![The half life of 7 Be in 4 host materials. The solid line represents the weighted average and the broken lines correspond to a ±1σ interval. Also shown is the adopted value in the literature [20]](https://www.researchgate.net/profile/Ulli-Koester/publication/2151346/figure/fig4/AS:669308472537094@1536586983614/The-half-life-of-7-Be-in-4-host-materials-The-solid-line-represents-the-weighted-average_Q320.jpg)
Content uploaded by Ulli Koester
Author content
All content in this area was uploaded by Ulli Koester on Jan 15, 2013
Content may be subject to copyright.
arXiv:nucl-ex/0612003v1 3 Dec 2006
Precision Measurement of the Decay Rate of 7Be in Host Materials
Y. Nir-El1, G. Haquin1, Z. Yungreiss1, M. Hass2, G. Goldring2, S.K. Chamoli2, B.S. Nara
Singh2, S. Lakshmi2, U. K¨oster3,4, N. Champault3, A. Dorsival3, G. Georgiev3,5,
V.N Fedoseyev3, B.A. Marsh6, D. Schumann7, G. Heidenreich8, S. Teichmann8
1Radiation Safety Division,
Soreq Nuclear Research Centre, Yavne, Israel
2Department of Particle Physics,
Weizmann Institute of Science, Rehovot, Israel
3ISOLDE, CERN, Geneva, Switzerland
4Institut Laue Langevin, Grenoble, France
5CSNSM, CNRS/IN2P3; Univ Paris-Sud,
ORSAY-Campus, France
6Physics Department,
University of Manchester, Manchester, UK
7Laboratory of Radiochemistry,
Paul Scherrer Institute, Vil ligen, Switzerland
8Target Facilities and Active Technique Section,
Accelerator Division, Paul Scherrer Institute,
Villigen, Switzerland
(Dated: February 8, 2008)
A controlled and precise determination of the cross-sections of the fusion reactions 7Be(p,γ)8B and
3He(4He,γ)7Be, which play an important role in determining the solar neutrino flux, necessitates
the knowledge of a precise value of the electron-capture half-life of 7Be. This half-life may depend
on the material hosting the 7Be atoms via small modifications of the electron density around the
7Be nucleus. In this brief communication we report on the measurement of 7Be implanted in four
materials: copper, aluminum, sapphire and PVC. The four results are consistent with a null host
dependence within two standard deviations and their weighted average of 53.236(39)d agrees very
well with the adopted value in the literature, 53.22(6)d. The present results may exhibit a slight
(0.22%) increase of the half-life at room temperature for metals compared to insulators that requires
further studies.
PACS numbers: PACS 25.40.Lw, 26.20.+f, 26.65.+t
The decay rate of radioactive nuclei that undergo or-
bital Electron Capture (EC) depends on the properties
of the atomic electron cloud around the nucleus. Hence,
EC may exhibit varying decay rates if the nucleus is im-
planted into host materials with different properties of
their corresponding electron clouds. The first sugges-
tion of this effect in 7Be, which is the lightest nucleus
that decays by EC, and reports of experiments trying
to investigate this phenomenon, have been presented by
Segr`e et al. [1, 2, 3]. This effect has been qualitatively
attributed in the past to the influence of the electron
affinities of neighboring host atoms [4]. The electron
density of the 7Be atom in a high-electron affinity mate-
rial such as gold is decreased via the interaction of its 2s
electrons with the host atoms, resulting in a lower decay
rate (longer half-life). Recently, the life-time modifica-
tion has been suggested to stem from differences of the
Coulomb screening potential [5] between conductors and
insulators (see below).
Several experimental and theoretical investigations
were conducted during recent years to study the host ma-
terial effect on the decay rate of 7Be [4, 6, 7, 8, 9, 10],
with a somewhat confusing scattering of experimental re-
sults. It was found that the half-life of 7Be encapsulated
in a fullerene C60 cage and 7Be in Be metal is 52.68(5)
and 53.12(5) days, respectively, amounting to a differ-
ence of 0.83(13)% [9]. A smaller effect of ≈0.2% was
measured for the half-life 53.64(22) d of 7Be in C60 and
53.60(19) d of 7Be in Au [10]. A recent theoretical eval-
uation shows that short and long half-lives 52.927(56)d
and 53.520(50)d were measured for 7Be in Al2O3and 7Be
in (average of BeO, BeF2and Be(C5H5)2), respectively
[4]. These results yield the magnitude of the effect to
be as large as 1.1%. Another experimental investigation
has shown that the half-life increases by 0.38% from 7Be
in graphite, 53.107(22) d, to 7Be in Au, 53.311(42) [7],
while a very recent investigation [11] has seen no effect
to within 0.4%. The great interest in this phenomenon
for 7Be arises also from the need to explore the possible
contribution of the half-life of 7Be to the measurement of
the cross section of the two fusion reactions, 7Be(p,γ)8B
and 3He(4He,γ)7Be, that play an important role in de-
termining the solar neutrino flux [12, 13].
The present work has been undertaken in order to
probe this phenomenon yet again in an experimental ap-
proach that takes full advantage of the experience gained
in measuring implanted 7Be activity in a controlled and
precise manner for cross section determinations of the
2
solar fusion reactions mentioned above [12, 13]. As a
demonstration of the quality of the γ-activity measure-
ment, we cite the results of [12, 15] where two inde-
pendent determinations of the absolute activity of 7Be,
at the Soreq laboratory and at Texas A&MUniversity,
were in excellent agreement to within 0.7%. The same
setup has also been used for determining the 7Be activ-
ity ensuing from the 3He(4He,γ)7Be reaction [13]. We
report the measurement of the half-life of 7Be implanted
in four host materials: copper, aluminum, aluminum ox-
ide (sapphire - Al2O3) and PVC (polyvinyl chloride -
[C2H3Cl]n]).
The primary source of 7Be for implantation was a
graphite target, from the Paul Scherrer Institute (PSI),
used routinely for the production of πmesons [14].
Many spallation products are accumulated in the tar-
get, including 7Be. Graphite material from the PSI me-
son production target was placed in an ion-source canis-
ter and was brought to ISOLDE (CERN); 7Be was ex-
tracted at ISOLDE by selective ionization using a reso-
nance laser ion source. Direct implantation of 7Be at 60
keV in the host material was subsequently followed. A
detailed description of the extraction and implantation
of 7Be at ISOLDE is provided in detail in Refs. [15, 16].
This procedure facilitated a precision measurement of the
cross section of the reaction 7Be(p,γ)8B. The implanta-
tion spot was defined by a 2 mm collimator positioned
at close proximity to the target for the Cu sample and
a 5 mm collimator for the other samples. This small
change in the ensuing counting geometry has been well
investigated for the measurement of 7Be activity [13]
and does not affect the results in any significant man-
ner. The implantation process provided full control of
the spot composition (7Be; 7Li) as well as a radial and
depth profiles. For earlier implantations, at a density of
7Be in Cu far exceeding that of the present experiment,
the spot was found to be robust and the 7Be inventory
in the spot was stable [15, 17], excluding naturally ra-
dioactive decay. The copper, aluminum and PVC host
material targets consisted of disks of 12 mm diameter and
1.5 mm thickness, while the sapphire target was a square
of 10.2 mm x 10.2 mm. The median implantation depth
of 7Be into these materials has been estimated using the
SRIM code [18] and found to be 12, 24, 470 and 37 µm,
respectively, i.e. all implantation depths were well below
the surface.
Reproducible counting geometry of the 7Be samples
was achieved by attaching them to plastic holders which
were mounted precisely on the detector endcap. Also at-
tached to the holders was a 133Ba source (T1/2= 3841(7)
d [19]) to correct for variations in the performance of
the detection system (geometry, detection efficiency). In
a separate set of measurements, an external 137 Cs source
(T1/2= 30.03(5)y [19]) was attached to a similar holder
and thus used to estimate the reproducibility of source
position by successive mountings of that holder.
Gamma-ray spectra were acquired by a p-type coaxial
HPGe detector of 63.7% relative detection efficiency, 1.78
keV energy resolution (FWHM) and 81.6 peak/Compton
ratio, all specified at the 1332.5 keV gamma-ray of 60 Co.
The detector was enveloped by a 5.1 cm mercury cylinder
and placed within a 10.2 cm thick lead shield. The elec-
tronic train following the detector consisted of standard
units, followed by a 8192 channels multichannel analyzer.
7Be decays by EC to the ground and first excited state
of 7Li at 477.6 keV. The branching ratio to 7Li*(477.6)
is 10.44(4)% and the adopted half-life is 53.22(6) d [20].
This general-use value of the half-life was intended by the
evaluator, the late R. Helmer, to be valid for Be and BeO
samples and adequate for various chemical forms [20].
Measurements of all 7Be samples were repeated ap-
proximately every two weeks and the total decay time
between the beginnings of first and last measurements of
a sample was 171.1 (copper), 146.0 (PVC), 163.0 (alu-
minum) and 180.6 d (sapphire). Measurements were
stopped when the statistical uncertainty of the 477.6 keV
peak reached 0.15 to 0.10 %. At the beginning of the
measurements, the activities of each sample were: 1900,
1800, 2600 and 3700 Bq, respectively and a typical count-
ing duration was 16 hours.
Since the extracted half-life values may depend slightly
on the analysis method used to compute peak areas, we
describe in some detail one such procedure of data anal-
ysis that was used to extract the present results. Other
analysis procedures were tried as well, without affecting
the conclusions in any significant manner.
The net number of counts in the 477.6 keV peak of 7Be
was calculated by summation after the integral counts of
the two scaled broad flat windows, to the left and right of
the peak, were subtracted from the gross integral counts
in the Region Of Interest (ROI) of the peak, as can be
seen in Fig. 1.
The edges of the windows were determined to avoid
overlap with the peaks at 437.0 keV (sum of 81.0 and
356.0 keV of 133Ba) and 511.0 keV (annihilation) and the
ROI was determined to include the low- and high-energy
tails of the peak (see Fig. 2).
The gross number of counts in the ROI is given by:
G=G1+G2+gwhere gis the number of counts in the
channel at the top of the peak.
The baseline to be subtracted is
B=m1+ 0.5
n1
B1+m2+ 0.5
n2
B2(1)
The net number of counts and its standard uncertainty
are N=G−Band σ(N) = [G+σ2(B)]0.5where the
variance of the baseline is given by
σ2(B) = m1+ 0.5
n12
B1+m2+ 0.5
n22
B2(2)
3
FIG. 1: Definition of 4 regions for the calculation of a net peak
area by the summation method. The widths are n1,m1,m2
and n2(in channels) and the integral numbers of counts are
B1,G1,G2and B2, respectively, depicting the case where at
the top there is a single channel of gcounts.
FIG. 2: An expanded view (in logarithmic scale) around the
7Be peak at 477.6 keV. The quality of the γspectrum, the
two flat regions around the 7Be line and the absence of any
interfering γlines can be well discerned.
If the peak is symmetrical, i.e. two channels of equal
height at the top, then g= 0 and the 0.5 terms in Eqs.
(1) and (2) must be removed.
The peak count-rate at the beginning of data acquisi-
tion is given by
R0=λN
1−[exp(−λT )] (3)
where Tis the acquisition Real-Time (in s) and the decay
constant (in s−1) of 7Be is λ=ln(2)
T1/2.T1/2is the half-life
(in s) of 7Be and its initial value in Eq. (3) can be chosen
as 53.22 d. The contributions of the small errors on T
and λto the propagated uncertainty are negligible. The
standard uncertainty of R0is then: σ(Ro) = Roσ(N)
N.
With R(o)
obeing the count-rate at the beginning of the
first measurement (t= 0) of a sample, the exponen-
tial decay can be expressed by the linear relationship
ln(Ro) = ln(R(o)
o)−λt . A weighted linear regression
of ln(R0) versus tgives the slope λand the standard
uncertainty σ(λ). Hence, T1/2and σ(T1/2) can be ob-
tained. The calculated value of λwas substituted in Eq.
(3), instead of the initial value, and the linear regression
was repeated. Convergence was achieved after one iter-
ation. The linear fitting procedure was examined by 3
criteria: (a) the correlation coefficient r, (b) the reduced
chi-square χ2/ν, and (c) the probability Pχ(χ2,ν) that
any random set of ndata points would yield a value of
chi-square as large as or larger than χ2. The goodness
of the fit is determined by how close are the extracted
criteria to the optimal values of -1, +1 and 100%. The
number of degrees of freedom νis equal to n-2 for the
fitting of a straight line (the single coefficient is the slope
and the constant term is the intercept).
The decay of the peak count-rate of the Al2O3sample
is shown as an example in Fig. 3. Uncertainties of count-
rates were of the order 0.10 to 0.16% and express the high
precision of the measurements. Fig. 3 shows also that
the calculated straight line fits well the measured results.
The goodness of the linear fit of the Al2O3sample is
FIG. 3: Left axis - (diamonds): The decay curve of the 477.6
keV line of 7Be imbedded in the Al2O3sample. The straight
line was fitted by a weighted linear regression. Right axis -
(squares): The deviation between the measured and the fitted
count rates, divided by the corresponding uncertainty, for the
10 measurements of the Al2O3sample (see text).
displayed in Fig. 3, which shows the difference between
measured and calculated (fitted) count-rates, in units of
the associated uncertainty of the measured value.
The geometrical uncertainty, found by the 137 Cs source
to be 0.035%, was applied to each data point in quadra-
ture addition to the statistical uncertainty σ(Ro). The
analytical uncertainty 0.062% was determined by run-
ning three different methods to analyze a peak area. This
uncertainty was added in quadrature to the provisional
uncertainty as calculated by the linear regression.
The weighted average of the measured half-lives of the
four host materials, presented in Table I and in Fig. 4,
4
TABLE I: The details of the half-life determinations and the
linear regression fits for the four samples. ris the correlation
coefficient defined in the text.
Host nT1
2(d) (r+1)106χ2
νPχ(χ2, υ)(%)
Material
Cu 10 53.353(50) 1.9 0.94 48.56
Al 10 53.257(44) 0.9 0.73 66.53
Al2O310 53.180(43) 0.4 0.39 92.73
PVC 10 53.181(45) 1.7 1.26 25.88
is 53.236(39) d, which agrees well with the adopted value
53.22(6) d [20], with no account being taken of the host
material.
Even though the statistical test of the present data
supports a null effect within ±1σ, the results of Fig. 4
may indicate a slight positive trend of the half-life versus
the electron affinity, where a host material with high-
electron affinity such as copper (conductor), exhibits a
longer half-life, compared to a lower electron affinity ma-
terial such as aluminum oxide (insulator).
FIG. 4: The half life of 7Be in 4 host materials. The solid
line represents the weighted average and the broken lines cor-
respond to a ±1σinterval. Also shown is the adopted value
in the literature [20]
A different possible interpretation of the life-time re-
sults follows a recent observation by Wang et al. [21]
of an approximately 1% increase in the lifetime of 7Be
in metallic vs. insulator environments at low tempera-
ture. This change is consistent with the Debye screen-
ing model [5] that has been successfully used to explain
the screening potential for nuclear reactions at very low
beam energies. The average life times for the two insula-
tors (PVC and Al2O3) and the two metals (Cu and Al)
are 53.180(31) d and 53.299(33) d, respectively, a differ-
ence of 0.22%. Indeed, the trend of the present data is
in basic agreement with the temperature dependence of
the screening model, as well as with the results of [11].
A further investigation of such a small trend and its de-
tailed temperature dependence is clearly called for.
We thank the PSI technicians Pedro Baumann and Al-
fons Hagel for the target handling and the ISOLDE staff
for their help. The work has been supported in part by
the Israel Science Foundation and the EU-RTD project
TARGISOL (contract HPRI-CT-2001-50033). We ac-
knowledge the support of the ISOLDE Collaboration.
[1] E. Segr`e, Phys. Rev. 71, 274 (1947).
[2] E. Segr`e and C. E. Wiegand, Phys. Rev. 75, 39 (1949).
[3] R.F. Leininger, E. Segr`e and C. Wiegand, Phys. Rev. 76,
897 (1949).
[4] P. Das and A. Ray, Phys. Rev. C71, 025801 (2005).
[5] K.U. Kettner, H.W. Beckker, F. Strieder and C. Rolfs,
J. Phys. G 32, 489 (2006); and references therein.
[6] A. Ray, P. Das, S. K. Saha, S. K. Das, B. Sethi, A. Mook-
erjee, C. Basu Chaudhuri, G. Pari, Phys. Lett. B455, 69
(1999).
[7] E.B. Norman, G.A. Rech, E. Browne, R.-M. Larimer,
M.R. Dragowsky, Y.D. Chan, M.C.P. Isaac, R.J. McDon-
ald, A.R. Smith, Phys. Lett.B519, 15 (2001).
[8] A. Ray, P. Das, S.K. Saha, S. K. Das, Phys. Lett. B531,
187 (2002).
[9] T. Ohtsuki, H. Yuki, M. Muto, J. Kasagi, K. Ohno, Phys.
Rev. Lett. 93, 112501 (2004).
[10] A. Ray, P.Das, S.K. Saha, S.K. Das, J.J. Das, N. Mad-
havan, S. Nath, P. Sugathan, P.V.M. Rao, A. Jhingan,
Phys. Rev. C73, 034323 (2006).
[11] B.N. Limata et al., Eur. Phys. J. A27, s01, 193-196
(2006).
[12] L. T.Baby et al., Phys. Rev. Lett. 90, 022501 (2003).
[13] B.S. Nara Singh, M. Hass, Y. Nur-El, G. Haquin, Phys.
Rev. Lett. 93, 262503 (2004).
[14] G. Heidenreich, Proc. AIP 642, 122 (2002 ).
[15] L.T. Baby et al., Phys. Rev. C67, 065805 (2003).
[16] U. K¨oster, M. Argentini, R. Catherall, V. N. Fedoseyev,
H. W. G¨oggeler, O. C. Jonsson, R. Weinreich and
ISOLDE Collaboration, Nuc. Inst. Meth. B204, 343
(2003).
[17] M. Hass et al., Phys. Lett. B462, 237 (1999).
[18] SRIM package from www.srim.org
[19] J.K. Tuli, Nuclear Wallet Cards, 7th ed., (2005),
www.nndc.bnl.gov
[20] D.R. Tilley, C.M. Cheves, J.L. Godwin, G.M. Hale, H.M.
Hofmann, J.H. Kelley, C.G. Sheu, H.R. Weller, Nucl.
Phys. A708, 3(2002).
[21] B. Wang et al., Eur. Phys. J. A28, 375-377; and refer-
ences therein (2006).
