Environmental Fluxes of Thermal Neutrons and Geophysics

Environmental fluxes of thermal neutrons originate from two sources: cosmic rays and natural radioactivity. Owing to a long lifetime of free neutrons, they are able to propagate over rather long distances in surrounding media prior to undergoing absorption, provided that these media do not contain elements that have large cross sections for neutron capture. The real lifetime of free neutrons and distances that they travel are determined by the properties of the medium with which they are in a dynamical equilibrium. At rather large depths under the ground, natural radioactivity associated with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha,n)$$\end{document} reactions on light nuclei of the Earth’s crust is the main source of neutrons. Radioactive gaseous radon, especially its long-lived isotope \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{222}\textrm{Rn}$$\end{document}, which is able to migrate over significant distances (several tens of meters in soil and several kilometers in the Earth’s atmosphere) plays a great role in this process. This means that the changes in the medium that are caused by various geophysical processes or by Moon–Solar–Earth phenomena should also be reflected in the neutron flux escaping from the Earth’s crust. The present article gives a brief survey of studies devoted to this subject and a discussion on them.


INTRODUCTION
Investigations into environmental neutron fluxes have a long history, which began in 1935 soon after the discovery of the neutron. For example, the first estimations of the neutron flux in the Earth's atmosphere were performed in [1]. It was shown that neutrons produced there by cosmic rays did not go far away from the production locus, undergoing a gradual moderation and thereupon capture by medium nuclei, after losing energy via inelastic and then elastic scattering.
In the early 1950s, an experimental investigation of neutron fluxes led to the creation of a neutron monitor (NM), an instrument intended for continuously monitoring low-energy cosmic rays producing secondary neutrons in a lead target surrounded by a moderator [2]. Not only does a thick moderator (paraffin or polyethylene) slow down neutrons, but it also screens boron gas proportional neutron counters positioned within the neutron monitor, shielding them from external thermal neutrons. The task addressed by NM designers was to create an instrument that would measure variations of cosmic rays and which would depend on meteorological and other environmental conditions to the minimum possible degree. Before long, this resulted in developing a global neutron monitor network, which is still operative. 1) Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia. * E-mail: stenkin@sci.lebedev.ru However, it is reasonable to formulate an inverse problem and to make an attempt at solving itnamely, the problem of studying the properties of a medium on the basis of recording the environmental flux of thermal neutrons in it. In fact, such problems have long since been solved in applied technical problems, where neutrons are employed as a tool rather than an object of investigations-for example, in neutron diffractometry or in neutron geophysical logging. We have only proposed extending the range of such investigations by employing neutrons as a tool for studying various geophysical and geodynamic processes. Below, we will give some examples of such investigations.

PRODUCTION AND DIFFUSION OF RADON AND NEUTRONS IN NATURE
Cosmic rays interacting with nuclei of air and the upper layer of soil (as well as with materials of the buildings housing the detector used) are the main source of neutrons in the Earth's atmosphere and at the surface of the Earth. Experimental data show that, at the surface of the Earth, about 90% of neutrons originate from cosmic rays. This estimate relies on measurement of the barometric coefficient, which is slightly less than its counterpart known for cosmic-ray hadrons. At depths that are larger than some 10 m under the ground and which cosmic-ray hadrons cannot reach, neutrons originate primarily from natural radioactivity , mostly that of uranium and thorium radioactive series. In this case, a dominant contribution to neutron production comes from (α, n) reactions on light nuclei of the Earth's crust, like Be, F, B, Na, Al, and Si. Obviously, there are no these nuclei in the Earth's atmosphere, so that this neutron source is absent there; on the contrary, they are the main source in the Earth's crust (the contribution of spontaneous fission of heavy nuclides to neutron production is negligible against them).
Neutrons produced in these reactions have energies in the MeV range, and their subsequent fate depends on the properties of the medium (soil): its humidity and the presence in it of rather rare elements absorbing neutrons such as Li, B, and Cd. Having been moderated, the neutrons are captured by nuclei of the medium. A typical neutron lifetime in a standard soil, which consists predominantly of SiO 2 , is about 1 ms. Over this time, they can traverse several meters of soil. The presence of soil waters may reduce this time, since the neutron lifetime in water is about 0.2 ms. Thus, we can see that, as was indicated in [1], neutrons do not go far away from their production locus, irrespective of the medium where they propagate.
The situation is totally different for inert gaseous radon 222 Rn, which has a substantially longer lifetime of more than five days. Its production proceeds over the whole soil volume, whence it can diffuse to rather long distances, forming mixtures with other underground gases, such as methane, carbon dioxide, and air. The coefficient of this diffusion depends substantially on the properties of soil-specifically, its temperature, the difference of the gas pressures between neighboring soil layers and the difference of the pressure in the soil layer nearest to the surface and the atmospheric pressure, fracturing, porosity, soil waters saturated with radon, etc. This is the circumstance owing to which the radon concentration at a given point depends on the properties of the medium and its changes. This in turn permits studying properties of media by measuring the environmental flux of thermal neutrons (geoneutrons), which is in dynamical equilibrium with the concentration of radon in matter surrounding the detector and having a thickness of several meters. Geophysical processes that change the properties of the medium include earthquakes, nearby volcanic eruptions, tidal waves in the Earth's crust, and Earth's free oscillations. It is noteworthy that this method has an undisputable advantage over the traditional method of a direct measurement of radon concentration in surrounding air. The point is that radon meter readings are highly unstable, since they are sensitive to any motion of air-that is, ventilation and air currents-as well as to the humidity of air. In the case of underground neutron detection, there is no such problems, since the neutrons are collected from soil layers of thickness about several meters around the detector used. As was indicated above neutrons are not produced in air.
But if a detector is positioned at the Earth's surface, it can be used there to study other geophysical phenomena-for example, hypothetical neutron production in lightning discharges, seasonal and Moon tidal waves, phenomena of Solar-Earth correlations of the Forbusch effect type, and GLE.

History of Investigations
Experimental investigations of geoneutrons began in the period spanning the late 1940s and the early 1950s, when, first, neutrons were found in extensive air showers (EAS) [3] and, then, in developing neutron monitors [2], numerous measurements of neutron fluxes were performed under various geological and geographical conditions. It turned out that precipitations and weather conditions affect substantially detector readings. In view of this, the designers of neutron monitors had to screen them from an external flux of thermal neutrons with a thick paraffin (polyethylene) layer. Thereupon, investigations of the environmental flux of neutrons by means of unshielded scintillation detectors were launched [4]. Also, a group headed by B.M. Kuzhevskii from Institute of Nuclear Physics at Moscow State University sporadically undertook attempts at searches for correlations between this flux and various geophysical phenomena [5] by means of gaseous helium counters. However, these counters did not possess required stability-the "neutron" counting rate exhibited jumplike changes within two orders of magnitude. This resulted in finding "correlations" of these outliers with many natural phenomena, such as remote earthquakes and Moon eclipses. Nevertheless, those studies gave impetus to performing similar investigations at a different experimental level.

Creation of En-Detectors
Within the PRISMA project [6], we developed a large scintillation detector for recording neutrons in EAS [7]. Owing to a high sensitivity and a high stability, this detector, called later an electron neutron detector (en-detector), turned out to be a convenient tool not only for measuring neutrons in EAS but also for continuously monitoring any environmental flux of thermal neutrons. It is based on a thin layer (50 mg/cm thick) of luminescent compound (alloy) formed by inorganic scintillator ZnS(Ag) and a boron-containing substance where boron was not subjected to enrichment. This scintillator is placed within a plastic tank of volume 200 l for water and is viewed by means of one photomultiplier tube whose photocathode has a diameter of 10 cm. A lightreflecting cone from an elastic plastic material characterized by a good light reflection is installed in order to enhance light collection. The scintillator area is 0.36 m 2 , and the detection efficiency for thermal neutrons is about 20%. It is of paramount importance that the scintillator in question has several luminescence time constants and that the respective intensities are particle-velocity-dependent, which made it possible to separate signals by the pulse shape. Via an analysis of the digitized-pulse shape, not only did we reliably get rid of noises and electromagnetic noise, but it was also possible to separate signals from neutron capture and signals from fast charged particles. A thin scintillator of the detector is yet another important property of this detector. As a result, fast charged particles generate in it a very weak signal lying in the keV region, which is below the detection threshold of approximately three particles (mip). This circumstance determines a very low detector background of about 1/s, since the detector is insensitive to an ordinary radioactive background and to single cosmic-ray muons. In addition to signals from neutron capture, it counts only group propagation of three or more charged particles such as those in EAS (this is used in the case of a detector in the composition of EAS arrays); muons or penetrating cosmic-ray protons together with particles accompanying them; and beta decays of radioactive nuclides near the detector, in which case the emitted electron is accompanied by series of gammas. The last circumstance opens yet another region of application for such detectors-specifically, the monitoring of the concentration of radioactive isotopes (predominantly, 214 Bi and 214 Pb) originating from radon decay [8].

Results Obtained by means of En-Detectors
In order to study variations of environmental fluxes of thermal neutrons, a global network of facilities operating under various geographical and geological conditions was created on the basis of en-detectors. They include those in Moscow (at Institute for Nuclear Research, Russian Academy of Sciences; National Research Nuclear University MEPhI; and Institute of Nuclear Physics, Moscow State University), in the North Caucasus (at Baksan Neutrino Observatory of Institute for Nuclear Research, Russian Academy of Sciences), in Tibet (first in Yangbajing and then in Lhasa at Tibet University), and in Kamchatka (Institute of Volcanology). Earlier, such facilities also operated in Italy (Gran Sasso, LNGS) and in Obninsk (Geophysical Survey of Russian Academy of Sciences). These facilities made it possible to obtain a number of interesting results. In particular, several previously unknown effects were discovered. A brief list of these results is presented below.
Hypothetical neutron production in lightning discharges during thunder storms was investigated by means of the Neutron facility at MEPhI and by means of ground-based facilities at Moscow State University, and LNGS [9]. In contrast to other similar studies, the detector pulse shapes were digitized and thereupon analyzed, which made it possible to get rid completely of noises and stray that are generated by powerful high-current lightning discharges and which are inevitable in such experiments. As a result, it was shown that, even in the case of a very close stroke of lightning, there is no excess of the neutron flux. Moreover, a moderately small decrease of a few percent in this flux because of copious precipitations was observed. The flux returned to an ordinary level next day.
The seasonal effect observed at all such facilities is also associated with precipitations. It manifested itself most clearly at the PRISMA-YBJ Tibet facility deployed at an altitude 4300 m, where there is no permanent snow blanket and where the winter and summer differ, apart from temperature, in the amount of precipitations: the winter is a dry season, while the summer is a wet season. Since water, which is a hydrogen-containing substance, slows down neutrons well and absorbs them rather strongly, the neutron flux reaches a maximum in winter there but decreases sharply in summer as soon as the season of rains begins [10]. The other component that is measured by en-detectors and which is sensitive to radon concentration in air behaves similarly but more smoothly. The graph of the synodic lunar month is presented in the same article, where it was obtained by the method of superimposition of epochs. In thats graph, one can clearly see the fourth harmonic of amplitude 0.5% and of period about 7.5 days. Lunar tidal waves were also observed at our other facilities. In particular, this concerns the M2 half-day wave of amplitude about 0.1%. Obviously, the detection of such weak variations requires fulfillment of the following two conditions. The detector used should possess a very high stability, and the data acquisition system should inevitably involve a complete digitizing of the pulse shape and its on-line analysis.
As was indicated above, the diffusion of radon in soil depends on its porosity and fracturing. Any shakeup caused by earthquakes is able to change these parameters, thereby changing the dynamics of radon diffusion and, hence, the neutron flux in the soil and near-ground air layer, as well as in underground rooms. During the operation of the PRISMA-YBJ facility (2013-2017) at a distance of about 600 km from Yangbajing, there occurred a catastrophic earthquake of magnitude 7.8 in Nepal on April 25, 2015.  [15]. The pressure readings are shifted ahead by 24 hours with respect to the readings of the gamma counter.
It was followed by a long series of aftershocks. The facility recorded the most powerful two earthquake tremors, but they manifested themselves in an irregular behavior of the diurnal neutron wave but not in the neutron counting rate. The averaged diurnal neutron wave has a maximum at around 17 : 00 of local solar time, while the concentration of heavy nuclides that is measured by en-detectors(at least in Yangbajing) has a maximum in the forenoon (that is, in antiphase with neutrons). In [11,12], where this result was published, a normalized parameter sensitive to the phases of the neutron (n) and radon (charged) diurnal waves was introduced in the form S = n norm + charged norm − 2. In ordinary days, the waves are in antiphase and compensate for each other, but, in the case of coincidence of the phases, a peak arises in the graph. Such peaks of amplitude in excess of six standard deviations (6σ) appeared six times over 3.5 years. Of these, three coincided with earthquakes and one was due to a geomagnetic storm. Only two events were not identified. The highest peaks (which have amplitudes greater than 9σ) were observed during the earthquake in Nepal. Thus, the method under discussion yields a very small number of spurious signals, but this is not so in the case of applying the method of directly measuring the radon concentration in air. Yet, the possibility of predicting earthquakes with the aid of en-detectors has not been proven-additional investigations of this possibility are required.

Barometric Pumping Effect for Neutrons and Gamma-Ray Background
The barometric pumping effect for underground gases has been known to physicists for a long time. It consists in pumping out underground gases into the Earth's atmosphere as the atmospheric pressure decreases. These gases contain radon among other components. Therefore, the effect in question should manifest itself for environmental neutrons as well, since the enhanced diffusion of radon from deeper layers of the soil, where it is always abundant, to the surface should intensify neutron production in the surface layer of the soil. This applies to any underground room, unless it is water-and gas-proof. This effect was indeed observed at the underground laboratory of the MSU EAS array (which is not gasproof) at a depth of 25 mwe, where a moderately small facility formed by one en-detector and one gamma detector on the basis of a CsI crystal is presently employed [13]. The difference of the neutron pumping effect from the respective effect for gases is that, on average, neutrons come from depths of several meters. Therefore, excessive radon going from larger depths should fill this volume. This requires some time, and the smaller the coefficient of radon diffusion in a given soil, the longer this time. In the aforementioned underground room, this time was close to two days. Thus, the barometric effect turns out to be delayed and manifest itself only after a two-day shift ahead with respect to neutron data. After that, the measured delayed barometric coefficient turned out to be very large-greater than 5% per mm Hg. Without this shift, it is close to zero. Note that this effect should be taken into account at underground low-background laboratories if the respective underground room is not equipped with a special gas insulation from the surrounding soil.
The presence of a gamma detector made it possible to discover yet another interesting effect with aid of this facility-a nonlinear pumping effect; its theory for geological parameters of the medium was described in [14]. The essence of this effect is the following: if, at the interface of two media (soil-air, soil-water, water-air, etc.), there occur harmonic oscillations of some macroscopic parameter-for example, temperature, pressure, or concentration of a material in a solution-then, at a rather large depth from the interface, this parameter takes a quasistationary value. If the amplitude of oscillations of this parameter at the interface undergoes a change, the quasistationary value in question will also changequadratically (!) rather than linearly. This quadratic effect was indeed observed but, so far, only for the gamma background [15]-not for neutrons-at an anomalously low atmospheric pressure in Moscow. It is noteworthy that this effect manifests itself only at anomalously low atmospheric pressures and has a threshold character, since, as we know, a parabola changes slowly near its zero value and then begins growing sharply (see Fig. 1). One can see that the experimental points fit in the respective parabola well. The asymmetry of the points is due to occurrence of the effect only at low pressures-that is, upon pumping out underground gases. Specifically, the effect appears only at pressures less than 725 mm Hg, which is an anomalously low value for Moscow. For neutrons, the nonlinear effect has not yet been observed, but, in the opinion of the present author, it is a matter of time-one should only wait for a long period of an anomalously low atmospheric pressure.
It is necessary to take into account this effect, as well as the linear effect, in performing measurements at underground low-background laboratories and to provide a gas insulation of underground laboratories in constructing them.

CONCLUSIONS
Environmental thermal-neutron (geoneutron) fluxes, which are in a dynamical equilibrium with the medium where they propagate, carry information about the medium and its dynamics. Radioactive gaseous radon, which is one of the links in the chains of radioactive uranium and thorium series, is permanently produced in the Earth's crust. In turn, it produces neutrons in (α, n) reactions on nuclei of light elements of the Earth's crust. As an inert gas, it may migrate, together with other underground gases, over rather long distances (tens of meters) in the soil. The rate of this migration, or diffusion, depends on the parameters of the surrounding soil. It follows that, by measuring variations of geoneutrons, we can get an idea of the state and variations of the surface layer of the Earth's crust. Thus, various geophysical processes can be studied by methods of nuclear (neutron) physics.
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