- Email: [email protected]
Numerical simulations of in situ production of terrestrial cosmogenic nuclides
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 259 (2007) 642–645 www.elsevier.com/locate/nimb
Numerical simulations of in situ production of terrestrial cosmogenic nuclides Jozef Masarik b
a,*
, Kyeong J. Kim b, Robert C. Reedy
c
a Department of Nuclear Physics, Komensky University, Sk-842 48 Bratislava, Slovakia NSF-Arizona AMS Laboratory, Department of Physics, University of Arizona, Tucson, AZ 85721, USA c Institute of Meteoritics, University of New Mexico, Albuquerque, NM 87131, USA
Available online 4 March 2007
Abstract A variety of geologic and environmental events and processes can be studied with the cosmogenic nuclides accumulated in terrestrial rocks. Reliable interpretation of the measured in situ-produced cosmogenic nuclides requires a good understanding of the involved nuclear processes and factors influencing them. The production rates of nuclides depend on many parameters. In this paper, calculations are reported and discussed on the influence of the air/ground interface and snow cover on production rates of in situ produced cosmogenic nuclides. 2007 Elsevier B.V. All rights reserved. PACS: 24.10.Lx; 96.40.Vw; 25.40.h Keywords: Cosmic rays; Cosmogenic nuclides; Neutrons; In situ production; Numerical simulations
1. Introduction The interactions of cosmic-ray particles with the Earth’s atmosphere produce a cascade of secondary particles and many cosmogenic nuclides [1]. Many secondaries have enough energy to undergo further collisions and to produce the next generation of secondary particles. Some of the particles produced in this cascade can reach the Earth’s surface and induce nuclear reactions in which a variety of cosmogenic nuclides are produced. The cosmogenic-nuclide concentration in a terrestrial sample depends on the sample’s composition, altitude, geomagnetic latitude and exposure geometry and their changes with the time. The character of the types of nuclear reactions and the energies of particles are determined by the energies of the incoming cosmic-ray particles and the elemental composition of the irradiated object. To make cosmogenic nuclides a common universal analytical tool in geosciences, it must *
Corresponding author. Tel.: +421 7 602 95456; fax: +421 7 654 25882. E-mail address: [email protected] (J. Masarik).
0168-583X/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.03.003
be applicable in broad range of sampling site characteristics. The goal of this paper is to investigate the influence of the air/ground interface and snow cover on production rates of in situ produced cosmogenic nuclides. We present a pure physical model approach to this problem. Similar studies employing some approximations and simplifications were published earlier [2,3]. 2. Model calculations Our numerical simulations of the interaction of primary and secondary cosmic-ray particles with matter are based on the GEANT [4] and MCNP [5] codes. As this code system is described in detail elsewhere [6,7], we repeat here only its main features that are relevant for the present study. In our simulations, only primary protons with energies between 10 MeV and 100 GeV were considered. The primary cosmic-ray particle flux at the Earth’s orbit consists of a galactic and a solar component. In this paper, we present only the results of cosmogenic-nuclide production
J. Masarik et al. / Nucl. Instr. and Meth. in Phys. Res. B 259 (2007) 642–645
simulation by the galactic cosmic rays. As solar cosmic-ray particles have low energies, they induce interactions only in the uppermost few g cm2 of the Earth’s atmosphere and only at high latitudes, where the geomagnetic field does not prevent them from entering the atmosphere. Therefore they contribute only to the total average cosmogenic nuclide production in the atmosphere [6,7]. The galactic cosmic-ray particles are a mixture of protons (87%), alpha particles (12%) and heavier nuclei (1%). The flux of cosmic rays varies with time, thus to calculate production rate as a function of time, the cosmic ray flux must be obtained as a function of time and energy. The GCR particle flux is modulated due to the interactions of incoming particles with the magnetic field convected outward by the solar–wind plasma. In recent years, the most frequently used models for primary GCR spectra were those of Castagnoli and Lal [8] and Webber and Higbie [9]. The spectral distributions of heavier particles present in primary cosmic rays are similar to the distribution of protons if energy per nucleon is considered. In these calculations, the model Earth was irradiated by a homogenous and isotropic flux of protons using the spectral shape of Castagnoli and Lal [8] and a modulation parameter of 550 MeV. The contributions from alpha (and heavier) particles were simply included in the final results by multiplying the proton calculations by a scaling factor, which was found to be 1.4 [6]. The characteristic feature of the GCR particle interactions is the production of the cascade of secondary particles. For these calculations, the Earth’s atmosphere was modeled as a spherical shell with an inner radius of 6378 km and a thickness of 100 km. The following elemental composition (in weight%) was used: 75.5% N, 23.2% O and 1.3% Ar. The total thickness of the atmosphere was 1033 g cm2. The elemental composition of the surface was assumed to be an average terrestrial one (in weight percent, 0.2% H, 47.3% O, 2.5% Na, 4.0% Mg, 6.0% Al, 29.0% Si, 5.0% Ca and 6.0% Fe). Except for very high contents of H, changes in this surface composition, or the addition of other elements such as K, Mn, Cr, have very little effect on the calculated fluxes. The surface density of the Earth was 2.0 g cm3. To investigate the depth dependence of particle fluxes, the sphere near the surface was divided into spherical shells. The fluxes of protons and neutrons within each cell were calculated. The production rate of a cosmogenic nuclide j at a depth D in the Earth is X XZ 1 P j ðDÞ ¼ Ni rijk ðEk Þ J k ðEk ; DÞ dEk ; ð1Þ i
k
0
where Ni is the number of atoms for target element i per kg material in the sample, rijk(Ek) is the cross section for the production of the cosmogenic nuclide j from the target element i by particles of type k with energy Ek and Jk(Ek, D) is the flux of particles of type k with energy Ek at depth D inside the Earth’s atmosphere. The particle fluxes Jk(Ek, D)
643
were calculated by the GEANT/MCNP code system. The statistical errors of the calculations were on the level of 4–6%. The systematic uncertainties of our calculated fluxes are estimated to be in the range of 10–15% and increase in the atmosphere with depth. For the cross sections rijk, we relied on the ones evaluated by us and tested by earlier calculations [6,7]. 3. Production of cosmogenic nuclides in the Earth’s surface In the interactions of primary cosmic-ray particles with the Earth’s atmosphere and during the development of particle cascades, particle fluxes undergo a continuous change in the sense of the spectral shape of their distribution and relative ratios of various particles. From the point of view of cosmogenic-nuclide production in the outermost few g cm2 of Earth’s atmosphere, the most important particles are neutrons and protons. Going deeper into the atmosphere, the proton fluxes decrease faster than the neutron fluxes, and therefore secondary cosmic rays become dominant. Secondary cosmic rays are produced through the interaction of primary cosmic rays with atmospheric and terrestrial nuclei and include strongly interacting particles (e.g. neutrons, protons and pions), weakly interacting particles (e.g. muons and neutrinos), electromagnetic radiation (photons), positrons and electrons. Secondary neutrons are responsible for the majority of nuclear transformations in which cosmogenic nuclides are produced [1]. Neutrons may be classified by energy or according the types of nuclear reactions in which they are involved [7]: • High-energy neutrons are produced through direct reactions of primary and secondary cosmic-ray particles with terrestrial nuclei. They can induce spallation reactions, and range from primary energies of several GeV down to 10 MeV. • Fast neutrons are produced primarily from the de-excitation of nuclei following compound nucleus reactions produced through interaction with high-energy neutrons. A common mode of de-excitation is nuclear evaporation: the emission of neutrons and protons with kinetic energies in the range of 0.1–10 MeV. • Slow neutrons have kinetic energies in the order of 1 keV, and are produced from the slowing down of fast neutrons, through elastic and inelastic collisions with nuclei. • Thermal and epithermal neutrons are produced from the slowing down of fast neutrons to energies similar to the vibrational motion of nearby molecules. An important characteristic of thermal neutrons is their relatively high probability of being absorbed by some nuclei. Thermal neutrons have an average energy of 0.025 eV at 293.16 K. At the Earth’s surface and at shallow depths, the largest contribution to the cosmogenic-nuclide production comes
J. Masarik et al. / Nucl. Instr. and Meth. in Phys. Res. B 259 (2007) 642–645 0.01 Fast (E>14.7 MeV) Thermal (E<0.045 eV)
Neutron flux [n/cm2 s]
from neutrons. From a few hundred meters above the Earth surface to near the top of the atmosphere, an equilibrium conditions exist, which means that the neutron energy spectrum remains almost unchanged [2,3] and only the total flux decreases exponentially. However, at the ground/air interface, a sharp change in the both neutron production and transport (due to the different compositions of air and surface) disturbs the equilibrium character of the neutron spectrum, which means that (besides attenuation) the shape of spectrum is changed. The presence of the water in the soil amplifies the changes in the spectral shape substantially. There are two principal mechanism involving neutrons by which cosmogenic nuclides can be produced in the Earth’s surface: (a) spallation of target nuclei by highenergy neutrons and (b) by neutron-capture reactions. Therefore, we investigated the behavior of thermal neutrons and high-energy neutrons near the Earth surface separately. The dependence of neutron fluxes on water content in the soil was also investigated. To obtain the neutron fluxes at air/ground interface, we began with the primary particles and calculated the fluxes at 200 g cm2 above the surface. The air/ground boundary is simulated as a semi-infinite interface between air and ground with each having a homogenous composition. Only the region near the interface, a 200 g cm2 thick region of air and 250 g cm2 thick region of the ground is considered for neutron transport. The assumed composition of atmosphere and soil are given above and, for the study of hydrogen effects on neutron fluxes, 1, 2 or 3% of water were added to the soil composition. The case with a 20 g cm2 thick water layer covering soil was also investigated. Our calculated total neutron flux at 50 cm above the air/ ground interface located at sea level altitude depends on chemical composition of surface. For the average composition of Earth surface given above, the total neutron flux corresponding to average solar activity is 9.1 neutrons cm2 s1. Addition of less than 5% of water into the surface composition leads to the increase of the neutron flux, higher water contents lead to the decrease of the total neutron flux. The total energy integrated neutron flux in the surface containing 1, 2 and 3% of water is 1.12, 1.20 and 1.29 times higher, respectively, than in the water free composition. The spectra of neutrons near the air/ground interface resemble the spectra in the air, except for thermal neutrons. The presence of the interface and water in the ground influences the thermal neutron spectra substantially. The key feature of the thermal neuron flux profile is an initial build-up of the thermal flux below the surface, the broad plateau of flux within 10% of its peak value for the depth between 15 and 75 g cm2 and the exponential decrease below this peak, see Fig. 1. The total neutron flux calculated at 50 cm above the air/ground interface differs from the free air by only about 25%. However, as is shown in Fig. 1, the thermal neutron flux rises by factor more than 10. As shown in Fig. 2, the amount of the thermal neutron flux rise depends on the water content of the surface. The
Ground
Air
0.001
0.0001
10
-5
-100
-50
0
50
100
2
Depth [g/cm ] Fig. 1. Cosmic-ray-induced thermal and fast neutron fluxes as a function of depth in ground and air. Calculations are done for the Earth’s surface at high latitudes, sea level and the chemical composition of ground and air given in the text.
0.01
Neutron flux [n/cm2 s]
644
Ground
Air
0.001
0.0001
Thermal (E<0.045 eV, with 3% water) Thermal (E<0.045 eV, without a water)
10
-5
-100
-50
0
50
100
2
Depth [g/cm ] Fig. 2. Comparison of the cosmic-ray-induced thermal neutron flux as a function of depth in ground and air. Calculations are done for the same conditions as in Fig. 1, but for two composition of ground: without water and with 3% of water added.
factor decreases with water content. The characteristic feature of the fast neutron flux is its flat profile for shallow depths (0–15 g cm2). This behavior is reflected also in nuclide production depth profiles in Figs. 3 and 4. Experimental data for Meteor Crater in Arizona [10] were fitted by least-square techniques. As seen from figures, the best agreement between data and fits is reached with a flat
J. Masarik et al. / Nucl. Instr. and Meth. in Phys. Res. B 259 (2007) 642–645
645
0.01
10
S]
X 10 5 atoms / g Sio 2
Thermal n with 3 % of water
Neutron flux [n/cm
10 Be
2
Ground
Fit to experimental data Fit to experimental data excluding the topmost one Calculated depth profile
0.001
W a t e r
1 0
20
40
60
80
100
120 0.0001 -100
—2
Depth [g cm ]
-50
Thermal with 3 % of water and 20 cm of water on top of soil 0
50
100
2
Depth [g cm ]
10
Fig. 3. Measured and calculated depth profile of Be in quartz separated from a boulder at Meteor Crater, AZ. The solid line is the least-squares fit to experimental data. The dot line is the least square fit to experimental data excluding the topmost one. The dot-dashed line is result of present simulations.
Air
Fig. 5. Comparison of the cosmic-ray-induced thermal neutron flux as a function of depth in ground, water and air. Calculations are done for the same conditions as in Fig. 2, but the ground with 3% of water in it in the second case is covered with a 20 cm thick layer of water.
10
X 101 atoms / g of Sio 2
simulations of thermal neuron flux for 20 cm thick water layer are in Fig. 5. In the presence of water cover on the ground surface, the neutrons near the boundary in rocks that otherwise leak out are thermalized more efficiently. This means that the water layer acts like both a moderator and reflector. When the thickness of water is increased, neutron production near the Earth surface decreases, and consequently the thermal neuron flux near the interface decreases.
26Al
Fit to experimental data Fit to experimental data excluding the topmost one Calculated depth profile
Acknowledgements
1 0
20
40
60
80
100
120
—2
Depth [g cm ] Fig. 4. Measured and calculated depth profile of 26Al in quartz separated from a boulder at Meteor Crater, AZ. The solid line is the least-squares fit to experimental data. The dot line is the least square fit to experimental data excluding the topmost one. The dot-dashed line is result of present simulations.
profile near the air/ground interface, as seen in the calculated neutron flux profiles. The snow cover and its influence on neutron moderation and reflection were simulated by covering the Earth surface with water layers of varying thickness. Results of our
Work at Komensky University in Bratislava was supported by Slovak Grant Agency grant 1/0207/03 and CRONUS-EU project. Work in the USA was supported by the NSF CRONUS-Earth project. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
D. Lal, Earth Planet. Sci. Lett. 114 (1991) 424. K. O’Brien et al., J. Geophys. Res. 83 (1978) 114. L. Dep et al., Nucl. Instr. and Meth. B 92 (1994) 321. B. Brun et al., CERN Report DD/EE/84-1 (1987) p. 584. J.F. Briesmeister, Los Alamos Report LA-12625-M (1993) p. 693. J. Masarik, J. Beer, J. Geophys. Res. 104 (1999) 12,099. J. Masarik, R.C. Reedy, Earth Planet. Sci. Lett. 136 (1995) 381. G.C. Castagnoli, D. Lal, Radiocarbon 22 (1980) 133. W.R. Webber, P.R. Higbie, J. Geophys. Res. 108 (2003) 1355. L. Dep, Thesis Purdue U. (1995) p. 155.
Nuclear Instruments and Methods in Physics Research B 259 (2007) 642–645 www.elsevier.com/locate/nimb
Numerical simulations of in situ production of terrestrial cosmogenic nuclides Jozef Masarik b
a,*
, Kyeong J. Kim b, Robert C. Reedy
c
a Department of Nuclear Physics, Komensky University, Sk-842 48 Bratislava, Slovakia NSF-Arizona AMS Laboratory, Department of Physics, University of Arizona, Tucson, AZ 85721, USA c Institute of Meteoritics, University of New Mexico, Albuquerque, NM 87131, USA
Available online 4 March 2007
Abstract A variety of geologic and environmental events and processes can be studied with the cosmogenic nuclides accumulated in terrestrial rocks. Reliable interpretation of the measured in situ-produced cosmogenic nuclides requires a good understanding of the involved nuclear processes and factors influencing them. The production rates of nuclides depend on many parameters. In this paper, calculations are reported and discussed on the influence of the air/ground interface and snow cover on production rates of in situ produced cosmogenic nuclides. 2007 Elsevier B.V. All rights reserved. PACS: 24.10.Lx; 96.40.Vw; 25.40.h Keywords: Cosmic rays; Cosmogenic nuclides; Neutrons; In situ production; Numerical simulations
1. Introduction The interactions of cosmic-ray particles with the Earth’s atmosphere produce a cascade of secondary particles and many cosmogenic nuclides [1]. Many secondaries have enough energy to undergo further collisions and to produce the next generation of secondary particles. Some of the particles produced in this cascade can reach the Earth’s surface and induce nuclear reactions in which a variety of cosmogenic nuclides are produced. The cosmogenic-nuclide concentration in a terrestrial sample depends on the sample’s composition, altitude, geomagnetic latitude and exposure geometry and their changes with the time. The character of the types of nuclear reactions and the energies of particles are determined by the energies of the incoming cosmic-ray particles and the elemental composition of the irradiated object. To make cosmogenic nuclides a common universal analytical tool in geosciences, it must *
Corresponding author. Tel.: +421 7 602 95456; fax: +421 7 654 25882. E-mail address: [email protected] (J. Masarik).
0168-583X/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.03.003
be applicable in broad range of sampling site characteristics. The goal of this paper is to investigate the influence of the air/ground interface and snow cover on production rates of in situ produced cosmogenic nuclides. We present a pure physical model approach to this problem. Similar studies employing some approximations and simplifications were published earlier [2,3]. 2. Model calculations Our numerical simulations of the interaction of primary and secondary cosmic-ray particles with matter are based on the GEANT [4] and MCNP [5] codes. As this code system is described in detail elsewhere [6,7], we repeat here only its main features that are relevant for the present study. In our simulations, only primary protons with energies between 10 MeV and 100 GeV were considered. The primary cosmic-ray particle flux at the Earth’s orbit consists of a galactic and a solar component. In this paper, we present only the results of cosmogenic-nuclide production
J. Masarik et al. / Nucl. Instr. and Meth. in Phys. Res. B 259 (2007) 642–645
simulation by the galactic cosmic rays. As solar cosmic-ray particles have low energies, they induce interactions only in the uppermost few g cm2 of the Earth’s atmosphere and only at high latitudes, where the geomagnetic field does not prevent them from entering the atmosphere. Therefore they contribute only to the total average cosmogenic nuclide production in the atmosphere [6,7]. The galactic cosmic-ray particles are a mixture of protons (87%), alpha particles (12%) and heavier nuclei (1%). The flux of cosmic rays varies with time, thus to calculate production rate as a function of time, the cosmic ray flux must be obtained as a function of time and energy. The GCR particle flux is modulated due to the interactions of incoming particles with the magnetic field convected outward by the solar–wind plasma. In recent years, the most frequently used models for primary GCR spectra were those of Castagnoli and Lal [8] and Webber and Higbie [9]. The spectral distributions of heavier particles present in primary cosmic rays are similar to the distribution of protons if energy per nucleon is considered. In these calculations, the model Earth was irradiated by a homogenous and isotropic flux of protons using the spectral shape of Castagnoli and Lal [8] and a modulation parameter of 550 MeV. The contributions from alpha (and heavier) particles were simply included in the final results by multiplying the proton calculations by a scaling factor, which was found to be 1.4 [6]. The characteristic feature of the GCR particle interactions is the production of the cascade of secondary particles. For these calculations, the Earth’s atmosphere was modeled as a spherical shell with an inner radius of 6378 km and a thickness of 100 km. The following elemental composition (in weight%) was used: 75.5% N, 23.2% O and 1.3% Ar. The total thickness of the atmosphere was 1033 g cm2. The elemental composition of the surface was assumed to be an average terrestrial one (in weight percent, 0.2% H, 47.3% O, 2.5% Na, 4.0% Mg, 6.0% Al, 29.0% Si, 5.0% Ca and 6.0% Fe). Except for very high contents of H, changes in this surface composition, or the addition of other elements such as K, Mn, Cr, have very little effect on the calculated fluxes. The surface density of the Earth was 2.0 g cm3. To investigate the depth dependence of particle fluxes, the sphere near the surface was divided into spherical shells. The fluxes of protons and neutrons within each cell were calculated. The production rate of a cosmogenic nuclide j at a depth D in the Earth is X XZ 1 P j ðDÞ ¼ Ni rijk ðEk Þ J k ðEk ; DÞ dEk ; ð1Þ i
k
0
where Ni is the number of atoms for target element i per kg material in the sample, rijk(Ek) is the cross section for the production of the cosmogenic nuclide j from the target element i by particles of type k with energy Ek and Jk(Ek, D) is the flux of particles of type k with energy Ek at depth D inside the Earth’s atmosphere. The particle fluxes Jk(Ek, D)
643
were calculated by the GEANT/MCNP code system. The statistical errors of the calculations were on the level of 4–6%. The systematic uncertainties of our calculated fluxes are estimated to be in the range of 10–15% and increase in the atmosphere with depth. For the cross sections rijk, we relied on the ones evaluated by us and tested by earlier calculations [6,7]. 3. Production of cosmogenic nuclides in the Earth’s surface In the interactions of primary cosmic-ray particles with the Earth’s atmosphere and during the development of particle cascades, particle fluxes undergo a continuous change in the sense of the spectral shape of their distribution and relative ratios of various particles. From the point of view of cosmogenic-nuclide production in the outermost few g cm2 of Earth’s atmosphere, the most important particles are neutrons and protons. Going deeper into the atmosphere, the proton fluxes decrease faster than the neutron fluxes, and therefore secondary cosmic rays become dominant. Secondary cosmic rays are produced through the interaction of primary cosmic rays with atmospheric and terrestrial nuclei and include strongly interacting particles (e.g. neutrons, protons and pions), weakly interacting particles (e.g. muons and neutrinos), electromagnetic radiation (photons), positrons and electrons. Secondary neutrons are responsible for the majority of nuclear transformations in which cosmogenic nuclides are produced [1]. Neutrons may be classified by energy or according the types of nuclear reactions in which they are involved [7]: • High-energy neutrons are produced through direct reactions of primary and secondary cosmic-ray particles with terrestrial nuclei. They can induce spallation reactions, and range from primary energies of several GeV down to 10 MeV. • Fast neutrons are produced primarily from the de-excitation of nuclei following compound nucleus reactions produced through interaction with high-energy neutrons. A common mode of de-excitation is nuclear evaporation: the emission of neutrons and protons with kinetic energies in the range of 0.1–10 MeV. • Slow neutrons have kinetic energies in the order of 1 keV, and are produced from the slowing down of fast neutrons, through elastic and inelastic collisions with nuclei. • Thermal and epithermal neutrons are produced from the slowing down of fast neutrons to energies similar to the vibrational motion of nearby molecules. An important characteristic of thermal neutrons is their relatively high probability of being absorbed by some nuclei. Thermal neutrons have an average energy of 0.025 eV at 293.16 K. At the Earth’s surface and at shallow depths, the largest contribution to the cosmogenic-nuclide production comes
J. Masarik et al. / Nucl. Instr. and Meth. in Phys. Res. B 259 (2007) 642–645 0.01 Fast (E>14.7 MeV) Thermal (E<0.045 eV)
Neutron flux [n/cm2 s]
from neutrons. From a few hundred meters above the Earth surface to near the top of the atmosphere, an equilibrium conditions exist, which means that the neutron energy spectrum remains almost unchanged [2,3] and only the total flux decreases exponentially. However, at the ground/air interface, a sharp change in the both neutron production and transport (due to the different compositions of air and surface) disturbs the equilibrium character of the neutron spectrum, which means that (besides attenuation) the shape of spectrum is changed. The presence of the water in the soil amplifies the changes in the spectral shape substantially. There are two principal mechanism involving neutrons by which cosmogenic nuclides can be produced in the Earth’s surface: (a) spallation of target nuclei by highenergy neutrons and (b) by neutron-capture reactions. Therefore, we investigated the behavior of thermal neutrons and high-energy neutrons near the Earth surface separately. The dependence of neutron fluxes on water content in the soil was also investigated. To obtain the neutron fluxes at air/ground interface, we began with the primary particles and calculated the fluxes at 200 g cm2 above the surface. The air/ground boundary is simulated as a semi-infinite interface between air and ground with each having a homogenous composition. Only the region near the interface, a 200 g cm2 thick region of air and 250 g cm2 thick region of the ground is considered for neutron transport. The assumed composition of atmosphere and soil are given above and, for the study of hydrogen effects on neutron fluxes, 1, 2 or 3% of water were added to the soil composition. The case with a 20 g cm2 thick water layer covering soil was also investigated. Our calculated total neutron flux at 50 cm above the air/ ground interface located at sea level altitude depends on chemical composition of surface. For the average composition of Earth surface given above, the total neutron flux corresponding to average solar activity is 9.1 neutrons cm2 s1. Addition of less than 5% of water into the surface composition leads to the increase of the neutron flux, higher water contents lead to the decrease of the total neutron flux. The total energy integrated neutron flux in the surface containing 1, 2 and 3% of water is 1.12, 1.20 and 1.29 times higher, respectively, than in the water free composition. The spectra of neutrons near the air/ground interface resemble the spectra in the air, except for thermal neutrons. The presence of the interface and water in the ground influences the thermal neutron spectra substantially. The key feature of the thermal neuron flux profile is an initial build-up of the thermal flux below the surface, the broad plateau of flux within 10% of its peak value for the depth between 15 and 75 g cm2 and the exponential decrease below this peak, see Fig. 1. The total neutron flux calculated at 50 cm above the air/ground interface differs from the free air by only about 25%. However, as is shown in Fig. 1, the thermal neutron flux rises by factor more than 10. As shown in Fig. 2, the amount of the thermal neutron flux rise depends on the water content of the surface. The
Ground
Air
0.001
0.0001
10
-5
-100
-50
0
50
100
2
Depth [g/cm ] Fig. 1. Cosmic-ray-induced thermal and fast neutron fluxes as a function of depth in ground and air. Calculations are done for the Earth’s surface at high latitudes, sea level and the chemical composition of ground and air given in the text.
0.01
Neutron flux [n/cm2 s]
644
Ground
Air
0.001
0.0001
Thermal (E<0.045 eV, with 3% water) Thermal (E<0.045 eV, without a water)
10
-5
-100
-50
0
50
100
2
Depth [g/cm ] Fig. 2. Comparison of the cosmic-ray-induced thermal neutron flux as a function of depth in ground and air. Calculations are done for the same conditions as in Fig. 1, but for two composition of ground: without water and with 3% of water added.
factor decreases with water content. The characteristic feature of the fast neutron flux is its flat profile for shallow depths (0–15 g cm2). This behavior is reflected also in nuclide production depth profiles in Figs. 3 and 4. Experimental data for Meteor Crater in Arizona [10] were fitted by least-square techniques. As seen from figures, the best agreement between data and fits is reached with a flat
J. Masarik et al. / Nucl. Instr. and Meth. in Phys. Res. B 259 (2007) 642–645
645
0.01
10
S]
X 10 5 atoms / g Sio 2
Thermal n with 3 % of water
Neutron flux [n/cm
10 Be
2
Ground
Fit to experimental data Fit to experimental data excluding the topmost one Calculated depth profile
0.001
W a t e r
1 0
20
40
60
80
100
120 0.0001 -100
—2
Depth [g cm ]
-50
Thermal with 3 % of water and 20 cm of water on top of soil 0
50
100
2
Depth [g cm ]
10
Fig. 3. Measured and calculated depth profile of Be in quartz separated from a boulder at Meteor Crater, AZ. The solid line is the least-squares fit to experimental data. The dot line is the least square fit to experimental data excluding the topmost one. The dot-dashed line is result of present simulations.
Air
Fig. 5. Comparison of the cosmic-ray-induced thermal neutron flux as a function of depth in ground, water and air. Calculations are done for the same conditions as in Fig. 2, but the ground with 3% of water in it in the second case is covered with a 20 cm thick layer of water.
10
X 101 atoms / g of Sio 2
simulations of thermal neuron flux for 20 cm thick water layer are in Fig. 5. In the presence of water cover on the ground surface, the neutrons near the boundary in rocks that otherwise leak out are thermalized more efficiently. This means that the water layer acts like both a moderator and reflector. When the thickness of water is increased, neutron production near the Earth surface decreases, and consequently the thermal neuron flux near the interface decreases.
26Al
Fit to experimental data Fit to experimental data excluding the topmost one Calculated depth profile
Acknowledgements
1 0
20
40
60
80
100
120
—2
Depth [g cm ] Fig. 4. Measured and calculated depth profile of 26Al in quartz separated from a boulder at Meteor Crater, AZ. The solid line is the least-squares fit to experimental data. The dot line is the least square fit to experimental data excluding the topmost one. The dot-dashed line is result of present simulations.
profile near the air/ground interface, as seen in the calculated neutron flux profiles. The snow cover and its influence on neutron moderation and reflection were simulated by covering the Earth surface with water layers of varying thickness. Results of our
Work at Komensky University in Bratislava was supported by Slovak Grant Agency grant 1/0207/03 and CRONUS-EU project. Work in the USA was supported by the NSF CRONUS-Earth project. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
D. Lal, Earth Planet. Sci. Lett. 114 (1991) 424. K. O’Brien et al., J. Geophys. Res. 83 (1978) 114. L. Dep et al., Nucl. Instr. and Meth. B 92 (1994) 321. B. Brun et al., CERN Report DD/EE/84-1 (1987) p. 584. J.F. Briesmeister, Los Alamos Report LA-12625-M (1993) p. 693. J. Masarik, J. Beer, J. Geophys. Res. 104 (1999) 12,099. J. Masarik, R.C. Reedy, Earth Planet. Sci. Lett. 136 (1995) 381. G.C. Castagnoli, D. Lal, Radiocarbon 22 (1980) 133. W.R. Webber, P.R. Higbie, J. Geophys. Res. 108 (2003) 1355. L. Dep, Thesis Purdue U. (1995) p. 155.