Radioactive decay speedup at T=5 K: electron-capture decay rate of (7)Be encapsulated in C(60).
ABSTRACT The electron-capture (EC) decay rate of (7)Be in C(60) at the temperature of liquid helium (T=5 K) was measured and compared with the rate in Be metal at T=293 K. We found that the half-life of (7)Be in endohedral C(60) ((7)Be@C(60)) at a temperature close to T=5 K is 52.47+/-0.04 d, a value that is 0.34% faster than that at T=293 K. In this environment, the half-life of (7)Be is nearly 1.5% faster than that inside Be metal at room temperature (T=293 K). We then interpreted our observations in terms of calculations of the electron density at the (7)Be nucleus position inside the C(60); further, we estimate theoretically the temperature dependence (at T=0 K and 293 K) of the electron density at the Be nucleus position in the stable center inside C(60). The theoretical estimates were almost in agreement with the experimental observations.
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ABSTRACT: A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.Physical review. B, Condensed matter 02/1988; 37(2):785-789.
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ABSTRACT: Diamond anvil presses of a new design were used to compress samples of beryllium-7 oxide to 120, 210, and 270 kilobars. The decay constant for the conversion of beryllium-7 to lithium-7 by electron capture was measured for compressed and uncompressed samples. A least-squares fit of the equation (lambda(c)-lambda)/lambda = KpP to the experimental data, where lambda(C) and lambda are the decay constants of the compressed sample and an uncompressed sample, respectively, and P is pressure, yields a value of (2.2 +/- 0.1) x 10(-5) kbar(-1) for the constant K(p).Science 10/1973; 181(4105):1164-5. · 31.03 Impact Factor
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ABSTRACT: The ratio of L- to K-shell electron captures in light nuclei is particularly sensitive to electron overlap and exchange effects. Calculations of these effects in (7)Be disagree by more than 20%. We report a measurement of the L/K ratio in (7)Be, using a cryogenic microcalorimeter which clearly separates L- and K-shell captures. The obtained L/K ratio of 0.040(6) is less than half that of existing predictions for free (7)Be. The discrepancy is likely due to in-medium effects distorting the L-shell electron orbitals.Physical Review Letters 02/2002; 88(1):012501. · 7.94 Impact Factor
Radioactive Decay Speedup at T ? 5 K: Electron-Capture Decay Rate
of7Be Encapsulated in C60
T. Ohtsuki,1K. Ohno,2T. Morisato,3T. Mitsugashira,4K. Hirose,1H. Yuki,1and J. Kasagi1
1Laboratory of Nuclear Science, Tohoku University, Mikamine, Taihaku-ku, Sendai 982-0826, Japan
2Department of Physics, Yokohama National University, Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
3Accelrys K.K., 3-3-1 Nishishinbashi, Minato-ku, Tokyo 105-0003, Japan
4IMR, Tohoku University, Narita, Oarai, Ibaraki 311-1313, Japan
(Received 14 September 2006; revised manuscript received 2 December 2006; published 18 June 2007)
The electron-capture (EC) decay rate of7Be in C60at the temperature of liquid helium (T ? 5 K) was
measured and compared with the rate in Be metal at T ? 293 K. We found that the half-life of7Be in
endohedral C60(7Be@C60) at a temperature close to T ? 5 K is 52:47 ? 0:04 d, a value that is 0.34%
faster than that at T ? 293 K. In this environment, the half-life of7Be is nearly 1.5% faster than that
inside Be metal at room temperature (T ? 293 K). We then interpreted our observations in terms of
calculations of the electron density at the7Be nucleus position inside the C60; further, we estimate
theoretically the temperature dependence (at T ? 0 K and 293 K) of the electron density at the Be nucleus
position in the stable center inside C60. The theoretical estimates were almost in agreement with the
DOI: 10.1103/PhysRevLett.98.252501PACS numbers: 21.10.Tg, 23.40.Hc, 27.20.+n, 36.40.Cg
In nuclear ?-decay and in the closely related process of
electron capture (EC), the decay curve is an exponential
function versus time with a constant decay rate. The decay
rate from any parent state, usually the nuclear ground state,
to any final daughter state is proportional to the product of
a nuclear matrix element and factors related to the phase-
space available to the neutrino and electron and to the
overlap between the initial electron and final nuclear
wave functions. Segre ´ et al. [1,2] were the first to suggest
that since the latter factors depend on the environment in
which the transmutation occurs, the decay rate should
depend on factors such as chemical form, pressure, and
temperature. It has been a long-standing challenge to es-
tablish the degree to which manipulation of these environ-
mental factors can, in practice, change nuclear decay rates
Recently we measured the half-life of7Be in endohedral
C60(7Be@C60) and reported that the decay rate increases
by almost 0.8% compared to that in Be metal [Be metal
(7Be)] [17,18]. This fact implied that the7Be atoms are
located in a unique environment inside C60. Several factors
contribute to this environment: the many ? electrons of
C60, special dynamic motions inside C60, etc. Therefore, it
is intriguing to study the temperature dependence of the
half-life of7Be inside C60. In the present study, in order to
suppress the dynamic motion of7Be inside C60, we mea-
sured the half-life of7Be in7Be@C60that had been cooled
to a temperature close to liquid helium (T ? 5 K). We also
present calculations of the electron density at the7Be
nucleus position at the site inside C60at different tempera-
tures (at T ? 0 K and 293 K). The theoretical estimates
reveal the stable position of the7Be nucleus inside C60and
the temperature dependence of the electron density at the
7Be nuclear position.
One way to produce atom endohedral C60is to insert
foreign atoms into preexisting C60[19–21]. We produced
an endohedral C60by nuclear recoil implantation [17,18].
Recently, we developed a reference method to measure the
half-life of7Be inside C60and that in Be metal, as shown in
Fig. 1(a). The method used to produce the7Be@C60and
7Be reference samples has been described previously .
In order to measure the half-life at T ? 5 K, the7Be@C60
sample was placed in the top of a He closed-cycle cryostat.
The two samples,7Be@C60(fastened in the cryostat) and
Be metal (7Be), were placed in a computer-controlled
sample changer, which moved the samples precisely in
front of a ?-ray detector as shown in the figure. The
measurement was started after the7Be@C60sample under-
went sufficient cooling at T ? 5 K in the vacuum state.
This arrangement allowed the decay rates of the two
samples to be measured in a consistent fashion while
reducing systematic errors. In the system, the internal
clock time of the computer for data acquisition was con-
stantly calibrated by a time-standard signal distributed via
a long-wave radio center in Japan. The 478 keV ? rays
emanating from the EC-decay daughter of7Be were mea-
sured using a high-purity germanium (HPGe) detector
(?EFWHMis 1.8 keV and has 50% relative efficiency)
coupled to a 2048- and/or 4096-channel pulse-height ana-
lyzer. Here, we set the specific measurement duration to
21600 s (21480 s for the live measurement time and 120 s
for the dead time of the measurement system plus the
sample exchange) for one data point. In Fig. 1(b), a typical
?-ray spectrum obtained in the measurement of the7Be
decay inside C60is shown as a function of ?-ray energy in
keV. The amount of radioactivity associated with the decay
through the identification of characteristic ? rays.
7Be (E?? 478 keV) could be uniquely analyzed
PRL 98, 252501 (2007)
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© 2007 The American Physical Society
Figure 2 shows two exponential decay curves of the7Be
radioactivities for samples of7Be@C60and Be metal (7Be)
plotted versustime (in days). In order to compare the decay
curves in Fig. 2, the data for the7Be@C60were normalized
to those for the Be metal (7Be) at Time ? 0, which was
5:17 counts=s (cps) for the7Be@C60and 5.65 cps for the
Be metal (7Be). Red and blue circles indicate the radio-
activities (decay rate in cps) for the samples of7Be@C60at
T ? 5 K and Be metal (7Be) at T ? 293 K, respectively.
The decay curves obtained in the present measurements
were fitted, byuse ofthe MINUITprogram distributed by the
CERN Program Library. The statistical error dominates the
uncertainty for each data point shown in Fig. 2. The un-
certainty of our measurement corresponds to the uncer-
tainty of the slope of the straight line fitted to the logarithm
of the counts (i.e., counts per second) of the decay spec-
trum. The reduced chi-square values of the exponential fits
are between 0.90 and 1.12. The uncertainty due to the dead
time was estimated to be less than 0.04%, and the system-
atic error in the measurements was estimated to be less
than half of the statistical error quoted above . We have
measured the decay rates and deduced the corresponding
half-lives of7Be in samples of7Be@C60(at T ? 5 K) and
in Be metal (7Be) (at T ? 293 K) in two separate mea-
surements with durations of 168 d and 143 d. In Fig. 3, the
red circles indicate the half-lives obtained for the sample of
7Be@C60at T ? 5 K and the blue circles indicate those of
the Be metal (7Be) at T ? 293 K. Green circles indicate
the half-lives in7Be@C60from the previous study .
The half-life of7Be in7Be@C60(at T ? 5 K) averaged
over two runs was 52:47 ? 0:04 d.
On the other hand, the half-life of
metal (7Be) averaged over many measurements was
7Be in the Be
Decay rate (cps)
Be metal( Be)
FIG. 2 (color).
the7Be@C60at T ? 5 K (red circles) and the Be metal (7Be) at
T ? 293 K (blue circles). Insets corresponding to the decay
intervals of 0–20 d and 140–170 d are displayed with an
Exponential decay curves of7Be in samples of
Be metal crystal (7Be)
FIG. 3 (color).
are plotted as red circles for the7Be@C60at T ? 5 K. The green
circles are half-lives measured previously at T ? 293 K (T ?
293 K) (previous work ). The blue circles represent the half-
lives used as reference samples of Be metal (7Be) (e.g., shown by
arrows). Points shown by the asterisk are the half-lives of Be
metal (7Be) samples compared to other samples . Half-lives
previously measured span the thick yellow bar.
Half-lives (T1=2) measured in this time period
470 480 490
Energy / keV
Counts / 21480 sec
Energy / keV
Counts / 21480 sec
He compressor system
FIG. 1 (color).
the half-lives of7Be in the7Be@C60and of the7Be reference
metal. (b) Typical ?-ray spectrum of
7Be@C60cooled down to T ? 5 K.
(a) Experimental setup for the measurement of
7Be in the sample of
PRL 98, 252501 (2007)
22 JUNE 2007
53:25 ? 0:04 d . The half-lives obtained for7Be in
several other host materials and chemical forms such as
graphite, gold, oxide, etc., have been presented by many
works [3–16]. In Fig. 3, half-lives previously measured are
alsoshownbyathickyellowbarasa comparison. The half-
lives mostly range between 53.10 and 53.40 d [6,10,12–
15]. Therefore, we find that our reference measurement of
the half-life for7Be in Be metal (7Be) is in satisfactory
agreement with other available data.
It is surprising to note that the difference between the
half-life of7Be in the7Be@C60at T ? 5 K and that in the
Be metal (7Be) at T ? 293 K was more dramatic than that
between the half-life of7Be in the7Be@C60at T ? 293 K
and that in the Be metal (7Be) at T ? 293 K as shown in
Fig. 3. Here, the former half-life at T ? 5 K was almost
1.5% shorter than that for the Be metal (7Be) sample at
T ? 293 K.Itcan beclearly seen inthe figurethat the half-
life of7Be in the7Be@C60(at T ? 5 K) is 0.34% shorter
than that in the7Be@C60under T ? 293 K and shorter
than any7Be half-life reported in any environment up to
Since the EC-decay rate depends on the electron density
at the nucleus position, we calculated the electron density
at the7Be nucleus position inside the C60. In order to
correctly express the cusplike profile of the electron den-
sity near the nucleus position, we adopted the first-
principles calculation program, DMOL3 , using numeri-
cal, localized orbitals as a basis set. Our calculation is
based on the generalized gradient approximation (GGA)
called BLYP [24,25] for the exchange-correlation potential
of the density functional theory. We used a double-numeric
quality basis set with polarization functions (DNP). We
first calculated the total energy of the Be atom for various
positions inside the C60. From this calculation, we identi-
fied four positions of the Be atom having relatively low
total energies; from the lowest to the fourth lowest in total
energy, the Be atom is located at the C60center, under a
five-membered ring, under a single bond, and under a six-
membered ring. Then, starting from these four Be geome-
tries, we performed a structural optimization of the whole
system and redetermined the total energy and the electron
density at the Be nucleus position after relaxation at T ?
0 K. We also determined the electron density (at the7Be
nucleus position) for an isolated Be atom and for Be metal.
All the results are listed in Table I. From Table I, it is clear
that the most stable position of the Be atom inside the C60
is the center, and the electron density at the Be nucleus
position is the highest in this case. The electron density at
the Be nucleus position changes from higher to lower
depending on the Be position as follows: C60center >
Be atom > Be metal > other sites inside C60.
At the C60center, the Be atom is almost isolated with no
bonds with the surrounding carbon atoms as seen in Fig. 4
(upper left). The electronic wave function of the Be2s
spread widely inside the C60and is somewhat compressed
relative to the situation in an isolated atom. As a result, the
electron density at the C60center is slightly higher than that
of an isolated Be atom. On the other hand, when the Be
atom is adsorbed under a single bond (Fig. 4, lower left),
the Be2s HOMO is hybridized with the unoccupied t1u
orbitals of the C60. When the Be atom is adsorbed under a
five-membered ring (Fig. 4, middle) or a six-membered
ring (Fig. 4, right), the system shows a spin polarization
with a magnitude of 2?B. Their majority spin HOMO and
HOMO-1 orbitals are also shown in Fig. 4. Unlike in the
other cases, one of the Be2s electrons transfers to the t1u
orbital and expands into a large area in the C60(the upper
figures show the majority spin HOMO), and the other
electron stays around the Be atom (the lower figures
show the majority spin HOMO-1). As a result, the electron
density at the Be nucleus position adsorbed underthe C60is
less than that of an isolated Be atom. By contrast, in a Be
metal, the Be2s electrons spread over the whole metal, but
each Be atom contains a net portion of the Be2s electrons.
Therefore, the electron density at the Be nucleus position
in a Be metal is higher than in the cases where the Be atom
is adsorbed under the C60, away from the center of the
Using the total energy E?r? and the electron density ??r?
calculated at each Be nucleus position r inside the C60, we
evaluate the electron density at Be nucleus position at
temperature (T) by taking average of the densities at
various Be positions according to the Boltzmann distribu-
tion. Details of the procedures for calculation will be
presented elsewhere . At the absolute zero temperature
(T ? 0 K), the Be atom is located at the C60center and the
electron density at the Be nucleus position is equal to
36:016e?=?A3, while at T ? 293 K, it is estimated as
35:899e?=?A3. (The7Be atom at T ? 293 K moves around
the local minima as seen in Fig. 4 and electrons sometimes
interact between Be2s and C60t1ustates.) Then, the rela-
tive difference between them amounts to 0.33%, which can
be compared with the relative difference of 0.34% for the
experimentally determined half-lives (52.47 d at T ? 5 K
and 52.65 d at T ? 293 K). On the other hand, if we com-
position in lower and/or the lowest total energy inside the C60.
The electron density of an isolated Be atom and of a Be metal is
also tabulated for comparison.
The calculated electron density at the7Be nucleus
Electron densityTotal energy
0.0 (most stable)
Under six-membered ring
Under five-membered ring
Under single bond
PRL 98, 252501 (2007)
22 JUNE 2007
pare the electron density of the7Be@C60at T ? 293 K
(35:899e?=?A3) with that of Be metal (35:423e?=?A3,
even also at T ? 293 K), the relative difference between
them amounts to 1.3%. This value can be also compared to
the relative difference 1.1% in the experimentally deter-
mined half-lives (52.65 d for the7Be@C60and 53.25 d for
the Be metal (7Be) on average in Fig. 3). The agreement
between the theoretical and the experimental results is
The L=K capture ratio (i.e. the ratio of electron density
of L?Be2s? and K?Be1s? orbits at the Be nucleus position)
is estimated to be almost 10% in the isolated Be atom
[27,28]. In our theoretical calculation, we also found that
the7Be atom stays at the center (potential minimum) of the
C60and the Be2s electrons can be fully restricted to the Be
nucleus at T ? 0 K as in an isolated Be atom (1s2, 2s2),
even though the calculated electron densities at the Be
nuclear position are somewhat different . On the other
hand, chemically and/or metallically bonded Be atoms
always lose Be2s electron to some degree, due to their
alkali-earth nature (relatively smaller electronegativity).
Therefore, the L=K capture ratio in the7Be atom is re-
duced when the7Be is chemically bonded and/or inside
host metal materials [3–16]. Here, the magnitude of the
average charge transfer from the L?Be2s? electrons of the
7Be atom may play an important role for such variation in
the decay constant in the environments.
In summary, the EC-decay rate of7Be in C60at T ? 5 K
and in Be metal (7Be) at T ? 293 K was measured with a
reference method. We found that the half-life of the7Be in
the7Be@C60cooled to T ? 5 K, 52:47 ? 0:04 d, breaks
the previous half-life record by more than 0.3%, and that
the7Be decay speed in the7Be@C60at T ? 5 K is nearly
1.5% faster than that in the Be metal (7Be) at T ? 293 K.
From the theoretical calculation, the most stable position
of the Be atom inside the C60is the center, and the electron
density at the Be nucleus position is the highest even at the
low temperature. In this case, we would like to emphasize
that we have observed the nuclear decay rate of a7Be
nucleus surrounded by a (1s2, 2s2) electron shell which
is almost that of an isolated atom.
The authors are grateful to the staff at the Accelerator
Divisions of the Laboratory of Nuclear Science and the
Cyclotron Radio-Isotope center, Tohoku University. This
workwas supported by Grants-in-Aid for Co-operative Re-
search No. 10640535, No. 12640532, and No. 17350024
from the Ministry of Education of Japan, the REIMEI
Research Resources of JAERI, and by the Mitsubishi
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FIG. 4 (color).
wave functions for the HOMO (and
HOMO-1) of the C60molecules with a
Be atom incorporated at the center
(upper left, front view, and side view),
below a single bond (lower left, front
view, and side view), below a five-
membered ring (middle, front view, and
side view), and below a six-membered
ring (right, front view, and side view).
Schematic view of the
PRL 98, 252501 (2007)
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