Indian Journal of Pure & Applied Physics Vol. 54, November 2016, pp. 739-743 Empirical relation between energy and angular deviation of muons transmitted through thick slabs Mausumi Sengupta Mitra a *, P K Sarkar b , T Bandyopadhyay a & D N Sharma c a HP Unit (HPD, BARC),Variable Energy Cyclotron Centre, 1/AF, Bidhannagar, Kolkata 700 064, India b Manipal Centre for Natural Sciences, Manipal University, Manipal 576 104, India c Health Safety and Environment Group, Bhabha Atomic Research Centre, Trombay, Mumbai, 400 085 India Received 5 August 2014; revised 20 July 2016; accepted 9 September 2016 To facilitate detection of materials of high atomic number buried inside materials of low atomic number using cosmic ray muons, Monte Carlo simulations have been carried out and an empirical relation has been developed to correlate energy with the most probable angular deviation of transported muons through slabs of different materials. This empirical relation describes the correlation between the energy distribution and the distribution of angular deviation of muons passing through slabs of different materials and of different thickness, and is expected to be useful in the field of cosmic ray muon radiography. Keywords: Empirical relation, Monte Carlo simulation, Cosmic ray muon radiography 1 Introduction Muons present in the cosmic ray shower are used for radiography of thick objects more effectively than X-rays or gamma-rays because of their large penetrating power. Most importantly, muon- radiography is free from unnecessary radiation hazards for the user, caused by X-rays or gamma- rays. Due to multiple Coulomb scattering, muons, while passing through any thick object, deviate in the direction and the amount of deviation depends on the atomic number Z and density of the material. Also, muons passing through slabs of materials suffer loss of energy, which depend on material Z as well as the thickness of the slab. These properties can be utilized for image reconstruction as well as material-Z discrimination. It is already claimed that utilizing this property of cosmic ray muons one can detect any high-Z material buried in low-Z surroundings, which is again useful in surveillance of cross border transport of nuclear and other heavy materials 1 . Therefore the high-energy cosmic ray muons (mean energy at sea level 3-4 GeV) may provide a way of discriminating materials of different densities and may be used to detect high-Z material in the presence of materials of low-Z. Recently there are several claims of utilizing muon imaging technique for imaging nuclear fuels inside reactor 2 which may be beneficial for investigation of the damaged core of reactors like those in Fukushima 3 . Muons passing through a material lose energy through different processes. The main processes of muon energy loss are: atom excitation and ionization (i.e., collision losses), bremsstrahlung, electron- positron pair production and inelastic scattering (photo-nuclear interaction). Collision losses are described by cross-sections comparable to atomic dimensions and occur very frequently along the path of any ion. Since energy loss per collision is small (about 10 eV), the resulting angular deviation per collision is also very small. This process of multiple scattering does not contribute much to the muon energy loss, so it is usually neglected in considering muon energy degradation. The other three interactions occur when the muon passes close to the nuclear protons and hence these are relatively rare, but since they involve much larger energy losses (about a few MeV) the muon scattering angle is quite large even in a single event. The mean free path for these large momentum transfers is called the radiation length, which decreases with increasing atomic number and density. These processes produce muon deflection from the initial direction and the resultant scattered angle depends on the radiation length of the material. Therefore, the Z-dependent distribution of angular —————— *Corresponding author (E-mail: mausumi@vecc.gov.in)