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In this work, it shows that nuclear reactions in lightning channel, which are produced by the deuterium-deuterium (D-D) and deuterium-tritium (D-T) nuclear reactions, represent a plausible mechanism for gamma-ray bursts observed at ground. Gamma-ray emissions from lightning can be explained by neutron inelastic scattering in the air. Neutrons (produced in lightning channel) will delay a definitive time (~33 ms) to cover the atmosphere before hitting a molecule and producing gamma rays, which is somewhat longer than the gamma-ray time delay (~20 ms) observed at ground.

Intense gamma-ray bursts on the ground, and produces in association with the initial-stage of rocket-triggered lightning, which have been recorded by Dwyer et al. [^{6} eV. The discrepancy is the same with the differences between the energy of a chemical explosive and an atomic bomb. Babich et al.^{ }[

On the other hand, experiments on board MIR orbital station (1991), ISS (2002), and Kolibri-2000 satellite (2002) at an altitude of 400 km detected neutron bursts (En ~ 0.1 eV - 1.0 MeV) in the equator regions connected with lightning discharges [^{14}(n, p)C^{14} by lightning [^{12} neutrons of 2.45 MeV energy by deuteron-deuteron fusion D(d, n)He^{3} in dense plasma [^{15} neutrons per lightning flash. Scientists have put forward a couple of potential explanations for the observed flux. One was that the high fields generated during lightning strikes were modifying the trajectories of muons from cosmic ray showers. The second was that the gamma rays emitted during the lightning strike generated neutrons, a photonuclear event. But new measurements show that neither of these explanations can explain the data [^{−3}∙s^{−1}. Unfortunately, lightning strikes only generate a tiny fraction of that.

In this work, it shows that nuclear reactions in lightning channel, which are produced by D-D or D-T reactions, represent a plausible mechanism for gamma-ray bursts observed at ground. We have estimated that gamma-rays appear in about ~ 33 ms after the vaporization of the triggering copper wire, in a good agreement with the time delay of gamma-ray bursts observed at ground, which is 22 ms. Gamma-ray emissions from lightning can be explained by neutron inelastic scattering in the air.

Let us consider thunderclouds exhibiting a dipolar electrical charge structure (

When the positive charge center is discharged by the rocket-triggered lightning, deuterium ions are accelerated downward, producing downward bursts of neutrons below the thunderclouds. In lightning channel, deuterons of water (each hydrogen has a probability of 1 in 6400 of being deuterium; this corresponds to the natural isotopic abundance, 0.015%) are transformed in ions D^{+} and are accelerated, producing neutrons by thermonuclear reactions. Neutrons with 2.5 MeV energy arise from the D(d, n)He^{3} branch of D-D fusion reaction. Since the D(d, p)T branch^{ }occurs with about equal probability at low deuteron energy [

Intense burst of MeV gamma-rays was observed by Dwyer et al. [

In laboratory experiments,^{ }neutron pulses are observed in a brief portion of time (~70 ns) after the discharge current peak [

thermalization period in air occurring subsequent to the fast neutron burst and a thermal equilibrium. According to Samworth [

where is the macroscopic neutron capture cross section. It is the effective cross-sectional area per unit volume of material for capture of neutrons (in cm^{2}/cm^{3} or cm^{−1}), given by [

where σ_{c} is the microscopic neutron capture cross section and n is the particle density (i.e., number of atoms or molecules per volume unity of the absorber). Only hydrogen and nitrogen have significant cross sections for thermal neutron capture (0.33 and 1.75 barns, respectively [

where is the arithmetic mean of neutron capture cross section for hydrogen (from water) and nitrogen. Considering particle density in humid air as being [

where N is the Avogadro number, M is the mean molar mass of air particles, p_{d} is the partial pressure of dry air (Pa), R_{d} is the specific gas constant for dry air, 287.05 J/(kg·K), T is air temperature on the Kelvin scale, R_{v} is the specific gas constant for water vapor, 461.495 J/(kg·K), is the relative humidity, and p_{sat} is the saturation vapor pressure. The saturation vapor pressure of water at any given temperature is the vapor pressure when relative humidity is 100%. A simplification of the regression used to find this, can be formulated as [

Inserting the numerical values in Equation (5), for T = 298 K and air humidity, we found n = 5 × 10^{25} m^{−3}. Thus, we have ~ 33 ms. The attenuation length or mean free path is the medium length of a path covered by a particle between subsequent impacts.^{ }The mean free path of neutron in an absorber (air) is given by [

where s_{T} is the total cross section of neutrons in the absorber. Thus, the time covered by a fast neutron between subsequent impacts is [

where ávñ is the mean speed of neutron. Thus [

where c is the speed of light, E_{k} is the kinetic energy of neutron, and m is its rest mass.

For 190 KeV neutrons (See _{T} ~ 4 barn [_{2} ~ 2 × 10^{−7} s (0.2 ms). Therefore, the time delay of gamma-ray bursts will be ms. Thus, gamma-rays should not be seen on the ground immediately after the rocket-triggered lightning because neutrons (produced in lightning channel) will delay a definitive time (~33 ms) to cover the atmosphere before hitting a molecule and producing gamma rays. This value is in a good agreement with gamma-ray time delay (~20 ms) observed at ground by Dwyer et al. [

where p_{a} is the partial pressure of air (Pa, N/m^{2}), and T is the absolute dry bulb temperature (K). The density of water vapor can be expressed as [

where p_{w} is the partial pressure water vapor (Pa, N/m^{2}), and T is the absolute dry bulb temperature (K). The amount of water vapor in air at ground level can vary between θ_{w} = 0% to about θ_{w} = 5% (for example, in thunderstorm conditions). On the other hand, the 2.31 MeV gamma-ray mass attenuation coefficients of dry air and water are respectively μ_{a} = 0.03 (cm^{2}/g) and μ_{w} = 0.02 (cm^{2}/g) [_{a} = p_{w} = 10^{5} Pa, T = 298 K, x = 650 m (burst of MeV gamma-rays was observed from a distance of 650 m from the lightning channel. See Ref. 1), and θ_{w}_{ }= 5%, we found I/I_{0} ~ 0.1. In the case of terrestrial gamma ray flashes (TGFs), assuming the photons are uniformly distributed over a disk of radius 300 km (given by the typical lightning-subsatellite distance), the 1 photon/cm^{2} fluence implies that of order 10^{15} photons reach satellite altitude. Full comparison of satellite observations to simulations of photon attenuation and scattering in the atmosphere requires a source of photons with 15 - 20 km altitude, and a total source of 10^{16} photons. This corresponds to a photon attenuation of I/I_{0} ~ 0.1. The amount of atmosphere above 6 km is about the same as the amount below that altitude [_{0} ~ 0.1), in a good agreement with our calculations. Thus, we expect a total source of 10^{16} photons and 10^{15} photons reach the ground.

Electrical discharges through polymer fibers have been shown to produce up to 10^{12} neutrons by deuteron-deuteron fusion in dense plasma, consistent with ion densities of about 10^{19} cm^{−3 }[^{18} cm^{−3} [^{ }with peak voltages between 10 and 100 MV across the plasma [

(0.015%) is identical in both water (for example, water droplets of cloud) and polymer molecules [

The “classical” lightning-triggering technique involves the use of a small rocket extending a thin grounded wire upward made of Kevlar-coated copper [^{7} and 10^{8} m/s) can be produced on the tip of the grounded copper wire (

In this case, natural deuterium atoms from Kevlar are transformed in relativistic ions, producing neutrons by nuclear reactions after the wire disintegration.

According to our work, gamma-rays are produced by collisions of fast neutrons with air molecules. In triggered lightning, gamma-rays appear in about 33 ms after the lightning, in a good agreement with gamma-ray time delay observed at ground, which is 20 ms [

tering of the line emission should occur for the spectrum reported.

According to our model, one should expect an excess of He^{3}—the other product of the D-D fusion reaction— near the lower levels of thunderclouds. If detection of this excess would be possible, it would provide further proof of the proposed mechanism. An effort in exploring such suggestion is in progress.

We acknowledge financial support from CNPq and Faperj (Brazil). The authors would like to express great appreciation to Dr. Sebastião Florentino da Silva (PROINFA from Eletrobrás, Rio de Janeiro, Brazil) for his encouragement and advice to this work.