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The average neutron lifetime value $\tau_n$ is an open problem in p...
[Weak force](https://en.wikipedia.org/wiki/Weak_interaction) is one...
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38 Scientific American, April 2016
L
UCKILY FOR LIFE ON EARTH, MOST MATTER IS NOT RADIOACTIVE. WE TAKE THIS FACT FOR
granted, but it is actually somewhat surprising because the neutron, one of the
two components of atomic nuclei (along with the proton), is prone to radioac-
tive decay. Inside an atomic nucleus, a typical neutron can survive for a very
long time and may never decay, but on its own, it will transform into other par-
ticles within 15minutes, more or less. The words “more or less” cover a disturb-
ing gap in physicists’ understanding of this particle. Try as we might, we have
not been able to accurately measure the neutron lifetime.
This “neutron lifetime puzzle” is not just embarrassing for us
experimentalists; resolving it is vital for understanding the na-
ture of the universe. The neutron decay process is one of the sim-
plest examples of the nuclear “weakinteraction—one of natures
four fundamental forces. To truly understand the weak force, we
must know how long neutrons live. Furthermore, the survival
time of the neutron determined how the lightest chemical ele-
ments first formed after the big bang. Cosmologists would like to
calculate the expected abundances of the elements and compare
them with astrophysical measurements: agreement would con-
firm our theoretical picture, and discrepancy could indicate that
undiscovered phenomena aected the process. To make such a
comparison, however, we need to know the neutron lifetime.
More than 10 years ago two experimental groups, one a Rus-
sian-led team in France and the other a team in the U.S., attempt-
ed separately to precisely measure the lifetime. One of us (Gelten-
bort) was a member of the first team, and the other (Greene) was
a member of the second. Along with our colleagues, we were sur-
prised and somewhat disturbed to find that our results disagreed
considerably. Some theoreticians suggested that the dierence
arose from exotic physics—that some neutrons in the experi-
ments might have transformed into particles never before detect-
ed, which would have aected the dierent experiments in diver-
gent ways. We, however, suspected a more mundane reason—per-
haps one of our groups, or even both, had simply made a mistake
or, more likely, had overestimated the accuracy of its experiment.
The U.S. team recently completed a long, painstaking project to
study the most dominant source of uncertainty in its experiment
in hopes of resolving the discrepancy. Rather than clearing up the
situation, that eort confirmed our earlier result. Similarly, other
re searchers later confirmed the findings of Geltenbort’s team.
This discrepancy has left us even more perplexed. But we are not
giving up—both groups and others continue to seek answers.
TIMING NEUTRONS
IN THEOR Y, measuring the neutron lifetime should be straightfor-
ward. The physics of nuclear decay are well understood, and we
have sophisticated techniques for studying the process. We know,
for instance, that if a particle has the possibility of transforming
into a lower-mass particle or particles while conserving such char-
acteristics as charge and spin angular momentum, it will. Free
neutrons display this instability. In a process called beta decay, a
neutron breaks up into a proton, an electron and an antineutrino
(the antimatter counterpart of the neutrino), which collectively
sum to a slightly lower mass but the same total charge, spin angu-
lar momentum and other conserved properties. These conserved
properties include “mass-energy,” meaning that the daughter
particles carry the dierence in mass in the form of kinetic ener-
gy, the energy of motion.
We cannot predict exactly when a particular neutron will de -
cay because the process is a fundamentally random quantum phe-
nomenon—we can say only how long neutrons live on average.
Thus, we must measure the average neutron lifetime by studying
the decay of many neutrons.
Investigators have employed two experimental methods—one
called the bottle” technique and the other the “beam” ap proach.
Bottle experiments confine neutrons in a container and count
how many are left after a given time. The beam method, in con-
trast, looks not for the disappearance of neutrons but rather for
the appearance of the particles into which they decay.
The bottle approach is particularly challenging because neu-
trons can pass easily through matter and thus through the walls
of most containers. Following a suggestion first explicitly made by
Russian physicist Yuri Zel’dovich, experimentalists who use the
bottle approach—as Geltenbort and his colleagues in France do—
get around the problem by trapping extremely cold neutrons
(that is, those with a very low kinetic energy) within a container of
very smooth walls [see box on page 40]. If the neutrons are slow
enough and the bottle smooth enough, they reflect from the walls
and hence remain in the bottle. To achieve this eect, the neu-
trons must move at speeds on the order of just a few meters per
second, as opposed to the roughly 10 million meters per second
neutrons travel when emitted during nuclear fission, for instance.
These “ultracold” neutrons are so slow that you could “outrun
Peter Geltenbort is a sta scientist at the Institut
Laue-Langevin in renoble, rance, where he uses
one of the most intense neutron sources in the world
to research the fundamental nature of this particle.
eorey . reene is a professor of physics at the University
of Tennessee, with a oint appointment at the Oak Ridge National
Laboratorys Spallation Neutron Source. He has been studying
the properties of the neutron for more than 40 years.
© 2016 Scientific American
April 2016, ScientificAmerican.com 39Graphics by Nigel Hawtin
them. The most accurate bottle experi-
ment to date took place at the Institut
Laue-Langevin (ILL) in Grenoble, France.
Unfortunately, no bottle is ever perfect.
If neutrons occasionally leak out of the
bottle, we will attribute this loss to beta
decay and will get the wrong lifetime. We
must therefore be sure to correct our cal-
culations so as to count only those parti-
cles that actually undergo beta decay.
To make that correction, we use a clev-
er technique. The number of neutrons lost
through the walls of the bottle de pends on
the rate at which neutrons bounce against
the walls. If the neutrons are slower or the
bottle is bigger, the bounce rate, and thus
the loss rate, will go down. By varying both
the size of the bottle and the energy (veloc-
ity) of the neutrons in successive trials, we
can ex trapolate to a hypothetical bottle in
which there are no collisions and thus no
wall losses. Of course, this extrapolation is
not perfect, but we do our best to account
for any error this calculation introduces.
In the beam method—used by Greene and others at the
National Institute of Standards and Technology (NIST) Center
for Neutron Research—we send a stream of cold neutrons
through a magnetic field and a ring of high-voltage electrodes
that traps positively charged particles [ see box on page 41 ].
Because neutrons are electrically neutral, they pass right
through the trap. If, however, a neutron decays within the trap,
the resulting positively charged proton gets “stuck.” Periodically
we “openthe trap and expel and count the protons. In princi-
ple, the proton trapping and detection are nearly perfect, and
we must make only very small corrections for the possibility
that we missed decays.
WHERE COULD WE GO WRONG?
TO BE USEFUL, a measurement must be accompanied by a reliable
estimate of its accuracy. A measurement of a persons height
that has an uncertainty of one meter, for example, is much less
meaningful than a measurement that has an uncertainty of one
millimeter. For this reason, when we make precision measure-
ments we always report an experimental uncertainty; an uncer-
tainty of one second, for instance, would mean our measure-
ment had a high probability of being no more than a second
shorter or a second longer than the true value.
Any measurement has, in general, two sources of uncertainty.
Statistical error arises because an experiment can measure only
a finite sample—in our case, a finite number of particle decays.
The larger the sample, the more reliable the measurement and
the lower the statistical error.
The second source of uncertainty—systematic error—is much
more dicult to estimate because it arises through im perfections
in the measurement process. These flaws may be something sim-
ple, like a poorly calibrated meter stick used to measure a persons
height. Or they can be more subtle, like a sampling bias—in a tele-
phone poll, for example, one might overly rely on calls to land
lines rather than to cell phones and thus fail to capture a truly
representative population sample. Experimentalists go to great
lengths to reduce these systematic errors, but they are im possible
to eradicate completely. The best we can do is carry out a detailed
study of all imaginable sources of error and then estimate the lin-
gering eect each might have on the final result. We then add this
systematic error to the statistical error to give a best estimate of
the overall reliability of the measurement. In other words, we put
great eort into estimating the known unknowns.
Of course, our great fear is that we have overlooked an “un -
known unknown”—a systematic eect that we do not even know
we do not know—hidden within the experimental procedure.
While we go to extreme pains to explore all possible uncertainties,
the only way to overcome this type of additional error with real
confidence is to perform another, completely independent mea-
surement using a totally dierent experimental method that does
not share the same systematic eects. If two such measurements
agree within their quoted uncertainties, we have confidence in the
results. If, on the other hand, they disagree, we have a problem.
For the measurement of the neutron lifetime we have two
such independent methods: the beam and the bottle. The most
recent result from the beam experiment at NIST gave a value for
the neutron lifetime of 887.7 seconds. We determined the statisti-
cal uncertainty in our estimate to be 1.2seconds and the system-
atic uncertainty 1.9seconds. Combining those errors statistically
gives a total uncertainty of 2.2 seconds, which means that we
believe the true value of the neutron lifetime has a 68 percent
probability of being within 2.2seconds of the measured value.
The bottle experiment at ILL, on the other hand, measured a
neutron lifetime of 878.5 seconds with a statistical uncertainty
of 0.7second, a systematic uncertainty of 0.3second and a total
uncertainty of 0.8second.
These are the two most precise neutron lifetime experiments
of each type in the world, and their measurements dier by
approximately nine seconds. Such a time span may not sound
like a lot, but it is significantly larger than the calculated uncer-
tainties for both experiments—the probability of obtaining a
How Neutrons Decay
Despite decades of trying, scientists hae not een ale to denitiel measre ho
long netrons lie otside o atomic ncleithe est eeriments in the orld rodce
conicting reslts lthogh the length othe netron lietime is ndetermined the
case o netron deca is ell knon hrogh a rocess called eta decaa netron
transorms into a roton and releases an electron and an antinetrino the antimatter
conterart to the netrino article he deca ensres that the nal articles charge
and sin anglar momentm tall to eal those o the original article
BASICS
Neutron
Proton
Electron
Antineutrino
Charge = –1
Spin angular
momentum =
+
½
Charge = +1
Spin angular
momentum =
+
½
Charge =
0
Spin angular
momentum =
+
½
Charge = 0
Spin angular
momentum =
+
½
Charge = 0
Spin angular
momentum = -½
{
{
© 2016 Scientific American
dierence of this size by chance alone is less than one part in
10,000. We must therefore seriously consider the possibility that
the discrepancy results from an unknown unknown—we have
missed something important.
EXOTIC PHYSICS
AN EXCITING explanation for the dierence could be that it actually
re flects some exotic physical phenomenon not yet discovered. A
reason to think such a phenomenon might exist is that although
the bottle and beam methods disagree, other beam studies show
good agreement among them selves, as do other bottle studies.
Imagine, for example, that in addition to the regular beta de -
cay, neutrons decayed via some previously unknown process that
does not create the protons sought in beam experiments. The bot-
tle experiments, which count the total number of lost” neutrons,
would count both the neutrons that disappeared via beta decay
as well as those that underwent this second process. We would
therefore conclude that the neutron lifetime was shorter than
that from “normal” beta decay alone. Meanwhile the beam exper-
iments would dutifully record only beta decays that produce pro-
tons and would thus result in a larger value for the lifetime. So
far, as we have seen, the beam experiments do measure a slightly
longer lifetime than the bottles.
A few theorists have taken this notion seriously. Zurab Berezhi-
ani of the University of LAquila in Italy and his colleagues have
suggested such a secondary process: a free neutron, they propose,
might sometimes transform into a hypothesized “mirror neutron
that no longer interacts with normal matter and would thus seem
to disappear. Such mirror matter could contribute to the total
amount of dark matter in the universe. Although this idea is quite
stimulating, it remains highly speculative. More definitive con-
firmation of the divergence between the bottle and beam meth-
ods of measuring the neutron lifetime is necessary before most
physicists would accept a concept as radical as mirror matter.
Much more likely, we think, is that one (or perhaps even both)
of the experiments has underestimated or overlooked a systemat-
ic eect. Such a possibility is always present when working with
delicate and sensitive experimental setups.
WHY THE NEUTRON LIFETIME MATTERS
FIGURING OUT WHAT WE MISSED will of course give us experimental-
ists peace of mind. But even more important, if we can get to the
bottom of this puzzle and precisely measure the neutron lifetime,
we may be able to tackle a number of long-standing, fundamen-
tal questions about our universe.
First of all, an accurate assessment of the timescale of neutron
decay will teach us about how the weak force works on other parti-
cles. The weak force is responsible for nearly all radioactive de cays
and is the reason, for instance, that nuclear fusion occurs within
the sun. Neutron beta decay is one of the simplest and most pure
Fill with
neutrons
Count #1
#1
#2
#3
Time
Number
of neutrons
observed
Count #2
Count #3
Dierent Techniques,
Dierent Results
Scientists have tried to main technies to measre the aerage
netron lietime the ottle and the eam methods he arios
ottle measrements oer the ears tend to agree ith one an
other ithin their calclated error ars as do the eam measre
ments he reslts rom the to technies hoeerconict
he discreanc aot eight seconds eteen the ottle and
eam aeragesma not seem like mch t it is signicantl
larger than the measrementsncertainthich means the
diergence rere sents a real rolem ither the researchers hae
nderestimated the ncertaint o their reslts ormore eciting
the dierence arises rom some nknon hsical henomenon
EXPERIMENTS
The Bottle Method
ne ay to easure ho long neutrons lie is to ll a ontainer ith
neutrons and empty it after various time intervals under the same con-
ditions to see ho any reain. hese tests ll in points along a ure that
represents neutron deay oer tie. ro this ure, sientists use a siple
forula to alulate the aerage neutron lifetie. eause neutrons oa-
sionally esape through the alls of the ottle, sientists ary the sie of
the ottle as ell as the energy of the neutronsoth of hih aet ho
many particles will escape from the bottle—to extrapolate to a hypothetical
ottle that ontains neutrons perfetly ith no losses.
See a video about neutron beta decay at Scienticmerican.comapr2016neutron-lifetime
SCIENTIFIC AMERICAN ONLINE
Neutron Lifetime (seconds)
Year of Experiment
Neutron Lifetime Measurements
Beam method
Bottle method
Beam method average* (blue zone):
888.0
+
2.1 seconds
1990
900
895
890
885
880
875
870
1995 2000 2005 2010 2015
Bottle method average (green zone):
879.6
+
0.6 seconds
Uncertainty
Disagreement
*The beam method average does not include the 2005 measurement, which was superseded by the 2013 beam study.
© 2016 Scientific American
April 2016, ScientificAmerican.com 41
examples of a weak force interaction. To calculate the details of
other, more complex nuclear processes involving the weak force,
we must first fully understand how it operates in neutron decay.
Discerning the exact rate of neutron decay would also help
test the big bang theory for the early evolution of the cosmos.
According to the theory, when the universe was about one second
old, it consisted of a hot, dense mixture of particles: protons, neu-
trons, electrons, and others. At this time, the temperature of the
universe was roughly 10 billion degrees—so hot that these parti-
cles were too energetic to bind together into nuclei or atoms.
After about three minutes, the universe expanded and cooled to a
temperature where protons and neutrons could stick together to
make the simplest atomic nucleus, deuterium (the heavy isotope
of hydrogen). From here other simple nuclei were able to form—
deuterium could capture a proton to make an isotope of helium,
two deuterium nuclei could join together to create heavier heli-
um, and small numbers of larger nuclei formed, up to the ele-
ment lithium (all the heavier elements are thought to have been
produced in stars many millions of years later).
This process is known as big bang nucleosynthesis. If, while
the universe was losing heat, neutrons had decayed at a rate that
was much faster than the universe cooled, there would have been
no neutrons left when the universe reached the right tempera-
ture to form nuclei—only the protons would have remained, and
we would have a cosmos made almost entirely of hydrogen. On
the other hand, if the neutron lifetime were much longer than the
time required to cool suciently for big bang nucleosynthesis,
the universe would have an overabundance of helium, which in
turn would have aected the formation of the heavier elements
involved in the evolution of stars and ultimately life. Thus, the
balance between the universal cooling rate and the neutron life-
time was quite critical for the creation of the elements that make
up our planet and everything on it.
From astronomical data we can measure the cosmic ratio of
helium to hydrogen, as well as the amounts of deuterium and other
light elements that exist throughout the universe. We would like to
see if these measurements agree with the numbers predicted by big
bang theory. The theoretical prediction, however, depends on the
precise value of the neutron lifetime. Without a reliable value for it,
our ability to make this comparison is limited. Once the neutron
lifetime is known more precisely, we can compare the observed
ratio from astrophysical experiments with the predicted value
from theory. If they agree, we gain further confidence in our stan-
dard big bang scenario for how the universe evolved. Of course, if
they disagree, this model might have to be altered. For instance,
certain discrepancies might indicate the existence of new exotic
particles in the universe such as an extra type of neutrino, which
could have interfered in the process of nucleosynthesis.
One way to resolve the dierence between the beam and bot-
tle results is to conduct more experiments using methods of com-
parable accuracy that are not prone to the same, potentially con-
founding systematic errors. In addition to continuing the beam
and bottle projects, scientists in several other groups worldwide
are working on alternative methods of measuring the neutron
lifetime. A group at the Japan Proton Accelerator Research Com-
plex (J-PARC) in Tokai is developing a new beam experiment that
will detect the electrons rather than protons produced when neu-
trons decay. In another very exciting development, groups at ILL,
the Petersburg Nuclear Physics Institute in Russia, Los Alamos
National Laboratory, the Technical University of Munich and the
Johannes Gutenberg University Mainz in Germany plan to use
neutron bottles that confine ultracold neutrons with magnetic
fields rather than material walls. This is possible because the neu-
tron, though electrically neutral, behaves as though it is a small
magnet. The number of neutrons accidentally lost through the
sides of such bottles should be quite dierent from that of previ-
ous measurements and thus should produce quite dierent sys-
tematic uncertainties. We fervently hope that, together, continu-
ing bottle and beam experiments and this next generation of
measurements will finally solve the neutron lifetime puzzle.
Time
Number of
neutrons going
through trap
Measured slope
Neutron beam
(known intensity)
passes through
Count the number of decays within the time interval
Trap
+ +
ProtonElectrodes
The Beam Method
In ontrast to the ottle ethod, the ea tehniue looks not for neutrons
ut for one of their deay produts, protons. ientists diret a strea
of neutrons through an eletroagneti trap ade of a agneti eld
and ring-shaped high-oltage eletrodes. he neutral neutrons pass right
through, ut if one deays inside the trap, the resulting positiely harged
protons ill get stuk. he researhers kno ho any neutrons ere in
the ea, and they kno ho long they spent passing through the trap,
so by counting the protons in the trap they can measure the number of
neutrons that deayed in that span of tie. his easureent is the deay
rate, hih is the slope of the deay ure at a gien point in tie and
hih allos the sientists to alulate the aerage neutron lifetie.
MORE TO EXPLORE
easureent of the eutron ifetie sing a raitational rap and a o-
eperature olin oating. A. Serebrov et al. in Physics Letters B, Vol. 605,
Nos. 1–2, pages 72–78; January 6, 2005.
he eutron ifetie. FredE.WietfeldtandGeoreyL.GreeneinReviews of Modern
Physics, Vol. 83, No. 4, Article No. 1173; October–December 2011.
Iproed eterination of the eutron ifetie. A. T. Yue et al. in Physical Review
Letters, Vol. 111, No. 22, Article No. 222501; November 27, 2013.
FROM OUR ARCHIVES
ltraold eutrons. R. Golub, W. Mampe, J. M. Pendlebury and P. Ageron; June 1979.
he roton adius role. Jan C. Bernauer and Randolf Pohl; February 2014.
scientificamerican.com/magazine/sa
© 2016 Scientific American

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