doi:10.1016/S0168-9002(03)00983-5 
Copyright © 2003 Elsevier Science B.V. All rights reserved.
Simulations of muon-induced neutron flux at large depths underground
V. A. Kudryavtsev
, 
, N. J. C. Spooner and J. E. McMillan
Department of Physics and Astronomy, University of Sheffield, Hicks Building, Hounsfield Rd., Sheffield S3 7RH, UK
Received 25 November 2002;
accepted 17 February 2003. ;
Available online 22 March 2003.
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Abstract
The production of neutrons by cosmic-ray muons at large depths underground is discussed. The most recent versions of the muon propagation code MUSIC, and particle transport code FLUKA are used to evaluate muon and neutron fluxes. The results of simulations are compared with experimental data.
Author Keywords: Underground muons; Neutron flux; Neutron production by muons; Dark matter experiments; Neutron background
PACS classification codes: 96.40.Tv; 25.40.Sc; 25.30.Mr; 28.20.−v
Fig. 1. Average number of neutrons produced by a muon per unit path length (1 gcm−2) in scintillator as a function of muon energy. Our results are shown by filled circles. The parameterisation with Eq. (1) is shown as a solid line. The parameterisation found in [13] is plotted by a dashed line. The measurements shown are as follows (in order of increasing energy): 20 mw.e. (minimal depth) [9 and 8], 25 mw.e. [4], 32 mw.e. [8], 316 mw.e. [4], 570 mw.e. [5], 3000 mw.e. [7], 5200 mw.e. [6]. Filled squares show the number of neutrons, produced in scintillator by muons with a real spectrum for depths of 0.55 kmw.e. and 3 kmw.e. in Boulby rock (mean energies 98 and 264 GeV, respectively).
Fig. 2. Dependence of neutron rate on the atomic weight of material. Materials and compounds used in the simulations and presented in the figure by filled circles are (in order of increasing atomic weight): C
10H
20 (
A
=10.4), C (
A=12.0), Na (
A=23.0), NaCl (
A=30.0), Fe (
A=55.9), Cd (
A=112.4), Gd (
A=157.3), Au (
A=197.0), and Pb (
A=207.2). A simple parameterisation by a power-law is given by the solid line. Also shown are the measurements of neutron rate by NA55 at CERN in three thin targets at two neutron scattering angles (open circles and open squares) (see text for details). These are normalised at small atomic weight (carbon) to our simulations with FLUKA for the muon spallation only (filled squares). For the muon spallation our result for lead is artificially shifted to
A=220 to avoid the overlaping with one of the CERN points.
Fig. 3. Neutron energy spectrum in scintillator (filled circles) and NaCl (open circles) obtained with muon spectrum at about 3 kmw.e. underground. Parameterisation proposed in [
13] for scintillator for muon energy 280 GeV is shown by the solid line, arbitrarily normalised to our simulations to reach visual agreement. Arbitrary units are used for all spectra, the normalisation being provided by the total neutron production rate (see
Fig. 1 and
Fig. 2).
Fig. 4. Neutron energy spectrum in scintillator (filled circles) in comparison with the LVD data [
7]. LVD data are normalised to the calculated spectrum to reach better visual agreement. The absolute normalisation is provided by the total neutron production rate (see
Fig. 1).
Fig. 5. Neutron energy spectrum at the boundary between salt and cavern.
Fig. 6. Simulated neutron rate as a function of distance from the muon track in scintillator (filled circles) in comparison with the LVD data [
7]. LVD data are normalised to the calculated distribution to get better visual agreement. The absolute normalisation is provided by the total neutron production rate (see
Fig. 1).
Table 2. Mean muon energies in GeV at various depths underground for standard and Boulby rock and two parameterisations of the muon spectrum at the surface
Column 1—depth in kilometres of water equivalent, km w.e.; column 2—mean muon energy for vertical muon flux in standard rock with parameterisation of the muon spectrum at sea level according to the best fit to the LVD data [20]; column 3—mean muon energy for global muon flux in standard rock for a flat surface with LVD parameterisation of the muon spectrum; column 4—mean muon energy for global muon flux in standard rock for a flat surface with Gaisser's parameterisation of the muon spectrum at sea level [19]; column 5—mean muon energy for global muon flux for Boulby rock with LVD parameterisation of the muon spectrum; column 6—mean muon energy for muon flux at 60o in standard rock with LVD parameterisation of the muon spectrum (for this column the values in column 1 show the slant depth instead of vertical depth).
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