Did nuclear transformations inside Earth form nitrogen, oxygen, and water?

Nitrogen and sea water concentrations have increased continuously from the Archean era. A rapid rise in oxygen concentration has been recorded from around 0.8 billion years ago. These phenomena cannot be completely explained by the collision of planetesimals with abundant nitrogen and the late veneer heavy bombardment of comets and meteorites with abundant water, and photosynthesis of heterotrophic plants, respectively. The formation of nitrogen, oxygen, and water are postulated to be the result of an endothermic nuclear transformation of carbon and oxygen nuclei confined in the carbonate aragonite lattice of Earth’s mantle or crust at high temperatures and pressures. This process was likely influenced by excited electrons generated by stick sliding during the evolution of supercontinents, mantle convection triggered by collisions of major asteroids, and nuclear fusion in Earth’s core. Thus, we show that calcium carbonates may have played a crucial role in the generation of atmosphere and sea water in Earth’s history.


Introduction
One of the most important aspects of Earth's evolution is the formation of the atmosphere followed by continuously altering composition of the gases contained in it. The atmosphere is also affected by the amount and temperature of sea water. The atmospheric composition and amount of water (H 2 O) are of obvious importance given their necessity for life on Earth. However, the processes that alter the atmospheric composition and generate water have not been fully comprehended yet. We study the composition changes of three important atmospheric gases, carbon dioxide (CO 2 ), nitrogen (N 2 ), and oxygen (O 2 ), and the increase of the sea level in Earth's history from 4 billion years (Ga) ago to present time. The composition changes of atmospheric CO 2 [1][2][3], N 2 [4][5][6], and O 2 [7][8][9] through geologic time, and the increase in sea level from around 2.3 Ga to the present, are shown in figures 1(a) and (b). The data were sourced from nine [1][2][3][4][5][6][7][8][9] and four research groups [10][11][12][13], respectively.
A parabolic decrease in CO 2 composition in the Archean era is accompanied by a gradual accumulation of N 2 until 2 Ga [1][2][3]. The majority of CO 2 removal can be explained by inorganic geochemical processes such as dissolution in a hot ocean environment and subsequent formation of carbonates as CO 2 reservoirs in seas by virtue of the weathering of igneous rocks [14]. The N 2 pressure increased parabolically until 2 Ga and converged to approximately 78% (the value seen presently), although the precise process leading to the change in N 2 concentration is not well established yet. Given that these changes cannot be solely contributed to the collision of planetesimals with abundant nitrogen (given the evidence provided by the higher N/Kr ratio [15]), we must look to transformation within the Earth's crust and mantle for a more credible answer.
On the other hand, changes in O 2 compositions can be divided into three time sections [7][8][9]: very low content before 2 Ga, rapid accumulation (popularly known as the 'Great Oxidation Event' (GOE) [9]) in the Precambrian era from 2 to 0.42 Ga, and saturation content from 0.42 Ga to the present time. The formation of the small amount of free O 2 on the sea surface by ultraviolet photochemical reactions [16] in the Archean era can be expressed as According to the present consensus [17], the generation is attributed to photosynthetic activity. After the first oxygenic photosynthesis by anaerobic cyanobacteria from 3.5 Ga onwards, aerobic photosynthesis by plants, algae, and cyanobacteria (eubacteria) produced O 2 and carbohydrates from H 2 O and CO 2 after 2.7 Ga. The photosynthetic reactions can be represented by a single well-recognized formula [18]: Studies on sea level changes have shown varied results. Kuenen [10] and Rubey [19] asserted a gradual accumulation, Conway [11] estimated a linear increase, whereas Twenhofel [12] and Walther [13] showed a parabolic rise from 0.5 Ga ( figure 1(b)). Turekian [20] accepted the hypothesis of an initial 'watering'. However, Craig [21] conducted an isotope analysis of δ 28 O and δD values in natural waters from many parts of the world, and showed evidence of circular water activity below the sea surface, far from Earth's interior. This evidence excludes speculations of sea level variations by Conway [11], Twenhofel [12], and Walther [13]. Even if the level has remained constant after the Archean era, high amounts of water impose restrictions on phased bioactivity. As per the present consensus, sea water originated from the bombardment of a late veneer of asteroids with water. These asteroids were supposedly 'main belt' asteroids orbiting between Mars and Jupiter, and they delivered some amount of water to the primitive dry Earth [22]. However, while it sounds interesting, this mechanism is unlikely to be the dominant source of sea water [23].
As can be seen from figure 1(a), since the formation of O 2 is likely related to the decrease in CO 2 and increase in N 2 levels, we consider two ratios in Earth's history: O 2 /CO 2 and O 2 /N 2 . Figures 2(a) and (b) present the timedependent ratios of O 2 /CO 2 and O 2 /N 2 , calculated using data from the nine research groups [1][2][3][4][5][6][7][8][9]   Ga to the present time. Since no directly observed geophysical data are available to explain the formation of these gases, these questions need to be analysed using circumstantial evidence and our understanding of Earth's atmosphere.

How Earth's atmospheric pressure can affect gas concentrations
According to Newton's law of universal gravitation, every point mass of matter in the Universe attracts every other point mass with a force directly proportional to the product of the two masses and inversely proportional to the square of their separation. The atmospheric gases on Earth's surface play a role here; the gravitational force is directly proportional to the product of the masses of Earth and the atmospheric gases, and inversely proportional to the square of the distance between them [25]. The altitude of the troposphere, which contains roughly 80% of the mass of Earth's atmosphere, extends to 12 km (0.19% of Earth's radius [25]). We consider time-dependent gas pressure for three main gases, CO 2 , N 2 and O 2 , assuming a total pressure of 1 atm, including pressure of Ar. We use the revised data of Kasting [3] and Bertaux [5] to generate the curves for CO 2 and N 2 , respectively, and the data from NESTA [8] are used to create the O 2 curve. The integrated N 2 without escape curve is calculated using the following equation of the integrated N 2 curve between 3.6 and 1.2 Ga.
where t denotes time in billion years. Note that R 2 for the integrated N 2 without escape curve is 0.9953. Since the pressure and composition of the first atmosphere before late heavy bombardment in the Archean era are unclear, we restrict our discussion to the formation period of N 2 and O 2 from 4 Ga to the present time. The calculated result is shown in figure 3(a). When the atmospheric pressure of N 2 and O 2 exceeds 1 atm, they escape to space from the upper atmosphere, aided by Earth's centrifugal force.
To investigate the formation of O 2 by photosynthesis, the differential pressure of CO 2 required for the formation of O 2 is calculated from the integrated O 2 pressure in figure 3(a). The result is presented in figure 3(b). The findings for the other groups appear in figures A1 and A2 in appendix A. According to equation (2), a considerable amount of CO 2 is required for the formation of O 2 in the time period from 0.7 to 0.2 Ga, which also corresponds to the appearance of animals on continents. Judging from the small amount of integrated CO 2 , the rapid generation of O 2 cannot be explained by photosynthetic activity alone. Thus, the consensus on the origin of the abundance of O 2 on Earth appears to be misplaced.
We offer an alternative intuition, namely, the possibility of nuclear transmutation of N 2 , O 2 , and H 2 O inside the Earth.

Dynamic nuclear transmutation between C and O atoms in calcium carbonate in Earth's lower mantle
In previous papers [26,27], the formation of N 2 was interpreted to be the result of an endothermic nuclear transmutation of C and O atom pairs in the calcium carbonate aragonite lattice of Earth's lower mantle from the Archean era to the present time. Since it is expected that the formation of nitrogen is distinctively associated with the formation of the carbonaceous rocks, we considered the dynamic reaction that the carbon and oxygen atoms in carbonate crystals interact to form nitrogen. The processes came about as a result of physical catalytic help of excited electrons (e * ) arising from plate tectonics and geoneutrinos (ν e ):  * ( ) When we reconsider transmutation reactions under high temperature and pressure, the following reaction comes to mind [26].
Deuteron fusions are generally expressed by the following reactions [28]. Thus equation (7) is an important reaction in the context of geoscience.  figure A3).

O 2 generated from processes other than photosynthesis
If the integrated N 2 gas curve in figure 3(a) is reasonable, we can unconditionally calculate the generation amounts m o of O 2 in Earth's history, using amounts of N 2 (m N ) from the integrated N 2 without escape curve over 1 atm, because N 2 is inert. m o =m N ×0.5×32/28 from equation (8), and the result is presented in figure 4(a). The curve shows a logarithmic increase from 3.6 Ga to the present time. The calculated value of 1.06×10 20 kg [24] is 387 times that of O 2 content in the present atmosphere (2.74×10 17 kg). The extra O 2 could react with the large amount of H 2 liberated from Earth's core, according to equation (9), resulting in the formation of additional water.

Possible generation of H 2 O by nuclear transmutation
According to equation (8) Thus, as per Earth's gravity, the total mass of atmospheric gas at 1 atm is 5.169×10 18 kg, including 6.67×10 6 kg (3.72×10 16 m 3, 0.934 vol %) for Ar [24]. The pressure exerted by each gas is calculated using its weight. These results are shown in figure 4(b), along with the curves for m w1 and m w2 . The results clearly show an expected and continuous rise in seawater level from 3.6 Ga to the present time. However, the total weight of water at the present time is around 3. 9×10 20 kg, which constitutes 28.9% of the current amount of sea water, 1.34×10 21 kg [30]. If Earth contains around 10 21 kg of N 2 , the total amount matches with Kuenen's estimation [10], although he used no data for the period before 2.3 Ga. The formation of water from the Proterozoic era contributed to the explosion in growth of cyanobacteria and vegetation.

Geological conditions for generation of N 2 , O 2 , and water
Considering the C-O distance (∼0.079 nm [31]) required for the dynamic nuclear transmutation of calcium carbonates in the lower mantle, higher temperature and pressure are necessary conditions for these reactions [26,27]. Since the relationship between critical temperature T and critical pressure P for the nuclear transmutation is expressed as 7,253×e −0.014P (31) , the formation of N 2 , O 2 , and H 2 O would be possible at temperatures 2,510 K and pressures 58 GPa. The region with this temperature-pressure profile corresponds to a zone known for diamond formation in an upper portion of Earth's lower mantle (see figure 4(S) in appendix B). Carbonaceous rocks are recognized to have been predominantly formed by weathering on land and inorganic reactions in the primitive sea during the Archean era, and by biological reactions in the Coral Sea during the Cambrian era. They are distributed on and near Earth's surface [32], and the large quantities of fresh calcium carbonate rocks are thought to have been delivered to the upper mantle by plate tectonics [33].
Next, we consider another attraction mechanism responsible for accelerating the confinement of C and O nuclei in the calcite lattice. We refer to physical catalysis by a neutral pion, which is recognized as a nonexchangeable component in a strong nuclear field [29] (see appendix B). The excited electrons and neutrinos in equation (3) are thought to have been generated by stick sliding [34,35] due to plate tectonics and the sliding of carbonate crystals, and are trapped in the interior portions of Earth, respectively. Neutrinos are known to be generated in the Universe by the Sun [36] or the flares of t-tauri stars [37] in the Archean era, and they are also generated by the collision of free electrons derived from pressure inonization, namely, the deuteronthermonuclear fusion in Earth's inner core [38][39][40]. Furthermore, the excited electrons may be also generated from existence of heavy holes which have rapid, small amplitude oscillations [41] in the lower temperature crust, rather than higher-temperature mantle. Therefore, we note that there is a very real possibility that nuclear transformation combined with physical catalysis may have occurred in Earth's crust and crust.

Asteroid collision-induced atmospheric evolution and liberation of atmospheric gases to space
The rise in the concentrations of N 2 , O 2 , and H 2 O in figures 2(b), 3(a), and 4, respectively, indicate the possibility that, from 3.5 Ga onwards, the liberation of O 2 into the atmosphere from 1.7 Ga onwards and the rapid increase in its levels in 0.5 Ga were caused by the collisions of asteroids in 3.4 Ga [42], the Vredefort collision in South Africa in 2 Ga [43], and the Sudbury collision in Canada in 1.85 Ga [44], and the Bedout collision in 0.3 Ga [45].  (8), water using equation (9), total water, and water using Kuenen's estimation, from 3 Ga to the present.
The extraterrestrial impacts aided the growth of the continents and intrusion of granitic magmas, and shifted mantle conversion patterns [46][47][48].
Inert N 2 and active O 2 was discharged into the atmosphere by volcanic activities and mantle plumes up to 1.2 and 0.5 Ga. Thereafter, the gases started escaping to space from 1.3 and 0.3 Ga, respectively. Indeed, recent research has reported that large amounts of terrestrial N 2 [49,50], noble gases [50], and O 2 [51] have been transported as far as the Moon by the Earth's wind. This is because atmospheric mass gets constantly dispersed into space, and without a continuous resupply of these gasses from Earth' interior portions, our atmosphere could not keep the pressure needed to support life on Earth. If N 2 , O 2 , and H 2 O were derived from C and O 2 , geologically active planets with abundant C and O 2 atoms could have generated these compounds. This is a very interesting possibility, since C and N 2 are two elements essential for all life forms [52].
In photosynthetic reaction of equation (2), the consumption of one molar carbon dioxide produces equivalent molar oxygen. To investigate formation effect of oxygen by photosynthetic reaction, the differential pressures of CO 2 required for formation of O 2 are calculated from integrated O 2 curves by Kasting [7] and Holland [9], using an equation of reduced pressure P CO2 =P O2 ×1.977/1.429, where 1.977 kg m −3 [53] and 1.429 kg m −3 [54] are density of CO 2 and O 2 gases, respectively. These data are shown in figures A1 and A2, respectively.
Both amounts of CO 2 required for formation of O 2 in time period from 1.9 Ga onwards in Kasting [7] and 0.9 Ga onwards in Holland [9] are larger than those of integrated CO 2 . CO 2 is reversely in excess at 0.2 Ga and present time. Thus the rapid generation of oxygen cannot be explained by photosynthetic activity only. Figure A1. Comparison with an integrated CO 2 curve and a differential pressure one of CO 2 reduced from O 2 one by Kasting [7]. Figure A2. Comparison with an integrated CO 2 curve and a differential pressure one of CO 2 reduced from O 2 one by Holland [9].  In previous papers [17,26], from wondering fact that the main binding energy per nucleon of stable nitrogen nucleus (7.5 MeV) is lower than those (7.7 and 8.0 MeV) of carbon and oxygen ones, respectively [55], the origin of nitrogen is interpreted to be the result of the endothermic nuclear transmutation: 12 16 14 ( ) This reaction is due to two-body confinement of carbon and oxygen nuclei in CaCO 3 carbonate lattice of the mantle, which is mediated by nuclear attraction caused by the catalysis of neutral pions, π ο , and taking into consideration the energy-momentum equilibrium [29]: which is based on an assumption that a parabolic increase in nitrogen content correlated to an abrupt decrease in carbon dioxide during the Archean era [1][2][3]. Pions are responsible for all low-energy nuclear interactions [56]; the pions within the nucleus allow the nucleonic species to bind together and transmute with each other [31].
Kenny [57] has termed equation (A2) as the 'electropionic reaction'. The neutral pion mass balance in equation (A2) is provided by emission of two excited electrons [58], which are derived from the carbonate lattice: where γ is photon. On the other hand, the electron reacts with deuteron to form neutral pion and an electron neutrino [29,59]: Fukuhara [59] has reported the following formula for the formation of helium:

* ( )
This reaction is facilitated by the electropionic attraction that is related to excited electron capture and neutral pion catalysis [29]. Since equation (A7) is a non-equilibrium (irreversible) equation, it does not obey the rules of parity and momentum balance. In the irreversible endothermic reaction proposed by Glansdorff and Prigogine [60], remarkable enhancement is expected on the basis of the thermal factor of exp (−ΔG/kT), where ΔG is the change of Gibbs energy for the whole system. In comparison with T 0 =300 K and T 1 =1,105, 1,439, 1,774, 2,109, 2,443 and 2,778 K, we get k 1 /k 2 in table A1. From the effect of temperature on the reaction rate k (equation (A8)) under the repulsive interaction potential between the atoms, we get the following example of shrunken distance at 80 GPa: @´=´´´= 2r 2 0.682r 2 0.862 0.86128 r 0.1554 nm A10 This radius (0.078 nm) is somewhat smaller than the critical radius (0.079 nm [31]) required for a dynamic nuclear reaction. Thus, the relationship between the critical temperature T and the critical pressure P for the reaction is expressed as = -+ T 33.47 P 4, 451.5 A11 ( ) Since the region with this temperature-pressure profile corresponds to the zone of diamond formation in mantle [67], the relationship in equation (A11) is shown in figure A4, along with the diamond formation lines, the actual temperature-pressure profile (T=10.95 P+1,875) of the Earth [68], and estimated P-T phase boundary line between aragonite and disordered calcite [64]. The critical temperature and pressure, which correspond to the critical radius for the dynamic reaction, are 2,510 K and 58 GPa, respectively, leading to depth of 1,290 km [69]. Therefore, it is possible that the dynamic reaction occurs in an upper portion of the lower mantle. Even if the convection current in the upper mantle is viscous fluid, the nuclear reaction could be promoted. In fact, fusion reaction 6 Li (d, α) 4 He and 2 H(d, p) 3 H with ∼6.83×10 6 K were measured in liquid Li acoustic (ultrasonic) cavitation [70]. The conditions required for the formation of nitrogen, oxygen and water are more stringent than those for diamonds.
Here, we must describe the natural conditions for diamond formation. It is well known that natural diamonds crystallize directly from kimberlite rock melts that are rich in calcite and found at depths of 1,500 km or more inside the Earth. The melts are essentially saturated in carbon dioxide gas at high pressures over 30 GPa and temperatures 763 K in deep in the Earth's mantle, since the 12 C/ 13 C ratio of a diamond shows that it arises from carbon dioxide [71]. Furthermore we note that platesets of poly-cyanogen (C 3 N) are dispersed in kimberlite rocks [72]. The type Ia diamond contains maximally 2%-mil nitro-gen [73]. Thus, the nitrogen impurities in diamonds may be the result of nuclear transmutation of CO 2 in the melt. Furthermore, it is known that nitrogen is distributed extensively throughout the silicate phase of the Earth's crust and mantle [74].