Resolution of the orthopositronium-lifetime puzzle.
ABSTRACT The long-standing discrepancy [G. S. Adkins, R. N. Fell, and J. Sapirstein, Ann. Phys. (N.Y.) 295, 136 (2002)]] between the theoretical calculations of the orthopositronium (o-Ps) annihilation decay rate (lambda(T)=1/lifetime) and some of the experimental measurements has been resolved. A focused beam of positrons incident on a special nanoporous silica film produces near-thermal energy o-Ps in vacuum that is slow enough to be virtually free of perturbing interactions. The fitted decay rate requires only a 500 ppm correction for nonthermal o-Ps effects. The new value of lambda(T)=7.0404(10)(8) micros(-1) is in excellent agreement with theory.
- SourceAvailable from: ArXiv[show abstract] [hide abstract]
ABSTRACT: The logarithmically enhanced alpha(3)ln(1/alpha) corrections to the para- and orthopositronium decay widths are calculated in the framework of dimensionally regularized nonrelativistic quantum electrodynamics. In the case of parapositronium, the correction is negative, approximately doubles the effect of the leading logarithmic alpha(3)ln (2)(1/alpha) one, and is comparable to the nonlogarithmic O(alpha(2)) one. As for orthopositronium, the correction is positive and almost cancels the alpha(3)ln (2)(1/alpha) one. The uncertainty in the theoretical prediction for the parapositronium decay width is reduced to 10(-2) &mgr;s(-1).Physical Review Letters 08/2000; 85(6):1210-3. · 7.94 Impact Factor
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ABSTRACT: The singlet decay rate has been measured using magnetic singlet-triplet state mixing for positronium formed in a [ital N][sub 2]-isobutane gas mixture. We find [lambda][sub [ital s]]=7990.9[plus minus]1.7 [mu]s[sup [minus]1]. At 215 ppm this result is 6.5 times more accurate than the previous measurement [D. W. Gidley, A. Rich, E. Sweetman, and D. West], and is the first measurement sensitive enough to test the relative order [alpha][sup 2]ln[alpha] term in the singlet decay rate calculation.Physical Review Letters 04/1994; 72(11):1632-1635. · 7.94 Impact Factor
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ABSTRACT: The vacuum decay rate lambdaT of orthopositronium (13S1) formed in a gas has been measured to be lambdaT=7.0514+/-0.0014mus-1. Measurements of lambdaT in four different gases, all in agreement, are averaged to obtain this result. As systematic tests, two entirely separate digital timing systems are simultaneously used throughout the experiment; the cross section for collisional quenching of the long-lived 2 3S1 excited state is determined; lambdaT is redetermined in two of the gases (N2 and Ne) using only high-gas-density measurements; and the collisional quenching rate of water vapor, the major residual gas contaminant, is directly measured. The final value of lambdaT from this gas experiment, which represents a factor of 4 improvement in accuracy over previous measurements, is 9.4 experimental standard deviations above the theoretical value.Physical Review A 12/1989; 40(10):5489-5499. · 3.04 Impact Factor
Resolution of the Orthopositronium-Lifetime Puzzle
R.S.Vallery,1,*P.W. Zitzewitz,2and D.W. Gidley1
1Randall Laboratory of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120, USA
2Department of Natural Sciences, University of Michigan-Dearborn, Dearborn, Michigan 48128, USA
(Received 18 March 2003; published 23 May 2003)
The long-standing discrepancy [G.S. Adkins, R. N. Fell, and J. Sapirstein, Ann. Phys. (N.Y.) 295, 136
(2002)] between the theoretical calculations of the orthopositronium (o-Ps) annihilation decay rate
(?T? 1=lifetime) and some of the experimental measurements has been resolved. A focused beam of
positrons incident on a special nanoporous silica film produces near-thermal energy o-Ps invacuum that
is slow enough to be virtually free of perturbing interactions. The fitted decay rate requires only a
500 ppm correction for nonthermal o-Ps effects. The new value of ?T? 7:0404?10??8? ?s?1is in
excellent agreement with theory.
DOI: 10.1103/PhysRevLett.90.203402 PACS numbers: 36.10.Dr, 11.10.St, 12.20.Fv
Precision measurements of the annihilation decay
rates of positronium (Ps) provide unique tests of quantum
electrodynamics (QED) (see Ref.  and references
therein).The triplet ground state decay rate, ?T, of ortho-
positronium (o-Ps) has a colorful history  of incon-
sistent experimental results and poor agreement with
theoretical calculations, the so-called o-Ps lifetime
puzzle (the lifetime, 1=?T, is about 142 ns). The theo-
retical value has recently been solidified by completion of
the full second order in ? QED corrections ( ? 230 ppm)
to yield [1,3] ?T?theory? ? 7:039979?11? ?s?1(1.6 ppm)
which includes additional higher-order logarithmic terms
. There is no longer any concern that the second order
corrections might be large ( ? 1000 ppm) and positive. (It
is interesting to note that there is no corresponding para-
positronium lifetime puzzle as the ground state singlet
decay rate measured in a buffer gas  is in excellent
agreement with theory  at the 215 ppm level of pre-
cision.) The fact that the QED theoretical value of ?Thas
been lower than the most precisely measured values has
spawned numerous (null) experiments  to search for
exotic, non-QED o-Ps decay processes involving axions,
C-odd bosons, millicharged particles, forbidden numbers
of gamma rays, and a mirror universe . In this Letter,
we present the results of a new measurement of ?Tthat
definitively resolves the o-Ps lifetime puzzle.
The most precise measurements of ?Tusing a buffer
gas  and a vacuum technique  are 7:0514?14? ?s?1
(200 ppm) and 7:0482?16? ?s?1(230 ppm), respectively.
They are 1200–1600 ppm above theory and a more re-
cent measurement  performed in silica powders,
7:0399?26? ?s?1(370 ppm). The Michigan buffer gas
experiment  has been shown to be subject to the prob-
lem of incomplete Ps thermalization  in low-pressure
gases, and this value should be corrected downward by at
least 700 ppm. The Tokyo experiment  in a fine-
grained insulating powder could be subject to small
Stark shifts that reduce the decay rate and are not ac-
counted for in their technique, but the experiment pri-
marily needs improved statistical precision. The 1990
Michiganvacuum experiment , wherein o-Ps is formed
in an evacuated cavity using a low-energy beam of
positrons, is attractive in eliminating gaseous and
powder formation media. It suffered statistically and
systematically from the presence of other intermediate
lifetime o-Ps decay processes that required fitting the
decay spectrum after 450 ns where only 4% of the o-Ps
decays remain. After further research on this additional
decay process , we have improved the vacuum
technique and performed a new, more accurate measure-
ment of ?T.
The positron beam and timing electronics are similar
to that described in Ref. . Briefly, a 35 mCi22Na source
is used to generate a primary positron beam of about 4 ?
105e?=s that is electrostatically focused onto a 3 mm
diameter Ni foil remoderator. A secondary beam of ?4 ?
104e?=s is generated from reemitted positrons and about
15% of these are time tagged by detecting secondary
electrons ejected from the remoderator by the incoming
positrons. The secondary beam has been improved to
permit delivery of the positron beam onto the Ps forma-
tion surface over a wide range of implantation energies
(1–5 keV), a key to performing systematic tests. The Ps
formation and confinement cavity has been completely
redesigned as shown in Fig. 1. New, more efficient anni-
hilation gamma detectors (fast plastic scintillator) are
centered on a small, two-chambered cavity. Timed posi-
trons are electronically gated through a final lens that
focuses them through two apertures into the second
chamber. Electric fields from the biased cavity walls
deflect the beam onto a special (see below) porous film
where Ps is formed with 30%–33% efficiency. Unlike the
1990 experiment, there is no MgO powder fumed on the
aluminum cavity walls. The time between the gated in-
jection of positrons and the subsequent detection of one of
the o-Ps annihilation gamma rays is measured and accu-
mulated as a decay histogram. As in previous measure-
ments, the decay rate is the fitted exponential slope of this
decay spectrum and represents the total rate of o-Ps
disappearance into all possible modes of decay.
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VOLUME 90, NUMBER 20
2003 The American Physical Society203402-1
The most significant improvement over the 1990 ex-
periment is the use of a porous silica film as the Ps
formation target. Developed as low-dielectric constant
materials by themicroelectronics
1 ?m-thick films have pores that are several nm in diam-
eter and fully interconnected to form a pore network .
A beam of keV positrons stop in the dense silica matrix
and form Ps that is expelled into the pores with a couple
eVof kinetic energy.With a mean-free path of 3.3 nm, Ps
is able to diffuse through the pore network over distances
much longer than the film thickness and escape through
the surface into vacuum . Having suffered on the
order of 104–106collisions with the silica pore walls
(depending on implantation depth), the Ps approaches
thermal equilibrium. (Ps confined to the pores by a thin
capping layer doesindeed fully thermalize since the fitted
lifetime is observed to have the expected strong depen-
dence on the film’s temperature .) We confirmed this
in a separate time-of-flight experiment of Ps emitted into
vacuum from a similar porous film. The energy distribu-
tion is nominally that of Maxwell-Boltzman emission
(with an effective kT ? 35–40 meV) joined with a
high-energy tail (see Fig. 2). This tail of thermalizing
Ps extends out at least to ?2 eV, the energy at which Ps
(formed from thermalized positrons in the silica) is ex-
pelled into the pores. In addition, there is a low-intensity
higher-energy tail of 2–20 eV Ps formed from back-
scattered positrons that never approached thermalization
. These Ps events are distinct from the thermal and
epithermal Ps that has diffused out of the film pores and
will be considered later.
There are several important consequences of having
near-thermal Psin the cavity.This Ps moves an average of
only1–2 cm in a lifetime and thus the surrounding cavity
should have comparably small size in order to confine Ps
to a region of highly uniform detection efficiency. (Ps
cannot be allowed to move over several lifetimes into
regions of systematically different gamma detection effi-
ciency as this would modulate the lifetime spectrum and
distort the fitted decay rate.) More importantly, even in a
small cavity Ps makes only 1–3 wall collisions per life-
time and thus collisional wall quenching is negligible.
(The Ps can clearly survive of order 106collisions in
diffusing through the silica film and a few more colli-
sions with the alumina cavity surface is negligible.) Thus,
thermal and epithermal Ps (energy <2 eV) sealed in a
1 cm cavity affords us the opportunity, in principle, to
measure the vacuum decay rate directly without extrap-
olations. In practice, however, our cavity must have an
aperture for the positron beam to enter. The escape/dis-
appearance of some Ps through this aperture into regions
of lower gamma detection efficiency (the major system-
atic effect in the 1990 experiment) systematically in-
creases the fitted total disappearance rate of o-Ps and
must be addressed.
With the above effects in mind, the double-chambered
cavity, shown in Fig. 1, was designed. Each chamber is a
cube with a side length of 1.5 cm corresponding to a
mean-free path of 1.0 cm. The two-chamber design is
based on the concept of differential pumping—i.e., the
inner 3 mm diameter aperture is small enough to allow
<1% of the thermal Ps to escape from the Ps formation
chamber. The subsequent escape probability from the
outer (second) chamber is 1%–2%, thus reducing the
thermal Ps escape probability through both apertures to
be less than 200 ppm. The tail of epithermal Ps will have
higher escape probability, but Monte Carlo simulations
porous silica film. Note that higher energy positrons implanted
more deeply (solid circles) in the film produce more thermal-
ized o-Ps with fewer events in the epithermal tail.
The energy distribution of o-Ps emitted from a typical
tagged positron beam is focused through apertures of 4 and
3 mm, respectively, and then deflected into a porous silica film
where ?30% form o-Ps. After many collisions in the inter-
connected 3.3 nm pores, most of the o-Ps that escapes the film
is nearly thermalized and, hence, too slow to escape from the
cavity or annihilate in wall collisions.
The o-Ps formation and confinement region.The time-
PH YSICA L R EVI EWL ET T ERS
23 MAY 2003
VOLUME 90, NUMBER 20
indicate that the overall disappearance effect of 0–2 eV
Ps on the fitted value of ? is expected to be less than
200 ppm. Pstransfer over time between the two chambers
has no effect because the gamma detectors are centered
on the dividing bulkhead rendering the two chambers to
be mirror images of each other.There are small (1%–2%)
axial and radial gradients in detector efficiency over each
chamber, but simulations indicate that the time-depen-
dent ‘‘filling’’ of the formation chamber is complete in
less than 200 ns (after which Ps is effectively averaging
over the gamma detector gradients).
The two-chambered cavity is designed to have negli-
gible Ps wall quenching and minimal entrance aperture
effects for the Ps with kinetic energy less than 2 eV.
However, this is not the case for the 2–20 eV tail of the
Ps energy distribution.The origin(s) of this ‘‘backscatter-
ing’’ component is backscattered or very shallowly im-
planted positrons that capture an electron at the film
surface to produce Ps with a broad range of energies.
Production of this high-energy Ps that does not undergo
thermalizing collisions within the film pores is well
documented in the literature dealing with positron beams
(see Ref.  and references therein).
The decay spectrum and relative intensity of the back-
scattered Ps events can be isolated by investigating non-
porous films where there is no outdiffusion of low-energy
Ps. We replaced the porous silica film with a thermal
oxide-grown dense silica film. The resulting backscat-
tered Ps typically produces two fitted lifetime compo-
nents  in the cavity: a fast moving (and fast decaying,
presumably by dissociation) component with a distribu-
tion of lifetimes in the 5–20 ns range and longer-lived,
several eV Ps with lifetimes predominately in the 70–
140 ns range.The fast Ps component decays away prior to
fitting the decay rate for times after 150 ns and, hence,
can be ignored, but the effect of the longer-lived compo-
nents for fits beginning as far out as 500 ns can be clearly
seen in Fig. 3. Fortunately, the relative intensity of these
events can be controlled by the positron beam implanta-
tion energy , E, as roughly 1=E. Thus, we have
acquired decay rate spectra at positron beam energies of
1–5 keV using both the porous and the nonporous films.
The nonporousfilm datawere used intwo complementary
ways to remove the collisional quenching effect of the
In the first method, the decay rates fitted at t ? 250 ns
in the full porous film spectrum are plotted versus the
measured relative intensity of the backscattered Ps com-
ponent (see Fig. 4). We assume the perturbation in the
fitted decay rate should be linear in this relative intensity
and extrapolate to zero backscattering. However, the
backscattered Ps decay spectrum is not exponential in
time (it is a broad distribution of exponentials). A second
method is used to remove backscattered Ps directly from
the time histogram prior to fitting the decay rate. From
the full porous film spectrum (slow Ps plus backscattered
Ps), an appropriately normalized dense oxide spectrum
(backscattered Ps only) is subtracted to produce a cor-
rected spectrum of purely slow Psdecay.The resulting fits
of the corrected spectrum are included in Fig. 3. The
corresponding fits at t ? 250 ns are also plotted in Fig. 4.
FIG. 3 (color online).
the start time of the fit for two of the positron implantation
energies used in this measurement. The decay rate for the full
spectrum (of all o-Ps decays) has a higher decay rate at lower
beam energy due to the increased relative intensity of
the backscattering component. The corrected spectra have
an appropriately normalized pure backscattering spectrum
The fitted decay rate as a function of
implantation energies, plotted as a function of backscattered Ps
over thermal o-Ps (IBS=Io-Ps). A linear fit to the full spectrum
decay rates is made to remove the effect of the backscattered
o-Ps. The decay time spectra are also corrected directly for
backscattering by subtracting an appropriately scaled back-
scattering spectrum from the full spectrum.
The fitted decay rates at t ? 250 ns for a range of Ps
PH YSICA LR EVI EW L ET T ERS
23 MAY 2003
VOLUME 90, NUMBER 20
This second method assumes that the spectrum of back-
scattered Ps from the dense silica is identical to that from
the porous silica, a reasonable but not precise approxima-
tion. Hence, extrapolation to zero backscattering for this
corrected spectrum as shown in Fig. 4 is appropriate and
yields 7:0412?8? ?s?1. This intercept is systematically
consistent at 30 ppm with that for the full spectrum
To determinethevacuumdecay rate,weneedtomakea
small additional correction for the effect of the disap-
pearance of Ps that has bounced through both apertures.
Simulations indicate this effect should be about 100–
300 ppm and is quite sensitive to the relative intensity
of epithermal Ps. To check this, we increased the first
aperture diameter from 4 to 8 mm and acquired spectra at
5 and 2 keV beam energy. The aperture disappearance
effect is deduced to be 0:0008?6? ?s?1(115 ? 85 ppm).
Our new value for the o-Ps decay rate is then ?T?
7:0404?10??8? ?s?1, where the first error is the statistical
error of 140 ppm and the second error of 115 ppm repre-
sents a combined systematic error associated with the
above extrapolation procedures and selection of the fitted
value of the decay rate at 250 ns. Errors due to time
calibration, spectrum linearity, and multiple o-Ps events
 are negligible.
Our current value for ?Tusing a porous silica thin film
for production of near-thermal Ps is in excellent agree-
ment with theory at a combined level of precision of
180 ppm. It also agrees well with the Tokyo  experi-
ment. There is no longer an o-Ps lifetime puzzle. The
problem with the 1990 vacuum experiment  is that
it failed to correctly account for and extrapolate over
the intensity of the backscattered Ps component. The
Michigangroupperformedtheextrapolationsof the fitted
decay rates vs the size of the confinement cavities (hence,
the wall collision rate) and versus the entrance aperture
area to account for Ps disappearance (see Ref. ), but
kept the beam energy constant at a low value of 700 eVto
keep the Ps formation high on the fumed MgO surface.
Not realized at the time was the need to extrapolate in the
positron beam implantation energy (and, hence, in the
intensity of the perturbing, nonexponential backscattered
Ps component) as done in the present measurement. The
fits shown in the top panel of Fig. 3, obtained at low
positron implantation energy, clearly illustrate the prob-
lem encountered in the1990 experiment. Even though the
decay rate appears to asymptotically approach a constant
value for fits beyond t ? 450 ns as in Ref. , the back-
scattered Ps component still raises the fitted decay rate at
all fitting times. Simulations confirm that increasing cav-
ity size (decreasing the wall collision rate) allows this
component to persist at longer and longer times. The
extrapolation in the intensity of the nonexponential back-
scattered Ps component is essential to eliminate its effect
on the fitted decay rate.
In summary, the major systematic effect in this experi-
ment is the backscattered o-Ps at approximately 2–20 eV
that requiresa 350 ppm correction (at 5 keV beam energy)
for collisional annihilation
Epithermal o-Ps extending up to ?2 eV requires a 100–
200 ppm correction for escape from the confinement
cavity. We are continuing data collection with the goal
of reducing both the 115 ppm systematic error related to
backscattered Ps and the 85 ppm uncertainty in the cavity
aperture effect. Our final value of ?Tshould achieve
statistical and systematic uncertainties that are each ?
We thank Mark Skalsey, G.W. Ford, Ralph Conti,
William Frieze, Aaron Leanhardt, Jianing Sun, Jason
Engbrecht, and Yifan Hu for many useful discussions.
We thank the National Science Foundation Grant
No. PHY-9731861 and the University of Michigan
for supportingthis research. We are grateful to
International Sematech for continuing support of low-
dielectric porous film research.
on the cavity walls.
*Electronic address: email@example.com
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