq.(1)
holds only when the decay curve Q ij (x) is defined as:

S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181 161
Q ij (x) =
Fig. 2. Schematic decay pattern of an excited nucleus.
U ij (x)
U ij (x) + S ij (x) , (2)
where U ij (x) and S ij (x) are the intensities of the Doppler-unshifted and Doppler-shifted
components of the γ -transition (L i → L j ), respectively. These components are often
called “stop” and “flight” peak, respectively.
The intensities I hi and I ij as well as the branching ratios b ij involved in the analysis
(see Eq. (1)) have been determined in the intensity measurement mentioned above. The
RDDS γ -singles spectra accumulated here were normalized to the intensity of the 260 keV
γ -ray of 109 Cd nucleus. The latter transition depopulates a very long lived 11 − /2isomeric
state with T 1/2 = 8 µs [20]. The intensities U ij (x) and S ij (x) used in Eq. (2) have
been determined from “difference spectra” according to the procedure described in [21].
“Difference spectra” have been obtained by subtracting each normalized spectrum i taken
at a distance d i from the properly normalized spectrum measured at the maximum targetto-stopper
distance d max . This subtraction leads to a smooth background over a wide energy
range in the resulting spectrum. The intensity of the remaining Doppler-shifted S ij (x) and
unshifted U ij (x) γ -rays have been simultaneously analysed in the difference spectra by
using the code LEONE [16,22]. The method of “difference spectra” simplifies considerably
the data analysis not only due to the resulting flat background but also because it enables to
detect contaminating lines by means of careful investigation of the (negative) stop peak and
the corresponding (positive) flight peak. Furthermore, the use of “difference spectra” has
the advantage of eliminating possible contributions in the stop peak intensities arising from
the fraction of the excited nuclei that decay already in the target. The determination of this
fraction is not a straightforward task. However, this effect can be checked by looking at the
spectra taken in large plunger distances for nonvanishing stop peaks of fast γ -transitions. In
case the fraction of the excited nuclei that decay already in the target is negligible, the stop
peaks of the γ -transition deexciting very short lived levels (τ

162 S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181
a v/c = 0.70(5)% was found. In addition, at large plunger distances no stop peaks have
been systematically observed for γ -transitions depopulating highly excited states mainly
of the 109 Cd nucleus.
As reported in [18] the first derivative dQ ij (x)/dx of an experimental decay curve
Q ij (x) can be either determined experimentally or it can be derived from the decay
curve Q ij (x) by calculating the first derivative dG ij (x)/dx of a continuously differentiable
function G ij (x),i.e.
dQ ij (x)
dx
:= dG ij (x)
. (3)
dx
The function G ij (x) is obtained by fitting several second order polynomials over
separate intervals to the measured Q ij (x) data points. In the present work, the quantities
dQ ij (x)/dx have been obtained via the latter (fitting) procedure. The experimental decay
curves Q ij (x) determined in the present work for the yrast band members up to 12 + 1 state
are shown in Fig. 3. The solid curves also shown in this figure represent the respective
fitted functions G ij (x) from which the derivatives dG ij (x)/dx, i.e. quantities dQ ij (x)/dx,
have been derived by using the code APATHIE [23].
From Eq. (1), it can be clearly seen that when analyzing plunger data according to
DDCM, one actually obtains a value for the mean lifetime τ of a given excited state at
each target-to-stopper distance x, i.e.asetofτ(x) data points, in the following called
“τ -curve”, is finally derived. This is actually the main advantage in applying DDCM
instead of carrying out a “conventional” data analysis, which is based on solving a set
of coupled differential equations (Bateman’s equations) for each excited level of interest.
When using DDCM the τ(x) data points obtained have to lie, within statistical errors,
on a straight line. Hence, when this is not the case, then either the decay curves have
not been corrected for various effects arising usually in plunger measurements (see, e.g.,
Ref. [24]), or other systematic errors are present in the data analysis. Decay curves have
to be usually corrected for relativistic aberration, solid angle and nuclear deorientation
effects. Furthermore, as shown in [25], systematic errors may arise in the analysis when
the contribution of the so-called side feeding, i.e. the feeding from continuum and/or by
unobserved weak discrete transitions, to the decay curves has not been assessed correctly.
In the present work, corrections due to relativistic aberration were negligible since the
recoil velocity v was small enough. In addition, the areas U ij (x) of the Doppler-unshifted
peaks were not affected by solid angle effects, since the stopper in the plunger device
was kept fixed during the experiment. As in the case of [26], the intensities S ij (x) of
the flight peaks have been affected by solid angle effects at target-to-stopper distances
x 1 mm. A reliable estimation of the influence of these effects on S ij (x) can be obtained
by comparing these intensities with the corresponding unshifted intensities U ij (x) in the
difference spectra: according to [21], in a difference spectrum the areas of U ij (x) and
S ij (x) are statistically equal, provided that stop and/or flight peak are not contaminated by
other γ -lines. This procedure has been followed in our case to correct, when necessary,
areas S ij (x). It has however to be pointed out that the values Q ij (x) measured for
x 1 mm were not significant in applying DDCM analysis.

Fig. 3. Experimental decay curves Q(x) (circles) measured in 110 Cd. The solid curves are the respective continuously differentiable function G(x)
obtained by fitting several second order polynomials over separate distance intervals. From the fitted G(x) functions the respective first derivatives
dQ(x)/dx := dG(x)/dx have been calculated and used to obtain the mean lifetimes by applying Eq. (1) and/or Eq. (6) (see text).
S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181 163

164 S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181
As pointed out in [27], nuclear deorientation is expected to have a significant influence
to the intensities of γ -transitions deexciting states with spin J 4. In addition, in the
case of E2 γ -transitions (J = 2) this influence is rather strong at 0 ◦ and rather weak
at 55 ◦ . Hence, the ratio of the decay curve of a given excited state derived at a certain
angle θ to this determined at 55 ◦ , provides a reliable check for possible influence of the
nuclear deorientation effect. In case this “anisotropy ratio” is constant, the decay curve
derived at the certain angle θ needs no corrections. In the present work, this check has
been partially hindered by the fact that during the experiment the detector placed at 55 ◦ has
provided spectra with long left tails in the γ -peaks, probably due to neutron damage, and
also irregular gain shifts, which in many cases occurred in the same single spectrum. Due
to these problems anisotropy ratios have been derived via following procedure: the “less
damaged” 55 ◦ -spectra, i.e. the γ -singles spectra including relatively short left tails and no
gain shifts, have been normalized to the 260 keV γ -transition of 109 Cd. From the latter
(normalized) spectra, the intensities of the unshifted peak of the 2 + 1 → 0+ 1
γ -transition
of the 110 Cd nucleus have been derived via a very careful integration procedure. This
procedure has also been carried out for the γ -singles spectra taken at 160 ◦ . Unfortunately,
the quality of the 55 ◦ spectra did not allow to obtain anisotropy ratios for the 4 + 1 → 2+ 1
γ -transition as well. In the following, the intensities of the unshifted peak of a γ -transition
i → j obtained from spectra normalized to the 260 keV γ -transition of 109 Cd, which have
beentakenatanangleθ, will be declared as R ij (x, θ). Hereby, it has to be pointed out that
R ij (x, θ) have not been determined from difference spectra like quantities U ij (x).
The intensities R ij (x, θ = 55 ◦ ) of the 2 + 1 → 0+ 1
γ -transition of 110 Cd have been
compared with the respective R ij (x, 0 ◦ ) and R ij (x, 160 ◦ ). The corresponding anisotropy
ratios are shown in Fig. 4. According to this figure, the decay curves determined at 0 ◦
and 160 ◦ are influenced from the nuclear deorientation effect at distances x 100 µm
and x 1000 µm, respectively. In addition, by fitting a single exponential function of the
form f(x)= a · exp(−x/τ R ) + c to the 0 ◦ /55 ◦ anisotropy ratio we obtained a relaxation
time-constant τ R = 410(120) ps. It has to be emphasized that the fit function used serves
only to correct the data measured at 0 ◦ , i.e. the data points of the decay curve determined
Fig. 4. Anisotropy ratios measured in the present work for the 2 + 1 → 0+ 1 γ -transition of the 110 Cd.
The solid curve shown in (a) has been obtained by the fitting of the single exponential function
f(x)= a · exp(−x/τ R ) + c to the data, which yielded a relaxation time-constant τ R = 410(120) ps.

S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181 165
at 0 ◦ have to be divided by the respective values f(x) yielded by the fitting procedure.
The fit function used does not necessarily describe in details the effect involved: the timeconstant
τ R could however serve for a comparison to other RDDS measurements in which
the nuclear deorientation effect has been taken into account in the analysis. Based on the
anisotropy ratios determined here, the data measured at 0 ◦ have been corrected as described
above. The resulting mean lifetimes were found to deviate less than 12% from the results
derived when no deorientation effect was taken into account. As the statistical errors of
most mean lifetimes obtained from our data analysis are much larger than 12%, it is rather
realistic to assume that, any uncertainties due to deorientation effects are not significant for
our final results.
In our analysis special care was focussed on side feeding: Its contribution to the decay
curves is according to [25] not à priori negligible, especially when the side-feeding
intensity Ii
sf of the level in consideration is not small enough, i.e. when Ii sf / ∑ j I ij 5%.
Quantity Ii
sf is calculated from the intensities I ij and I hi that have already been defined
above, according to the following equation:
I sf
i
= ∑ j
I ij − ∑ h
I hi . (4)
As shown in [25] the time distribution of side feeding of a given discrete level L i
is approximately the same as the average time distribution of the discrete γ -transitions
(L h → L i ) feeding this level. According to the findings of [25], the side feeding of level
L i can be simulated by an “effective” side feeding decay curve, noted here as Q sf
i (x),
which is to be obtained as the weighted average of the decay curves Q hi (x) of the discrete
transitions (L h → L i ) feeding the level L i . Hence, Q sf
i
(x) is to be calculated according to
the following equation:
∑
Q sf
i (x) = h I hi · Q hi
∑
h I . (5)
hi
The “effective” side feeding decay curve Q sf has to be taken into account when applying
Eq. (1). In this case and by taking into account Eq. (4), one obtains following equation:
[
( ∑
( ) (
Ihi
I
sf ) )]/[
i
τ(x)=− Q ij (x) − b ij Q hi (x) + Q sf
i
I
h ij I (x) v · dQ ]
ij (x)
ij dx
[ ∑ ]/[ ]
=− Q ij (x) −
. (6)
h I hi · Q hi
∑
h I hi
i
v · dQ ij (x)
dx
The relative side feeding intensities, i.e. the ratio I sf
i
/ ∑ j I ij , of all levels in 110 Cd and
109 Cd studied in the present work are given in Tables 2 and 3 respectively. As it can be
seen there, the side-feeding intensities of the ground band members of 110 Cd up to 8 +
state were small enough, so that the contribution of side feeding to the decay curves of
these states could be neglected. This, however, was not the case for the 10 + 1 and 12+ 1 states
of 110 Cd and for almost all levels of 109 Cd. For these cases an effective side-feeding decay
curve was calculated according to Eq. (5), and Eq. (6) has been further applied in order to
determine the respective mean lifetime.

166 S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181
4. Results
4.1. The nucleus 110 Cd
For the data analysis in 110 Cd, the level scheme reported in [8,28] has been adopted. Part
of this level scheme, in which all the γ -transitions involved in our analysis are included,
isshowninFig.5.Theτ -curves obtained for the yrast band members in 110 Cd are shown
in Figs. 6 and 7. As shown in these Figs. the τ(x)-values of all levels investigated, do not
indicate any systematic errors: the data points τ(x) lie indeed, within statistical errors, on
a straight line. Due to statistics, these errors are, especially in the case of 4 + 1 and 6+ 1 states,
relatively large. The mean lifetimes τ displayed in parts (c) of these figures have been
deduced as the weighted average indicated by a straight line of the respective τ(x) values.
The results are summarized in Table 2.
The mean lifetime of the 2 + 1
state (τ = 8.7(12) ps) determined here, is statistically in
agreement with that reported by Piiparinen et al. (τ = 9.2(6) ps) in [28] as well as that
adopted in the most recent data compilation of A = 110 nuclei (τ = 7.78(10) ps) [29].
For the 4 + 1
state, the DDCM analysis of our data yielded a mean lifetime τ = 1.0(5) ps.
The corresponding value in [29] is τ = 1.05(13) ps. It has to be noticed that the mean
lifetimes adopted in [29] for the 2 + 1 and 4+ 1
levels have been derived in Coulomb excitation
measurements. Our result for the 4 + 1
state is further in agreement with that obtained
recently by Lobach et al. (τ = 1.18 +0.32
−0.18 ) [30]. This applies also for the 6+ 1
level for which
Fig. 5. Partial level scheme of 110 Cd (from Refs. [8,28]). The width of the arrows represents the
relative intensity measured in the present work for the corresponding transition (see also text). The
excitation energy of each of the three different 8 + states is given in parenthesis. The mean lifetimes
or mean lifetime limits determined in the present work are also displayed.

Table 2
Mean lifetimes τ and B(E2) values determined in the present work for 110 Cd in comparison to other measurements. The excitation energy of the levels
is given by E x . The relative side-feeding intensity adopted in the DDCM analysis for the corresponding excited state is given by I SF . The energy of the
γ -transitions deexciting the levels is given by E γ . The spin and parities of the respective initial and final states are given by Ji π and Jf π respectively. I i→f
and b i→f are the relative intensities and γ -branchings, respectively, measured in the present work for the corresponding γ -transitions
Level I SF τ (ps) J π
i → J π f E γ I i→f b i→f B(E2) [W u]
E x (keV) (%) this work others a (keV) (arb. units) (%) this work others a
658 0.5(24) 8.7(12) 7.78(10) b 2 + 1 → 0+ 1 658 100 100 24(3) 27(1) b
9.2(6) c 23(2) c
1542 3.5(21) 1.0(5) 1.05(13) b 4 + 1 → 2+ 1 885 99.5(2) 100 48(24) 46(6) b
1.18 +0.32
−0.18 d 40(8) d
2480 2.4(22) 0.9(5) 0.58 +0.22
−0.13 d 6 + 1 → 4+ 1 938 82.1(1) 100 40(22) 62.3(175) d
3275 0.1(25) 1.5(5) 0.90(30) b 8 + 2 → 6+ 1 795 50.5(8) 100 55(18) 91(30) h
1.2 < ···< 4 d 44.0(238) d
3440 1.6 < ···< 4 d 8 + 3 → 6+ 1 960 7.4(10) 9.8(42) d
3611 20.2(36) 670(25) 670(35) e 10 + 1 → 8+ 2 335 40.5(9) 72(3) 6.6(4) 6.0(3) e
650(144) f 7.7(18) f
→ 8 + 3 171 11.5(13) 20(3) 45(5) 26(2) e
33.5(85) f
→ 8 + 1 424 0.9(3) 2(1) 0.05(2) 0.04(1) e
→ 9 − 265 3.4(5) 6.0(5)
0.054(18) f
S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181 167

Table 2 —continued
Level I SF τ (ps) J π
i → J π f E γ I i→f b i→f B(E2) [W u]
E x (keV) (%) this work others a (keV) (arb. units) (%) this work others a
4172 23.1(38) 11.4(6) 12.0(6) c 12 + 1 → 10+ 1 561 44.9(11) 100 41(2) 39(2) c
5026 < 4 2.0(2) c 14 + 1 → 12+ 1 854 34.5(12) 100 > 14 29(3) c
4078 < 5 1.0(3) c 10 + 2 → 8+ 2 802 10.0(5) 100 > 16 74(24) c
1.2 +0.5
−0.3 d 60.4(186) d
4889 2.0(2) c 12 + 2 → 10+ 2 811 10(3) 37(2) c
2540 0.90 +0.40
−0.25 d 5 − → 4 + 998 13.9(6)
2879 < 1250 750(40) e 7 − → 6 + 399 22.1(5)
866(144) f → 5 − 339 11(1) g > 1.2 2.3(3) e
1.6(3) f
3346 71(4) c 9 − → 7 − 467 14.3(10) g 15.1(9) c
a A recent data compilation can be found in Ref. [29].
b From Ref. [29].
c From Ref. [28].
d From Ref. [30].
e According to [30], after a reanalysis of the data of Ref. [28].
f From Ref. [32].
g Estimated value since doublet γ -line.
h B(E2) value calculated using the mean lifetime given in [29].
168 S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181

S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181 169
Fig. 6. DDCM analysis of the three lowest yrast states of 110 Cd. For a given level, the respective data
in (a) correspond to the numerator of Eq. (6), i.e. the time distribution of the “difference” between
the depopulation and the population of the level in consideration. Data in (b) correspond to the
denominator of Eq. (6) multiplied by −1, i.e. the opposite values of the first time derivative of the
respective decay curve. By dividing data points shown in a) by the corresponding data points shown
in (b) one obtains the τ(x) values shown in (c). The solid straight lines shown in parts (c) correspond
to the displayed mean lifetimes τ . These have been obtained by averaging the respective τ(x) values.
our analysis yielded a mean lifetimes of 0.9(5) ps, whereas Lobach et al. have derived
τ = 0.58 +0.22
−0.13 [30]. For the 8+ 2
state a mean lifetime of 1.5(5) ps has been here determined.
For this level, a τ = 0.9(3) ps has been adopted in the compilation of De Frenne and
Jacobs [29].
At this point it has to be mentioned that the presence of the 164 keV γ -ray, which
according to [28] depopulates the 8 + level at E x = 3440 keV excitation energy and feeds
the 8 + 2
state at E x = 3275 keV, was not present in our γ -singles spectra. Hence, no such
feeder was taken into account in the analysis of the latter state. Furthermore, in accordance
to [28], a 707 keV γ -ray depopulates an 8 + state at E x = 3187 keV and feeds the 6 + 1
level. In the γ -singles spectra taken here, this γ -transition is a member of a multiplet of
γ -lines, so that no decay curve could be obtained. Hence, it was not possible to consider
the 707 keV γ -transition in the analysis of the 6 + 1
level. From the intensity balance of this
state however (see Table 2), it can be seen that the intensity of the 707 keV γ -ray relative
to this of the 938 keV γ -transition (6 + 1 → 4+ 1
) is less than 2.2%. Hence, the mean lifetime
determined for the 6 + 1 state is rather weakly dependent on the decay time of the 8+ 1 level

170 S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181
Fig. 7. Same as Fig. 6 for the 8 + 2 ,10+ 1 and 12+ 1 states of 110 Cd.
at E x = 3187 keV, which is deexcited by the 707 keV γ -line: in case the latter feeder had
been taken into account in the analysis, one would have obtained a slightly shorter mean
lifetime τ for the 6 + 1
state. Such a decrease in τ of this state however would not have
changed the final conclusions concerning this level.
The mean lifetime determined in the present work for the 10 + 1
state (τ = 670(25) ps) do
not justify the findings of the measurement reported in [28], where a longer mean lifetime
(τ = 800(40) ps) was reported. However, a reanalysis of the data of the latter measurement
yielded according to [31] a mean lifetime τ = 670(35) ps, which is in excellent agreement
with our result, with which the findings of [32] (τ = 650(144) ps) also agree. The mean
lifetime of the 12 + 1
state measured in our work (τ = 11.4(6) ps) is statistically in agreement
with the respective mean lifetime reported in [28] (τ = 12.0(6) ps). For the 14 + 1
and the
10 + 2
levels only upper limits of τ 4psandτ 5 ps, respectively, could be determined in
the present work, since the decay curves of their precursor states could not be measured.
These upper limits have been determined by fitting a single exponential function to the
decay curves of the 854 keV and 802 keV γ -transitions, respectively. Here, it has to be
pointed out that the 637 keV γ -ray, which according to [28], deexcites the 10 + 2
level and
feeds the 8 + 3 level at E x = 3440 keV (see Fig. 5) was not present in our γ -spectra.
No DDCM analysis could be performed for the 7 − state since the 467 keV γ -ray feeder
from the 9 − level is a doublet and therefore no decay curve could be derived for the
precursor 9 − state. The fitting of a single exponential function to the decay curve of the 7 −

S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181 171
state yielded τ = 1050(100) ps. This, delayed feeding from the 7 − level has “obscured”
the decay curve of the 998 keV γ -transition deexciting the 5 − state. Hence, it was not
possible to extract a mean lifetime for the 5 − level.
4.2. The nucleus 109 Cd
In order to analyze the data concerning excited states in 109 Cd, the level scheme
reported by Juutinen et al. [11] has been adopted. Part of this level scheme is shown in
Fig. 8. Hereby, only the excited states and γ -transitions, which are relevant for our data
analysis, are included. The relative intensities of the transitions shown in Fig. 8 have been
determined from the γ -singles spectra taken in the present intensity measurement. In order
to facilitate the discussion, the level scheme shown in Fig. 8 has been arbitrarily divided in
level sequences labeled with numbers ranging from 1 to 7. The results of the present work
concerning the nucleus 109 Cd are summarized in Table 3. The corresponding τ -curves of
the DDCM analysis are shown Figs. 9–11.
Fig. 8. Partial level scheme of 109 Cd adopted from [11]. Only the excited states and γ -transitions,
taken into account in the data analysis, are shown. The widths of the arrows are proportional to the
relative intensities measured in the present work for the respective γ -transitions. The level scheme
has been arbitrarily divided in level sequences labeled with numbers ranging from 1 to 7. The mean
lifetimes or mean lifetime limits determined in the present work are also displayed.

172 S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181
Table 3
Mean lifetimes τ and B(E2) values determined in the present work for 109 Cd. The numbers in the
first column indicate the level sequences (see Fig. 9) in which the corresponding states are placed.
The rest notation is the same as in Table 2
Placed Level I SF τ J π
i → J π f E γ I i→f b i→f B(E2)
in E x (keV) (%) (ps) (keV) (arb. units) (%) [W u]
1 3911 < 19 25/2 + → 23/2 + 527 1.6(2) 28.9(44) a
→ 21/2 + 851 1.8(2) 32.5(37) >1
→ 23/2 − 1048 1.5(5) b 28.3(66) a
2 4725 < 4.5 31/2 + → 29/2 + 478 0.9(1) 13.0(11)
→ 27/2 + 785 6.0(2) 87.0(34) >16
2 3940 54.5(47) 5.5(5) 27/2 + → 25/2 + 415 4.8(1) 36.4(17)
→ 23/2 + 557 8.4(5) 63.6(46) 57(8)
2 3383 11.5(67) 17.5(13) 23/2 + → 21/2 + 324 4.2(2) 37.2(22)
→ 21/2 − 340 0.8(2) 7.0(14)
→ 19/2 + 441 6.3(5) 55.8(48) 51(7)
2 2942 19.2(20) d < 5 19/2 + → 17/2 − 776 1.2(2) 17.9(21)
→ 15/2 + 801 0.9(2) 13.4(31) >2
→ 19/2 − 1121 4.6(2) 68.7(37)
3 4247 < 5.5 29/2 + → 25/2 + 722 10.1(2) 100 > 25
3 3525 23.8(27) 17.5(17) 25/2 + → 21/2 + 466 13.5(4) 69.5(27) 48(6)
→ 23/2 − 663 5.9(1) 30.5(10)
3 3060 1.4(35) 1.2(7) 21/2 + → 17/2 + 372 0.4(1) 2.0(2) 62(37)
→ 19/2 − 1238 19.7(8) 98.0(34)
4 2862 30.1(23) < 1.7 23/2 − → 19/2 − 1041 28.4(5) 100 > 13
4 1821 20.6(27) 0.85(20) 19/2 − → 15/2 − 836 83.3(13) 100 76(19)
4 986 8.6(26) 14.4(6)) 15/2 − → 11/2 − 522 100 100 47(3)
5 5280 46(16) < 11 29/2 − → 27/2 − 649 2.2(1) 63.4(97) a
→ 25/2 − 1249 0.4(1) 11.0(29) a
5 4631 62(18) < 6 27/2 − → 25/2 − 600 5.7(4) 66.2(96) a
5 4031 27.3(74) < 4 25/2 − → 23/2 − 482 3.5(2) 61.8(26)
→ 23/2 − 1169 2.2(2) 38.2(20)
5 3549 17.8(48) < 3 23/2 − → 21/2 − 195 1.3(3) 29.5(42)
→ 23/2 − 687 3.1(3) 70.5(47)
6 3043 84.6(80) < 5 21/2 − → 17/2 − 877 2.9(2) 55.8(43) >5
→ 19/2 − 1221 2.3(1) 44.2(35)
6 2974 < 11 21/2 − → 17/2 − 808 0.8(3) 29.6(66) >2
→ 19/2 − 1152 1.9(1) 70.3(55)
6 2166 39(5) 0.7(4) 17/2 − → 13/2 − 741 1.1(1) 19.0(15) 32(19)
→ 15/2 − 1181 4.8(1) 81.0(33)
7 3371 < 5 23/2 − → 19/2 − 780 2.1(3) 44.5(71) >7
→ 19/2 − 1549 2.6(3) 55.5(82) >0.2
7 2591 37(15) 1.2(5) 19/2 − → 15/2 − 1605 3.3(4) 100 2.1(9)
7 2867 1820(280) 21/2 (+) → 19/2 − 1045 6.7(8) 100
a Branching calculated including also γ -transitions either not displayed in Fig. 8 or not given in
Table 3.
b Estimated value since doublet γ -line.

S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181 173
Fig. 9. Same as Fig. 6 for some excited states of level sequences “2” and “3” of 109 Cd.
4.2.1. The level sequences “1”, “2” and “3”
In the level sequence “1” only the “effective” lifetime (in the following noted as τ e ), of
the excited state having spin J π = 25/2 + could be obtained: Due to statistics the decay
curves of the γ -transitions feeding into this state could not be derived from the spectra
measured. Hence, by fitting a single exponential function to the decay curve determined
for the 527 keV γ -transition, a τ25/2 e + = 13(3) ps was derived. According to this value, and
using the conventional 2σ -limits, the mean lifetime of this state has to be shorter than 19 ps.
The 851 keV and 1048 keV γ -rays deexciting the J π = 25/2 + level were not sufficiently
resolved in the γ -spectra. This was also the case for the 562 keV, 679 keV and 759 keV γ -
transitions, which depopulate the J π = 23/2 + state of sequence “1”. Consequently, the
intensities deduced via a gaussian fitting procedure for these γ -transitions were rather
uncertain. Due to these uncertainties, the DDCM analysis of the J π = 19/2 + state of
sequence “2” yielded only an upper limit for its mean lifetime: since the feeding from the
levels of sequence “1” into this state was rather uncertain, only the 441 keV discrete feeding
γ -transition having a relative intensity of 80.8(20)% has been considered in the analysis.
The feeding into the J π = 21/2 + state of sequence “3” arises mainly from the
deexcitation of the J π = 23/2 + and J π = 25/2 + states of sequence “2” and “3”
respectively: the relative total intensity of the 324 keV and 466 keV γ -transitions is
98.6(35)%, whereas the rest arises from the γ -rays depopulating the levels of sequence “1”.
Consequently, corrections due to the latter rather weak feeding from sequence “1” were
negligible. The DDCM analysis of the J π = 21/2 + state of sequence “3” yielded a mean
lifetime τ = 1.2(7) ps.

174 S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181
Fig. 10. Same as Fig. 6 for some excited states of level sequence “4” of 109 Cd. In the case of the
23/2 − state one can clearly see that not all τ(x)-values lie statistically on a straight line. This is due
to the fact that the strongest γ -transition feeding into this level could not be taken into account in the
analysis (see also text).
For the 23/2 + and 27/2 + states of sequence “2” the DDCM analysis yielded mean
lifetimes of 17.5(13) ps and 5.5(5) ps respectively, whereas for the 25/2 + level of sequence
“3” a mean lifetime of 17.5(17) ps has been derived. For the 31/2 + and 29/2 + states only
effective lifetimes have been obtained: due to statistics, the decay curves of their discrete
feeding transitions could not be extracted from the spectra measured. Hence, by fitting a
single exponential function to the decay curves of the 785 keV and 722 keV γ -transitions
we obtained τ e 31/2 + = 3.5(5) ps and τ e 29/2 + = 4.5(5) ps, respectively.
4.2.2. The level sequence “4”
In the DDCM analysis of the J π = 15/2 − state three discrete γ -feeding transitions,
namely the 836 keV, 1181 keV and 1605 keV γ -transitions, have been taken into account.
According to our intensity measurement these γ -transitions feed into the level considered
with a relative total intensity of 91.4(25)%. Here, it has to be mentioned that Juutinen et
al. have reported in [11] a 1701.8 keV γ -transition deexciting the 17/2 + state of sequence
“3”, which feeds into the 15/2 − level. In our work the latter γ -feeder was found to have
negligible relative intensity of less than 1%. Hence, a relative side feeding intensity of
8.6(26)% has been adopted. The DDCM analysis yielded a mean lifetime τ = 14.4(6) ps
for the 15/2 − level.
According to [11], the 19/2 − state of level sequence “4” is populated via several discrete
γ -transitions. Here, seven discrete feeders with a total relative intensity of 79.4(19)%have

S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181 175
Fig. 11. Same as Fig. 6 for some excited states of level sequences “6” and “7” of 109 Cd.
been considered in the analysis of this state. These feeding transitions are all shown in
Fig. 8. The remaining discrete feeding transitions reported in [11] were in our work rather
weak: their decay curves could not be obtained in the present work. Hence, they have been
treated as side feeding with a relative intensity of 20.6(27)%. The DDCM analysis of the
19/2 − state yielded a mean lifetime τ = 0.85(20) ps.
For the 23/2 − state of level sequence “4” only an upper mean lifetime limit was derived:
the strongest discrete feeder (1160 keV γ -ray from the 27/2 − state) was obscured by other
transitions in the γ -singles spectra. Hence, the decay curve of the latter feeding transition
could not be determined and its influence to the decay of the 23/2 − could not be assessed.
In such a case, as already shown in details in [18], the τ(x)values are expected to decrease
asymptotically down to a constant value, with increasing distance x. This was indeed
observed in the τ -curve of the level in consideration (see Fig. 10), which decreases down
to τ = 1.3(2) ps. This value yields an upper limit of 1.7 ps for the mean lifetime of the
23/2 − level.
4.2.3. The level sequences “5”, “6”, and “7”
Most of the γ -transitions shown in Fig. 8 for the level sequence “5” were not sufficiently
resolved in the γ -singles spectra. Consequently, the gaussian fitting procedure carried
out to determine their intensities and/or their decay curves yielded rather large statistical
errors. Due to these uncertainties several feeding assumptions have been tested in the
DDCM analysis of these states. Since the results were strongly influenced from the feeding
assumption used, only upper mean lifetime limits can be reported (see Table 3). A striking

176 S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181
Fig. 12. Experimental decay curve of the 21/2 (+) excited state of level sequence “7” in 109 Cd. The
data points are the intensity of the Doppler unshifted component of the 1045 keV γ -transition which
deexcites the level considered. The solid curve is obtained by fitting a single exponential function to
the data points which yields a mean lifetime of 1.82(28) ns.
feature of the decay curves measured for the members of this level sequence is that they all
have the same effective lifetime, i.e. τ e ≈ 9(1) ps. This may suggest that the mean lifetimes
of the levels considered are rather short, i.e. τ

S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181 177
5. Discussion
The B(E2) values determined in the present work for the lowest E2 yrast band
γ -transitions of 110 Cd are given in Table 2. The B(E2) values determined in the present
work for the 2 + 1 → 0+ 1 and 4+ 1 → 2+ 1
γ -transitions are in rather good agreement with
those reported in Ref. [29]. The latter B(E2) values have been determined in previous
Coulomb excitation measurements. In addition, the B(E2) values derived in our work for
the 2 + 1 → 0+ 1 and 4+ 1 → 2+ 1
γ -transitions are in rather good agreement with those reported
in Refs. [28] and [30], respectively.
According to the transition probabilities obtained in 110 Cd, an increase of the B(E2)
values occurs up to the 8 + 2
state at E x = 3275 keV. Above this level one distinguishes
between a “fast” and a “slow” pathway (see Fig. 5). The former proceeds via the
802 keV γ -transition, through which the 10 + 2
level is deexcited. For this γ -transition
Piiparinen et al. [28] as well as Lobach et al. [30] have reported high B(E2) values of
74(24) W.u. and 60.4(186) W.u., respectively. In the present work only a lower limit of
B(E2; 802 keV)>16 W.u could be determined. The “slow” pathway proceeds via the
335 keV γ -ray deexciting the 10 + 1
state. For the 335 keV γ -ray a B(E2; 335 keV) =
6.6(4) W.u. has been obtained in the present work. Above the 10 + 1
state the collectivity
“recovers”: a high transition probability of B(E2) = 41(2) W.u has been here determined
for the 12 + 1 → 10+ 1 γ -transition (E γ = 561 keV).
An interesting feature in the level scheme of 110 Cd, is the existence of three closelying
8 + states. These states are shown in Fig. 5, in which the respective excitation
level energies are given in parenthesis. According to [7,8,28] the lowest lying 8 + state
at E x = 3187 keV is fed by the 10 + stateviaa424keVγ -ray and is further deexcited to
6 + 1
state through a 707 keV γ -transition. The B(E2) value obtained here for the 424 keV
populating γ -transition is rather low: B(E2; 424 keV) = 0.05(2) W.u. This value clearly
indicates a significant difference between the configurations of the 8 + 1 at 10+ 1
states. On the
other hand the high transition rate (B(E2; 171 keV) = 45(5) W.u) determined here for the
171 keV γ -ray deexciting the 10 + 1 state and feeding into the 8+ 3 level at E x = 3440 keV
is a strong argument for assigning the same character in both states. Unfortunately, due to
statistics and the fact that the decay curve measured in the present work for the 960 keV
γ -ray (8 + 3 → 6+ 1 ) is “obscured” by the strong slow feeding from the 10+ 1
state, it was not
possible to extract a mean lifetime for the 8 + 3
level and further obtain the B(E2) value of the
8 + 3 → 6+ 1
γ -transition. However, Lobach et al. [30] have reported for this γ -ray a B(E2)
value of 9.8(42) W.u. which suggests different configurations for the 8 + 3 and 6+ 1 states.
In Fig. 13(i) the relative B(E2) values measured here for 110 Cd are compared with the
respective ratios predicted by the U(5)-limit of IBM-1. Hence, in Fig. 13(i), the ratios
[ B(E2; I → I − 2)
R = R exp. B(E2; 2 + 1
=
→ 0+ 1
]exp.
[ ) R U(5) B(E2; I → I − 2)
(7)
B(E2; 2 + 1 → 0+ 1 ) ]U(5)

178 S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181
Fig. 13. (i): Plot of the ratio R = R exp /R U(5) of the experimental relative B(E2) values in 110 Cd
to the respective relative B(E2) values predicted by the U(5) limit of IBM-1 vs. spin I (see text for
explanations). (ii): Same as part (i) for the even–even Cd nuclei with mass number A ranging from
106 to 116 (see also text).

S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181 179
are plotted vs. (initial) spin I . Hereby, the data points shown are the weighted average values
of the respective B(E2) values given in Table 2, except that of the B(E2; 14 + 2 → 12+ 2 )
which has been deduced from the Q 2 t values, i.e. the square of the transition quadrupole
moments, given in Ref. [33]. It has to be noticed that the 14 + 2 → 12+ 2
γ -transition is not
showninFig.5.ForI 8, the involved γ -transitions are given in parenthesis. According
to Eq. (7), if the measured relative B(E2) values were equal to the respective ones predicted
by the vibrational limit (U(5)-limit) of IBM-1, then the respective data points had to lie on
the straight line labeled in Fig. 13(i) with letter “a”. This line correspond to R = 1. Curve
labeled “b” represents the ratio of the relative B(E2) values predicted by the SU(3) limit
of IBM-1 (rotational limit) to those predicted by the U(5) limit. As it can be seen in Fig.
13(i) the data points for I = 2, 4, 6 ¯h lie statistically on the straight line “a”. For I = 8 ¯h
one has to distinguish between both weak 8 + 1 → 6+ 1 and 8+ 3 → 6+ 1
γ -transitions from the
strong 8 + 2 → 6+ 1 γ -ray (E γ = 795 keV). The data point of the latter transition lies indeed
on line “a”, whereas the data points of the former γ -rays deviate strongly from R = 1.
For I = 10 ¯h only the relative B(E2) value of the 10 + 2 → 8+ 2
γ -transition is close to the
respective U(5) predictions. For I = 12 ¯h the relative B(E2) value of both the 12 + 1 → 10+ 1
and 12 + 2 → 10+ 2
γ -transitions lie close to the straight line “a”. This also applies for the
both the 14 + 1 → 12+ 1 and 14+ 2 → 12+ 2 γ -rays.
Based on Fig. 13(i), and provided that the 8 + 2 → 6+ 1
(E γ = 795 keV) γ -line, together
with the “unfavoured” pathway consisted of the 10 + 2 → 8+ 2 ,12+ 2 → 10+ 2 , and 14+ 2 →
12 + 2
γ -transitions are the continuation of the ground band, one clearly sees that the level
sequence
2 + 1 , 4+ 1 , 6+ 1 , 8+ 2 , 10+ 2 , 12+ 2 , 14+ 2
forms a nice vibrational band with intraband B(E2) values being in agreement with the
predictions of the U(5) limit of IBM-1.
Recently, Regan et al. [34] have carried out a g-factor measurement of the 10 + 1
state that
yielded g 10
+ =−0.09(3). This result clearly elucidate the neutron nature of the 10+ 1 1 state.
Hence, as claimed in [7] the level sequence 10 + 1 ,12+ 1 ,14+ 1
can be attributed to excitations
due to the alignment of an h 11/2 neutron pair. In such a case the 8 + 3
state, which is fed by the
10 + 1
level via the 171 keV γ -ray, must also have neutron character due to the high transition
rate of the 10 + 1 → 8+ 3
γ -transition (B(E2; 171 keV) = 45(5) W.u). Such an assignment is
not in agreement with the proton character proposed for the 8 + 3
state in [7].
By considering all the B(E2) values reported so far [4,5,28–30,33] for the yrast bands
of the even even Cd nuclei with A = 106–116 and then calculating the ratio R defined
in Eq. (7) one obtains Fig. 13(ii), in which R is plotted vs. initial spin I for all the above
mentioned Cd isotopes. Hereby, it has to be noticed that all the ratios R shown in Fig. 13(ii)
have been deduced from Coulomb excitation measurements except those of 110 Cd. The
latter ratios have been taken from the present RDDS work, from the RDDS measurements
of Piiparinen et al. [28] as well as from the DSAM measurements of Lobach et al. [30].
From Fig. 13(ii), it can be clearly seen that the measured transition probabilities in the even
even Cd nuclei, are in a remarkably good agreement with the respective predictions of the
U(5) limit of IBM-1.

180 S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181
The reduced transition probabilities determined in 109 Cd are rather large. Especially
in level sequence “4” it was found that B(E2; 15/2 − → 11/2 − ) = 47(3) W.u. In
107 Cd, Häusser et al. [13] have obtained B(E2; 15/2 − → 11/2 − ) = 32(2) W.u. This is
indeed a drastic change when considering that the respective γ -transitions differ only by
7 keV. In the weak coupling scheme, it is expected that B(E2; 15/2 − → 11/2 − )109 Cd ≈
B(E2; 2 + → 0 + )110 Cd , whereas in the rotational aligned coupling the B(E2; 15/2− →
11/2 − )109 Cd value is slightly larger. In our case B(E2; 15/2− → 11/2 − )109 Cd ≈ 2 ·
B(E2; 2 + → 0 + )110 Cd . Hence, our result deviates significantly from the values expected.
An interesting feature of level sequences “2” and “3” in 109 Cd, is that the B(E2) values
deduced from the mean lifetimes of the respective depopulating E2 γ -transitions do not
change significantly with increasing spin. According to the B(E2) values obtained for the
21/2 + → 17/2 + ,23/2 + → 19/2 + ,25/2 + → 21/2 + , and 27/2 + → 23/2 + γ -transitions
the collectivity in these level sequences is almost constant (≈ 50 W.u).
6. Conclusions
In the present work the mean lifetimes of 9 excited states in 109 Cd have been determined
for the first time. The corresponding B(E2) values are rather large.
In 110 Cd, the mean lifetimes of the lowest 6 yrast band members have been measured.
Hence, it was possible to follow the evolution of the B(E2) values along the yrast line of
110 Cd. Based on the relative B(E2) values determined here and in [28] one could claim that
the 110 Cd is one of the best examples of nuclei resembling the U(5) symmetry of IBM-1.
This has been also shown by Kern et al. [2] in terms of the energies of the excited states in
110 Cd.
The comparison of all experimental B(E2) values reported so far for the E2 γ -transitions
deexciting the lowest lying collective states in the even even Cd nuclei, are in a remarkably
good agreement with the respective predictions of the U(5) limit of IBM-1. Certainly, it
would be very interesting to determine more B(E2) values along the yrast lines of these
nuclei in order to check further the U(5) character of these isotopes.
References
[1] A. Arima, F. Iachello, Ann. Phys. 99 (1976) 253.
[2] J. Kern, D.E. Garrett, J. Jolie, H. Lehmann, Nucl. Phys. A 593 (1995) 21.
[3] F.K. McGowan, R.L. Robinson, P.H. Stelson, J.L.C. Ford Jr., Nucl. Phys. 66 (1965) 97.
[4] W.T. Milner, F.K. McGowan, P.H. Stelson, R.L. Robinson, R.O. Sayer, Nucl. Phys. A 129
(1969) 687.
[5] C. Fahlander, A. Bäcklin, L. Hasselgren, A. Kavka, V. MIttal, L.E. Svensson, B. Varnestig,
D. Cline, B. Kotliski, H. Grein, E. Grosse, R. Kulessa, C. Michel, W. Spreng, H.J. Wollersheim,
J. Stachel, Nucl. Phys. A 485 (1988) 327.
[6] I. Thorslund, C. Fahlander, J. Nyberg, S. Juutinen, R. Julin, M. Piiparinen, R. Wyss,
A. Lampinen, T. Lönnroth, D. Müller, S. Törmänen, A. Virtanen, Nucl. Phys. A 564 (1993)
285.
[7] J. Kern, A. Bruder, S. Drissi, V.A. Ionescu, D. Kusnezov, Nucl. Phys. A 512 (1990) 1.

S. Harissopulos et al. / Nuclear Physics A 683 (2001) 157–181 181
[8] S. Juutinen, R. Julin, M. Piiparinen, P. Ahonen, B. Cederwall, C. Fahlander, A. Lampinen,
T. Lönnroth, A. Maj, S. Mitarai, D. Müller, J. Nyberg, P. Simecek, M. Sugawara, I. Thorslund,
S. Törmänen, A. Virtanen, R. Wyss, Nucl. Phys. A 573 (1994) 306.
[9] M. Deleze, S. Drissi, J. Jolie, J. Kern, J.P. Vorlet, Nucl. Phys. A 554 (1993) 1.
[10] D.C. Stromswold, D.O. Elliott, Y.K. Lee, L.E. Samuelson, J.A. Grau, F.A. Rickey, P.C. Simms,
Phys. Rev. C 17 (1978) 143.
[11] S. Juutinen, P. Simecek, C. Fahlander, R. Julin, J. Kumpulainen, A. Lampinen, T. Lönnroth,
A. Maj, S. Mitarai, D. Müller, J. Nyberg, M. Piiparinen, M. Sugawara, I. Thorslund,
S. Törmänen, A. Virtanen, Nucl. Phys. A 577 (1994) 727.
[12] F.S. Stephens, R.M. Diamond, S.G. Nilsson, Phys. Lett. B 44 (1973) 429.
[13] O. Häusser, D.J. Donahue, R.L. Hershberger, R. Lutter, F. Riess, H. Bohn, T. Faestermann,
F. v. Feilitzsch, K.E.G. Löbner, Phys. Lett. B 52 (1974) 329.
[14] G. Alaga, V. Paar, V. Lopac, Phys. Lett. B 43 (1973) 459.
[15] T.K. Alexander, J.S. Foster, Adv. Nucl. Phys. 10 (1978) 197.
[16] H. Hanewinkel, Diplomarbeit, Institut für Kernphysik, Universität zu Köln, Köln, 1981,
unpublished.
[17] T.K. Alexander, A. Bell, Nucl. Instrum. Methods 81 (1970) 22.
[18] A. Dewald, S. Harissopulos, P. von Brentano, Z. Phys. A 334 (1989) 163.
[19] G. Böhm, A. Dewald, P. Petkov, P. von Brentano, Nucl. Instrum. Methods A 329 (1993) 248.
[20] C.M. Lederer, V.S. Shirley (Eds.), Table of Isotopes, Wiley, New York, 1978.
[21] A. Dewald, U. Kaup, W. Gast, A. Gelberg, H.W. Schuh, K.O. Zell, P. von Brentano, Phys. Rev.
C 25 (1982) 226.
[22] S. Albers, A. Clauberg, A. Dewald, C. Wesselborg, A. Zilges, Verhandl. DPG(VI) 23 (1988)
227.
[23] F. Seiffert, Program APATHIE, Institut für Kernphysik, Universität zu Köln, Köln, 1989,
unpublished.
[24] K.W. Jones, A. Schwarzschild, E.K. Warburton, D.B. Fossan, Phys. Rev. 178 (1969) 1773.
[25] S. Harissopulos, A. Dewald, A. Gelberg, P. von Brentano, K. Loewenich, K. Schiffer, K.O. Zell,
Nucl. Phys. A 467 (1987) 528.
[26] P. Petkov, S. Harissopulos, A. Dewald, M. Stolzenwald, G. Böhm, P. Sala, K. Schiffer,
A. Gelberg, K.O. Zell, P. von Brentano, W. Andrejtscheff, Nucl. Phys. A 543 (1992) 589.
[27] P. Petkov, R. Krücken, A. Dewald, P. Sala, G. Böhm, J. Altmann, A. Gelberg, P. von Brentano,
R.V. Jolos, W. Andrejtscheff, Nucl. Phys. A 568 (1994) 572.
[28] M. Piiparinen, R. Julin, S. Juutinen, A. Virtanen, P. Ahonen, C. Fahlander, J. Hattula,
A. Lampinen, T. Lönnroth, A. Maj, S. Mitarai, D. Müller, J. Nyberg, A. Pakkanen, M. Sugawara,
I. Thorslund, S. Törmänen, Nucl. Phys. A 565 (1993) 671.
[29] D. De Frenne, E. Jacobs, Nucl. Data Sheets 89 (2000) 481.
[30] Yu.N. Lobach, A.D. Efimov, A.A. Pasternak, Eur. Phys. J. A 6 (1999) 131.
[31] M. Piiparinen, private communication.
[32] L.K. Kostov, W. Andrejtscheff, L.G. Kostova, L. Käubler, H. Prade, R. Schwenger, Eur. Phys.
J. A 2 (1998) 269.
[33] R. Julin, Phys. Scr. T 56 (1995) 151.
[34] P.H. Regan, A.E. Stuchbery, S.S. Andersen, Nucl. Phys. A 591 (1995) 533.