Half-life of^{221} Fr in Si and Au at 4 K and at millikelvin temperatures

Abstract

The half-life of the α-decaying nucleus 221Fr was determined in different environments, that is, embedded in Si at 4 K, and embedded in Au at 4 K and about 20 mK. No differences in half-life for these different conditions were observed within 0.1%. Furthermore, we quote a value for the absolute half-life of 221Fr of t1/2=286.1(10) s that is of comparable precision to the most precise value available in the literature.

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arXiv:1010.6250v1 [nucl-ex] 29 Oct 2010
The half-life of221Fr in Si and Au at 4K and at mK temperatures.
F. Wauters,1B. Verstichel,2,1, ∗M. Breitenfeldt,1V. De Leebeeck,1V. Yu. Kozlov,1I. Kraev,1
S. Roccia,1G. Soti,1M. Tandecki,1E. Traykov,1S. Van Gorp,1D. Z´ akouck´ y,3and N. Severijns1
1Instituut voor Kern- en Stralingsfysica, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium
2CERN, CH-1211 Gen` eve 23, Switzerland
3Nuclear Physics Institute, ASCR, 250 68ˇReˇ z, Czech Republic
(Dated: November 1, 2010)
The half-life of the α decaying nucleus221Fr was determined in different environments, i.e. em-
bedded in Si at 4 K, and embedded in Au at 4 K and about 20 mK. No differences in half-life for
these different conditions were observed within 0.1 %. Furthermore, we quote a new value for the
absolute half-life of221Fr of t1/2= 286.1(10) s, which is of comparable precision to the most precise
value available in literature.
I. INTRODUCTION
The half-life of α and β decaying nuclei have always
been considered as constant, independent of their sur-
roundings. Recently, however, it has been claimed that
the half-life of a radioactive isotope would change if em-
bedded in a metallic host.
model applied to quasi-free metallic electrons [1–3], a
1/√T dependence for the screening energy UDwas pre-
dicted. When cooled down to a few Kelvin, the half-life
of β−(β+) decaying nuclei would then increase (decrease)
by several tens of percent and the half-life of α decaying
nuclei would even be shortened by several orders of mag-
nitude. This hypothetical mechanism was proposed as
a possible solution for long lived transuranic waste pro-
duced by fission reactors [1].
A series of subsequent experiments claimed to have ob-
served changes in the half-lives of both β∓and α decays,
although the effects were less profound than predicted
by the Debye plasma model. The half-life of α-decaying
210Po implanted in copper was reported to shorten by
6.3(14) % when cooled down to 12 K [4], the half-life of
β+decaying22Na embedded in Pd was observed to be
1.2(2) % shorter at 12 K [5], the half-life of β−decay-
ing198Au embedded in Au was observed to be 4(2) %
longer at 12 K [6], and for7Be (EC-decay), an increase
of about 1 % was reported [7]. Note that electron capture
decay rates may depend on the material hosting the ra-
dioactive isotope via small modifications of the electron
density around the EC decaying nucleus (see e.g. [8] and
references therein). In contrast to the above results, sev-
eral experiments carried out at a later stage on the β
decaying isotopes198Au [9–12],22Na [11, 12],64Cu [13],
and74As [14], and on the EC decaying7Be [10], did not
observe any changes of the half-lives up to the permille
level when these isotopes were embedded in a metallic
environment and cooled down to 10-20 K.
As to α decay, it was demonstrated theoretically that
taking into account not only the electron screening effect
Using the Debye plasma
∗Present address: Center for Molecular Modeling, Ghent Univer-
sity, Technologiepark 903, 9052 Zwijnaarde, Belgium
on the α particle’s tunneling potential, but also on its
binding energy inside the nucleus, the half-life would not
significantly change [15]. Further, it was argued [16, 17]
that if the Debye plasma model would be applicable to
α decays, the effect should have been observed previ-
ously already in Low Temperature Nuclear Orientation
experiments (LTNO) [18]. In this type of experiments
radioactive isotopes are implanted in a metallic foil, typ-
ically Fe, and cooled to milliKelvin temperatures. It was
claimed [4, 6] that no appreciable effect on nuclear half-
lives can be observed in LTNO experiments, as the ra-
dioactive ions implanted at typically 60 keV would end
up in the oxidized surface layer of the sample foil, which
acts as an insulator. This claim is clearly incorrect as the
LTNO technique is precisely based on the fact that the
radioactive nuclei end up at substitutional sites in a pure
bcc Fe lattice, where they experience a unique hyperfine
interaction. Nuclei that end up in an oxide surface layer
cannot be oriented and thus also do not show anisotropic
emission. To avoid a surface oxide layer, the foils used in
LTNO measurements are carefully prepared by polishing
and annealing procedures prior to inserting them in the
vacuum of the setup [19, 20]. Substitutional fractions of
about 70 % to 95 % are generally observed for 60 keV
implantations into a cold (i.e. 4 K or lower) Fe foil (e.g.
[21–24]). In LTNO experiments on α decaying isotopes
implanted in Fe, no half-life changes at the percent level
were observed between room temperature and 1 K [17],
and between 4 K and 50 mK [16].
Here, we report a dedicated half-life measurement of the
α decaying nucleus221Fr implanted in Si at 4 K, and in
Au at 4 K and at 20 mK. The three different half-life val-
ues obtained agree witch each other within 0.1 % and also
agree with the literature room temperature value. Previ-
ously, it was shown that the half-life of221Fr is constant
to less than a percent at room temperature, regardless to
its chemical environment [25].
II. THE EXPERIMENT
The
221Fr activitywasproduced atthe
ISOLDE/CERN facility by spallation reactions in-

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duced by a 1.4 GeV proton beam impinging on a UCx
target [26]. After diffusing out of the target, the221Fr
nuclei were ionized in a W surface ion source [27],
accelerated to 60 keV, and mass selected by the General
Purpose Separator (GPS) [28].
were subsequently transported to the NICOLE LTNO
setup [24, 29] where they were implanted into the cooled
Au or Si sample. A SRIM calculation [30] showed that
the implantation depth of221Fr ions with an energy of
60 keV is 80˚ A for Au and 330˚ A for Si, respectively.
In previous LTNO experiments, it was shown that
under these implantation conditions about 80 % of the
221Fr ions end up in a fully metallic environment in a
well-prepared Fe sample foil [23, 31].
The decay α particles were detected with three 500 µm
thick Si PIN diode detectors which were positioned at
an angle of 15◦relative to the surface of the sample foil
and at an angle of 90◦relative to each other.
type of detectors have previously been tested under the
conditions of this experiment and showed good behavior
[32].A high efficiency coaxial germanium detector,
place outside the cryostat, was used for γ ray detection.
Further, standard NIM electronics and a PC-based data
acquisition system were used.
The measurements consisted of a succession of implan-
tation and data-taking periods, where in the latter
every 30 s a spectrum was recorded during at least 10
221Fr half-lives.First, nine such measurements were
performed with an Au foil at milliKelvin temperatures,
after which the temperature of the foil was raised to
4 K and another five measurements were carried out.
Thereafter, the Au sample foil was removed and a Si
sample was loaded into the system to carry out five
measuring cycles at 4 K. During all measurements, a
1 kHz pulser was used to monitor the dead time. Only
data for which the dead time was below 5 % and the
shorter-lived beam contaminant221Ra (t1/2= 28(2) s
[33]) had decayed, were considered for analysis.
A typical α spectrum is shown in Fig. 1. After the
The radioactive ions
These
Channel
2000 250030003500 4000
Counts
0
500
1000
1500
2000
Exp. data
Entries
Mean
RMS
8192
2767
626.5
Experimental data
213Po
8.38 MeV
217At
7.07 MeV
221Fr
6.34 MeV
221Fr
6.13 MeV
213Bi
5.87 MeV
Pulser
FIG. 1. A typical α spectrum, taken a few minutes after the
end of the implantation of the mass 221 beam. The integral
of the pulser peak was used to correct for dead time.
221Ra activity has decayed, the only α lines appearing
in the spectrum originate from the decay of221Fr and
its daughter nuclei. The α line at 6.34 MeV, which will
be used to determine the half-life of221Fr, showed an
energy resolution of 32 keV (FWHM). The α lines of
217At and213Po were broadened to respectively 43 keV
and 57 keV because of the relocation of the recoiling
daughter nuclei following the α decay of221Fr and217At,
respectively, leading to a larger scattering for the decay
α particles and even allowing part of nuclei to leave the
host foil. Therefore, only the α lines of221Fr, which was
directly implanted, were considered for analysis.
The γ spectrum shown in Fig. 2 confirmed that, after
Channel
200 400600800 1000
Counts
0
5000
10000
15000
Exp. data
Entries
Mean
RMS
8192
316
168.3
Experimental data
57Co
122 keV
57Co
136 keV
221Fr
218 keV
213Bi
440 keV
209Tl
465 keV
FIG. 2. Typical γ-ray spectrum. Apart form the two γ lines
of57Co, only γ lines originating from the decay of221Fr or its
daughter nuclei were observed.
the isotope221Ra had decayed,221Fr and its daughters
were the sole activities present in the sample foil. The
two γ lines at 122 keV and 136 keV originate from the
57CoFe nuclear thermometer [34] which was soldered on
to the back side of the sample holder so as to monitor
the temperature in the milliKelvin range.
III. ANALYSIS AND RESULTS
In order not to be sensitive to possible small gain
shifts during the measurements, the
α peak was integrated using reasonably wide markers,
including in fact both α lines of221Fr (at 6.34 MeV and
6.13 MeV [35]), as well as the weak 5.87 MeV α line of
213Bi [36]. The background contribution to this integral
originates from this213Bi α line and from the long tail
of the 8.38 MeV α line from the decay of213Po [36],
which has the same effective half-life as213Bi.
correcting the integrals for the dead-time by normalizing
to the pulser peak (see Fig. 1), it was checked that the
background indeed decays according to the literature
value of the half-life of213Bi, i.e. 2735(4) s [36] (Fig. 3).
221Fr 6.34 MeV
After

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FIG. 3. A fit with a single exponential of the background
of the221Fr α peak integral. The resulting half-life coincides
with the literature value of the half-life of213Bi.
To fit the
was used:
221Fr decay curve, the following function
Ae−(t+B)ln2
C
+ D
?
e−(t+B)ln2
E
− e−(t+B)ln2
C
?
,(1)
which takes into account the build-up and decay of the
213Bi background activity. The free parameters in the
fit were the amplitudes of the counts from221Fr, A, and
from213Bi, D, as well as the half-life of221Fr, C. The
fixed parameter B expresses the start of the ingrowth
of the213Bi activity and is determined by a fit of the
ingrowth curve of the 440 keV γ line in the β decay of
213Bi. For the parameter E, the above mentioned litera-
ture value of the213Bi half-life was used [36]. A typical
example of a fit to determine the half-life of221Fr using
Eq. (1) is shown in Fig. 4.
time?(s)
00
2000
4000
6000
8000
counts
10
10
2
10
3
10
4
t =286.0(4)?s
/ =?0.97
? ?
1/2
2
221Fr?decay
213Bi?background
FIG. 4. Fit to the221Fr half-life, t1/2, of the decay curve of the
combined
to the half-life of213Bi (see Fig. 3).
221Fr α peaks. The background decays according
For the integration of the peaks in the γ spectrum, a lin-
ear background subtraction was carried out taking into
account the amplitude of the background to the left and
right of the peak. As the integral of the 218 keV γ line
in the decay of221Fr went to zero, a single exponential
could be fitted to extract the half-life (Fig. 5).
All fits were performed using the MINUIT package [37]
inside the publicly available ROOT framework. Nearly
all fits resulted in reduced χ2values, χ2/ν, close to unity.
This also demonstrates that the integrations and dead-
time corrections were being dealt with correctly. When-
ever the χ2/ν of the fit was larger than unity the error
on the corresponding t1/2was multiplied by
?χ2/ν.
time?(s)time?(s)
00
20002000
4000 4000
6000 6000
counts
1010
22
10 10
33
10 10
44
counts
t =286.1(8)?s
/ =?1.6
? ?
1/2
2
FIG. 5. Single exponential fit to the decay curve of the221Fr
218 keV γ line.
The results from all four detectors, three α parti-
cle detectors and one γ detector, as well as the results
of successive decay measurements in one given material
and for a given temperature, all turned out to be mutu-
ally consistent, thus demonstrating the stability of our
experiment.This is illustrated in Figs. 6, 7, and
where all t1/2values extracted from the three different
data sets are shown. The evolution of the temperature
of the sample during one of the measurements at mil-
liKelvin temperatures is shown in Fig. 9.
Table I summarizes the results for the three different
measurement conditions.Within 2.5 standard devia-
tions, no difference is observed between the half-lives of
221Fr embedded in the non-metallic Si environment at
4 K, in Au at 4 K, and in Au at milliKelvin tempera-
tures. Our results therefore do not support the claimed
temperature or host material dependence for α decay.
The weighted average value of all three results in Table
I is t1/2(221Fr) = 286.12(9) (χ2/ν = 1.6).
The quoted error on this value is purely statistical. To
quote an absolute half-life of221Fr, systematic errorshave
still to be taken into account. The systematic error re-
sulting from the dead-time correction by pulser normal-
ization was estimated by varying the markers which de-
fine the integral of the pulser peak, yielding a 0.5 s vari-
ation on the half-life of221Fr. In addition, the integrals
during the first half-life of221Fr were the most sensitive
to the dead-time correction, as at later times the amount
8,

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4
282
284
286
288
290
292
detector 1
detector 2
detector 3
! detector
measurement
half-life (s)
1
2
34
5
6
7
89
10
FIG. 6.
α particle detectors (using the most intense α lines in the decay of211Fr) and the 218 keV γ line. The last block (labeled ’10’)
shows the weighted average values for all 9 results for each detector.
221Fr half-life values obtained in the 9 measurements at milliKelvin temperatures in the Au host foil, for the three
TABLE I. Half-life values for
mK region or at 4 K, and in different environments, i.e. Au and Si. The values presented in the fifth column are the weighted
averages of the values of all four detectors. The last column indicates the difference of the half-life values obtained, compared
to the reference Si measurement. The quoted errors are purely statistical. Whenever the χ2/ν of the weighted average was
larger than unity, the error bar was increased by a factor
?χ2/ν.
221Fr measured by observing the decay α and γ rays at different temperatures, i.e. in the
Measurement condition
mK / Au
Detector
α1
α2
α3
γ
t1/2(221Fr) (s)
285.89(13)
286.10(11)
286.52(13)
286.43(36)
?χ2/ν
0.8
1.2
0.8
1.1
t1/2(221Fr) (s)
?χ2/ν∆t1/2(%)
286.17(8)0.90.01(5)
4 K / Au
α1
α2
α3
γ
285.91(13)
285.96(18)
286.22(43)
284.92(95)
1.2
1.4
3.0
3.6
285.93(11)1.40.09(6)
4 K / Si
α1
α2
α3
γ
286.11(40)
286.14(21)
286.25(25)
288.38(60)
1.2
1.5
0.9
-
286.19(12)1.1-
of dead time rapidly dropped below 1 %. Varying the
starting point of the fit reveals another systematic error,
related to the dead-time correction, of 0.7 s. The sys-
tematic error related to the presence of counts from the
decay of213Bi was estimated to be 0.5 s by varying the
value used for the half-life of213Bi, i.e. parameter B in
Eq. (1), within one standard deviation. Finally, an 0.11 s
systematic error comes from the accuracy of our timing
system which was determined by calibrating it with a ex-
ternal clock.
Adding all systematic errors in quadrature, our final
value for the half-life of221Fr becomes:
t1/2(221Fr) = 286.1 ± (0.09)stat± (1.0)systs .(2)
This value is in agreement with and more precise than
the value of 294(12) s quoted in Refs. [36, 38], and is in
agreement with and even slightly more precise than the
value of 287.4(12) s quoted in Ref. [25].
IV. CONCLUSION
Because of the findings reported in [16] and [17], it
comes as no surprise that our results are not supporting
the Debye-H¨ ucker model [1–3], which predicts (based on
the calculations of [11, 12]) a reduction of the half-life of
221Fr in a metal at 4 K with a factor of about 50, and at

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5
282
286
290
294
measurement
half-life (s)
detector 1
detector 2
detector 3
! detector
1
2
34
5
6
FIG. 7.
at 4 K in the Au host foil. The last block (labeled ’6’) shows
the weighted average values for all 5 results for each detector.
221Fr half-life values obtained in the 5 measurements
282
286
290
measurement
half-life (s)
detector 1
detector 2
detector 3
detector
1
2
34
5
6
FIG. 8.
in the Si host foil. During the last four measurements of this
series, the gamma spectra were corrupted. The last block
(labeled ’6’) shows the weighted average values for all 5 results
for each detector.
221Fr half-life values obtained in the 5 measurements
20 mK with a factor of many orders of magnitude more.
No dependency on the solid-state environment and tem-
perature of this α decaying isotope is observed up to a
level of 1 × 10−3, which is at variance with the reported
6 % change of the activity of213Po nuclei implanted in
Cu at 12 K [4]. Our result supports the theoretical cal-
culations of [15], which predicted no significant change
of the half-life. These dedicated half-life measurements
bring down the level to which no temperature and host-
material effect is observed on nuclear half-lives for α de-
cays to the same level of precision as was already estab-
lished for β decays and EC decays in Refs. [8–14].
0
1500
3000
4500
6000
Temperature?(mK)
10
15
20
25
30
35
Time?(s)
FIG. 9. Temperature evolution of the Au sample during one
of the measurements at mK temperatures deduced from the
57CoFe nuclear orientation thermometer. During the implan-
tation period, the sample warms to several tens of milliKelvin
due to the power deposited by the mass 221 beam and the
subsequent radioactive decay of the source that is gradually
increasing in strength. About 200 s after the end of the im-
plantation period, all of the short lived211Ra activity is gone
and the sample foil quickly cools down to below 20 mK, after
which the half-life measurement was started.
V.ACKNOWLEDGMENTS
This work was supported by the Fund for Scientific
Research Flanders (FWO), project GOA/2004/03 of the
K. U. Leuven, the Interuniversity Attraction Poles Pro-
gramme, Belgian State Belgian Science Policy (BriX net-
work P6/23), and the grant LA08015 of the Ministry of
Education of the Czech Republic.
Riisager, Hans Fynbo, Luis Fraile, and the ISOLDE col-
laboration for their support.
We thank Karsten
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