SEARCH FOR THE MUON CATALYZED d 3He-FUSION
PNPI participants in the MuCF collaboration*):
D.V. Balin, V.A. Ganzha, E.M. Maev, O.E. Maev, G.E. Petrov, G.G. Semenchuk,
G.N. Schapkin, A.A. Vasiliev, A.A. Vorobyov, N.I. Voropaev
*)
Austrian Academy of Sciences, A-1090 Vienna, Austria;
Institut de Physique de l'Universite , Perolles, 1700 Friburg, Switzerland;
Technical University of Munich (TUM), D-85747 Garching, Germany;
Paul Scherrer Institut (PSI), CH-5232 Villigen , Switzerland;
University of California and LBNL, Berkeley CA 94720, USA
1. Introduction
The nuclear fusion reaction
d + 3He → 4He (3.66 MeV) + p (14.64 MeV)
(1)
is interesting for various reasons: as a mirror reaction of the d(t,4He)n fusion process and as a perspective
source of thermonuclear energy. This fusion process was involved in the primordial nucleosynthesis of light
elements in the early universe. For these reasons, it is important to know the cross section for this reaction at
low collision energies, E < 10 keV. The phenomenon of the muon catalysis opens an opportunity to study
this reaction at practically zero collision energy, when fusion occurs in the 3Hedµ mesomolecule:
3
Hedµ→ 4He (3.66 MeV) + p (14.64 MeV) + µ.
(2)
Formation of the 3Hedµ molecule occurs in collisions of slow dµ atoms with 3He atoms:
dµ + 3He → [(3Hedµ)e]+ + e.
(3)
This process was first predicted theoretically [1] as an intermediate step in the muon transfer from
the deuterium mesoatom to helium. This prediction was confirmed in our experiments at PNPI [2] where
the dµ + 3He → 3Heµ + d transfer rate was measured at the room temperature for the first time:
λd3He (300K) = (1.24 ± 0.05)∙108 s–1, in close agreement with the predicted rate. The discovered formation of
the 3Hedµ molecules allowed to search for the muon catalyzed d 3He-fusion reaction, similar to the ddµ- and
dtµ-fusions. However, a serious complication arises from competition of this fusion reaction with very fast
decay of the 3Hedµ molecule:
[( Hedµ)e] →
3
+
[(3Heµ)e] + d + γ
[(3Heµ)e] + d
3
Heµ + d + e.
(4)
According to the theoretical calculations [3], the decay rate is λdec ≈ 7∙1011 s–1. The nuclear fusion rates
f (J) in the 3Hedµ molecule depend on the value of the molecular angular momentum J. The theoretical
predictions are: f (0) = (1.9–2.1) 105 s–1 and f (l) = 6.5·102 s–1 [4]. About 99% of the initially produced
3
Hedµ molecules are in the J = 1 state. However, as Men’shikov noted [5], the transition
(3Hedµ)J=l → (3Hedµ)J=0 is possible in ion-molecular reactions between the 3Hedµ and D2 molecules via
formation of the muonic molecular complex [(3Hedµ)eD2]+ [6]:
[(3Hedµ)J=1 e]+ + D2 → [(3Hedµ)J=1 eD2]+ → [(3Hedµ)J=0 e]+ + D2+ + e.
PAGE
(5)
According to theoretical estimates [6], the formation rate of the complex [(3Hedµ)J=1eD2]+ is
λ1 ≈ 3٠1013φ s–1 (where φ is the D2 density normalized to the Liquid Hydrogen Density (LHD)), and
the decay rate of this complex is λ2 ≈ 5٠1011 s–1 Such estimates show that one can expect quite efficient
transfer (3Hedµ)J=l → (3Hedµ)J=0 and, as a consequence, a detectable 3Hedµ-fusion process.
The first experimental limit on the 3Hedµ-fusion rate f < 4·108 s–1 was set at PNPI in 1990 [7]. In 1996,
the MuCF collaboration performed a short test run in the intense muon beam at PSI [8] and reduced
the upper limit for the 3Hedµ-fusion rate: f < 1.6·106 s–1. Later in 1997, there was a special physics run
dedicated to the 3Hedµ-fusion search [9]. Below we present a brief description of that experiment and
the final results of the data analysis.
2. Experimental method and data analysis
The experiment was performed in the µE4 beam of the meson factory at PSI with the experimental set-up
used at that time by the MuCF collaboration for studies of the muon catalyzed dd-fusion [10]. The basic
element of the set-up was a high-pressure cryogenic hydrogen ionization chamber (HIC) operating as
an active target in the time-projection mode to detect both the proton and 4He from reaction (1). The chamber
was filled with the gas mixture HD + 3He (5.6%) at 50K and 13.2 bar pressure (φ = 9.21% of the LHD).
The pure HD gas with a minimal D2 content (0.52%) was obtained using a special technology developed at
PNPI [11]. These conditions were chosen to optimize the formation of the 3Hedµ molecules and to minimize
background from the ddµ-fusion. The chamber was exposed to an intense negative muon beam of PSI, and
9.7·108 muon stops were selected during three weeks of data taking.
The muons were stopped in the sensitive volume of the HIC which was defined by the 12 mm drift
distance (from the cathode to the grid) and the anode area of 10 cm2 subdivided into 13 pads (Fig. 1).
The HIC operated at –35 kV on the cathode and –4 kV on the grid. The maximum drift time of electrons was
2 µs. For detection of signals from the anodes, a fast (100 MHz, 8 bit) Flash ADC based electronics was
used. It allowed to receive full information about the signals (amplitude, duration, time and energy) from all
the charged particles which were detected inside the HIC. The energy resolution (rms) and the energy
threshold were 30 keV and 120 keV, respectively.
The strategy of the measurements was to select a clean sample of muon stops (Nµ) in the fiducial volume
inside the HIC. The muon signals had to satisfy a set of amplitude, duration and energy criteria that provided
reliable selection of such muon stops avoiding completely (on a level of 0.01%) any wall effects in
the measurements. Then we had to look for events with a large signal on the muon-stop anode, separated in
time from the muon signal. Such events correspond to detection of 4He with the energy of 3.66 MeV. Then
it was required that the 4He signal was accompanied by signals on at least two neighbouring anodes, that
constitute a continuous track, with the energy deposit corresponding to the track of a 14.64 MeV proton. This
combined registration of the 4He and proton signals drastically suppressed most of the background, where
one of the reaction products was the long-range charged particle, e.g., from µ-capture on the wall materials
or from the breakup reactions in µ3He-capture. One candidate for the d 3He-fusion event is presented in
Fig. 1.
According to the kinetics of the processes in the HD + 3He gas mixture, the following reactions can occur
after a muon stop: pdµ-, ddµ- and 3Hedµ- fusions, as well as muon capture on nuclei (3He and gaseous
impurities: O2, N2, etc.). The HIC detected all the charge products of these reactions with an energy higher
than 200 keV. Figure 2 shows the measured amplitude distribution of pulses which follow the muon signals.
In this spectrum, one can see the peaks corresponding to the products of the following processes: the ddµfusion channels with 3He + n, 3Heµ + n, t + p; the channel with 3He + µ from the pdµ-fusion, and the triton
peak from the muon capture on 3He. The interpretation of this spectrum requires to take into account
the effect of ion-electron recombination in the ionization chamber gas that shifts the observed peaks towards
lower amplitudes. The quantitative evaluation of these shifts is known from our previous measurements.
The number of the 3Hedµ molecules formed after the muon stops is given by the expression:
N 3Hedμ =Nµ·Cdµ·Λd3He /tot,
PAGE
(6)
where tot is the disappearance rate of the dµ atoms, Λd3He is the 3Hedµ molecule formation rate, and Cdµ is
the fraction of the stopped muons which had reached the dµ-atom ground state. All these three parameters
were measured directly in our experiment.
Fig. 1. a) Display of the Flash ADCs for a candidate event of d 3He-fusion. The dotted lines show the threshold levels.
b) Top view of the anode pad plane
The rates tot and Λd3He were obtained from the analysis of time distribution of t + p signals from
the ddµ-fusion. In order to select such events, we analysed the part of the energy spectrum around the peak
in the region 2.8–3.2 MeV (see Fig. 2). The disappearance rate of the dµ atoms determined from the slope of
the time distribution proved to be tot = (1.907 ± 0.037)∙106 s–1. The rate Λd3He was determined by
the formula:
Λd3He = tot – 0 – Λddµ – Λpdµ – ΛµZ,
(7)
where = 0.455∙106 s–1 is the muon lifetime.
The rates Λddµ = (2.18 ± 0.046)∙103 s–1, Λpdµ = (2.5 ± 0.1)∙105 s–1 and ΛµZ ≤ 3∙103 s–1 were measured in our
previous experiments. This gives λd3He = (1.197 ± 0.046)∙106 s–1. Finally, normalizing to the LHD, we
obtain [12]:
λd3He(50K) = Λd3He / (φ C3He) = (2.32 ± 0.09)∙108 s–1,
(8)
where φ = 9.21% is the HD + 3He gas density and C3He = 5.6% is the 3He concentration.
This result could be compared with the d 3He formation rate measured at the room temperature in our
previous experiment [2]: λd3He(300K) = (1.24 ± 0.05)∙108 s–1. Both results are in good agreement with
the theoretical predictions based on the resonant exchange mechanism [13]. The value of Cdμ was estimated
in the measurement of the triton yield (Yt) from the reaction of µ3He-capture. The triton events from
the µ3He-capture correspond to the peak in the region 1.1–1.5 MeV of the amplitude spectrum in Fig. 2.
The method of Yt determination was totally identical to that used in our experiment for precise measurement
of the rate of the muon capture on 3He [14]. After an analysis of the amplitude and time distributions of these
events, we obtained Yt = (1.88 ± 0.04)∙10–3. The triton yield Yt depends directly on the value of Cdμ, on
the rates of the pdµ and ddµ fusions, and on the rate of the µ3He-capture. All the rates necessary for
calculations of Yt are well known from our previous measurements or have been measured in the present
experiment. Finally, from the measured triton yield Yt we obtain the value of Cdμ = 0.82 ± 0.06. Using
the measured values of Λd3He, λtot, and Cdµ, we have calculated from Eq. (6) the number of 3Hedµ molecules
formed in our experiment by the selected stopped muons:
N 3Hedμ = (4.9 ± 0.4) 108.
PAGE
The background processes, which can in principle imitate signals from the d 3He-fusion in the HD + 3He
gas mixture are: the muon catalyzed dd- and pd-fusions, the muon capture on 3He, and the muon capture on
gas impurities. Also, a possible source of background is the pile-up of signals from these reactions with each
other and with muons. The important background reactions are:
a) channel t + p of ddµ-fusion (the energy and the range of the emitted particles are Ep = 3.02 MeV,
Rp = 0.9 cm, Et = 1.01 MeV, Rt = 0.06 cm).
b) channel 3He + n of ddµ-fusion (E 3He = 0.82 MeV). This channel is dangerous because it produces d 3Hefusions in flight in collisions of 3He with deuterium atoms, especially since the cross section for the d 3Hefusion has a maximum near 0.8 MeV. To suppress these channels of background, we replaced D2 in
the experimental gas mixture by HD and reduced the target temperature to 50K. By this, we decreased
the yield of the ddµ-fusion events by a factor of ~50.
c) µ-capture on 3He, namely, the breakup reactions with long-range protons and deuterons. These reactions
can imitate the d 3He-fusion only in the case of pile-up with the products of other reactions, e.g., t + p.
However, the probability of such pile-ups is very low.
d) µ-capture on impurities accompanied by long-range protons.
It turned out that the process d) is the main source of background in the experiment (this we understood
after special investigations) and really can imitate signals from the products of the 3Hedµ-fusion reaction.
To study the background from the µ-capture reactions, we performed an additional experiment with high
concentration of nitrogen admixture (H2 + N2, 140 ppm, φ = 0.0872). Also, in order to estimate
the probabilities of background events from ddµ-fusion and µ-capture on 3He, we analysed the data from our
experiments with the HD-mixture (φ = 0.0941) and from the experiment devoted to a study of the µ-capture
on 3He (φ = 0.0656). All these measurements were performed in similar experimental conditions with
the same experimental set-up.
Fig. 2. Amplitude spectrum of pulses after the muon signals
PAGE
No candidates for the 3Hedµ-fusion events in either pure HD or pure 3He gas targets were found in our
analysis. The background due to the ddµ-fusion and 3Heµ-capture reactions was shown to be negligible.
In contrast, the experiment with H2 + N2 (140 ppm) yielded such candidate events. They imitated the signals
which we anticipated from the 3Hedµ-fusion events. These signals could appear due to charged products of
µ capture on nitrogen: protons, deuterons, α, etc. Nitrogen was the main admixture in our case (on a level of
~l ppm).
However, the time distribution of such µ-capture events is very different from that of the d 3He-fusion
events. About 95% of the fusion events should be earlier than 1.8 µs after the stopped muon, however
the µN-capture events appear mostly after 1.8 µs. We applied this criterion to three selected candidates for
the d 3He-fusion events in the experiment with the HD + 3He gas mixture and found that only one of them
was in the (0–1.8) µs interval.
Finally, in the course of our experiment, 4.9·108 3Hedµ-molecules were formed with only one event
which passed the selection criteria as a candidate for the 3Hedµ-fusion event. On the other hand, the expected
background was also one event. Following the PDG recommendations, we have concluded that the number
of the d 3He-fusion events detected in our experiment is Nf < 3.3 on the 90% confidence level. From this,
the effective fusion rate f is determined:
f = Nf dec / (N 3Hedµ ε),
(9)
where Nf is the number of the d 3He-fusion events (Nf < 3.3), N 3Hedµ is the number of the 3Hedµ-molecules
(4.9·108), dec is the decay rate of the 3Hedµ-molecules (dec ≈ 7∙1011 s–1), and ε is the detection efficiency of
the products of the 3Hedµ-fusion reactions. This efficiency was defined as ε = ετ·εS. The factor εS was
determined mostly by the efficiency of registration of the 3Hed-fusion protons (their range was 16.4 cm),
according to the geometry of the HIC and the selection criteria on the amplitude and duration of signals in
a proton track (the detection efficiency of the 3.66 MeV alpha particles was 100%). The value of εS was
calculated by Monte-Carlo simulations: εs = 0.13 ± 0.01. The factor ετ takes into account the dead time
resulting from pile-ups of signals of the fusion products with the muon signals. To define the factor ετ, we
used the experimental time distribution of the t + p signals of the dd-fusion, which in our experimental
conditions was similar to the expected time distribution of the d 3He-fusion events. Besides, we used
the results of Monte-Carlo simulations of durations of signals from the products of the d 3He-fusion to take
into account the selection criteria which were applied in the search of the candidates for the 3Hedµ-fusion
events. In this way, we have evaluated ετ = 0.63 ± 0.05 and the total efficiency ε = ετ·εS = (8.2 ± 0.8)%.
Finally, from Eq. (9) we obtain the upper limit for the effective fusion rate f :
f < 6∙104 s–1 at 90% C.L.
In addition, we can deduce the upper limit of the fusion rate f (0) from the J = 0 state of the 3Hedµ-molecule
using the theoretical value for the population P(0) of this state [4]:
f (0) < 5·105 s–1.
The obtained upper limit is still higher than the theoretical prediction f (0) ≈ 2·105 s–1 [4].
Recently, new results were published [15] from an experiment that was performed with
the D2 + 3He (5%) gas mixture at two densities (φ = 5.21 % and φ = 16.8% of the LHD). From an analysis of
their data, the authors obtained the following values of the effective fusion rate: f = (4.5 + 2.6 – 2.0)∙105 s–1
at φ = 5.21%, and f = (6.9 + 3.6 – 3.0)∙105 s–1 at φ = 16.8% . In spite of a rather low (~40%) accuracy of
these data, the estimated values of f seem to exceed by an order of magnitude the upper limit for f set in
our experiment. Assuming this difference is not due to some problems in either of the experiments, but rather
due to differences in the experimental conditions, this might be an interesting interpretation of
the experimental results indicating a way for further investigations.
PAGE
3. Conclusion
A new upper limit for the d 3Heµ-fusion rate, f < 6∙104 s–1, was experimentally set in the experiment
performed with the HD + 3He (5.6%) gas mixture at the 50K temperature and gas density φ = 9.21%
of the LHD. From this result, we have derived an upper limit for the d 3Heµ-fusion ratef (0) from the J = 0
state of the 3Hedµ molecule: f (0) < 5∙105 s–1. In addition, the dµ → 3Heµ transfer rate λd3He was measured
for the first time at 50K: λd3He (50K) = (2.32 ± 0.09)·108 s–1. This value could be compared with the result of
our previous measurement at the room temperature: λd3He (300K) = (1.24 ± 0.05)∙108 s–1 [2]. Both values are
in agreement with the theoretical prediction [13] based on the resonant formation of the 3Hedµ molecule.
The measured upper limit f < 6∙104 s–1 for the d 3Heµ-fusion rate looks to be in strike disagreement with
the reported in Ref. [15] observation of the d 3Heµ-fusion signals with the rate f ≈ 5∙105 s–1. However, that
experiment was performed with another gas mixture, namely with D2 + 3He(5%), and we do not exclude that
the difference between the results of these two experiments might be due to a possible difference in
the formation rates of the [(3Hedµ)J=1 eHD]+ and [(3Hedµ)J=1 eD2]+ clusters. To clarify the situation, some
new measurements are desirable. For example, using the existing set-up of the MuSun experiment (see
the article devoted to the MuSun experiment in this edition), one could increase the sensitivity for the search
of the muon catalyzed d 3He-fusion by an order of magnitude with a quite low background.
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