In-beam fast-timing measurements in 103,105,107Cd

Abstract

Fast-timing measurements were performed recently in the region of the
medium-mass 103,105,107Cd isotopes, produced in fusion evaporation reactions.
Emitted gamma-rays were detected by eight HPGe and five LaBr3:Ce detectors
working in coincidence. Results on new and re-evaluated half-lives are
discussed within a systematic of transition rates. The $7/2_1^+$ states in
103,105,107Cd are interpreted as arising from a single-particle excitation. The
half-life analysis of the $11/2_1^-$ states in 103,105,107Cd shows no change in
the single-particle transition strength as a function of the neutron number.

Full text

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arXiv:1105.1688v1 [nucl-ex] 9 May 2011
In-beam fast-timing measurements in103,105,107Cd
S. Kisyov1, S. Lalkovski1∗, N. Mˇ arginean2, D. Bucurescu2, L. Atanasova3, D. L. Balabanski3, Gh. Cˇ ata-Danil2,
I. Cˇ ata-Danil2, J.-M. Daugas4, D. Deleanu2, P. Detistov3, D. Filipescu2, G. Georgiev5, D. Ghit ¸ˇ a2, T. Glodariu2,
J. Jolie6, D.S. Judson7, R. Lozeva5, R. Mˇ arginean2, C. Mihai2, A. Negret2, S. Pascu2, D. Radulov1†,
J.-M. R´ egis6, M. Rudigier6, T. Sava2, L. Stroe2, G. Suliman2, N.V. Zamfir2, K.O. Zell6and M. Zhekova1
1Faculty of Physics, University of Sofia ”St. Kliment Ohridski”,
1164 Sofia, Bulgaria;
2Horia Hulubei National Institute for Physics and Nuclear Engineering,
77125 Bucharest-Magurele, Romania
3Institute for Nuclear Research and Nuclear Energy,
Bulgarian Academy of Science, 1784 Sofia, Bulgaria
4CEA, DAM, DIF, 91297 Arpajon, France
5Centre de Spectrom´ etrie Nucleaire et Spectrometrie de Masse,
91405 Orsay-Campus, France
6Institut f¨ ur Kernphysik,
University of Cologne, Cologne, Germany
7Department of Physics, University of Liverpool,
Liverpool, United Kingdom
(Dated: May 10, 2011)
Fast-timing measurements were performed recently in the region of the medium-mass103,105,107Cd
isotopes, produced in fusion evaporation reactions. Emitted γ-rays were detected by eight HPGe
and five LaBr3:Ce detectors working in coincidence. Results on new and re-evaluated half-lives are
discussed within a systematic of transition rates. The 7/2+
arising from a single-particle excitation. The half-life analysis of the 11/2−
shows no change in the single-particle transition strength as a function of the neutron number.
1states in103,105,107Cd are interpreted as
1states in103,105,107Cd
PACS numbers: 21.10.k, 21.10.Hw, 21.10.Tg, 23.20.Lv, 27.60.+j
I. INTRODUCTION
Cadmium isotopes have two protons less than the50Sn
nuclei, presenting a good test case for the robustness of
the shell structure. Shell model calculations successfully
describe the experimentally observed level energies and
level lifetimes in the extreme neutron-rich and neutron-
deficient cadmium isotopes proving the persistence of
the shell structure below the doubly magic132Sn and
100Sn [1–4]. Fingerprints of collectivity, however, start
to emerge when moving away from the neutron shell clo-
sures. They can be found in the decrease of the 2+
and in the increase of the respective B(E2;2+
ues when approaching the neutron mid-shell [5].
Due to the neighbourhood of the shell model tin
isotopes and the presence of weak collectivity in the
neutron-mid shell cadmium isotopes, both single particle
and collective states are expected to occur in the medium
mass odd-A Cd nuclei. Moreover, there are several cases
where the structure of the state is ambiguous. In the
103,105,107Cd [6–8], for example, the lowest-lying excited
Jπ= 7/2+state can arise from a collective excitation
built on the 5/2+ground state or from a single-particle
excitation. A model independent approach to the prob-
1energy
1→ 0+
1) val-
∗E-mail address: stl@phys.uni-sofia.bg
†Present address: Katholieke Universiteit, Leuven, Belgium
lem is to evaluate the B(E2) transition strengths within
a systematical study involving even-even well deformed
and spherical nuclei, where the structure is well estab-
lished.
In order to study the structure of the low-lying ex-
cited states in
were performed. The half-lives are directly related to the
transitions rates and hence to the structure of the state.
The present paper reports on new results, obtained with
eight HPGe detectors working in coincidence with five
LaBr3:Ce detectors.
103,105,107Cd fast-timing measurements
II.EXPERIMENTAL SET UP
The low-lying excited states, placed on and close to
the yrast line in103Cd,105Cd and107Cd were populated
via fusion evaporation reactions. A carbon beam, ac-
celerated to 50 MeV by the Tandem accelerator of the
National Institute for Physics and Nuclear Engineering
at Magurele, Romania, impinged on self-supporting 10
mg/cm2thick94,96Mo targets and on a 1 mg/cm2thick
98Mo target with 20 µm Pb backing. The three targets
were isotopically enriched up to 98.97% in94Mo, 95.70%
in96Mo and 98% in98Mo, respectively.
The cross section for the
tion was calculated to be 100 mb, while for the
96Mo(12C,3n)105Cd and98Mo(12C,3n)107Cd reactions it
was approximately 400 mb. The typical beam intensity
94Mo(12C,3n)103Cd reac-

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was of the order of 8 pnA. Besides the 3n channels, the 4n,
2np, 4np and 2nα- fusion evaporation channels also have
significant cross sections which contaminate the spectra
of interest.
The half-lives of the levels of interest were deduced by
using a fast-timing set up consisting of 5 LaBr3:Ce scin-
tillator detectors working in coincidences with 8 HPGe
detectors [9]. Five of the HPGe detectors were placed
at backward angles with respect to the beam axis, two
were placed at 90◦and the eighth HPGe detector was
placed at a forward angle.
tors were mounted bellow the target chamber on a ring
of approximately 45◦degrees with respect to the beam
axis. The five LaBr3:Ce crystals had a cylindrical shape
and 5% Ce doping. One of the LaBr3:Ce detector was a
commercial integral detector. Its size was 2”×2”. Two
of the LaBr3:Ce detectors had 1” height and a diam-
eter of 1”. Two LaBr3:Ce crystals had dimensions of
1.5”×1.5”. Each of the four crystals was optically cou-
pled to XP20D0B photomultiplier and mounted in alu-
minum casing. The readout, from each of the four non-
comercial detectors, was made via a VD184/T voltage
divider. The voltage divider issues a negative anode sig-
nal and a fast positive dynode signal. The anode signal
was used for timing, while the dynode signal was used to
obtain energy signal. This non conventional choice was
made to avoid the saturation of the dynode signal [9],
which facilitates the analysis of the energy spectra.
The energy signals from the HPGe detectors were am-
plified and then digitized by 8k Analog to Digital Con-
verters (ADC) AD413A. The timing signals from the
HPGe detectors were processed by 4k 4418/T Time-to-
Digital converters. The energy signals from the LaBr3:Ce
detectors were amplified by spectroscopic amplifiers and
then digitized by 8k ADC AD413A. The timing signals
from the LaBr3:Ce detectors were sent to a Quad Con-
stant Fraction Discriminator, model 935. Each of the five
timing signals was used to start a Time-to-Amplitude
Converter (TAC) operating in a common stop mode.
Then the five TAC output signals were sent to 8k ADCs.
The acquisition was triggered when two LaBr3:Ce and
one HPGe detectors were fired in coincidences.
The five LaBr3:Ce detec-
III. DATA ANALYSIS
Data was stored in event-by-event mode in 100 MB
long files, which were grouped in runs of approximately
2 hours. Then the data was analyzed using the GASP-
Ware and Radware [10] packages. Because of the instabil-
ity of the LaBr3:Ce detectors observed with time, a gain
matching procedure was applied run-by-run. To correct
the CFD for the walk effect, observed at low energies,
analysis of the time responce as a function of energy was
performed with a60Co source [9] and in-beam. Then the
data was sorted in gated energy spectra, two-dimentional
energy-energy (Eγ− Eγ) and three-dimentional energy-
energy-time (Eγ− Eγ− ∆T) matrices, where Eγ is the
0 200400600 8001000
5e+05
1e+06
1.5e+06
2e+06
2.5e+06
3e+06
HpGe
LaBr
1044
0 200 4006008001000
Energy [keV]
5000
10000
15000
20000
counts
131
260
331
392
511539
668
786
832
886
131
668
(a)
(b)
705
FIG. 1: (Colour online)105Cd energy spectra: (a) Total pro-
jection from all HPGe and LaBr3:Ce detectors; (b) LaBr3:Ce
energy spectrum gated on a 886-keV transition in any of the
HPGe detectors. The labels denote transitions in105Cd
γ-ray energy detected by a LaBr3:Ce detector and ∆T
is a time difference between two gamma rays detected in
coincidence.
The (Eγ− Eγ− ∆T) matrices were constructed as
fully symetric in energy, i.e.
rays of energies Eγ1and Eγ2are detected the matrix ele-
ments (Eγ1,Eγ2) and (Eγ2,Eγ1) are incremented, while
the time intervals associated with these two points are
calculated as ∆T = (t1−t2)+t0and ∆T = −(t1−t2)+t0
respectively. Here, t1−t2> 0 is the time difference mea-
sured with two TAC converters and t0 is an arbitrary
offset. In the cases where the two γ-rays feed and de-
excite a state with a half-life longer than the electronics
resolution, which in the present work is 6 ps/channel,
then the time distributions associated with the two ma-
trix elements (Eγ1,Eγ2) and (Eγ2,Eγ1) will be shifted
by 2τ, where τ is the lifetime of the level of interest.
This procedure represents the centroid shift method [11],
which has been successfully used in the past [12] and re-
cently applied with LaBr3:Ce detectors [9]. In the cases,
where the level half-life is much longer than the detector
time resolution, a tail emerges on the right hand side of
the time distribution. In these cases the slope of the tail
has been used to determine the half-life of the level. De-
convolution of Gaussian and exponent was applied in the
cases where the half-life of the level is of the order of the
FWHM of the prompt distribution.
In order to select a particular reaction channel and
particular γ-decay branch leading to the state of interest,
the matrices were constructed with a condition imposed
on prompt γ-rays detected in any of the high-resolution
HPGe detectors.
Fig. 1(a) shows the energy total projection for
the
LaBr3:Ce detectors. At low energies, the higher effi-
ciency of the LaBr3:Ce with respect to the HPGe de-
tectors is remarkable. The energies of105Cd are marked
for each event where γ-
12C+96Mo→105Cd+3n reaction for all HPGe and

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3
-10
-5
0
5
10
1
10
100
counts
-2 0246 8 10
(d)
1
10
100
-4 -2024
Time [ns]
1
10
-3-2
-1
0
1
23
1
10
100
(a)
(b)
(c)
FIG. 2: (Colour online) Time spectra, obtained for the decay
of the 7/2+
the 11/2−
1states in107Cd (a),105Cd (b),103Cd (c) and for
1state in105Cd (d)
with numbers.
ergy spectrum, gated on the 886-keV transition from
105Cd in the HPGe detectors, which improves the peak-
to-background ratio. Similar spectra were constructed
for the other two reactions12C+94Mo→103Cd+3n and
12C+98Mo→107Cd+3n.
Fig. 2 presents time spectra obtained after two dimen-
sional energy gates imposed on Eγ-Eγ− ∆T matrices,
gated on prompt transitions with HPGe detectors. To in-
crease the statistics, in each of the cases, several prompt
gates were imposed on the HPGe detectors. Here, the
procedure will be ilustrated by using the lowest lying
prompt and delayed transitions shown on Fig. 3.
Fig. 2(a) presents the time distributions for the decay
of the 7/2+
ted in full lines, is obtained with a (205γ,641γ) energy
gate, while the symmetric (641γ,205γ) gate is plotted
with dots. The half-life of 0.68 (4) ns, obtained from the
centroid shift method, is consistent with the NNDC value
of T1/2=0.71 (4) ns [8]. Gates on 798-keV or 956-keV
transitions (Fig. 3) were applied with HPGe detectors in
order to clean the time spectra from background events.
Fig. 2(b) presents the time curves for the decay of the
7/2+
tained in the present study, was measured from the slope
of the time distribution gated on (639γ-131γ) with the
LaBr3:Ce detectors and cleaned with a gate on the 886
γ-ray or 705-keV γ-ray (Fig. 3) imposed on any of the
eight HPGe detectors. It agrees the 1.75 (11) ns value,
adopted by NNDC [7], which is based on a γ(t) measure-
ment with one NaI(Tl) detector [13].
Fig. 2(c) presents the time curves for the decay of the
7/2+
The half-life of 0.37 (3) ns was
obtained from the centroid shift of the two time distribu-
tions generated with gates on the 188-keV and 720-keV
transitions (Fig. 3) imposed on any two of the LaBr3:Ce
detectors in coincidence with the 921-keV or 623-keV γ-
Fig. 1(b) represents the LaBr3:Ce en-
1state in107Cd. The time distribution, plot-
1state in105Cd. The half-life of 1.66 (12) ns, ob-
1state in103Cd.
103Cd
105Cd
107Cd
5/2+
0
7/2+
188
11/2+
908
15/2+
1829
19/2+
2452
9/2+
740
11/2–
1671
15/2–
2314
5/2+0
7/2+
131
11/2+ 799
15/2+
1685
17/2+
2390
9/2+770
11/2–
1162
15/2–
1702
19/2–
2488
5/2+0
7/2+
205
11/2–
846
15/2–1361
19/2–
2159
23/2–
3115
188
720
921
623
740
931
643
131
668
886
705
639
392
539
786
205
641
515
798
956
FIG. 3: Partial level schemes of103,105,107Cd
TABLE I: First excited 7/2+state in103,105,107Cd and decay
properties
IsotopeEi
T1/2
Eγ
[keV]
188
LλδB(λL)
[W.u.]
0.0089 (8)
2.27 (19)
0.0058 (5)
2.93 (22)
[keV]
188
103Cd0.37 (3) ns M1
E2
M1
E2
M1 0.25 (1) 0.00331 (20)
E2
≤ 0.1
105Cd1311.66 (12) ns 131
≤ 0.1
107Cd2050.68 (4) ns 205
4.2 (4)
rays (Fig. 3) detected in any of the HPGe detectors.
The half-life of the 11/2−
obtained by gating on the 539-keV feeding and 392-keV
de-exciting transitions (Fig. 3), detected by any two of
the five LaBr3:Ce detectors. An additional gate on the
786-keV γ-ray, which is in coincidence with the 392-keV
and 786-keV transitions (Fig. 3), was imposed on any
of the HPGe detectors. The half-life, deduced from the
centroid shift of the two mirror time spectra, is 149 (12)
ps.
1state in105Cd Fig. 2(d) was
IV.DISCUSSION
7/2+
listed in Table I along with the level energy Eiand the
spin/parity assignments Jπ. In order to calculate the
partial half-lives and the reduced transition probabilities
the γ-ray energies Eγ, multipolarities Lλ, and mixing
ratios δ, adopted by NNDC [6–8], are also listed. The
Jπ= 7/2+state is the first excited state in all three
isotopes and decays via M1+E2 transition to the ground
state. An upper limit of the mixing ratio δ ≤ 0.1 for
the 7/2+
by the NNDC [6]. The mixing ratio, adopted for the
M1+E2 transition in107Cd, is δ =+0.25 (1) [8]. It has
been suggested that the respective transition in105Cd is
of almost pure M1 nature, however a small E2 admixture
1: The half-lives T1/2, of the levels of interest, are
1→ 5/2+
1transition in103Cd has been estimated

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4
5355 5759
61 63
65
0.02
0.04
0.06
0.08
BM1 (W.u.)
53555759
61 63
65
neutron number
10
20
30
40
BE2 (W.u.)
even-A Cd
odd-A Cd
(a)
(b)
FIG. 4: (Colour online) Systematics of (a) B(M1;7/2+
5/2+
5/2+
pared to the B(E2;2+
cores (triangles)
1
→
1) values for odd-A cadmium nuclei and (b) B(E2;7/2+
1) values for odd-A cadmium isotopes (diamonds) com-
1→ 0+
1→
1) values in even-even cadmium
is assumed [7]. For the purpose of the current discussion
an upper limit of δ ≤0.1 was adopted in the present study.
The reduced transition probabilities, calculated with
RULER [5], are given in the last column of Table I.
Fig. 4 shows the systematic trend of the B(M1)
(Fig. 4(a)) and B(E2) values for the 7/2+
sitions in103−111Cd55−63 (Fig. 4(b)), compared to the
B(E2;2+
1) for their even-even Cd cores. Fig. 5
shows the evolution of the B(E2;2+
rates with the neutron number for all even-even nuclei in
the 40 ≤Z≤ 50 region.
In the103−107Cd55−59nuclei, because of the low mixing
ratio, the B(E2;7/2+
significantly suppressed in comparison to the B(E2;2+
0+
1) values for the even-even Cd cores (Fig. 4(b)). More-
over, they are two orders of magnitude weaker than
the B(E2;2+
1) values for the most deformed neu-
tron mid-shell Zr and Mo nuclei (Fig. 5). In fact, the
103,105,107Cd B(E2;7/2+
the reduced transition probabilities for the magic tin nu-
clei (Fig. 5) suggesting a single-particle nature of the
7/2+
1state, most probably arising from νg7/2configu-
ration.
In109Cd61, the 7/2+
1state appears 203 keV above the
5/2+ground state and decays via a pure, according to
NNDC, M1 transition giving rise to B(M1)(W.u.)=0.068
12 [14], which is an order of magnitude higher than the
respective value in103−107Cd. However, the odd behavior
of the B(M1) point on Fig. 4 suggests a significant E2
component. In fact, such an increase of the B(E2) value,
and hence in the collectivity of the state, is observed in
111Cd. There, the 5/2+
keV and 416 keV respectively [15]. The 7/2+
life of 0.12 ns and decays to the 5/2+
M1+E2 transition. The mixing ratio δ = −0.144 of this
transition leads to B(E2;7/2+
1→ 5/2+
1tran-
1→ 0+
1→ 0+
1) transition
1→ 5/2+
1) transition strenghts are
1→
1→ 0+
1→ 5/2+
1) values are similar to
1and 7/2+
1states appear at 245
1has a half-
1state via 171-keV
1→ 5/2+
1)=23 6 (2) W.u.,
5456 58
606264 666870727476
number of neutrons
1
10
100
BE2(W.u.)
Sn
Cd
Pd
Ru
Mo
Zr
FIG. 5: (Colour online) Systematics of B(E2;2+
sition rates for the even-even nuclei with 40≤ Z ≤ 50
1→ 0+
1) tran-
which approaches the B(E2;2+
even cadmium cores (Fig. 4(b)) and hence the 7/2+state
becomes collective.
11/2−
1states appear in all odd-
cadmium isotopes from103Cd to123Cd [5]. It is observed
at 1671 keV in103Cd [6] and decreases in energy when
approaching the neutron mid-shell. In117Cd69it appears
at 136 keV above the ground state.
The big energy gap between the 11/2−
ground state in103−111Cd opens space for several states
of single-particle and collective nature to appear. Among
those levels is the 9/2+
decays via an E1 transition. For medium mass odd-A
Cd isotopes the energy of the 11/2−
ground state where only low-spin states are populated. In
this mass region the 11/2−
1state decays via low-energy
transitions of higher multipolarity leading to increase of
its half-life to T1/2 =14.1 y in113Cd [5]. Further in-
creases of the energy of the 11/2−
the ground state leads to a decrease of the half-life. The
isomeric 11/2−
1state in all neutron-rich cadmium nuclei
with A≥113 decay via β-decay process to the respective
indium isobars. In spite the half-life of the state decreases
and the energy of the isomeric state increases with the
mass number, isomeric decays have not been observed so
far.
The half-life of the excited 11/2−
measured in present work, allows a systematical study of
the E1 transitions strenghts as a function of the neutron
number. The half-life T1/2=71 ns of the 11/2−
107Cd has been previously measured [13]. This level de-
cays via a branch of E1, M2 and E3 transitions to 9/2+,
7/2+and 5/2+states with partial half-lives 2.4×10−7,
1.0×10−7and 4.5×10−6s respectively.
The 11/2−
decays via two E1 transitions to two 9/2+states. The
partial half-lives for the two transitions are 2.7×10−10
and 3.3 × 10−10s respectively.
The 11/2−state in103Cd decays via a 931-keV E1
1→ 0+
1) value in the even-
1: The Jπ= 11/2−
1state and the
1state to which the 11/2−
1state
1drops closer to the
1state with respect to
1state in103,105Cd,
1state in
1state in105Cd, which has a T1/2= 149 ps,

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5
transition to a 9/2+. No time structure of the decaying
transition was observed in the present work. Therefore,
an upper limit of 6 ps was deduced.
The Weisskopf estimates for the 931-keV E1 γ-ray in
103Cd is TW.e.
1/2
= 3.8 × 10−16s, for the 330-keV E1 tran-
sition and 392-keV E1 γ-ray in105Cd are 8.40×10−15s
and 5.00 × 10−15s. and TW.e.
1/2
37-keV E1 transition in107Cd. For all four transitions
the E1 hindrance factor FW= T1/2,γ/TW.e.
104. Given that the 11/2−is an intruder state, the simi-
lar hindrance factor observed in all three odd-A cadmium
nuclei103,105,107Cd suggests similar structure of the final
9/2+state.
= 6.14 × 10−12s for the
1/2
is of order of
V.CONCLUSION
Excited states in103,105,107Cd have been populated via
fusion-evaporation reactions. Half-lives of several excited
states were measured by using the delayed coincidence
technique. The half-life of the 7/2+
105Cd were confirmed. The half-life of the first excited
state in103Cd and of the 11/2−
tained allowing a systematical study of the transitions
strenghts. The B(E2;7/2+
in103−107Cd are strongly hindered with respect to the
B(E2;2+
1) values, observed in the most deformed
nuclei in the region, suggesting a single particle nature
for the 7/2+
1states. The hindrance factors, calculated for
E1 transitions in103,105,107Cd, suggest similar structure
of the 9/2+states.
1state in107Cd and
1in105Cd are newly ob-
1→ 5/2+
1) transitions strenghts
1→ 0+
VI. ACKNOWLEDGMENTS
The work is partly supported by the Bulgarian Science
Fund under contracts DMU02/1, DRNF02/5, DID-05/16
and by a contract for Bularian-Romanian partnership,
number BRS-07/23.
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