Spontaneous creation of muons and destruction of protons in ultra- dense hydrogen H(0)

doi:10.21203/rs.3.rs-3403096/v1

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Spontaneous creation of muons and destruction of protons in ultra- dense hydrogen H(0)

https://doi.org/10.21203/rs.3.rs-3403096/v1

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A patented laser-induced muon generator (Holmlid 2017) is here used to observe also the spontaneous formation of muons from ultra-dense hydrogen H(0). The muons are detected by their interaction with converters and scintillators both inside and outside the vacuum apparatus containing the muon generator. This interaction creates x-ray radiation which then gives beta e+e- pairs with a zero energy cutoff of 510 ± 10 keV. The e+e- energy distributions are matched by a statistical model. It is concluded that muons are formed by spontaneous annihilation nuclear processes in H(0) primarily creating mesons. The lifetime before the spontaneous proton destruction by annihilation is estimated from the results to be of the order of 1011 years, thus much shorter than theoretical proton lifetimes.

Physical sciences/Energy science and technology

Physical sciences/Physics/Applied physics

Physical sciences/Physics/Nuclear physics

Physical sciences/Physics/Particle physics

ultra-dense hydrogen

muons

The formation of muons by laser-induced nuclear processes has been described in several publications [1–10]. Sceptical comments without any proof have been published [11, 12] as well as responses [13, 14]. The use of a laser for inducing the nuclear processes means that the experiment appears a little complex and some critics believe that the laser energy is used to create the muons. To give unambiguous proof, the present contribution focuses on the spontaneous creation of muons in nuclear processes in H(0). It is obvious that the energy for the particle creation is from the baryon annihilation [6.7,10,15]. The patented muon generator [1] is the most intense muon source which has been described, with 10¹³ muons created per laser pulse [2] when used with laser induction. It is used previously in a few publications employing energy spectroscopy of the emitted leptons [3–5]. The nuclear processes which produce the muons are baryon annihilation reactions [6, 7] which initially form kaons and pions [10]. These mesons decay rapidly mainly to muons. The decay time of epithermal muons from H(0) was measured and shown to agree accurately with the accepted life-time of 2.2 µs [8]. The zero-signal high-energy cut-off in Kurie plots of MCA energy spectra from H(0) is constant close to the electron mass of 511 keV. This indicates e⁺e⁻ emission. This maximum energy in the Kurie plots is independent of the converter or scintillator material in the detector [3–5]. This shows that neither muon capture nor muon decay is the source of the energetic particles. Instead, it clearly indicates e⁺e⁻ pair production.

The physics of ultra-dense hydrogen H(0) was summarized in a review paper in 2019 [16]. The molecular mechanisms involved in the production of H(0) were summarized in another more recent review [17]. Thus, the properties of H(0) and of its formation are not described extensively here but the reader is referred to these summaries.

The H-H bond distances in H(0) are given by d = 2.9 r_q s², with r_q = 0.192 pm (quantum mechanical electron radius [16, 18]). The most often studied value of the spin quantum number s in the laboratory is s = 2 which has bond distances of 2.245 ± 0.003 pm [19, 20]. A relatively weak disturbance by a laser pulse with energy < 0.4 J transfers H(0) in spin state s = 2 to s = 1, with internuclear distance of 0.56 pm. At such short internuclear distances in similar systems, nuclear processes take place within 1 ns [21]. Both laser-induced nuclear processes [3] and spontaneous nuclear processes [4] in H(0) generate mesons (kaons and pions) [10, 22–26], which decay to form mainly muons, gammas and neutrinos. A novel detection method [5] was also developed to detect the muons. The correct decay time of the muons formed was verified [8]. The photo multipliers with a thin metal layer in front, used for muon detection in the T2K experiment [27], are similar to the detectors used here.

Mesons can be formed by pulsed-laser impact on H(0) [10, 16]. The mesons are observed by their decay to muons in a vacuum [10, 22–25] and also after deflection in magnetic fields [25]. They are identified by their characteristic decay times [6, 7, 10]. Charged pions with τ = 26 ns as well as neutral long-lived kaons with τ = 52 ns and charged kaons with τ = 12.4 ns [28, 29] are easily observed from their decay to muons. The particle energy spectra due to the muons (and particles formed by them) from the experiments with H(0) are studied in a few publications from our group [3–5]. The muons formed by meson decay create high-energy photons in materials and these photons give numerous electron-positron pairs.

The e⁺e⁻ (electron-positron) pairs formed interact with the internal structure of the PMT. As shown below, the particle kinetic energy is in the range up to 510–520 keV. Such electrons (and positrons) have a range in the PMT glass of only 1 mm [30] and much less in the copper dynodes in the PMT. They will thus dissipate their energy in the PMT structure giving secondary electrons. The calibration of the PMT directly with the external 512 keV beta-decay electrons from ¹³⁷Cs [4, 5] gives 3.0 keV per channel (at main amplifier gain = 1). Since the zero signal cut-off in the Kurie plots is constant, close to 175 channels, the Q value for most processes observed is close to 520 keV. This observation is significant and close to the electron mass of 511 keV.

A simple statistical theory of the energy distributions for the light leptons formed by pair- production from the muon annihilation can be formulated in the classical limit which means no quantization for the kinetic energy [26]. Such a theory is here built on the so called RRK (Rice-Ramsperger-Kassel) theory used in chemical reaction kinetics [31, 32]. This description only assumes that the energy available for a certain process, in this case the e^± pair-production process, is limited and is distributed between several energy terms statistically. This is a microcanonical ensemble. This type of theory is a general theory used to describe arbitrary reactions [33, 34]. The probability distribution for one such energy term out of N terms is [26, 33]

P(ε) = K(E' - ε)K-1/ (E')K with K = N-1, N-2.... (1)

with E' the remaining non-distributed energy, equal to the real distributable total energy Etot for the first calculated energy distribution term. The energy term ε is the distributed energy in this energy term. Instead deriving the similar function for two such terms out of N terms gives [26.33]

P(ε) = const × ε (E' - ε)K-2/ (E')K with K = N-1, N-2.... (2)

While the distribution for one energy term in Eq. (1) is peaked at zero energy, the distributions for two terms are peaked at intermediate energy, below the maximum at Etot where the distribution goes to zero. A distribution of two energy terms out of total five to six terms resembles the typical beta-decay distribution [35] and is also very similar to the experimental distributions given below. The two energy terms are the kinetic energy terms for electron and positron motion to the detector while the six terms are for all directions for these two particles.See further in the Results section.

Typical experimental setups with dimensions are shown in Fig. 1. More details are given in each figure caption.

In the H(0) generator[1], several iron oxide catalyst samples with main composition K₂Fe₂₂O₃₄ 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 molecular processes involved in forming H(0) were recently reviewed [17]. The ultra-dense material is assembled on the upper surface of the generator. The gas pressure in the chamber is 0.1–100 mbar (uncorrected Pirani reading at low pressure) with or without constant pumping.

The particle signal is measured with a detector often consisting of an Al foil converter [5] and a photomultiplier (PMT) as shown in Fig. 1. Another common form employs a stainless steel plate with 0.2 mm thickness instead of the Al converter. Both constructions are used either attached to the vacuum chamber with a plastic scintillator or the steel plate as vacuum wall, or separated from the chamber by a distance up to 3 m. The converter is normally a pillow of 20 µm thick Al foil folded and compressed by hand to a few mm-thick clump with 3–5 layers of foil. The 5 cm long plastic scintillator (PS) (BC-408, Saint-Gobain Crystals) has diameter 40 mm. A pin-hole free Al foil of thickness 20 µm is mounted in front of the PS giving a light-tight enclosure when attached to the chamber. Sometimes another plastic scintillator (BC-720, Saint-Gobain Crystals) was used. It has a similar diameter (38 mm) but only 1.6 cm thickness. This type of scintillator is especially intended for detecting fast neutrons while being insensitive to gamma radiation. The PMT used is 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 PMT is mounted outside the vacuum in a light-tight metal container. PMT high voltage is normally 1600 V. A preamplifier (Ortec VT120) with bandwidth 10–350 MHz and gain 200 or 20 and a pulse-shaping main amplifier (Ortec 440A) with shaping time 0.5 µs were used for the measurements. The signal from the PMT was analyzed by a 2048 channel multi-channel analyzer (MCA) (Ortec EASY-MCA-2k with Maestro software) normally with total acqusition time per spectrum of 500 s. In the figures, the amplifier gain is sometimes given as 200 (preamplifier)×1 (main amplifier).

The calibration of the energy spectra for the PMT detector for electrons directly into the PMT employed a beta radiation emitter of 137Cs (37 kBq, Gammadata, Uppsala, Sweden) to find the zero-signal cutoff in straight-line Kurie plots [35]. This procedure was also described in Ref. [4]. With this cutoff corresponding to Q = 512 keV, the calibration of 3.0 keV per channel was found (with preamplifier gain 200 and gain 1 in the main amplifier. This calibration is identical with that for earlier PMT tubes of the same type [5]. With a CSDA range of approximately 0.21 g cm-2 for 500 keV electrons in glass [30], the range is of the order of 1 mm, thus giving penetration of most of the electrons and positrons into the PMT. The signal caused by the 137Cs emitter (with blank experiment subtracted) sitting 20 cm from the PMT without a metal enclosure is shown in Fig. 2, giving the cutoff close to 174 channels in the MCA. It should be observed that this beta electron calibration without enclosure provides a correct energy calibration for electrons and positrons formed within the detector enclosure. A calibration employing the 137Cs source externally to the metal enclosure surrounding the PMT gives a different energy distribution due to energy loss of the electrons when they pass through the metal wall into the PMT.

An approximate intensity calibration can also be performed using the known source intensity. It shows that most electrons penetrate through the glass into the PMT and become detected.

The positrons formed in the multi-pair production process give detectable annihilation gamma photon peaks. The detector used for such measurements was a NaI(Tl) scintillator with length 4 cm and diameter 4 cm (Saint-Gobain) with a PMT 9125B (Electron Tubes). The signal was analyzed by the same amplifiers and MCA as described above. A positron source, a ²²Na source (37 kBq, Eckert & Ziegler) was used for calibration.

The published results from experiments similar to the ones described here show a zero-signal cutoff in Kurie plots at 510–520 keV close to the electron mass of 511 keV [3–5, 26], indicating electrons and/or positrons as the particles formed in large numbers by the detection process. The initial suggestion [3, 4] to explain this apparent beta decay process was that the muon decay gave rise to this signal. When other experimental features were observed, like the strong increase in signal by using glass or metal converters [5], a simple muon decay scheme was clearly no longer a possible explanation. A pair production of the observed type requires apparently bosons with high energy.

A mechanism which agrees with experimental findings indeed exists.The muons have high energy of the order of 100 MeV and give gammas and x-ray photons in interaction with matter for example in the converter. These photons then create numerous e⁺e⁻ pairs in materials around the detector and these pairs are detected in the PMT.

4.1. Constant zero-signal cut-off

The shape of the MCA energy spectrum and its high-energy cutoff, which indicates pair production, is unchanged during changes in source intensity, as shown in Fig. 3. Numerous spectra have also been published which show that the cut-off is constant close to 511 keV [3–5]. Such experiments show the intensity variation of the source with several source parameters. Another straight-forward experiment is to change the distance between the converter where the e^± pairs are formed and the PMT detector. Such an experiment is shown in Fig. 4. The conditions for both panels in Fig. 4 are the same, with the bottom panel measured after a 10 min rebuilding time, moving the PMT 10 cm away from the steel plate giving 100 times lower signal but still the same signal cut-off.

With the PMT close to the stainless steel plate in the vacuum flange in front of the detector part, the cutoff is observed in the Kurie plot to be at around 180 channels or 540 keV. This slightly higher value than in most experiments is apparently, as seen in the upper panel of Fig. 4, due to a higher background intensity from another process which has its cutoff at around 1 MeV. This could be a slightly different process where complete lepton pairs i.e positronium at 1.02 MeV total energy are detected. This cutoff is then due to the maximum positronium kinetic energy of 1.02 MeV in the energy distribution. At a large converter distance as in the bottom panel in Fig. 4, these positroniums have annihilated giving only gamma radiation, with the known lifetime for the singlet state of 0.12 ns and of the triplet state of 142 ns [28, 36].

The published spectra contain several examples of the constant cut-off for different converter materials [3–5]. That the cut-off is independent of the converter material supports a muon-gamma-e^± pair model. The nuclei in the converters do not influence or take part in this process.

4.2. Muons are not ambient but from the generator

The signal in the experiments varies in size with many different parameters. One example is shown in Fig. 5 where the signal is shown to depend strongly on the amount of D(0), being deposited in the source by gas admission prior to the experiment and then removed by heating in vacuum. Renewed gas admission increases the signal again. This process is reproducible and is used routinely. This proves that the muons originate in the source and are not ambient, for example from nuclear processes in the upper atmosphere as most mouns on Earth are.

The PMT-MCA signal in the region above 1 MeV is intense and complex. An example of the signal with the detector mounted on the chamber and also separate from the chamber is shown in Fig. 6. The low-energy muon part below 1 MeV is almost unchanged when the detector is moved away from the chamber. The high-energy part is however strongly reduced at long distance, suggested to be so since it is caused by the more shortlived kaons and pions from the annihilation reactions [10].

4.3. Function of the converter

The importance of the converter is demonstrated by an experiment in Fig. 7. At 1 MeV energy, the signal is increased a factor of 1000 by the converter plus NaI snintillator in front of the PMT, and at 500 keV about a factor of 20. The Al converter is placed between the scintillator and the PMT, thus no visible photons from the scintillator can reach the PMT.The intensity at 2.5 MeV in Fig. 7 is not changed by the converters. This behaviour agrees with that expected for muons at low energy. Kaons and pions, which are not influenced strongly by the converters, give the signal at high energy as mentioned above.

The best Al converter is a compressed “pillow” of a few layers of 20 µm thick Al foil. In the results shown in Fig. 8, it should be noted that also the process of transport of the final e^± leptons to the PMT is of importance for the size of the observed signal. A dense converter material like Ta will give less penetration of the e^± particles relative to glass and Al. Another drastic example of this transport effect is shown in Fig. 9. The use of two plastic scintillators of length 5 cm in front of the converter gives a signal which is 10–100 times lower than without the scintillators. The non-conducting organic scintillator material prevents the transport of the electrons and positrons to the PMT.

4.4. Lifetime of H(0)

The spontaneous nuclear process in H(0) implies a lifetime of H(0). So we need to estimate this lifetime from the results found here. In Fig. 4 upper panel the total intensity of muons is approximately 10⁵ particles per 200 channels, thus 2×10⁷ particles during 500 s or 4×10⁴ s^− 1. The total volume of H(0) on the generator is estimated to be a 4 mm diameter layer with a thickness of 1 µm or a volume of 6×10^− 12 m³. With a bond distance of 2 pm in spin state s = 2, each atom in H(0) occupies a volume of 8×10^− 36 m³. This means 8×10²³ atoms in the layer on the muon generator which produces 4×10⁴ reactions s^− 1. So the reaction rate per atom becomes 5×10^− 20 s^− 1 or a life time of 10¹¹ y thus longer than the assumed lifetime of the universe but much shorter than the lifetime of a proton outside H(0) which is thought to be > at least 10³² y [37]. The spontaneous nuclear processes giving the mesons and the muons are probably the same as for the laser-induced nuclear orocesses, thus baryon annihilation [6, 7]. This process is initiated by a transfer in H(0) from spin state s = 2 to s = 1 creating mesons, muons and finally only gamma photons, electrons (positrons) and neutrinos. Thus a mechanism exists for proton ”decay” to mesons and muons.

4.5. Statistical energy distributions

A statistical theory was described above which gives energy distributions of a few kinetic energy terms out of larger number of terms, assuming a fixed total energy to be distributed among this larger number of energy terms. This is an energy distribution for a so called microcanonical ensemble of systems. An energy distribution which is peaked at an intermediate energy is found for two terms out of for example six terms (N = 6). An even better agreement is here found with N = 5.5. Such a distribution is shown in Fig. 10, with the total energy limit put equal to 175 channels. In this way, a simple comparison is possible with the normal MCA plots. This type of distribution is similar to a beta-decay distribution [35], which also has a fixed total energy to distribute between several particles and thus between several energy terms.

For an accurate comparison with the Kurie plots shown in Figs. 3 and 4 and in previous publications [3–5], the square root of the statistical energy distribution is also calculated. The best result giving linear plots for this (P(ε))½ function is shown in Fig. ,10 for this case N = 5.5.

One might expect the best agreement for N = 6, thus six quadratic energy terms in total. Two velocity vectors are involved in each pair production step (one electron and one positron). Each such vector is associated with three quadratic kinetic energy terms for v_x, v_y and v_z respectively. However, they are not all independent since linear momentum needs to be conserved for each electron and positron pair. Such restrictions often give lower values for the apparent number of terms in this type of statistical energy distribution [33]. The energy distributions observed may be thought to correspond to three terms. However, the third term will tend to deflect the particle away from the detector, so two terms for the observed energy is more correct. Thus, the observed energy distributions should correspond to two terms out of 5 or 6. Here, the plot in Fig. 10 shows a linear Kurie plot to the theoretical cut-off introduced in the statistical formulas, thus giving agreement with experimental results for two terms out of 5.5.

An experimental energy distribution is included in Fig. 11, using a theoretical distribution with N = 5. At high energy, the tail of the experimental distribution does not go to zero since another type of signal is found there as seen also in Figs. 3 and 4 which was described above.. In the range of 40–150 channels, the two curves agree quite well.

The observed particle energy is thus distributed to two terms out of five - six for an electron or a positron with a maximum energy of 511 keV. This indicates that the pair-production process is sequential for each pair produced. How energy is conserved in an annihilation process which generates many pairs simultaneously does not seem to be well understood, probably since such processes have not been investigated. Another annihilation process with several different particle pairs formed was recently studied, showing excellent energy conservation [6, 7].

The linear Kurie plots shown here and previously [3–5] are thus interpreted as due to e^± pair-production.

Muons are created by spontaneous nuclear processes in H(0). They have statistical energy distributions with a zero-signal cut-off at 510 ± 10 keV.The spontaneous annihilation processes mean that a lifetime is observed for protons inside H(0), of the order of 10¹¹ years.

Acknowledgment

Part of the equipment used here was constructed and built with support from GU Ventures AB, The holding and incubator company at University of Gothenburg.

There was no direct funding for this project.

Data availability

The data that support the findings of this study are available upon reasonable request from the author Leif Holmlid.

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No competing interests reported.

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Spontaneous creation of muons and destruction of protons in ultra- dense hydrogen H(0)

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Abstract

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1. Introduction

2. Theoretical background

3. Experimental

4. Results and discussion

4.1. Constant zero-signal cut-off

4.2. Muons are not ambient but from the generator

4.3. Function of the converter

4.4. Lifetime of H(0)

4.5. Statistical energy distributions

5. Conclusions

Declarations

References

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