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Decay of muons generated by laser-induced processes in ultra-dense
hydrogen H(0)
Leif Holmlid
a
,
*
, Sveinn Olafsson
b
a
Atmospheric Science, Department of Chemistry and Molecular Biology, University of Gothenburg, SE-412 96, G€
oteborg, Sweden
b
Faculty of Physical Sciences, University of Iceland, Reykjavik, Iceland
ARTICLE INFO
Keywords:
Condensed matter physics
Nuclear physics
Particle physics
Quantum fluids
Superfluid
Experimental nuclear physics
Charged particle emission by condensed matter
Nuclear particle phenomenology
Ultra-dense hydrogen
Muon
Meson
Laser-induced Processes
ABSTRACT
This work reports identification of muons by their characteristic life-time of 2.20
μ
s after laser-induction of their
precursor mesons, both kaons K
and K0
Land pions
π
in ultra-dense hydrogen H(0). The pair-production signal
from scattered muons at a metal converter in front of a photo-multiplier detector is observed with its decay. The
observed signal intensity is decreased by a metal beam-flag which intercepts the meson and muon flux to the
detector. Using D(0), the observed decay time is (2.23 0.05)
μ
s in agreement with the free muon lifetime of 2.20
μ
s. This signal is apparently due to the preferential generation of positive muons. Using p(0), the observed decay
time is in the range 1–2
μ
s, thus shorter than the free muon lifetime, as expected when the signal is mainly caused
by negative muons which interact with matter by muon capture.
1. Introduction
Nuclear processes [1] induced by ns pulsed lasers in ultra-dense
hydrogen H(0) and also similar spontaneous nuclear processes [2]
were previously shown to generate mesons (both charged and neutral
kaons K
and K0
Las well as pions
π
)[3,4,5], which decay to muons [6].
A novel muon detection method [6] was developed to cope with the
requirement of improved and selective methods for muon detection.
Recently, an extensive study of the precursor mesons using magnetic
deflection was published [7]. Here, further results are presented on the
decay of the muons following laser-induced meson generation. An
average decay time constant of (2.23 0.05)
μ
s, in agreement with that
for free muons [8,9], is observed in the experiments.
Ultra-dense hydrogen H(0) [10,11,12,13] has been shown to exist in
at least two different forms by experiments in the G€
oteborg group:
ultra-dense deuterium D(0) [14,15] and ultra-dense protium p(0) [16].
Also mixed forms pD(0) have been studied. The interatomic distance of a
few pm, normally at 2.3 pm in spin state s¼2, has been proven by
laser-induced neutral time-of-flight and time-of-flight mass spectrometry
studies [14,15,16]. Recently, also rotational spectroscopy with a reso-
lution of a few cm
1
has been used: this gives the interatomic distances
with high precision and with a resolution of a few femtometers in
agreement with theory and previous experiments [17]. Due to the short
distances between the hydrogen atoms in these materials, laser-induced
nuclear reactions can be initiated by relatively weak pulsed lasers with
peak intensity of the order of 10
13
Wcm
-2
[18,19].
Muon generation and muon beams are of interest at present for
several experiments, mainly in experiments using large laboratories like
muon storage rings, muon colliders and muon cooling experiments (for
example MICE) [20]. In muon spin spectroscopy (
μ
SR, muon spin rota-
tion), low-energy positive muons formed by decay of positive pions are
implanted in materials [21]. The bench-top approach that we take here
and in our previous studies is likely to give useful results on
muon-catalyzed fusion energy production [22,23]. For such a process,
negative muons are needed at large intensities at low cost and with low
energy consumption [24]. Our published results on muon generation [1,
2,6] indicate that such a development is possible. A recent patent [25]
summarizes the specific details of the muon generator. Neutron genera-
tion from muon-catalyzed fusion was in fact recently reported with this
muon generator [26].
* Corresponding author.
E-mail address: holmlid@chem.gu.se (L. Holmlid).
Contents lists available at ScienceDirect
Heliyon
journal homepage: www.heliyon.com
https://doi.org/10.1016/j.heliyon.2019.e01864
Received 17 August 2018; Received in revised form 1 February 2019; Accepted 29 May 2019
2405-8440/©2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-
nc-nd/4.0/).
Heliyon 5 (2019) e01864
Please cite this article as: L. Holmlid, S. Olafsson, Decay of muons generated by laser-induced processes in ultra-dense hydrogen H(0), Heliyon,
https://doi.org/10.1016/j.heliyon.2019.e01864
2. Background
The material ultra-dense hydrogen H(0) exists in at least two different
forms namely ultra-dense protium p(0) [16] and ultra-dense deuterium
D(0) [14,15]. Also mixed pD forms exist. A few different spin states have
been found for H(0) from time-of-flight (TOF) and time-of-flight mass
spectrometry (TOF-MS) studies, with s¼1, 2 and 3 [15,16]. Recently,
spin states s¼2, 3, and 4 were studied with a resolution of a few cm
1
by
rotational spectroscopy in the visible [17,27]. The spin state determines
the interatomic bond distance as d¼2.9 r
q
s
2
, with r
q
¼0.192 pm
(quantum mechanical electron radius [15]). The interatomic distance in
the most common form of ultra-dense hydrogen H(0) with s¼2is
approximately 2.3 pm [10,11,12]. The molecular structure of H(0) is
given by chain clusters H
2N
with Ninteger, formed by H–H pairs rotating
around a common axis [28,29]. Also small clusters H
3
(0) and H
4
(0)
occur very frequently [13,27,30,31]. The best low-temperature TOF
experiments done on clusters of the forms D
3
and D
4
gave 2.15 pm 0.02
pm [13] for s¼2, while theory gives 2.23 pm [15]. Rotational spec-
troscopy in D
2N
(0) gives 2.245 pm 0.003 pm for s¼2, recalculating
from the best data found for s¼3[17]. The density of H(0) is close to
10
29
cm
3
or 100 kg cm
-3
[10,11,12]. H(0) forms thin superfluid layers
on metal and metal oxide surfaces [32,33]. On non-metal surfaces like
glass and plastic, a superfluid film is not formed [33]. H(0) is stable on
suitable supports for days and weeks in a vacuum [12] and can be
detected by the first probing laser pulse in the experiments.
There are many different levels in the theoretical description of these
systems: the classical potential energy [1,15] and the normal
one-electron pictures immediately at hand of course give only partial
answers concerning the stability and properties of H(0). The best
description so far is based on the theory for superfluids and supercon-
ductors, especially the description given by Hirsch [34]. Another pre-
diction can be found in the theory for Compton-scale composite particles
by Mayer and Reitz [35]. Such small systems are not easily solved or
described by any known quantum mechanical method. In some experi-
ments the smallest basic block that needs to be considered is a pair H
2
,as
part of and coupled to the chain clusters H
2N
. This entity of four particles
with at least two significant spins is the smallest part that can be
described approximately as H(0). We do not assume that a complete
theoretical description is within close reach, but the experimental results
are quite decisive.
Mesons and muons are released from the ultra-dense hydrogen ma-
terial H(0) by pulsed laser-beam radiation but occur as well due to
spontaneous nuclear reactions with no laser. The energy spectra of the
muons are studied in three recent publications from our group [1,2,6].
Spontaneous muon generation far above the natural background can be
detected for weeks after the formation of H(0), if the material is kept in a
vacuum. Mesons are observed by direct time-of-flight using flight dis-
tances up to two meters [3,4,5,7]. They are identified by their typical
decay times in the studies cited. Charged pions
π
at
τ
¼26 ns as well as
long-lived neutral kaons K0
Lat
τ
¼52 ns and charged kaons K
at
τ
¼12.4
ns are all observed [3,4,5,7]. See also the experiment in Fig. 1 for decays
due to K0
Land K
. Magnetic deflection proves that most laser-ejected
particles from H(0) are neutral, thus probably neutral kaons K0
L. The
charged particles ejected are shown by the magnetic deflection to have
masses slightly less than unity, thus being kaons and pions [7]. Their
velocities are typically 0.75–0.9 cthus relativistic with an energy above
500 MeV u
1
[7].
3. Experimental
The experimental setup used for the decay time experiments is shown
in Fig. 2 with dimensions. The laser used is a Nd:YAG laser with pulse
energy <0.4 J at 1064 nm and pulse length 7 ns with pulse repetition rate
10 Hz. The laser beam was focused with an f¼50 mm lens on the H(0)
surface layer on a H(0) generator in a small vacuum chamber of 100 mm
diameter and length 1–2 m. The laser beam waist was <20
μ
mas
calculated for a Gaussian beam meaning a laser intensity of <410
13
W
cm
-2
. The experimental behavior and results do not vary with the
focusing. Normally, the visible plasma area on the generator surface is a
few mm in diameter independent of the laser spot size. In the H(0)
generator, several potassium-doped iron oxide catalyst samples [36,37]
form D(0) from deuterium gas (99.8% pure) or p(0) from natural
hydrogen gas (99.9995% pure hydrogen, naturally containing only
0.016% D). The ultra-dense material is formed on the upper surface of the
H(0) generator. This laser target surface is not rotated. With an H(0) layer
on this surface the laser ablation of the metal target is quite weak, and the
setup can be used for daily experiments during several weeks with no
change in performance. The gas pressure in the chamber is 0.1–10 mbar
(Pirani reading uncorrected for gas composition) with or without con-
stant pumping, normally in the lower part of this range if not specially
remarked in the figure captions. Since the gas composition is quite
complex with large amounts of H(0) clusters, no easy pressure reading
correction is possible.
The particle signal is measured with a detector consisting of a plastic
scintillator (PS) used as vacuum window [38], an Al converter [6] and a
photomultiplier (PMT). The Al converter is normally at a distance of 75
cm from the H(0) generator. It consists of a piece of 20
μ
m thick Al foil
folded and compressed by hand to a mm-thick clump with around five
layers of foil. A pinhole free Al foil of thickness 20
μ
m is mounted in front
of the PS giving a light-tight enclosure and no scattered visible light
photons (laser light) to the PMT. The PMT is an Electron Tubes 9128B
with single electron rise time of 2.5 ns, electron transit time 30 ns,
end-window cathode, and linear focused dynode structure. The dark
count rate is 100 Hz according to the manufacturer. The Al converter
gives high-energy electrons to the PMT by a few different processes [6,
39,40], mainly by pair production. PMT high voltage is normally 1600 V.
The PMT is mounted outside the vacuum in a light-tight metal container.
Thus penetration of He atoms formed by any nuclear processes in the
Fig. 1. Time variation of particle signal to an Al foil collector observing muons,
instead of the PMT detector in Fig. 2. Oscilloscope measurements, same data in
both panels with different vertical axes. The signal pulse has two parts, from
charged kaons K
at 12.4 ns decay time and neutral long-lived kaons K0
Lat 52 ns
decay time. Linear vertical scale in top panel displays the charged kaon decay
and log scale in bottom panel displays the long-lived neutral kaon decay. 0.2
mbar D
2
.
L. Holmlid, S. Olafsson Heliyon 5 (2019) e01864
2
apparatus into the PMT is prevented and there will be no He pressure at
the external PMT.
The signal current from the PMT is taken out via a short 50 Ωcoaxial
cable to the 50 Ωinput of a fast digital two-channel oscilloscope (Tek-
tronix TDS 3032, 300 MHz, 1.2 ns risetime). A 50 ΩRF attenuator is used
in the case of off-screen signals to give a factor of nine (-20 dB) lower
signal on the oscilloscope. A multi-channel scaler (MCS) with 5 or 20 ns
dwell time per channel is used for the pulse counting decay time constant
measurements (EG&G Ortec Turbo-MCS). Each MCS spectrum consists of
the sum from 1000-5000 laser shots. A preamplifier (Ortec VT120A) with
bandwidth 10–350MHz and gain 200 is used for the MCS measurements.
A single discriminator level is used in the Turbo-MCS. Since the pulse
count time distributions are measured with an Al foil in front of the PMT
as also in the MCA energy spectra, the signal is not caused by visible
photons from the scintillator into the PMT but by electrons and positrons
from pair-production by the fast muons. This means that any scintillator-
internal decay process giving photons in the scintillator cannot generate
the signal observed.
A beam-flag can be rotated to vertical or horizontal orientation, as
indicated in Fig. 2. It is a 1.5 mm thick Al plate at a distance of 64 cm from
the H(0) generator. When rotated to the vertical orientation, it allows
passage of most of the particles from the generator to the detector [4].
Positive muons and neutral kaons will pass through the beam-flag while
the charged precursor kaons and pions will mainly be blocked.
4. Results
4.1. Principle of the experiment
To observe the muon decay directly, the detector or collector should
in principle be placed at a large distance from the generator, so that the
muons can decay to electrons or positrons at or before reaching the de-
tector. Such a detector would also need to distinguish between the decay
leptons from muons and from their precursor mesons. Due to the broad
electron energy distributions from the muon decay, this principle is
rather difficult to use in a setup which generates meson showers of the
complexity which is seen here. (Alternatively, the detector needs to be
selective to muons [6]). Further, if the muons move with a velocity close
to c, the distance to the detector should be more than several hundred
meters. In general, the muons may move through matter without strong
ionization [39]. However, since the muons with the kinetic energy
observed here scatter in the laboratory equipment and in the surrounding
walls, a decaying muon cloud exists in the laboratory after the laser pulse.
Of special interest are the scattering properties of a layer of H(0) [19,29].
Such a layer reflects charged particles even at high energy, due to the
extreme density of this layer. This means that muons may have their final
scattering interaction at such a layer on the target before moving to the
detector.
The negative muons may be captured [40] after collisional deceler-
ation and may have a shorter lifetime than free muons [8]. Positive
muons will only scatter with energy loss and cannot be captured and will
thus more likely display the free muon lifetime. The muons interact with
the converter at the PMT mainly by pair production, giving electron -
positron pairs which can be detected by the PMT detector, before they
decay (submitted). Thus, the density of the positive muon cloud around
the apparatus will decay correctly with the free muon lifetime, after the
laser pulse forms the precursor mesons which have relatively short life-
times. If the positive muons initially have high kinetic energy, their
observed lifetime will be longer than the stationary free lifetime of 2.20
μ
s[8] due to relativistic effects. If the rate of electron-positron pair--
production varies appreciably with the kinetic energy of the muons,
non-exponential decays may be found. Since the decay time distributions
are measured with an Al foil in front of the PMT as in the MCA energy
spectra, the signal is not caused by visible photons from the scintillator
but by electrons and positrons. This means that any internal decay pro-
cess giving photons in the scintillator used cannot generate the signal
observed.
Thus, a direct measurement of the free muon decay-time requires that
mainly positive muons can be created, since such muons will not interact
too much with materials, and will not be captured by the nuclei in the
materials even if they thermalize. However, the muons should probably
not be allowed to decelerate too much by collisions, since then the pair-
production rate decreases appreciably. The electrons and positrons
released by the positive muons at the detector during their passage there
will be easily observed by the detector as in previous studies [1,2,6].
Thus, a method exists for observing the free decay of positive muons
released from the H(0) generator.
4.2. Meson decay to muons
The laser pulse gives emission of mesons, both kaons and pions [4,5,
7], from the H(0) generator. When a metal foil collector is mounted at a
distance of 1–2 meters as in these references, the signal to the collector
shows one or a few intermediates. One example is given in Fig. 1. It shows
in this case two intermediates in a decay chain, with a rise time close to
Fig. 2. Principle of the apparatus used, vertical cut. The inner diameter of the
tube is 100 mm and the distance between generator and converter is 75 cm.
L. Holmlid, S. Olafsson Heliyon 5 (2019) e01864
3
the laser pulse rise time and a decay time typical for the mesons formed,
in this case charged kaons K
and neutral long-lived kaons K0
L. Extensive
studies [4,5,7] show that the kaons and pions ejected from the generator
are relatively slow and decay to muons before reaching the collector.
These muons are normally the particles which give the signal current in
these studies by impinging on the collector foil, and the signal decay is
due to the disappearance of the mesons after the laser pulse has ended.
This means that the decay times of the mesons can be determined
accurately, and a relativistic increase of the decay time is not normally
observed. Thus, the signal decays with a time constant of 12–52 ns due to
the meson decay. This shows directly that mesons are generated by the
laser impact and it can safely be concluded that muons are formed by the
meson decay within approximately 100 ns.
4.3. Muon MCA spectra
Energy MCA spectra due to muons show that the muon interaction
with matter is mainly electron-positron pair production. Such spectra
have been measured with a similar PMT detector with a converter in
front of the PMT cathode [2,6]. The converter is made from Al foil or
other solid material [2,6]. The distance from the H(0) generator is up to
5 m in air, and 1–2 m in vacuum. One example is shown in Fig. 3. The
bottom panel in the figure shows the MCA data in the form of a Kurie plot
[1,2,6]. The calibration of the energy scale used
137
Cs beta electrons at
513 keV [1,2,6]. The MCA spectra do not vary with the direction of the
detector in the laboratory, but vary slightly in intensity with detector
position in the laboratory, normally being higher at larger distance from
the H(0) generator. Thus, the particles detected are muons which scatter
freely, even elastically, in the laboratory environment.
4.4. Signal decay
Pulse count time distributions or MCS spectra with the PMT at the top
of the apparatus as in Fig. 2 show a time variation as a decay of the signal
after the laser pulse interacted with the H(0) layer. This decay is due to
the decreasing number of muons in the cloud at the apparatus. The decay
is exponential and often close to the known decay-time of muons at 2.20
μ
s. It varies between a factor of two shorter than this value and slightly
longer, as expected due to muon capture processes as the cause of the
shorter times, and relativistic velocity of the muons as the cause of the
longer times. An example of the decay observed with D(0) in the source is
shown in Fig. 4. The calculated curve there is an exponential with decay
time (2.04 0.04)
μ
s. Note that this is data taken with the Al pillow in
front of the cathode, thus with mainly leptons to the PMT and no light
from the scintillator. The fitted decay time constants are given at
convergence, using the non-linear Marquardt-Levenberg fit procedure in
the program SigmaPlot 13. The error limits are the standard errors given
by this program.
4.5. Beam flagging
The signal intensity to the detector in the decay time experiments is
strongly influenced by the beam flag shown in Fig. 2. This is shown in
Fig. 5 in an experiment with p(0) in the generator and short decay time
close to 1.4
μ
s, thus probably mainly with negative muons. In this case,
the signal with the flag closed is strongly decreased and does not have an
obvious exponential decay. Of course, with mainly negative muons on
their way from the target to the converter, they are expected to interact
with the thick beam flag and they may be scattered more strongly than
positive muons are.
When instead D(0) is used a longer decay time close to 2.2
μ
sis
observed and the beam flag does not decrease the signal as much as in the
case above with p(0). This case is shown in Fig. 6. In this case as assumed
with mainly positive muons, the interaction with the beam flag is smaller
and more of the muons may pass through it. Of course, the energy of the
muons may also be slightly different from the case in Fig. 5 for other
reasons, so that the transmission through the flag is different.
Fig. 3. MCA spectra showing muon detection by pair-production with
maximum energy around 510 keV in one experiment. Same data plotted with
two different vertical scales, log scale in the top panel to show the overall
appearance and square root of counts in the bottom panel to give a Kurie-like
plot with a linear part to the energy cut-off. Energy calibration used
137
Cs
beta electrons at 513 keV [1,2,6]. Red curves use only a steel plate converter,
black curves use PS þAl converter as in Fig. 2.H
2
at 0.1 mbar.
Fig. 4. Laser-induced pulse counting MCS decay signal with D(0). Decay time
(2.22 0.03)
μ
s in range 0.9–10
μ
s in separate fit. SigmaPlot 13 was used for the
fit. 1000 shots per spectrum, 5 ns dwell time. PS and Al converter. The spectrum
at the bottom is found with laser off.
L. Holmlid, S. Olafsson Heliyon 5 (2019) e01864
4
There are also other factors which may influence the interpretation of
the experiments with beam flagging. In all experiments, the beam flag
can remove the major part of the signal. This indicates that the signal
observed originates from below in the chamber, from the source region.
If the decaying muons have stayed in the vicinity through several scat-
tering events before they pass to the detector region and give the
electron-positron pairs which are detected, they could be thought to
arrive from arbitrary directions, not only from the source region. How-
ever, their last scattering event before passing close to the detector is
likely to be somewhere in the structure of the vacuum chamber, for
example on the walls and at the source which parts are covered by an
ultra-dense hydrogen H(0) layer. Such layers give very efficient scat-
tering for various particles, as is observed directly in previous experi-
ments [19,29].
Other experiments with beam flagging [1] conclude that the particles
blocked by the beam flag are not muons but rather their precursor me-
sons. In these experiments, the MCA energy spectra showed that high
energy particles were removed by the beam flag, but that the normal
muon signal at lower energy (due to pair production) was not influenced
by the flag. Such a case is shown in Fig. 7. As can be seen in Fig. 5, this
signal at short times (where the meson signal exists) is also in the present
case strongly decreased by the beam flag. Thus, these results show that
the direct meson signal at short times as well as the muon signal at longer
times (which is studied here) are decreased by the beam flag.
4.6. Decay time measurements
A nice decay from the MCS measurements with D(0) in the muon
generator is shown in Figs. 6and 8. The single time constant appears
clearly at approximately 2.3
μ
s, close to the decay time for free muons. In
Fig. 8 the measured points and the least-squares fitted exponential curve
are shown. The program used for the fit was Sigma-Plot 13 using a model
with one exponential decaying term. The measured lifetime of 2.33
μ
s
0.08
μ
s is slightly larger than the best muon life-time value of 2.196981
μ
s[8]. By combining this measured value with the result in Fig. 4,a
better value of (2.28 0.04)
μ
s is obtained. This measured decay time is
longer than the best lifetime of 2.20
μ
s. If this longer lifetime observed
here is due to a relativistic effect, it corresponds to a relatively low
average kinetic energy of 3.8 MeV for the muon during its decay time.
Since some muons may receive an initial kinetic energy of several hun-
dred MeV [7], this indicates that the energy loss to the apparatus mate-
rials is relatively fast, probably taking less than 1
μ
s[23]. The
background without laser is approximately 0.2 counts per channel,
insignificant relative to the signal studied, as shown in Fig. 4. These re-
sults show directly that the decay process is due to particles created by
the laser pulse at the generator and that these particles are scattered in
the apparatus. Such a long time constant cannot be due to gamma pho-
tons from the laser-induced plasma, which decays in approximately 20 ns
as observed by collectors in Refs. [4,5].
The measured decay time should be corrected slightly by subtracting
the average meson lifetime from the total time observed after the laser
pulse. The most common meson observed is the long-lived neutral kaon
K0
Lwith lifetime 51–52 ns from hundreds of experiments (with one
example in Fig. 1) giving this as the most common meson decay time in
the experiments. This type of meson decays to charged pions and muons,
and the pions also give muons after a decay time of 26 ns. This means that
the final result for the of muon lifetime after subtracting 52 ns here is
(2.23 0.05)
μ
s, where the error limit is increased slightly due to
possible contributions from other precursor mesons. This gives the final
value found here into agreement with the best value of the muon lifetime
[8] within the error limits.
Using p(0) instead of D(0) normally gives shorter decay times, often
closer to 1.5
μ
s with one example in Fig. 5. This indicates that positive
muons are fewer in this case and that as expected the decay-time of
negative muons is shortened due to interaction of the muons with matter
[40]. This implies that mainly negative muons reach the converter in this
case. These decay results confirm that muons are due to the laser-induced
processes in H(0) as concluded previously from the energy spectra [2,6].
Fig. 5. Laser-induced pulse counting MCS signal from p(0), with open and
closed beam-flag. Dwell-time 5 ns, 5000 shots per spectrum. PS and Al con-
verter. 0.3 mbar H
2
.
Fig. 6. Laser-induced pulse counting MCS signal from D(0), with open and
closed beam-flag. Dwell-time 20 ns, 1000 shots per spectrum. PS and
Al converter.
Fig. 7. Beam flag effect on MCA signal. Energies up to 4 MeV (
137
Cs beta
electron calibration) are observed with beam flag open. Signal of mesons and
muons. PS and Al converter. <0.1 mbar D
2
.
L. Holmlid, S. Olafsson Heliyon 5 (2019) e01864
5
5. Discussion
The particle signals observed here are clearly caused by laser-induced
nuclear processes in H(0). A few steps in these processes have been
identified. The first one is the laser-induced transfer of the H
2
(0) pairs in
H(0) from excitation state s¼2 (with 2.3 pm H–H distance) to s¼1 (at
0.56 pm H–H distance) [15]. The state s¼1 may lead to a fast nuclear
reaction, and the internuclear distance for s¼1 is in fact similar to that
known to give muon catalyzed fusion with a high rate within a few ns
[23]. The nuclear process may involve two protons. The first particles
observed after a short distance [3,4,5,7] are indeed kaons, both neutral
and charged, but the initial formation also of pions cannot be excluded
completely. From the six quarks in the two protons, three kaons may be
formed. Two protons have a mass of 1.88 GeV while three kaons have a
mass of 1.49 GeV. Thus, the reaction 2 p →3 K releases 390 MeV, thus
around 130 MeV per kaon on average. The kaons formed decay to pions
within 52 ns and then to muons.
The difference between the results using D(0) and p(0) needs to be
discussed. From several experiments, it seems likely that positive kaons
are formed at lower density of H(0), while negative kaons are formed
preferentially at higher density. In the present experiments, that should
mean that positive muons should be formed using D(0), since the signal
in Figs. 5and 6is slightly lower for D(0). This agrees with the conclusion
that D(0) here gives more positive muons and thus a time constant close
to the free muon decay. The reason for this density effect is however not
obvious. One might speculate that in D(0) only every second nuclei is a
proton, and thus that the 2 p →3 K transition is less likely, but this does
not give any clue to why positive muons should be formed more often in
that case. Another possibility would be that at high density, neutral kaons
are formed preferentially and at low density, charged kaons are more
common. However, charge asymmetry is required to explain the obser-
vations in such a case.
6. Conclusions
The laser-induced pulsed signal previously concluded to be due to
muons is now found to have a decay time constant in the expected range
1.0–2.3
μ
s. The best known decay time for free muons is 2.20
μ
s, and the
measured decay time of (2.23 0.05)
μ
s from D(0) is concluded to be due
to positive muons. Using p(0), the decay time is shorter than 2.2
μ
sas
expected for negative muons due to their more intense interaction with
matter (muon capture).
Declarations
Author contribution statement
Leif Holmlid: Conceived and designed the experiments; Performed
the experiments; Analyzed and interpreted the data; Wrote the paper.
Sveinn Olafsson: Conceived and designed the experiments; Analyzed
and interpreted the data; Wrote the paper.
Funding statement
This work was supported by GU Ventures AB, The Holding Company
at University of Gothenburg.
Competing interest statement
The authors declare no conflict of interest.
Additional information
No additional information is available for this paper.
Acknowledgements
Part of the equipment was constructed and built with support from
GU Ventures AB, The Holding Company at University of Gothenburg. LH
thanks his wife, Ulla Holmlid, for help with checking the proof.
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