# Calculations of Cross-Sections for Positron Scattering on Benzene
## 1 Introduction  
Positron interactions with organic molecules play a vital role in medical physics, materials science, and astrophysics [1, 2, 3, 4, 5, 6, 7]. In medical physics, particular interest is focused on the positronium (Ps) and its role in positron emission tomography (PET) [1]. Ps atoms, which are short-lived bound states of an electron and its antiparticle, the positron, can be created when a positron is emitted inside the human body and does not annihilate directly with one of the electrons of the examined organism. As research shows, about 40% of the positrons in PET scans decay through Ps formation rather than direct annihilation [1]. Hence, the Ps is being explored as a crucial component of new-generation PET devices. In materials science, positron annihilation spectroscopy methods yield information about defects localizing positrons and can provide identification of neutral or negatively charged vacancy-related defects in materials [2]. It is also possible to identify specific point defects by comparing the experimentally determined lifetimes with Density Functional Theory (DFT)-calculated values for the perfect material state and states localized at specific vacancy-related defects [3]. Furthermore, positron lifetime measurements, which are performed using high-intensity positron beams, enable the determination of a depth profile of vacancy-related defects [3]. Positrons in space are created mainly in the interstellar medium (ISM), when photons or high-energy particles from cosmic radiation trigger a cascade of processes, and positrons are one of the final products [4]. Other sources of these particles are massive stars, as well as red giants and Wolf-Rayet stars [5]. Potential sources also include pulsars, neutron stars, and black holes, as well as dark matter [6]. The spectrum of the photons, created due to positron annihilation in our galaxy, has been examined over a wide range of energies, from 50 keV to over 100 GeV [7]. In the low-energy region (from 50 keV to10 MeV), photon emissions can be explained with good accuracy [8], while in the high-energy region, from 1.5 to 100 GeV, the results of observations suggest an excess of ultra-relativistic positrons in cosmic rays in relation to theoretical models [9; 10]. Furthermore, a yet-unresolved problem is to find an explanation for the annihilation radiation map in the ISM. The known astronomical objects in the ISM do not possess the capability to produce such a high rate of positrons that could stay in agreement with the photon emission resulting from their annihilation [9]. A possible explanation could be positron scattering on polycyclic aromatic hydrocarbon (PAH) molecules, which were found in the composition of the interstellar dust [10]. Experimental results of positron-PAH molecule annihilation cross-sections, which show that these increase by several orders of magnitude, seem to confirm the possible importance of such reactions in the ISM [11]. For the theoretical study of positron interaction with matter, knowledge of scattering cross-sections is crucial. In particular, positron-transport Monte Carlo simulation studies, e.g., [12; 13], need a set of input data describing the interaction of the positron beam with the target. The cross-sections describe different physical phenomena that occur during the interaction of positrons with the target atoms or molecules. Elastic and inelastic processes particularly need to be considered. For low-energy positron interactions with atoms and molecules, the processes of interest include elastic scattering, electronic and vibrational excitation, ionization, Ps formation, and annihilation [13]. There have been a number of earlier review articles involving cross-sections for positron scattering, e.g., [14]; however, the benzene molecule, which is the simplest aromatic hydrocarbon, has not received considerable attention in positron scattering studies.