Precision Mass Measurements beyond $^{132}$Sn: Anomalous behaviour of odd-even staggering of binding energies

TLDR: An empirical neutron pairing gap expressed as the odd-even staggering of isotopic masses shows a strong quenching across N = 82 for Sn, with a Z dependence that is unexplainable by the current theoretical models.

Abstract: Atomic masses of the neutron-rich isotopes $^{121--128}\mathrm{Cd}$, $^{129,131}\mathrm{In}$, $^{130--135}\mathrm{Sn}$, $^{131--136}\mathrm{Sb}$, and $^{132--140}\mathrm{Te}$ have been measured with high precision (10 ppb) using the Penning-trap mass spectrometer JYFLTRAP. Among these, the masses of four $r$-process nuclei $^{135}\mathrm{Sn}$, $^{136}\mathrm{Sb}$, and $^{139,140}\mathrm{Te}$ were measured for the first time. An empirical neutron pairing gap expressed as the odd-even staggering of isotopic masses shows a strong quenching across $N=82$ for Sn, with a $Z$ dependence that is unexplainable by the current theoretical models.

Figures

TABLE I. Cyclotron frequency ratios r and ground state mass excess values in keV based on this work. Masses of reference Xe isotopes in column 1 for given A are from Refs. [20–22]. Results from other direct mass measurements are from ISOLTRAP [8,23,24] or an experimental storage ring (ESR) at the fragment separator (FRS) [25]. Otherwise, the value from Atomic Mass Evaluation 2003 (AME2003) [20] is given.

FIG. 2 (color online). A time-of-flight resonance from the JYFLTRAP setup for 135Snþ. A two-fringe Ramsey pattern of 25-350-25 ms (on-off-on) was used in this case.

FIG. 5 (color online). Odd-even staggering for the N ¼ 81 and 83 isotones as measured in experiment (a) and estimated within the spherical (b), deformed (c), and deformed particle-numberconserving (d) self-consistent calculations.

FIG. 1. Neutron-rich isotopes with Tz 13 whose masses have been determined by Penning trap (PT) or Q measurements. Letter r denotes r-process nuclei according to Ref. [10].

FIG. 4 (color online). The same as in Fig. 3 but for the calculated (spherical HFB) odd-even mass staggering in (a) Sn, Te, and Xe isotope chains and mixed pairing force and (b) Sn isotope chain and surface, mixed, and volume pairing forces.

FIG. 3 (color online). Experimental odd-even mass staggering for Sn, Te, and Xe isotope chains. For clarity, odd-N points have been connected with lines and the error bars have been omitted when ð ð3ÞÞ< 10 keV. The open symbols present the experimental values around the shell-gap prior to this work. The data points for N ¼ 82 are beyond the scale.

Full text

This is an electronic reprint of the original article.
This reprint may differ from the original in pagination and typographic detail.
Author(s):
Title:
Year:
Version:
Please cite the original version:
All material supplied via JYX is protected by copyright and other intellectual property rights, and
dupli
cation or sale of all or part of any of the repository collections is not permitted, except that
material may be duplicated by you for your research use or educational purposes in electronic or
print form. You must obtain permission for any other use. Electronic or print copies may not be
offered, whether for sale or otherwise to anyone who is not an authorised user.
Precision mass measurements beyond ^{132}Sn: Anomalous behaviour of odd-even
staggering of binding energies
Hakala, Jani; Dobaczewski, Jacek; Gorelov, Dmitry; Eronen, Tommi; Jokinen, Ari;
Kankainen, Anu; Kolhinen, Veli; Kortelainen, Markus; Moore, Iain; Penttilä, Heikki;
Rinta-Antila, Sami; Rissanen, Juho; Saastamoinen, Antti; Sonnenschein, Volker; Äystö,
Juha
Hakala, J., Dobaczewski, J., Gorelov, D., Eronen, T., Jokinen, A., Kankainen, A.,
Kolhinen, V., Kortelainen, M., Moore, I., Penttilä, H., Rinta-Antila, S., Rissanen, J.,
Saastamoinen, A., Sonnenschein, V., & Äystö, J. (2012). Precision mass
measurements beyond ^{132}Sn: Anomalous behaviour of odd-even staggering of
binding energies. Physical Review Letters, 109(3), 032501.
https://doi.org/10.1103/PhysRevLett.109.032501
2012

Precision Mass Measurements beyond
132
Sn: Anomalous Behavior of Odd-Even
Staggering of Binding Energies
J. Hakala,
*
J. Dobaczewski, D. Gorelov, T. Eronen,
†
A. Jokinen, A. Kankainen, V. S. Kolhinen, M. Kortelainen,
I. D. Moore, H. Penttila
¨
, S. Rinta-Antila, J. Rissanen, A. Saastamoinen, V. Sonnenschein, and J. A
¨
ysto
¨
‡
Department of Physics, P.O. Box 35 (YFL), FI-40014 University of Jyva
¨
skyla
¨
, Finland
(Received 5 March 2012; published 16 July 2012)
Atomic masses of the neutron-rich isotopes
121–128
Cd,
129;131
In,
130–135
Sn,
131–136
Sb, and
132–140
Te have
been measured with high precision (10 ppb) using the Penning-trap mass spectrometer JYFLTRAP.
Among these, the masses of four r-process nuclei
135
Sn,
136
Sb, and
139;140
Te were measured for the first
time. An empirical neutron pairing gap expressed as the odd-even staggering of isotopic masses shows a
strong quenching across N ¼ 82 for Sn, with a Z dependence that is unexplainable by the current
theoretical models.
DOI: 10.1103/PhysRevLett.109.032501 PACS numbers: 21.10.Dr, 21.60.n, 27.60.+j
The doubly magic
132
Sn nucleus has been probed inten-
sively by nuclear spectroscopy over the last two decades. It
has been found to exhibit features of exceptional purity for
its single particle structure [1,2]. This provides an ideal
starting point for exploring the detailed evolution of nuclear
structure of more neutron-rich nuclei beyond the N ¼ 82
closed shell in the vicinity of Sn. Only a few experimental
and theoretical attempts along these lines have been per-
formed recently. No experimental data exist for excited
states or masses for nuclides below Sn with N>82. The
experimental situation is slightly better for the Z>50
isotopes of Sb and Te because of their easier access.
Recent data on the BðE2Þ transition strengths for
132
Te,
134
Te, and
136
Te isotopes [3], and their interpretation using
a quadrupole-plus-pairing Hamiltonian and the quasipar-
ticle random phase approximation [4] suggested the need
for reduced neutron pairing to explain the observed anoma-
lous asymmetry in the BðE2Þ values across the N ¼ 82
neutron shell. This behavior was not observed in standard
shell model calculations [3]. Another shell model calcula-
tion of the binding energies of heavy Sn isotopes with
A>133 [5] suggested the importance of pairing correla-
tions and the strength of the pairing interaction in general
for weakly bound nuclei. Therefore, it would be necessary
to probe the evolution of odd-even staggering of masses [6]
around the N ¼ 82 neutron shell to learn about the magni-
tude of pairing and its variation as a function of Z and N
beyond
132
Sn.
The high precision of present-day ion-trap mass spec-
trometry combined with the high sensitivity [7] can pro-
vide the needed information on mass differences such as
one- and two-nucleon separation energies, shell gaps, and
empirical pairing energies. For example, the masses of
neutron-rich Sn and Xe isotopes were recently measured
up to
134
Sn and
146
Xe with the Penning-trap mass spec-
trometer ISOLTRAP at the CERN ISOLDE facility [8,9].
In this Letter we wish to present new data of high-precision
mass measurements of neutron-rich Cd, In, Sn, Sb, and Te
isotopes across the N ¼ 82 neutron shell by using the
JYFLTRAP Penning trap. These nuclides are also of inter-
est for nuclear astrophysics models of element synthesis, in
particular, to explain the large r-process abundance peak at
A ¼ 130 [10] (see Fig. 1). In more general context, a vast
body of nuclear data on neutron-rich isotopes is needed for
r-process nucleosynthesis predictions. Such data include
masses, single particle spectra, pairing characteristics, as
well as decay properties and reaction rates. In all of these
the binding energies or masses of ground, isomeric, and
excited states play key roles [10].
The measurements were performed using the JYFLTRAP
Penning-trap mass spectrometer [11] which is connected to
the Ion Guide Isotope Separator On-Line (IGISOL) mass
separator [12]. The ions of interest were produced in
proton-induced fission reactions by bombarding a natural
uranium target with a proton beam of 25 MeV energy. A
thorium target was used in the case of
129
In and isotopes
of Sb.
Fission products stopped in a helium-filled gas cell at a
pressure of about 200 mbar as singly charged ions were
transported out of the gas cell, accelerated to 30 keV
energy, and mass separated. A gas-filled radio frequency
74 76 78 80 82 84 86 88 90 92
46
48
50
52
54
rr
rr r
r
r
rr
r
r
r
r
r
r
rr
r
r
r
r
r
r
r
r
Stable isotope
Mass from PT
Mass from Q
β
only T
1/2
known
Proton number
Neutron number
r
Cs
Xe
I
Te
Sb
Sn
In
Cd
Ag
Pd
FIG. 1. Neutron-rich isotopes with T
z
 13 whose masses
have been determined by Penning trap (PT) or Q

measure-
ments. Letter r denotes r-process nuclei according to Ref. [10].
PRL 109, 032501 (2012)
PHYSICAL REVIEW LETTERS
week ending
20 JULY 2012
0031-9007=12=109(3)=032501(5) 032501-1 Ó 2012 American Physical Society

quadrupole cooler and buncher prepared the ions for the
Penning-trap setup.
In a Penning trap an ion has three different eigenmo-
tions: axial motion (
z
) and two radial motions, magnetron
(

) and modified cyclotron (
þ
) motion. The frequencies
of the radial motions sum in first order to the cyclotron
frequency 
c
¼
1
2
q
m
B. Here q and m are the charge and
mass of the ion, and B is the magnetic field.
JYFLTRAP consists of two cylindrical Penning traps,
the purification and precision trap, which are located inside
a 7-T superconducting magnet. Both traps were used to
purify the samples, first with the sideband cooling tech-
nique [13] for isobaric separation and then, if prompted by
the presence of isomers or other contaminants, with the
Ramsey cleaning technique [14]. After a cleaned sample
was trapped in the precision trap, the time-of-flight ion-
cyclotron resonance technique [15] was applied in order to
determine the resonance frequency. The Ramsey method of
separated oscillatory fields [16], which makes the side-
bands more pronounced and narrower, was used in the
250
300
350
-8 -6 -4 -2 0 2 4 6 8
Time of Flight [µs]
Excitation frequency - 796410.46 [Hz]
ν
c
(
135
Sn
+
) = 796410.46(1)
data fit
FIG. 2 (color online). A time-of-flight resonance from the
JYFLTRAP setup for
135
Sn
þ
. A two-fringe Ramsey pattern of
25-350-25 ms (on-off-on) was used in this case.
TABLE I. Cyclotron frequency ratios

r and ground state mass excess values in keV based on this work. Masses of reference Xe
isotopes in column 1 for given A are from Refs. [20–22]. Results from other direct mass measurements are from ISOLTRAP [8,23,24]
or an experimental storage ring (ESR) at the fragment separator (FRS) [25]. Otherwise, the value from Atomic Mass Evaluation 2003
(AME2003) [20] is given.
Xe
Nuclide

r ¼

c;ref

c;meas
JYFLTRAP Literature
Ref.A keV keV
130
121
Cd
b
0.930 790 292(23)
81 074:2ð28Þ81 060ð80Þ [20]
122
Cd
0.938 492 175(22)
80 610:8ð27Þ80 616:6ð44Þ [24]
123
Cd
b
0.946 216 645(22)
77 414:4ð26Þ77 367ð93Þ [24]
124
Cd
0.953 920 584(26)
76 702ð4Þ76 697ð10Þ [24]
125
Cd
b
0.961 646 357(24)
73 348:1ð29Þ73 360ð70Þ [20]
126
Cd
0.969 353 430(25)
72 257ð3Þ72 256:5ð42Þ [24]
127
Cd
0.977 082 59(11)
68 493ð13Þ68 520ð70Þ [20]
128
Cd
0.984 791 049(83)
67 234ð10Þ67 250ð17Þ [24]
129
In
0.992 442 788(22)
72 838:0ð26Þ72 940ð40Þ [20]
131
In
1.007 878 672(22)
68 025:0ð26Þ68 137ð28Þ [20]
130
Sn
1.000 080 552(28)
80 133ð4Þ80 134ð16Þ [23]
132
131
Sn
0.992 516 774(26)
77 262ð20Þ
a
77 264ð10Þ [8]
132
Sn
1.000 103 654(26)
76 543ð4Þ76 547ð7Þ [8]
134
133
Sn
0.992 670 308(18)
70 874:4ð24Þ70 847ð23Þ [8]
134
Sn
1.000 173 910(25)
66 432ð4Þ66 320ð150Þ [8]
130
135
Sn
1.038 731 983(25)
60 632ð3Þ
131
Sb
1.007 763 324(18)
81 982:5ð21Þ81 988ð21Þ [20]
132
Sb
b
1.015 480 774(22)
79 635:6ð27Þ79 674ð14Þ [20]
133
Sb
1.023 184 733(31)
78 921ð4Þ78 943ð25Þ [20]
134
Sb
b
1.030 923 280(17)
74 021:1ð21Þ74 170ð40Þ [20]
135
Sb
1.038 657 131(24)
69 689:6ð29Þ69 710ð100Þ [20]
136
Sb
1.046 397 992(52)
64 510ð7Þ
132
Te
1.015 434 872(33)
85 190ð4Þ85 182ð7Þ [20]
133
Te
b
1.023 151 534(18)
82 938:2ð22Þ82 945ð24Þ [20]
134
Te
1.030 852 922(27)
82 535ð4Þ82 559ð11Þ [20]
135
Te
1.038 590 701(22)
77 727:9ð26Þ77 725ð123Þ [20]
136
Te
1.046 316 045(24)
74 425:7ð29Þ74 430ð50Þ [20]
137
Te
1.054 056 424(21)
69 304:2ð25Þ69 290ð120Þ [25]
138
Te
1.061 784 295(36)
65 696ð5Þ65 755ð122Þ [25]
139
Te
1.069 527 729(29)
60 205ð4Þ
140
Te
1.077 257 59(23)
56 357ð27Þ
a
Corrected for 65.1 keV isomer; see Ref. [20].
b
Isomer separated.
PRL 109, 032501 (2012)
PHYSICAL REVIEW LETTERS
week ending
20 JULY 2012
032501-2

majority of measurements. The experimental setup and the
measurement technique are described in more detail in
Ref. [17].
A sample resonance is shown in Fig. 2. When the
cyclotron frequencies of an unknown species (m
meas
) and
a well-known reference ion (m
ref
) are known, and both are
singly charged ions, the atomic mass can be determined as
follows:
m
meas
¼

c;ref

c;meas
ðm
ref
 m
e
Þþm
e
; (1)
where m
e
is the mass of the electron. The data analysis
procedure was almost identical compared to Ref. [18]. In
this work, the systematic uncertainties due to the magnetic
field fluctuations were minimised by applying so-called
interleaved frequency scanning, described in Ref. [19].
The results are given in Table I. Excitation times be-
tween 100 and 800 ms were used depending on the half-life
of the isotope. In the case of Ramsey excitations, excitation
patterns with two 25 ms pulses separated by a waiting time
were used. Table I lists only the masses of the ground states
which are relevant for the further discussion of the results.
A paper containing the isomeric data will be submitted
separately. The new data agree with the earlier ion-trap
measurements and present significant improvement in ac-
curacy for all Sn, Sb, and Te isotopes beyond N ¼ 82.
The high precision of Penning-trap mass measurements
enables for the first time a critical evaluation of odd-even
staggering of binding energies and related empirical pair-
ing gaps across the N ¼ 82 shell gap. The most simple
example is the three-point odd-even-mass-staggering
formula [6]

ð3Þ
ðNÞ¼ð1Þ
N
½EðN þ 1Þ2EðNÞþEðN  1Þ=2;
(2)
where N is the number of nucleons (neutrons or protons)
and E the binding energy. The 
ð3Þ
staggering mostly
depends on the intensity of pairing correlations in nuclei,
but, as we discuss below, it is also affected by the polar-
ization effects.
Figure 3 shows the experimental neutron 
ð3Þ
staggering
for Sn, Te, and Xe isotopes crossing the N ¼ 82 shell
closure. The difference between the values at N ¼ 81
and 83 shows a large asymmetry for Sn but a much smaller
one for Te and Xe. This indicates a considerably stronger
quenching in the pairing gap for Sn than for Te and Xe,
suggesting the importance of core polarization effects. A
similar asymmetry observed for BðE2Þ values of n-rich Te
isotopes was also traced to reduced neutron pairing above
the N ¼ 82 shell closure [4].
In order to probe this question theoretically, we per-
formed self-consistent calculations of varying complexity,
by using the Sly4 [26] energy density functional and contact
pairing force. To make a meaningful comparison, in each
variant of the calculation, the pairing strength (equal for
neutrons and protons) was adjusted so as to give the average
pairing gap in
120
Sn equal to 1.245 MeV. The pairing
channel was described within the Hartree-Fock-
Bogoliubov (HFB) approximation and the blocking and
filling approximations [27,28] were used to treat odd nuclei.
First, to provide a baseline for further analyses, in Fig. 4
we show the neutron 
ð3Þ
staggering calculated within the
spherical approximation [29]. Such an approximation al-
lows us to look at pure effects of pairing correlations,
whereby the binding energies of odd isotopes are decreased
due to one pair being broken. Otherwise, in this approx-
imation, effects due to deformation polarizations exerted
by valence particles are completely switched off. From
Fig. 4(b) we see that for the volume (vol) or mixed (mix)
pairing forces [30], the experimental decrease of 
ð3Þ
when
crossing the N ¼ 82 gap in Sn is very well reproduced,
whereas the data exclude the pure surface pairing force.
Such pairing decrease is due to a lower level density above
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
70 72 74 76 78 80 82 84 86 88 90
∆
(3)
(N) [MeV]
Neutron number
Sn
Te
Xe
FIG. 3 (color online). Experimental odd-even mass staggering
for Sn, Te, and Xe isotope chains. For clarity, odd-N points have
been connected with lines and the error bars have been omitted
when ð
ð3Þ
Þ < 10 keV. The open symbols present the experi-
mental values around the shell-gap prior to this work. The data
points for N ¼ 82 are beyond the scale.
Sn sur
Sn mix
Sn vol
70 80 90
(b)
0.5
1.0
1.5
Sn
Te
Xe
70 80 90
Neutron Number N
∆
∆
∆
∆
(3)
(N) [MeV]
SLy4 + HFB(sph)
(a)
FIG. 4 (color online). The same as in Fig. 3 but for the calcu-
lated (spherical HFB) odd-even mass staggering in (a) Sn, Te,
and Xe isotope chains and mixed pairing force and (b) Sn isotope
chain and surface, mixed, and volume pairing forces.
PRL 109, 032501 (2012)
PHYSICAL REVIEW LETTERS
week ending
20 JULY 2012
032501-3

the N ¼ 82 gap [4] (the surface pairing force is unable to
discriminate between the two surface-type orbitals h
11=2
and f
7=2
located below and above the N ¼ 82 shell gap,
respectively). Spherical calculations miss the experimental
values in Te and Xe isotopes [Fig. 4(a)], which indicates
that the polarization effects must here be taken into account
explicitly.
To better illustrate the trends in Z>50 nuclei, in Fig. 5
we show the experimental neutron 
ð3Þ
staggering in Sn,
Te, and Xe isotopes along the N ¼ 81 and 83 lines, com-
pared with theoretical results. In experiment [Fig. 5(a)], the
difference between the N ¼ 81 and 83 isotones smoothly
decreases from about 0.5 MeV in Sn to almost zero in Xe,
whereas spherical results [discussed above and repeated in
Fig. 5(b)] show no such decrease at all.
To analyze the effects of polarizations induced by de-
formation, we have performed two additional HFB calcu-
lations. First, by using the code
HFODD (v2.51i) [31], we
allowed valence particles or holes to induce self-
consistently deformed shapes. Then, the even isotones,
N ¼ 80, 82, and 84, turn out to be spherical anyhow;
namely, neither do the closed-core N ¼ 82 systems be-
come deformed, nor do the paired two neutron particles or
holes induce nonzero deformations. Only the polarization
effects exerted by unpaired odd neutron particles or holes
are strong enough to induce nonzero deformations in the
odd isotones, N ¼ 81 and 83.
In this way, the odd-particle polarizations lead to lower
values of the 
ð3Þ
staggering solely through increased
binding energies of odd isotones. Since such polarization
increases with adding protons, the obtained values of 
ð3Þ
decrease with Z, as illustrated in Fig. 5(c). However, this
trend does not depend on whether deformation is induced
by odd particles or holes; therefore, on both sides of the
N ¼ 82 shell gap we obtain an identical decrease with Z,at
variance with experiment.
To test if the above results may be affected by the
particle-number nonconservation inherent in the HFB the-
ory, we have repeated all calculations by using the
HFBTHO
code [32,33]. Here, within the Lipkin-Nogami method, we
were able to include the approximate particle-number
projection after variation. Moreover, the obtained solutions
were next exactly projected on good particle numbers.
Such a projected Lipkin-Nogami method was extensively
tested [33] and proved to be very efficient in describing
pairing correlations in near-closed-shell systems.
The obtained results are shown in Fig. 5(d). We see that the
general pattern is not qualitatively changed. The dynamic
pairing correlations, which are now nonzero even in the
N ¼ 82 isotones, lead to larger values of the 
ð3Þ
staggering,
which in the N ¼ 81 isotones perfectly well reproduce the
experimental trend. However, in the N ¼ 83 isotones, the
disagreement with data remains a puzzle. Indeed, the asym-
metry of the trend of the staggering, measured below and
above the N ¼ 82 gap, points to specific effects related to
orbitals occupied beyond N ¼ 82 or to their weak binding,
which are not captured by the current state-of-the-art theo-
retical approaches.
This work has been supported by the Academy of
Finland under the Centre of Excellence Program 2006–
2014 (Nuclear and Accelerator Based Physics Program at
JYFL) and the FIDIPRO program.
Note added in proof.—Recently, another Penning trap
study [34] appeared where some isotope masses overlap-
ping with our data set were measured showing excellent
agreement.
*jani.hakala@phys.jyu.fi
†
Present address: Max-Planck-Institut fu
¨
r Kernphysik,
Saupfercheckweg 1, 69117 Heidelberg, Germany.
‡
juha.aysto@phys.jyu.fi
[1] P. Hoff et al. (ISOLDE Collaboration), Phys. Rev. Lett. 77,
1020 (1996).
[2] K. L. Jones et al., Nature (London) 465, 454 (2010).
[3] D. C. Radford et al., Phys. Rev. Lett. 88, 222501 (2002).
[4] J. Terasaki, J. Engel, W. Nazarewicz, and M. Stoitsov,
Phys. Rev. C 66, 054313 (2002).
[5] M. P. Kartamyshev, T. Engeland, M. Hjorth-Jensen, and
E. Osnes, Phys. Rev. C 76, 024313 (2007).
[6] W. Satuła, J. Dobaczewski, and W. Nazarewicz, Phys. Rev.
Lett. 81, 3599 (1998).
[7] K. Blaum, Phys. Rep. 425, 1 (2006).
[8] M. Dworschak et al., Phys. Rev. Lett. 100, 072501 (2008).
[9] D. Neidherr et al., Phys. Rev. C 80, 044323 (2009).
[10] M. Arnould, S. Goriely, and K. Takahashi, Phys. Rep. 450,
97 (2007).
[11] A. Jokinen, T. Eronen, U. Hager, I. Moore, H. Penttila
¨
,S.
Rinta-Antila, and J. A
¨
ysto
¨
, Int. J. Mass Spectrom. 251, 204
(2006).
[12] H. Penttila
¨
et al., Eur. Phys. J. A 25, 745 (2005).
[13] G. Savard, St. Becker, G. Bollen, H.-J. Kluge, R. B.
Moore, Th. Otto, L. Schweikhard, H. Stolzenberg, and
U. Wiess, Phys. Lett. A 158, 247 (1991).
(b)
SLy4 + HFB(sph)
50 52 54
SLy4 + PLN(def)
(d)
0.0
0.5
50 52 54
(c)
Proton Number Z
SLy4 + HFB(def)
0.0
0.5
1.0
N=81
N=83
∆
∆
∆
∆
(3)
(N) [MeV]
EXP
(a)
FIG. 5 (color online). Odd-even staggering for the N ¼ 81 and
83 isotones as measured in experiment (a) and estimated within
the spherical (b), deformed (c), and deformed particle-number-
conserving (d) self-consistent calculations.
PRL 109, 032501 (2012)
PHYSICAL REVIEW LETTERS
week ending
20 JULY 2012
032501-4