An Experimental Study on Deuterium Production from Titanium Hydride Powders Subjected to Thermal Cycles

Abstract

An extensive multi-year experimental study was conducted to investigate the potential production of deuterium from titanium hydride TiH_x powders subjected to specific thermal cycles. Mass spectrometry was performed, focusing on the variation in signal intensities at $m/z$ = 2, 3, 4, 18, 19, 20, and 21, corresponding to fragments primarily involving deuterium, during the degassing of titanium hydride powders as the sample temperature was raised from room temperature to approximately 1100 °C. The results reveal an anomaly in the deuterium-to-hydrogen ratios, with the analysis indicating an increase in deuterium concentration by a factor of approximately 280 compared to its natural concentration on Earth. Three independent methods confirmed the excess deuterium. Simultaneously, flow calorimetry was performed during the degassing process, which did not show any measurable excess heat produced in the configuration used. This study was motivated by our novel theoretical predictions, based on the standard electroweak theory with gauge symmetry, suggesting the generation of slow neutrons within metal hydrides when exposed to coherent excitations. Our findings align with direct measurements of neutron emission by TiH_x powders under cavitation in liquid water, as recently published by Fomitchev-Zamilov.

1. Introduction

The transmutation of elements at low temperatures has been a subject of intense study for more than thirty years. In this work we describe new experimental evidence of the production of deuterium from titanium powder loaded with hydrogen. We will also discuss the theoretical hypothesis that this deuterium is produced by a reaction in which protons in an excited coherent state generate slows neutrons via electronic capture; it naturally follows that these neutrons are also able to cause a wide range of nuclear transmutations involving heavy elements. In the first part of this introduction we are thus going to recall the main experimental evidence of transmutations occurring in various low-energy conditions, as we believe that their explanation is strictly related to the hypothesized coherent neutron generation.

Evidence of the emission of neutrons from a titanium–deuterium system was reported as early as in 1989 by De Ninno et al. [1]. Reports by Ohmori, Mizuno, and co-workers in 1997–1998 [2,3] described the formation of Fe from an Au electrode during electrolysis. In the 2000s, Iwamura et al. [4,5,6] further advanced the field by demonstrating the generation of Ru and Pr following the permeation of D₂ gas through a Pd membrane. Around the same period, Celani et al. [7,8] reported the detection of new elements in Th-Hg-Pd-D(H) electrolytic systems. For an extensive review of related studies, see [9].

Later, Iwamura et al. found transmutation phenomena induced by deuterium gas permeation through nanosized Pd multilayers doped with Cs and other elements [10,11,12,13]. They observed the transmutation of Cs into Pr by this method at the laboratory of Mitsubishi Heavy Industries Ltd. These results have been independently reproduced [14].

Ref. [15] offers a recent detailed analysis of neutron production in low-energy experiments. The collected experimental evidence supports the hypothesis of a new class of nuclear reactions, prompting recent interest from the US Department of Energy’s ARPA-E program, which has launched a new initiative to investigate this phenomenon further. In Ref. [16], Fomitchev-Zamilov reported clear observations of neutron emission during the acoustic cavitation of deuterated titanium powder.

Huang et al. have recently conducted experiments using two reactors made from a concentric multiple-pipe heat exchanger and found that, when water is flowing through a tiny space and heated, it produces peculiar excess heat probably by cavitation and the dynamic implosion of nanobubbles [17]. Possible nuclear transmutation was found by SEM/EDX inspection of ruptured copper pipe samples (C increases 200–500%, O 300–600%, Fe 400%, and new elements P, S, and Ca appear).

Very recently, in a correlated study [18], one of the authors (L.G.) illustrated the theoretical viability of generating neutrons through electron capture (EC) (Figure 1) at room temperature and low energy within a metal sample (e.g., Ni, Ti) heavily loaded with hydrogen. This was accomplished by utilizing the coherence properties of the quantum plasma created by dissolved protons within a metal [19,20,21]. When suitably excited coherently, this plasma can provide enough de-excitation energy to generate a neutron from one of the protons through electronic capture. These predictions are based on the standard model of electroweak interactions, relying on the fundamental $SU{\left(2\right)}_L\times U\left(1\right)$ gauge symmetry.

Previous publications have discussed the production of ultra-slow neutrons in metals [22], but they do not provide a comprehensive treatment of the energy exchange required to overcome the mass gap for neutron production.

The novel underlying principle supporting the theory developed in [19] is that, through a coherent process, the energy required to reach the threshold for neutron production can be supplied by a coherent superposition of energy quanta associated with highly populated low-energy degrees of freedom. These degrees of freedom encompass the vibrational modes of the electron and/or proton plasmas.

Specifically, electron capture becomes possible because the coherent plasmas of protons and electrons present in the metal [19] in particular conditions, when coherently excited to an elevated vibrational state, possess an energy that is significantly higher compared to typical thermal energies. This is because the plasmas are composed of a vast number of particles, resulting in sufficient energy to overcome the mass gap between the combined mass of a proton and an electron and the mass of a neutron, enabling the production of a neutron and an electronic neutrino.

In simple terms, there are two different ways to quantum mechanically describe a set of N identical particles. The first approach utilizes the density matrix formalism, which represents a statistical ensemble of independent particles whose quantum phases are completely uncorrelated. The second approach involves representing the N particles as a coherent system, wherein all particles share the same quantum phase and are described by a single quantum state.

In the first case, when interacting with another field, the conservation of energy in the transition is associated with the energy of a single particle, which is generally a fraction of an eV. In the second case, the energy associated with the coherent quantum state is the sum of the single particle energies and is equal to N times the energy of a single particle. Consequently, in calculating the transition rate, the energy conservation condition to be imposed contains a coherent energy that is N times larger than that of a single particle and can reach values in the order of MeV.

Thus, it becomes possible for a process to generate a neutron and a neutrino from a coherent state of electrons and protons, as the required energy is 782 keV, corresponding to a very small vibrational energy per proton and per electron. This condition would be impossible to achieve in the case of incoherent transitions and is the reason why, in our opinion, it is impossible to describe LENR phenomena through single-particle theories.

In reference [19], we have shown how these coherent proton states can form spontaneously within a metallic matrix. Considering that electrons in the metal are also in coherent configurations, as shown in reference [23], it becomes possible to rigorously write, within the standard model, a coherent transition rate for neutron production.

The formalism of coherent states for particles of spin 1/2 in a state of high density is not frequently used and requires special care. For this reason we will discuss in more detail these theoretical issues in a separate work.

The neutrons produced in this manner, being generated just above the energy threshold, have a very small momentum and their cross-section of interaction with surrounding nuclei is very high, leading to immediate binding through nuclear capture. This forms metastable nuclear states that quickly decay to their ground state, releasing an energy equal to the nuclear binding energy of the incoming neutron. This energy is not emitted in the form of $\gamma$ rays because the emitted $\gamma$ during de-excitation is coherently absorbed by the electron plasma in the crystal. The excitation of the coherent electronic state, being shared by a macroscopic number of electrons, can be effectively dissipated as heat through a downconversion process similar to latent heat production in a phase transition.

As this study is experimental in nature, we will delve deeper into a rigorous theoretical description of the processes outlined in a dedicated work aimed at establishing the foundations for a comprehensive theory of nuclear phenomena in condensed matter.

The objective of this experimental study is to validate the possibility of exciting these coherent configurations to an extent that generates measurable quantities of ultra-low momentum (ULM) neutrons. This is achieved by subjecting Ti micropowders loaded with natural hydrogen ($D/H\sim {10}^{-4}$) to thermal cycles.

To this end, we have employed a custom-built reactor, two independent vacuum systems, a residual gas analyzer (RGA), and a mass-flow calorimeter. The experimental procedure was repeated seven times over a time span of more than one year. The gas outgassed from the active samples was analyzed and compared to the gas of a reference hydrogen tank.

Mass spectrometry measurements have revealed an excess of deuterium in comparison to the natural background in all the tests performed. Following the theory described in [18], this excess is thought to be a direct consequence of the generation of slow neutrons in the coherent electron capture reactions described above. More details about this process and further expected consequences of the coherent electron capture are given in the next section.

2. Expected Consequences of Neutron Generation in Our Experimental Environment

The presence of ULM neutrons in the metal naturally induces neutron capture processes [24] by the nuclei present in the surrounding environment, typically hydrogen nuclei and titanium nuclei. The products of the expected reactions will therefore be mainly deuterium nuclei, tritium nuclei, and titanium isotopes, of which the most abundant isotope is ${}^{48}Ti$ with 73.7%.

Since the stable isotopes of Ti range from 46 to 50 in mass number, the addition of a neutron will predominantly produce an isotopic abundance shift without producing observable nuclear effects. Only ${}^{50}Ti$ with a natural abundance of 5.2% would transmute to ${}^{51}Ti$ which is a beta-emitter with a decay time of 5.8 min to ${}^{51}V$ which is again stable.

The produced deuterium has the advantage of being released from the metal in gaseous form and is therefore detectable by an RGA after escaping from the metal. The produced tritium would have a much lower abundance than deuterium since it requires the interaction of a neutron with a deuterium nucleus which, being less abundant than hydrogen, implies much suppressed tritium production.

The incoherent (single-particle) process of neutron capture by hydrogen nuclei can be described by the following equation:

$$n+H⟶D^{*}⟶D+\gamma ,$$

(1)

where n is a neutron, H is a hydrogen nucleus, $D^{*}$ is a deuterium nucleus in an excited state, D is a deuterium nucleus in its ground state, and $\gamma$ is the outgoing photon. The reaction is exothermic, releasing approximately 2.2 MeV of energy. The only available mechanism for energy dissipation is electromagnetic de-excitation, resulting in the emission of a $\gamma$ photon of approximately 2.2 MeV within a characteristic time given by $\tau \simeq {\displaystyle \frac{1}{E}}\simeq 2·{10}^{-21}$ s. Consequently, the single-particle process is inherently radioactive.

Likewise, the process of neutron capture by titanium nuclei can be described by the following equation:

$$n+{}^{A}Ti⟶{}^{A+1}Ti^{*}⟶{}^{A+1}Ti+\gamma$$

(2)

where ${}^{A+1}Ti^{*}$ is an excited state of titanium. The reaction is also exothermic, releasing an approximately 1.5 MeV photon.

Finally, the production of tritium can be described by the following equation:

$$n+D⟶T^{*}⟶T+\gamma ,$$

(3)

where $T^{*}$ and T are tritium nuclei in the excited and ground states.

In all these cases, the $\gamma$ rays produced by the de-excitation of the metastable state of the newly formed isotopes denoted by an asterisk, that would normally be radiated away in the vacuum in a timeframe of order $\tau \sim {10}^{-6}$ eV⁻¹ = ${10}^{-22}$ s, are not detected outside the host metallic matrix because they are coherently absorbed by the coherent state of electrons present in the metal. The coherent nature of this interaction implies an amplification factor for the electromagnetic coupling constant in the order of $\sqrt{N_e}\sim {10}^4$ where $N_e$ is the number of electrons in the coherent state, implying an amplification of the interaction probability of a factor ∼${10}^8$. The $\gamma$ energy is thus distributed among a large number of electrons, so each acquires a small fraction of an electron volt, which can then be efficiently converted into thermal energy. The result is the absence of $\gamma$ emissions and an increase in the crystal’s temperature due to the conversion of the $\gamma$ energy into heat.

One might wonder why a metal irradiated by $\gamma$ rays does not exhibit the same absorption efficiency as observed in the case of photons emitted during the de-excitation of nuclei produced through the previously described mechanism. The reason lies in the fact that, for the reaction to occur, both energy and momentum must be conserved in the interaction with the coherent state of electrons, which effectively makes the phase space nearly zero. In contrast, during the absorption process of the $\gamma$ photon, since the photon is virtual, energy conservation is not required at the electromagnetic vertex. This results in a much higher interaction rate compared to the first scenario.

In summary, the described reactions primarily generate heat and stable isotopes, with only a minimal fraction of the energy produced in the form of energetic radiation. The produced tritium, due to its radioactivity, should be subsequently observable. However, the quantity produced is expected to be very small, resulting in negligible levels of radioactivity, as will be further discussed in the following sections. A specialized apparatus should be implemented to detect it.

For completeness, we note that, under certain circumstances, the coherence of the process may not be complete, particularly in situations of strong disequilibrium and impulsive excitation. In these cases, the emission of highly energetic particles can occur, as has been experimentally observed in some setups [25].

Coherent correlated states and low-energy nuclear reactions in nonstationary systems have been analyzed in refs. [26,27].

The authors of [28] investigate possible low energy nuclear reactions arising due to the conversion of proton to neutron through weak interactions, in which the resulting neutron forms a short-lived virtual state, according to the framework of second-order perturbation theory.

3. Methods

The experiment is designed to detect an increase in the concentration of deuterium relative to its natural abundance, which is in the range of $1.5·{10}^{-4}$–$2.5·{10}^{-4}$, in the gas degassed from a $Ti{H}_x$ sample subjected to thermal cycles ranging from 20 °C to 1100 °C. This measurement is carried out by monitoring the relative heights of signals from an RGA for various hydrogen compounds, typically $H_2$, $HD$, $H_{2}O$, and $HDO$. The following subsections describe the experimental setup and the procedures for conducting the experiments.

3.1. Experimental Setup

The experimental apparatus (Figure 2) is composed of a reactor, two independent vacuum systems, a mass spectrometer, and a mass-flow calorimeter. The reactor is depicted in Figure 3 and is composed of several components:

• A reactor core (RC), made out of a Swagelok 1/4” 25 cm long pipe, closed at one end by a vacuum tight TIG welding. The sample is 1 g of hydrated Ti powder (SAES Getters Group) and is placed inside the reactor core. In a second series of experiments a 1/4” custom-made alumina tube, closed at one end, has been used in place of the Swagelok tube to avoid steel melting at high temperature.
• Four N-type, Nicrosil-armored thermocouples of a thickness of 1.5 mm (TC1, TC2, TC3, and TC4).
• A flange equipped with 5 vacuum tight feed-through (F1).
• A hollow cylindrical heater (H1), inner diameter 10 mm, 15 cm length, made of 80 coils of Niconel wire, 1 mm diameter, and able to deliver up to 1 kW of thermal power. The RC can reach up to 1200 °C. H1 surrounds RC so that the middle point of H1 is at the same height of the bottom of RC.
• An external vacuum chamber (C1), 56 mm diameter and 250 mm long, surrounding the reactor core and the heater, and filled with an insulating wool. C1 is sealed at its top by flange F1 and evacuated by the pump S1 (Figure 4). The temperature of the side walls and of the flange remains below 50 °C even when RC reaches 1200 °C thanks to the cooling system. Figure 5 shows the power–temperature calibration curve.
• An external plexiglass cylinder (C2) surrounding the external vacuum chamber where a water flow is allowed to circulate so that the reactor is cooled.
• Two PT100 water-resistant sensors (PTin, PTout) used for measuring the temperature of the inlet and outlet water.
• A water flow meter (FM), used for measuring the flow rate of the cooling water.
• A DC power supply, PS1, programmable from 0 to 500 V, 1 kW to feed H1.
• An amperometric resistance R1 of 1 $\Omega$.
• Two Agilent multimeters, MM1 and MM2, model 2000, equipped with multiplexer cards.
• An RGA MS1, model Pfeiffer Prisma 80, equipped with TalkStar software, Version 1.40.
• A rotative+turbo pump connected directly downstream the MS1, capable of reaching a vacuum ∼${10}^{-7}$ mbar in the detection volume of MS1.
• A micro-needle, K1, that, together with valve G2, allows for a pressure drop from atmospheric down to the range of ${10}^{-7}$ mbar in the section directly connected to T1 and MS1.
• A PC running the LabView program that acquires all the digital data coming from MM1 and MM2 and stores them into a file for offline analysis.

The thermocouple TC1 is positioned inside RC so that the tip is 1 cm from the bottom of RC and about 2 cm below the top of the $Ti{H}_x$ powder.

RC is connected to F1 through a vacuum fitting in its turn connected to the primary vacuum system (see Figure 4). This flange seals a secondary vacuum chamber encompassing the reactor core. This arrangement establishes two distinct vacuum systems. The first, connected to RC (primary), is linked to the MS system, while the second (secondary) is connected to C1. The secondary system serves the dual purpose of enhancing thermal insulation for RC against the external environment (see Figure 5) and evacuating the intermediate chamber C3 upstream of the needle valve. A scroll, oil-free pump, S1 (Agilent SH-110 dry scroll vacuum pump, with a minimum pressure of $7·{10}^{-2}$ mbar), is employed to pump the secondary vacuum system.

All tubing from RC to C3 consists of 1/4” Swagelok vacuum tubes. The remaining tubes are standard KF32 vacuum tubes equipped with a heating wire for degassing during the pump-down phase. A pressure gauge, P1, is situated on the vacuum manifold between RC and G1, measuring the pressure of gases released by the sample. Voltage measurements, V1 and V2, are recorded at the ends of H1 and R1, respectively, to precisely quantify the power supplied to H1.

Within the high-vacuum section of the primary vacuum system, near the MS, a Pirani vacuum gauge, P2, is installed to monitor vacuum quality during MS measurements. TC1, TC2, TC3, TC4, P1, V1, and V2 are connected to MM1 and MM2, which, in turn, are linked to a PC via the GPIB communication protocol. The experiment is orchestrated by a LabView program tailored for this purpose, capable of recording the complete set of raw data for subsequent offline analysis. The data acquisition is conducted at intervals of approximately 4 s.

The MS measurement is interfaced via RS-232 to the PC, and real-time acquisition data is stored in a text data file. H1 heats the RC, with its connections passing through the upper flange. In the interstice between RC and H1, TC2 and TC3 are positioned at different heights, with their connections also passing through the vacuum fittings present on F1. Finally, TC4 measures ambient temperature.

The gases released by the heated Ti powder are collected in C3 and can be sampled by MS1 thanks to the adjustable micro-needle valve (G2+K1 in Figure 4) that allows for a pressure drop from atmospheric down to the range of ${10}^{-7}$ mbar.

3.2. Experiment

The aim of the experiment was to subject $Ti{H}_x$ powders to thermal cycles in the range of 20–1100 °C in order to induce rapid hydrogen degassing fluxes. During this process, the RGA monitored the isotopic composition of the gases in the vacuum chamber. The expected result was that, following the intense hydrogen degassing, the coherent vibrational states in the metal would be sufficiently excited to produce ULM neutrons. The excess neutrons were then identified by detecting an increase in the isotopic abundance of deuterium.

The experiment commenced with the $Ti{H}_x$ powder at room temperature, while the primary vacuum system was maintained at approximately 90 °C and evacuated for three days with all G1, G2, and G3 valves open. The water contamination level was monitored using mass spectrometry (MS). Once the partial pressure of water reached around $5·{10}^{-7}$ mbar, the vacuum system was returned to ambient temperature, and the experiment began. Valves G1, G2, and G3 were closed, and the power supplied to the heater was gradually increased, causing the temperature of the resistance coil (RC) to rise. Upon reaching a temperature of approximately 200 °C, the hydrogen loaded into the $Ti{H}_x$ sample began to degas.

During the degassing process, valves G1 and G2 were operated to maintain the pressure inside the MS manifold within the operating range of the MS. The pressure reading $P2$ was kept in the range of ${10}^{-7}$–${10}^{-5}$ mbar, and peaks at $m/z=1$, 2, 3, 4, 18, 19, 20, and 21 were continuously monitored.

The parameters of the experiment were recorded every 4 s and stored for later analysis. The temperature of the sample was gradually increased, as displayed in Figure 6, up to a maximum of approximately 1100 °C. At this point, the reactor core (RC in Figure 3) underwent a meltdown, contaminating the analyzed gas with air from chamber C1, which concluded the experiment.

The choice of a wide temperature range (20–1000 °C) was made to ensure that the entire degassing process of ${\mathrm{TiH}}_2$ was covered. Titanium hydride undergoes significant degassing over a broad temperature range, with hydrogen release beginning around 400 °C and continuing through 700 °C, as described in the literature. This range was also chosen to perform calorimetry over the full temperature spectrum to ensure that any potential anomalous heat generation could be detected. As shown in Figure 6, no measurable excess heat was observed throughout the experimental range. The experiment aimed to investigate any calorimetric anomalies during the degasification process, and the wide temperature interval was necessary to capture all relevant phase transitions and potential thermal effects.

The experiment was conducted seven times using both the gas outgassed from the cell and a reference $H_2$ tank, with careful attention to maintaining consistent experimental conditions throughout all trials. The results consistently reflected those obtained from both the active cell and the reference, highlighting the differences between the outcomes with the active powder and the reference gas, which will be detailed in the following section.

4. Results

The experimental results using mass spectrometry suggest the production of deuterium in Ti powders with a high loading ($x\simeq 2$) of natural hydrogen. The gas released from the powders is injected into the RGA to analyze the relative abundance of gas species present in the chamber during the thermal cycles. The detection of deuterium excess is obtained with a number of independent methods, all relying on low-resolution mass spectrometry analyses. The methods are as follows:

• Monitoring of the peak intensity at $m/z$ = 3 compared to the peak intensity at $m/z$ = 2;
• Monitoring of the peak intensity at $m/z$ = 4 compared to the peak intensity at $m/z$ = 2;
• Monitoring of the peak intensity at $m/z$ = 19 and $m/z$ = 21 compared to the peak intensity at $m/z$ = 18.

These methods will be described in detail in the following.

4.1. Signal Intensity of $HD$

Figure 7 illustrates the typical mass spectra obtained before and after melting of the reactor at approximately 1100 °C. Figure 8 depicts the intensity ratio between $m/z$ = 3 ($HD$) and $m/z$ = 2 ($H_2$) species for the gas produced in the reaction and for the gas from an $H_2$ bottle used as a reference. The labels “exp1” and “exp2” correspond to experiments conducted with the active cell, while the “ref1” and “ref2” labels are relevant to the tests using the gas from the $H_2$ reference tank. All measurements are conducted under identical conditions. A noticeable discrepancy of ${\eta }_3$ is evident when the powder is present, compared to the value measured using an $H_2$ tank. However, anomalous behavior for the case of atomic hydrogen (${\eta }_1$) is not observed in this context. A significant increase in the relative abundance of the ${\eta }_3$ = ($m/z$ = 3)/($m/z$ = 2) signal is observed compared to the same quantity ${\eta }_3^{ref}$ measured in the reference gas in identical conditions. Figure 8 shows that the measurements have been performed several times, always giving consistent results.

Figure 9 illustrates the variation in the peak ratios ${\eta }_3$ and ${\eta }_4$ for the species at $m/z$ = 3 and $m/z$ = 4 measured during the experiment, along with the corresponding values ${\eta }_3^{ref}$ and ${\eta }_4^{ref}$ obtained for the reference $H_2$ bottle. The evident excess signal observed during the experiment compared to the reference signal is noteworthy. Furthermore, it is notable that the variations in ${\eta }_3$ and ${\eta }_4$ with pressure align with the anticipated behavior. Specifically, the partial pressure variation for HD is expected to demonstrate a linear relationship with the pressure of $H_2$, while the partial pressure of $D_2$ is expected to vary quadratically. Consequently, ${\eta }_3$ is anticipated to remain constant with changes in the pressure of $H_2$, while ${\eta }_4$ is expected to be directly proportional to the pressure of $H_2$. The observation confirms such an outcome within the experimental error.

4.2. The $H_3^{+}$ Problem

In Refs. [29,30], the investigation reveals that the measurement of $HD$ abundance in mass spectroscopy requires correction due to the formation of $H_3^{+}$ in the ionized plasma within the mass spectrometer. This formation is a result of the following reaction:

$$H_2^{+}+H_2⟶H_3^{+}+H^{*}.$$

(4)

Given that $H_3^{+}$ is not distinguishable from $H{D}^{+}$ by typical isotope ratio mass spectrometers, a correction becomes necessary. The concentration of $H_2^{+}$ is directly proportional to the partial pressure of $H_2$; consequently, the generation of $H_3^{+}$ is proportional to the square of the partial pressure of $H_2$. To correct the height of the $m/z$ = 3 peak, the following formula is applied:

$$P_{HD}=P_3-K{P}_2^2$$

(5)

Here, $P_{HD}$ represents the partial pressure in mbar of the $H{D}^{+}$ ion, while $P_2$ and $P_3$ are the intensities measured in mbar at $m/z$ = 2 and $m/z$ = 3, respectively. The correction constant K has been determined to be approximately 5000–30,000 ${\mathrm{mbar}}^{-1}$ (see Ref. [30]), assuming a sensitivity of 1 mA/mbar.

Equation (5) indicates that, when $P_2\sim 8·{10}^{-6}$ mbar, the correction due to $H_3$ is in the order of $P_{H_3}\sim 3·{10}^{-7}$–$2·{10}^{-6}$ mbar. This value can potentially overshadow the contribution of the $HD$ signal. In the absence of a high-resolution mass spectrometer, an alternative method for detecting $HD$ concentration involves monitoring the intensity ratio ${\eta }_3=P_3/P_2$ as a function of the $H_2$ pressure, proportional to $P_2$. Using Equation (5), we can express ${\eta }_3$ as follows:

$${\eta }_3={\displaystyle \frac{P_{HD}}{P_2}}+K{P}_2$$

(6)

This allows the extraction of the interesting quantity ${\eta }_3^0={lim}_{P_2\to 0}{\displaystyle \frac{P_3}{P_2}}$, which represents the real estimate of the abundance ratio of deuterium, by linearly fitting the values of ${\eta }_3$ measured at various $H_2$ pressures.

Continuing along the same line of thought, we can theoretically formulate the relationship between the pressure of $H_2$ and the peak ratio ${\eta }_4=P_4/P_2$, which represents the ratio of intensities at $m/z$ = 4 and $m/z$ = 2. Given the minimal signal contribution from ${}^{4}He$, we attribute the observed value to the presence of $D_2$. The concentration of $D_2$ is expected to vary in direct proportion to the square of the pressure of $H_2$ (refer to

Table 1. Most relevant reactions involving hydrogen, deuterium, and oxygen.

Reactants		Products	Reaction Rate
$H_1+H_1$	⟷	$H_2$	$\left[H_2\right]=k_1{\left[H_1\right]}^2$
$D_1+D_1$	⟷	$D_2$	$\left[D_2\right]=k_1{\left[D_1\right]}^2$
$H_2+H_1$	⟷	$H_3$	$\left[H_3\right]=k_2\left[H_2\right]\left[H_1\right]$
$H_2+H_2$	⟷	$H_3+H_1$	$\left[H_3\right]\left[H_1\right]=k_3{\left[H_2\right]}^2$
$HD+DH$	⟷	$D_2+H_2$	$\left[H_2\right]\left[D_2\right]=k_4{\left[HD\right]}^2$
$HDO$	⟷	$D+OH$	$\left[D_1\right]\left[OH\right]=k_5\left[HDO\right]$
$HDO$	⟷	$HD+O$	$\left[HD\right]\left[O\right]=k_6\left[HDO\right]$
$H_{2}O$	⟷	$H+OH$	$\left[H_1\right]\left[OH\right]=k_7\left[H_{2}O\right]$

) being $\left[D_2\right]\propto {\left[D_1\right]}^2\propto {\left[H_2\right]}^2$, in the absence of any linear contribution. Consequently, if ${\eta }_4$ is contingent upon the concentration of $D_2$, an anticipated linear variation with $P_2$ emerges.

Figure 8 shows the variation in ${\eta }_3$ and ${\eta }_4$ together with the ratios with the $m/z$ = 1 peak for the experiment and reference case.

Figure 9 shows the variation in ${\eta }_3$ and ${\eta }_4$ with varying $H_2$ pressures. Both quantities are shown in the case of gas released during the experiment and of gas originated from a $H_2$ tank, taken as the reference for the natural abundance and measured in completely identical conditions. The variation in ${\eta }_3$ is linear within the experimental errors and displays an intercept different from zero, as expected from theory. The variation in ${\eta }_4$ is also linear within the experimental errors and displays an intercept compatible with zero, as expected from theory. The results of the linear fits are shown in

Table 2. Linear fit of the data shown in Figure 9 with 95% confidence intervals.

Experiment	${\mathit{\eta }}_3^0$ with Interval	${\mathit{\eta }}_4^0$ with Interval	Adjusted	Adjusted
	at 95% Confidence Level	at 95% Confidence Level	R-Square 3	R-Square 4
Experiment 1	0.045 (0.037, 0.053)	1.04 $·{10}^{-5}$ (−2.6 $·{10}^{-5}$, 4.7 $·{10}^{-5}$)	0.95	0.98
Reference 1	0.008 (0.006, 0.011)	−4.75 $·{10}^{-6}$ (−2.1 $·{10}^{-5}$, 1.2 $·{10}^{-5}$)	0.49	0.84

. The value of ${\eta }_3^0$ represents the expected relative abundance of deuterium compared to normal hydrogen, 280 times larger than the natural value 160 ppm.

The comparison with the reference gas shows an excess in the concentration of $HD$ and $D_2$ well above the experimental errors, thus confirming the hypothesis of deuterium production during the experiment.

4.3. Observation of Deuterated Water

Another independent indication of the presence of an excess of deuterium compared to the natural abundance can be detected by measuring the relative intensity of the peaks associated with the water molecule.

The possible isotopic combinations for the water molecule are listed in

Table 3. Natural abundance of mass peaks of the water molecule (derived from [31,32,33]).

$\mathit{m}/\mathit{z}$	Relative Intensity	Isotopic Combinations
18.0106	100	$H_2{}^{16}O$
19.0148	0.0401	$H_2{}^{17}O$
19.0169	0.032	$HD{}^{16}O$
20.0148	0.2001	$H_2{}^{18}O$
20.0211	$1.284·{10}^{-5}$	$HD{}^{17}O$
20.0231	$2.56·{10}^{-6}$	$D_2{}^{16}O$
21.0211	$6.42·{10}^{-5}$	$HD{}^{18}O$
21.0273	$1.03·{10}^{-9}$	$D_2{}^{17}O$
22.0274	$5.13·{10}^{-9}$	$D_2{}^{18}O$

, together with their natural relative intensities.

In

Table 4. Observed peak intensities in the range 18–22 $m/z$ during the experiment and after reactor meltdown with air contamination, along with the possible attribution to chemical species (see Figure 7).

$\mathit{m}/\mathit{z}$	Partial Pressure (mbar)	Partial Pressure (mbar)	Identification
	During the Experiment	After Meltdown
18	$5.5·{10}^{-7}$	$5.1·{10}^{-7}$	$H_2{}^{16}O$
19	$3.5·{10}^{-8}$	$1.1·{10}^{-9}$	$HD{}^{16}O$, $H_2{}^{17}O$
20	$3.1·{10}^{-9}$	$2.4·{10}^{-8}$	$H_2{}^{18}O$, $HD{}^{17}O$, $D_2{}^{16}O$, ${}^{20}Ne$, ${}^{40}Ar^{++}$
21	$1.3·{10}^{-10}$	0	$HD{}^{18}O$, $D_2{}^{17}O$, ${}^{21}Ne$
22	$1.1·{10}^{-10}$	$3.8·{10}^{-10}$	$D_2{}^{18}O$, ${}^{22}Ne$, $C{O}_2^{++}$
40	$1.6·{10}^{-8}$	$1.9·{10}^{-7}$	${}^{40}Ar$

are shown the measured intensities during the experiment and after the meltdown of the reactor with air contamination. The peak of ${}^{40}Ar$ increases after meltdown due to the air contamination, allowing for a determination of the intensity ratio $r_{Ar}$ between ${}^{40}Ar^{++}$ and ${}^{40}Ar^{+}$. We find $r_{Ar}=0.1268$ that can be used to subtract the unknown contribution of ${}^{40}Ar^{++}$ from the intensity of the peak at $m/z$ = 20 measured during the experiment. The procedure is facilitated by the notable increase in the ${}^{40}Ar^{+}$ signal post-meltdown, leading to a substantial predominance of ${}^{40}Ar^{++}$ over the $H_2{}^{18}O$ signal.

After the correction, we compute the ratios of the measured intensities with the corresponding natural values as shown in

Table 5. Ratio of the measured intensities with the natural intensities. An isotopic excess for deuterium is detected. The increased signal observed at $m/z=20$ after the meltdown is attributed to ${}^{40}Ne^{++}$ and ${}^{20}Ne$, which were practically absent during the experiment but significantly increased after air contamination due to their presence in the atmosphere.

$\mathit{m}/\mathit{z}$	Before Meltdown	After Meltdown	Species
18	1.00	1.00	$H_2{}^{16}O$
19	87.7	2.98	$HD{}^{16}O$
20	0.998	23.5	$H_2{}^{18}O$
21	233	0	$HD{}^{18}O$

that shows a very large increase in deuterium abundance compared to the natural abundance. The ratios at $m/z$ = 19 and $m/z$ = 21 are both notably higher than 1, contrasting with the corresponding values measured after the reactor meltdown. This discrepancy suggests an excess of deuterium during the reaction compared to the natural abundance. Despite the anticipation that their values should be equal, the observed difference remains unexplained. It is likely that unidentified contributions are introducing additional signals, adding complexity to the interpretation of the sought-after signal.

Figure 10 presents the temporal evolution of ${\eta }_{19}=P(m/z=19)/P(m/z=18)$ throughout the experiment, shown by the red line, spanning from the start of the heating ramp until the cell melts at temperatures between 1100 and 1200 °C, coinciding with air contamination. A marked increase in ${\eta }_{19}$ appears as the degassing of the $Ti{H}_x$ powder begins. To sustain optimal RGA functionality, the pressure is regulated by adjusting the needle valve, ensuring that the $H_2$ partial pressure remains within an acceptable range. Also included in Figure 10 is ${\eta }_{19}^{ref}$, representing the analogous ratio measured from gas released by the reference $H_2$ bottle, which shows no significant fluctuations in this case.

The ${\eta }_{19}$ value rises rapidly with increasing cell temperature, then returns to its initial level after the cell meltdown. This behavior suggests an increase in deuterium nucleus concentration within the gases released by the $Ti{H}_x$ sample. These gases react with $O{H}^{-}$ radicals to produce $HDO$, with a mass peak at $m/z$ = 19. No notable variation in the ratio is observed when reference $H_2$ is introduced from the $H_2$ tank (blue line). The likelihood that the peak at $m=19$ amu arises from $H_{3}O$ is considered highly improbable [33], making an actual increase in D concentration the most probable cause of this rise.

To summarize this section, we have shown in three independent ways a significant increase in deuterium concentration well above the natural background after the intense degassing of $Ti{H}_x$ powders subjected to rapid thermal excitations.

5. Discussion

This study marks a significant advancement in developing a unified scientific framework to comprehend nuclear phenomena in deuterated or hydrated metals, integrating both experimental and theoretical perspectives.

The theoretical process under investigation in this work does not exhaustively account for all mechanisms that could lead to nuclear processes at low energy. Rather, it represents one potential pathway for initiating nuclear transmutations. Notably, an alternative process that could induce nuclear reactions at low temperatures is the fusion of deuterium nuclei within palladium, as outlined in [34]. Further theoretical contributions have been made by Hagelstein et al. [35]; yet, a unifying aspect across these diverse mechanisms is the quantum coherence that underpins such processes [36].

A critical aspect of these processes, particularly in scenarios involving a limited number of participating particles, is the challenge of dissipating the substantial energy released (in the order of several MeV) as thermal heat. In contrast, only processes involving a large ensemble of particles can effectively mitigate the emission of highly energetic particles, a stark difference from traditional nuclear reactions observed in conventional nuclear reactors. Energetic radiation in low-energy nuclear reactions becomes detectable only under specific non-equilibrium conditions, as evidenced by the work of G. Carpinteri and colleagues [25], who observed reproducible bursts of neutrons during controlled rock fracturing experiments.

This study integrates theoretical insights with experimental findings, offering a comprehensive analysis of deuterium production from titanium hydride powders subjected to thermal cycling. The theoretical framework suggests the possibility of neutron generation via electron capture within metal samples heavily loaded with hydrogen, a process enabled by the coherence properties of the quantum plasma formed by dissolved protons in the metal.

The central premise of this study, alongside the work referenced in [18], posits that a deeper understanding of low-energy nuclear reactions (LENRs) hinges on the stimulation of coherent configurations. These configurations facilitate either weak or strong interactions that would be otherwise unattainable in few-body dynamics due to the insufficient energy available. In the specific case examined, the existence of ultra-low momentum (ULM) neutrons triggers neutron capture processes, leading to the production of deuterium, tritium, and various titanium isotopes.

The experimental results reveal an anomaly in deuterium–hydrogen ($HD$) ratios, emphasizing the potential production of deuterium in Ti powders. Mass spectrometry analyses show an increase in deuterium abundance, with three independent methods confirming the deuterium excess. The isotopic anomaly is further supported by the observation of deuterated water and the analysis of water molecule peaks.

One critique that could be raised against the obtained result is that the measured excess concentration of deuterium is not due to the actual production of deuterium nuclei in the metal matrix, but rather to the isotopic effect in titanium desorption rates, which favors the concentration of deuterium in the outgassed gas that reaches the mass spectrometer. However, this criticism is refuted by previous experimental observations, which demonstrate that titanium shows no diffusion and degassing differences among the various isotopes of hydrogen, deuterium, and tritium [37], or, in some cases, the diffusion is slower for deuterium than for hydrogen [38].

The question may arise whether the obtained results can be influenced by the chemical activity of hydrogen with the reactor core at high temperatures. However, no matter how complex the reactions involving hydrogen may be, the variation in peak heights will be the same for hydrogen and deuterium. Consequently, the ratio of the peak heights corresponding to hydrogen and deuterium cannot depend on such chemical reactions. Therefore, a change in temperature cannot alter this ratio. Any observed variation in this ratio should thus be attributed to actual changes in the concentration of deuterium relative to that of hydrogen.

It is also crucial to note that the entire vacuum system, RGA, reactor, or any other part of the experimental equipment has never been directly exposed to a source of deuterium that could explain the obtained findings as a result of mere deuterium contamination.

6. Conclusions

This work demonstrates, for the first time to our knowledge, the production of deuterium through the thermal excitation of titanium powders loaded with hydrogen. This experimental result was motivated by theoretical studies predicting the generation of neutrons within the metal under appropriate stimulation. The presence of neutrons implies deuterium production, creating a coherent link between the experimental results and theoretical predictions that mutually reinforce each other. The main conclusions of our study are as follows:

• Experimental Evidence: Mass spectrometry analyses revealed an unexpected increase in the deuterium-to-hydrogen ratio in the degassing gases from the titanium hydride samples, with the deuterium concentration rising up to 280 times its natural abundance. These results were confirmed through three independent measurement methods.
• Novelty of the Work: The primary innovation of this research lies in confirming the coherence-driven electron capture mechanism that leads to neutron production and subsequent deuterium synthesis in metal hydrides. This previously unobserved neutron generation opens new avenues in understanding low-energy nuclear reactions (LENRs) within solid-state physics.
• Theoretical Consistency: The observed experimental results are in agreement with a theoretical framework based on electroweak interaction theories, specifically employing gauge symmetry to predict ultra-low momentum neutron generation through coherent vibrational excitations.
• Technological and Scientific Implications: This work presents a pathway for applications in isotope production, nuclear waste remediation, or advanced energy devices utilizing solid-state nuclear reactions. The potential for neutron generation via this method could significantly impact energy and material sciences.
• Future Directions: Further research is planned to expand our understanding of the conditions enabling these coherent states that facilitate nuclear transformations. Proposed experiments will investigate similar processes in alternative metal matrices and explore practical applications with a focus on sustainable energy and environmental solutions.

In line with these findings, further experiments are proposed to validate the applicability of the theory described in [18] to other nuclei beyond deuterium. To test this hypothesis and assess the method’s potential for practical applications, such as isotope production and nuclear waste remediation, the reactions listed in

Table 6. Possible reactions involving neutrons whose final products are noble gases.

${}^{7}Li+n\to {}^{8}Li,\left({\beta }^{-}\right)\to {}^{8}Be,\left(\alpha \right)\to 2{,}^{4}He$

${}^{19}F+n\to {}^{20}F\left({\beta }^{-}\right)\to {}^{20}Ne$

${}^{37}Cl(24\%)+n\to {}^{38}Cl\left({\beta }^{-}\right)\to {}^{38}Ar$

${}^{79}Br(50\%)+n\to {}^{80}Br\left({\beta }^{-}\right)\to {}^{80}Kr$

${}^{81}Br(50\%)+n\to {}^{82}Br\left({\beta }^{-}\right)\to {}^{82}Kr$

${}^{127}I+n\to {}^{128}I\left({\beta }^{-}\right)\to {}^{128}Xe$

${}^{129}I\left({\beta }^{-}\right)+n\to {}^{130}I\left({\beta }^{-}\right)\stackrel{12.6\mathrm{h}}{\to }{}^{130}Xe$ (demonstrates radioactivity reduction)

have been selected. These reactions aim to produce noble gases, which are ideal for detection due to their chemical inertness and minimal interaction with the system materials, thus ensuring reliable analysis. The specific noble gas of interest depends on the isotopes which are supposed to be present in the initial samples. Notably, transmuting the long-lived isotope ${}^{129}I$ into stable ${}^{130}Xe$ could demonstrate the ability to inertize radioactive substances, further underlining the method’s practical relevance for waste management.

In conclusion, this study integrates theoretical insight with experimental validation, marking a significant step forward in the scientific understanding of nuclear processes in metal hydrides. By bridging theory with experimental findings, it establishes a foundation for future work in LENR and solid-state nuclear technology, with applications in isotope production, environmental sustainability, and nuclear waste management.