The main neutral kaon decay processes which produce muons and gamma photons are [8–11],
\({\text{K}}_{S}^{0} \to {\pi ^0}+{\pi ^0} \to 2\gamma +2\gamma {\text{ }} \to {\text{n (}}{e^+}+{e^ - }){\text{ (1)}}\)
\({\text{K}}_{S}^{0} \to {\pi ^+}+{\pi ^ - } \to {\mu ^+}+{\mu ^ - } \to i({e^+}+{e^ - }{\text{) (2)}}\)
\({\text{K}}_{L}^{0} \to {\pi ^0}+{\pi ^0}+{\pi ^0} \to 2\gamma +2\gamma +2\gamma {\text{ }} \to {\text{m (}}{e^+}+{e^ - }){\text{ (3)}}\)
\({\text{K}}_{L}^{0} \to ({\text{metal}}) \to {\text{K}}_{S}^{0} \to {\pi ^0}+{\pi ^0} \to 2\gamma +2\gamma {\text{ }} \to {\text{n (}}{e^+}+{e^ - }){\text{ (4)}}\)
\({\text{K}}_{L}^{0} \to ({\text{metal}}) \to {\text{K}}_{S}^{0} \to {\pi ^+}+{\pi ^ - } \to {\mu ^+}+{\mu ^ - } \to i({e^+}+{e^ - }{\text{) (5)}}\)
Neutrinos are also formed but omitted here. The decays differ for \({\text{K}}_{L}^{0}\) and \({\text{K}}_{S}^{0}\) by the emission of six or four photons, respectively, which is here used to discriminate between them. The muonic channels Eqs. (2) and (5) provide evidence for the neutral kaons. Eqs. (1) and (4) with 4 gamma photons show evidence for the short-lived neutral kaon \({\text{K}}_{S}^{0}\). Eq. (3) with 6 gamma photons provides evidence for the long-lived neutral kaon \({\text{K}}_{L}^{0}\). As described further below, three different gamma photon peaks are observed, which correspond to two, four and six gamma photons, thus providing evidence for both \({\text{K}}_{S}^{0}\)(four gamma photons) and \({\text{K}}_{L}^{0}\)(two and six gamma photons).
The two gamma photons from each neutral pion decay do not generally move in opposite directions as they would do if the pion was at rest in the lab system. This is caused by the momentum of the neutral pion π0 which is of a size similar to that of the gamma photons. Further, the photons do not in general have an energy of 135/2 = 67.5 MeV due to the large kinetic energy of the neutral pion. Thus, the energy and momentum conservation results in different directions for the initial pion and the resulting two gamma photons.
The kaon decay processes in Eqs. (4) and (5) take place in contact with the metal parts around the detector and especially in the Al foil pillow converter used in some of the experiments. Each gamma photon with energy of the order of 70 MeV can create numerous lepton pairs, since each such pair requires only 1.02 MeV for its production. The number of leptons in each pulse will vary mainly with the number of neutral pions decaying, resulting in a crude spectrum in the PMT with photopeaks for each set of pions (primarily two and three sets as in Eqs. (1) and (3)). There exists also another decay channel (12%) for \({\text{K}}_{L}^{0}\) [10]
\({\text{K}}_{L}^{0} \to {\pi ^0}+{\pi ^+}+{\pi ^ - } \to 2\gamma +{\mu ^+}+{\mu ^ - }+...{\text{ }} \to {\text{m (}}{e^+}+{e^ - })+i({e^+}+{e^ - })+...{\text{ (6)}}\)
In this process, a signal corresponding to just one neutral pion π0 will probably be observed by the detector employed. A similar signal from just one π0 may also be obtained from charged kaons K± [10] (21%), so it is expected to observe three equally spaced photopeaks, indicating the gamma photons from one, two or three neutral pions π0. This is confirmed below, with peaks centered close to 19.2 MeV, 19.2×2 = 38.4 MeV, and 19.2×3 = 57.6 MeV energy observed by the PMT detector. Thus, evidence for both types of neutral kaons is obtained.
The method of detection used is selective: charged mesons will not easily pass through the stainless steel enclosure of the PMT, and the PMT detector only reacts to charged particles Thus, the charged particles must be formed inside the detector enclosure. The energy calibration of the PMT as described above uses a beta (electron) emitter outside the PMT, so the photocathode is not involved in the signal generation. This means that neutral particles which can penetrate into the detector enclosure and form charged particles there will be detected preferentially. This is the detection process needed for identification of neutral kaons, being either short-lived or long-lived, and also for neutral pions, which create leptons in the interaction of the gamma photons with the detector structure. The final signal observed is due to charged leptons formed or released inside the PMT. These leptons induce secondary cascades in the multiplier dynode structure when a high voltage is applied over the PMT.
4.1. Muon and kaon detection with scintillator
The results presented in this section are found with the thin scintillator detector separated from the meson generator chamber. It is at a distance of less than 2 m from the generator in air. Thus the particles reaching the detector have penetrated 2 mm of stainless steel in the vacuum chamber wall and a similar thickness of stainless steel in the detector enclosure. The signals observed are mainly spontaneous and decrease in time for weeks after formation and deposition of H(0) in the generator. Also signals caused by laser impact in the generator can be observed, but due to the short pulse length and low laser repetition rate of 10 Hz, also in these cases the main part of the observed signal is due to spontaneous processes in H(0). However, the pulsed laser impact in the generator chamber causes recognizable energy spectrum effects even when the detector part is separated from the generator by up to 2 m of air and 4 mm of steel, as shown below. This proves that the signal is not due to any other sources outside the apparatus. The spontaneous signal (i.e. a signal that is not directly related in time to an external stimulus) is influenced by the prior or concurrent laser use, thus also the spontaneous signal is from the inside of the apparatus. A typical signal using the thin scintillator BC-720 is shown in Fig. 3. There are three different signal contributions apparent in this figure: 1) the dominant muon signal at low energy which was studied in previous publications [7, 17], 2) a slightly lower signal at intermediate energy and 3) an even less intense signal at high energy above 1 MeV. The high energy signal will be studied further in the next section. It is there shown to be due to neutral kaon decay. An intermediate energy signal was concluded in experiments inside the vacuum chamber [27] to be due to charged particles. Here, however only muons and long-lived neutral kaons can penetrate the steel walls and reach the detector outside the chamber, to create leptons in the detector part. The black spectrum in Fig. 3 shows the signal remaining after running the laser for a few minutes. This process decreases the kaon signal, both at high and intermediate energy, after partial destruction of the H(0) in the generator. This effect shows once more that the signal observed is due to spontaneous sources inside the apparatus which can be influenced by the laser, not due to any external or cosmic sources.
The signal at intermediate energy is observed at relatively high intensity in the experiments. One example is shown in Fig. 4. There the total signal corresponding to neutral kaons at intermediate energy is of the order of 100 s− 1. This large dignal size excludes once more that the signal is due to cosmic or other external sources. The black curve in Fig. 4 shows the signal a few days earlier, before long-time preparation in D2 gas which gave a large amount of D(0) in the apparatus. Kurie-like plots (square root of intensity against particle energy) here generally show a good linear variation with energy. This indicates a muon signal and shows a constant cut-offs at 1.1 MeV on the PMT energy scale (Fig. 5). This indicates a pulse size corresponding not only to one muon (as described in previous publications [7, 17, 27] with a 0.52 MeV cutoff) but an energy corresponding to two simultaneously detected muons. This agrees with a decay process of short-lived neutral kaons as in Eqs. (2) and (5) [8, 9]. The two almost simultaneously formed muons (certainly both appearing within the 500 ns shaping time of the amplifier) will result in double the pulse size in the PMT relative to the one muon case studied previously [7, 17]. This explains the behaviour at intermediate energies found in Fig. 5. The long-lived kaon oscillation to shortlived kaons means that each long-lived neutral kaon decays to one positive and one negative muon with 69% probability [8–11]. This detection process forms a large signal contribution due to the metal enclosure of the detector as described above. If short-lived neutral kaons are formed at the meson generator, they will decay rapidly and there is little signal in the detector. With no oscillation to a shortlived neutral kaon, a long-lived neutral kaon should form a pair of charged pions with 12% probability which decay to muons and one charged pion with either positive or negative charge with 66% probability. These decays also form muons. These small differences between the processes for 1. long-lived neutral kaons oscillating to short-lived (69%)) or 2. (not oscillating (66 + 12 = 75%)) cannot be observed in the results found. The kaon interaction with the steel walls close to the detector makes it highly likely that shortlived kaons are formed there from the long-lived kaons. The probability that a long-lived neutral kaon will decay by itself inside the detector volume (52 ns decay time passing through the detector) is much smaller than the probability of decay as a short-lived neutral kaon (0.1 ns decay time) after oscillation due to the metal walls. Unfortunately, this oscillation probability does not appear to be known from theory or experiment but from the present results it appears to be of the order of 0.1 or larger.
This neutral kaon signal increases with the amount of D(0) in the generator, and it increases by heating of the generator and by D2 admission. The most striking observation is that the kaon signal increases with time (of the order of days) using D2 gas at high pressure (many mbar) in the generator, with one example in Fig. 4. Further, this signal is slowly decreased by laser impact on the generator, in the time range of minutes to hours with an example in Fig. 6. Thus, the structure of D(0) which forms most neutral kaons is created by self-organization in the D(0) material but it is destroyed by the (probably subsidiary) effects of the impacting laser, possibly by gamma photon emission from the laser-induced nuclear processes. This special structure is concluded to be the small molecules H3(0) and H4(0) [37].
The detection of neutral kaons does not depend on the special properties of this scintillator. The same type of spectra as in Figs. 3 and 4 can be found also with a metal converter in the setup used in the next section. Thus, the detection of neutral kaons described here is due to kaon decay in dense materials followed by almost the same detection mechanism of the muons generated as reported for muons previously. A coverage of the scintillator end with a PE box does not reduce the neutral kaon signal at intermediate energy while the normal muon signal at low energy decreases as expected. A removal of the scintillator from the detector tube strongly decreases both the muon and the kaon parts of the signals. Thus, the kaon signal is due to both the metal wall and the scintillator: the kaons decay to pions in the walls around the PMT, and the pions finally form electrons and positrons in the scintillator and in the PMT tube. Thus, neglecting neutrinos and gamma photons, \({\text{K}}_{L}^{0} \to ({\text{metal wall}}) \to {\text{K}}_{S}^{0} \to {\pi ^+}+{\pi ^ - } \to {\mu ^+}+{\mu ^ - }{\text{ (scintillator) }} \to i({e^+}+{e^ - })\)
is the main signal generating process as in Eq. (5).
4.2. Gamma photon detection with metal converter
In the so called converter type of experiment, the PMT detector part is mounted on the vacuum apparatus which contains the meson generator, as shown in Fig. 2. The vacuum wall in front of the PMT part is a steel plate of 0.2 mm thickness. Thus, the particles pass through the 0.2 mm steel plate to the Al foil converter at the PMT cathode as shown in Fig. 2. This converter [17] is used to form electrons and positrons by pair production from muons (as in [7, 15, 17, 27]) but here it is also used for lepton pair production from the gamma photons created by the decay of neutral kaons as shown in Eqs. (1), (3) and (4). The signals observed are spontaneous, no inducing field or particles are used. To observe the large energy signal, the preamplifier used has low gain, normally G = 20. Typical experimental results with two of the main peaks observed are shown in Fig. 7. These peaks are in the energy range up to 70 MeV for electrons using the calibration 46 keV/channel, which was described in the experimental section. The energies found are thus very large and show directly that decaying particles with large masses like kaons are involved and that an efficient process has transferred energy to the leptons which enter the PMT. The interpretation of these results is that long-lived neutral kaons \({\text{K}}_{L}^{0}\)are emitted from the generator. After entering the stainless steel plate facing the PMT part and partial transformation at the steel plate to short-lived kaons \({\text{K}}_{S}^{0}\), they decay to neutral pions π0 which then form high-energy gamma photons. These gamma photons produce several lepton pairs (electron-positron pairs) at the PMT detector. Of course, these complex processes may produce a varying appearance of the peaks due to the exact direction of the kaons entering the detector part. A reasonable calibration for the efficiency of this setup can however be found from the results in Fig. 7, if the two main peaks are interpreted as due to two and three neutral pions each, from the processes in Eqs. (3) and (4). This means that each neutral pion with at least 135 MeV energy on average deposits 19.2 MeV as electron energy in the detector (19.2×2 = 38.4 MeV, 19.2×3 = 57.6 MeV for the other peaks). This will be discussed below.
A typical low-energy distribution is shown in a logarithmic plot and a square-root (Kurie-like) plot in Fig. 8. The prior use of the laser decreased the kaon signal level. The distribution in Fig. 8 does not show a clear beta-like shape, which distinguishes this kaon-type signal from the normal muon signal observed in the same system at lower energy [7, 17, 27]. Beta-like signals were observed in the scintillator experiments described above. Thus, a broad energy distribution exists for the leptons from the decay of neutral pions, as expected. The typical zero cutoff energy in Fig. 8 is around 19 MeV. This corresponds to one gamma photon from one neutral pion coming from the process in Eq. (6). The reason for the distribution is likely that several particles (lepton pairs) are formed from each photon with variable energy in the range around 70–100 MeV.
These high-energy signals are not quenched at a gas pressure of the order of 10 mbar in the chamber. The pressures used are indicated in the figure captions. Charged mesons like charged kaons and pions are quenched at such pressures. This shows that the signal here is caused by neutral particles, thus neutral kaons as was concluded from the gamma photon spectra.
By changing the conditions at the generator it is also possible to observe further high-energy features. In Fig. 9, a small amount of Ga metal is added on the muon generator surface. The liquid Ga metal absorbs H(0) and forms a larger amount of H(0) on the generator. This results in a visibly stronger white plasma with impinging laser pulse. In the top panel Fig. 9(a), a typical photopeak with Compton minimum is observed, at an edge corresponding to 67 MeV thus close to the expected average gamma photon energy (135/2 = 67.5 MeV). This peak corresponds well to a pair of photons with 135 MeV total energy, which creates the peak just below 67 MeVand the peak at 63.5 MeV which may be close to the Compton edge. This means that the gamma photopeak can be observed for the neutral pion decay. This photopeak has also been reproduced without Ga using 20 mbar H2 pressure. By moving the generator to a slightly lower position, shown in Fig. 2 (thus introducing more material in the path to the detector), the peak at 58 MeV from Fig. 7 is found together with the photopeak in Fig. 9. This peak at 58 MeV corresponds to three pions. A similar effect may be observed for the lower energy 38 MeV (two pions) peak in Fig. 7, where both a relatively sharp photopeak clearly indicating gamma photons and a broader peak are shown.
The changes in peak structure for example between Figs. 7, 9 and 10 are apparently due to changes in the kaon distributions to the detector, due to variations in the location and structure of the emitting H(0) material inside the generator. If more information about the scattering of the kaons is needed for the design of kaon detectors, more specific experiments can be performed.
An important non-intuitive result is shown in Fig. 10, providing further proof for the signal generation process. Two spectra are shown, one with and one without the usual Al converter between the steel plate and the PMT. In the case without converter the signal is very low and does not show any high-energy particles. With the Al converter in place, the signal is high and shows a typical photopeak at 38 MeV as in Fig. 7, attributed to four gamma photons from \({\text{K}}_{S}^{0}\) as in Eqs. (1) and (4). It is apparent that intense showers of leptons enter the PMT or are formed in it. This creates the intense pulses observed at the anode output of the PMT. If the signal pulses would be due to photons entering the PMT instead, the signal in Fig. 10 would be higher with the Al converter removed (not blocking the entrance to the PMT), not a factor of > 300 lower without converter as found here. Thus, the Al converter interacts with the kaons and forms the neutral pions and finally the gamma radiation and the lepton pairs observed.
It is also possible to distinguish between gamma photons originating at the muon generator and in the steel plate and the Al converter in front of the PMT. Due to the large distance between the generator and the detector, the number of gamma photons reaching the PMT should be decreased by a factor < 4 when the PMT is moved away 10 cm (to the double distance). In Fig. 11, it is shown instead that the signal decreases a factor of 90 or more by this change in PMT position. This indicates that the gamma photons are formed at the steel plate in the wall or in the converter at the PMT by particles generated in the steel plate by neutral kaons. If these particles from the steel plate are very short-lived neutral pions π0 the loss in signal by moving the PMT away 10 cm will be very strong. The angular coverage of the converter relative to the steel plate decreases strongly through the 10 cm move, and even more important the neutral pions will decay long before they reach the converter, emitting gamma photons which have just a small probability to reach the converter or the PMT. Thus, the gamma photons observed are formed close to the detector, not at the generator. The particles which can reach the steel plate from the generator are (possibly) charged kaons and long-lived neutral kaons\({\text{K}}_{L}^{0}\). The long-lived neutral kaons oscillate at the steel plate to form short-lived neutral kaons\({\text{K}}_{S}^{0}\)which decay to neutral pions inside the detector housing. The pions decay to gamma photons which produce lepton pairs inside or just outside the PMT. This experiment in Fig. 11 thus shows all the important steps in the signal generation.